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\,
,\
Females Females
, ._2,, ,
,\
,\ \ ,
,\
,x
~
.�
:::J en >. :;;; - 1, consists of of the the reproductive reproductive values values of of individuals individuals in in the the respective respective habitats habitats (Caswell, (Caswell, 11989; 989; Rousset, 999a). The Rousset, 11999a). The importance importance of of habitat-specific habitat-specific reproductive reproductive values values is is discussed discussed in in the the following following section. section. The The number number of of individuals individuals that that disperse disperse from from habitat habitat h to to other other habitats habitats at at equilibrium equilibrium is is =
=
hfh( fzh) L Ehh = nnhfh(nh) E ~ mhi mhi d i :/:hh =
((16.3) 16.3)
while while the the number number of of immigrants immigrants to to habitat habitat h from from other other habitats habitats is is
Ih - ~
nifi(ni)mih.
((16.4) 1 6.4)
i :/:h
According 1 9 8 8 ) definition, According to to Pulliam's Pulliam's ((1988) definition, habitat habitat h is is aa sink sink if if E Ehh < < h. Ih. Noting 1 6.2) {;(ni)mi Noting that, that, from from Eq. Eq. ((16.2) fi(~i)mihh = aahi(ni), and that, that, from from the the definition definition hi(ni), and
SOURCE-SINKPOPULATION POPULATION DYNAMICS DYNAMICS 116. 6. SOURCE-SINK
= h (fh( fzh) � Eh Eh--- Ih Ih == n;~b(fb(~tb) ~ mmhi b i - --1 ) )
391 391
of of right right eigenvector, eigenvector, lia ] ~ i a hh ii(ni)ni ( ~ i ) ~ i = nh, one one can can show show that that the the difference difference between between the numbers numbers of of emigrants emigrants and and immigrant immigrant at at equilibrium equilibrium equals equals the 1
((16.5) 1 6.5)
l
Thus, Thus, habitat habitat hh is is aa sink sink (following (following Pulliam's Pulliam's definition) definition) if if ffh(~h)Eimhi < 1. 1. h(nh)limhi < (;(ni), lim If If mortality mortality during during dispersal dispersal is is negligible negligible or or is is absorbed absorbed into into/~(ni), ~,imhi hi == 1. In In this this case, case, Pulliam's Pulliam's definition definition of of aa sink sink implies implies that that ffh(~/#) < 11,, i.e., i.e., that that the the h (nh) < local local density density in in aa sink sink habitat habitat is is above above the the local local carrying carrying capacity capacity [defined [defined as as the density density at at which which fft,(nl,) the ]. h (nh ) = 11].
=
Reproductive Value Value and and the the Definition Definition of of Sources Sources and and Sinks Sinks Reproductive Equation 1 6.5) formalizes Equation ((16.5) formalizes the the definition definition of of source source and and sink sink habitats habitats as as net net exporters exporters and and importers importers of of dispersing dispersing individuals. individuals. However, However, as as noted noted by by Kawecki 1 993) and Rousset ((1999a), 1 999a), habitat-specific Kawecki and and Stearns Stearns ((1993) and Rousset habitat-specific reproductive reproductive values values may may be be more more closely closely related related to to the the ecological ecological and and evolutionary evolutionary conse consequences quences of of environmental environmental heterogeneity heterogeneity than than the the difference difference between between emigra emigration and immigration. First, First, the the reproductive reproductive value value measures measures the the expected expected long-term long-term contribution contribution of Caswell, of an an individual individual to to population population growth growth and and the the future future gene gene pool pool ((Caswell, 11989). 9 8 9 ) . The The asymptotic asymptotic contribution contribution of of the the local local population population in in habitat habitat h h to to aa future gene pool is is U u~vt, (note the the analogy analogy between this quantity and the the patch patch future gene pool between this quantity and hVh (note value value as as defined defined in in Chapter Chapter 4; 4; the the two two are, are, however, however, not not identical identical as as the the latter latter focuses focuses on on colonization colonization of of empty empty patches) patches).. Local Local populations populations in in habitats habitats with with > I1 contribute contribute more expected based Vv~h > more to to future future generations generations than than would would be be expected based on on their share habitats with with v~ Vh > 11 would be sources, sources, whereas whereas those with Vh vh < < 11 would be avoid contributing would be sinks. sinks. To To avoid contributing to to terminological terminological confusion, confusion, this this redef redefinition is not advocated here. here. However, However, it it is is useful useful to to see see when the definition definition inition is not advocated when the based would classify based on on the the reproductive reproductive value value would classify habitats habitats differently differently than than the the one based on First, note one based on net net immigration. immigration. First, note that that from from definition definition of of the the left left eigen eigenh, then vector Hence, if vector Vh vh = kiviaih. ~,iviaih. Hence, if Vh vh = = 11 for for all all h, then kiaih Eiaih = = fhkimhi fhEimhi = = 11 for for all all h. In words, if emigration in habitats ((i.e., i.e., the h. In words, if immigration immigration balances balances emigration in all all habitats the system system does not reproductive values values in does not have have aa source-sink source-sink structure), structure), then then the the reproductive in all all habitats immigration balances habitats are are 11.. However, However, if if immigration balances emigration emigration in in some some habitats habitats but others, the but not not in in others, the reproductive reproductive values values in in those those habitats habitats will will generally generally be Second, if be different different from from 11.. Second, if there there are are only only two two habitats, habitats, then then ((11 and and 2) 2) ff1(m11 (m + mu) > 1 > h(m2I + m ) implies VI > 1 > V , i.e., the reproductive 22 implies Vl > 1 > v2, 2 i.e., the reproductive I ll + m12) > 1 > f2(m21 + m22) value habitat classified source according according to value is is greater greater in in the the habitat classified as as source to Pulliam's Pulliam's defi definition 999a). This nition (Rousset, (Rousset, 11999a). This is is not not any any more more the the case case when when there there are are more more than than two 1 999a) illustrated two habitats. habitats. Rousset Rousset ((1999a) illustrated this this with with an an example example with with one-way one-way dispersal. However, dispersal. However, aa discrepancy discrepancy between between Pulliam's Pulliam's source-sink source-sink definition definition and values may and the the pattern pattern of of habitat-specific habitat-specific reproductive reproductive values may also also occur occur when when i). Such a case is illustrated in dispersal dispersal rates rates are are symmetric symmetric (i.e., (i.e., mi mii; = = m mji). Such a case is illustrated in ; Fig. 6 .2. In example, habitat habitat 11 and Fig. 116.2. In that that example, and habitat habitat 2 2 are are both both sources sources according according to excess of emigration over to Pulliam's Pulliam's definition, definition, with with the the excess of emigration over immigration immigration being being greater habitat 2 (in absolute greater for for habitat 2 than than for for habitat habitat 11 (in absolute terms terms and and relative relative to to equilibrium equilibrium population population sizes) sizes).. Consistent Consistent with with this, this, the the net net reproductive reproductive rate rate habitat 2. 2. Yet, Vb reflecting at at equilibrium, equilibrium, fh(nh), fh(t/h), is is largest largest in in habitat Yet, Vv22 < < 11 < < vl, reflecting the the fact which is fact that that most most emigrants emigrants from from habitat habitat 2 2 end end up up in in habitat habitat 33,, which is aa strong strong sink. sink. To summarize, summarize, the the application application of of the the concept concept of of source-sink source-sink population population To structure habitat types. structure is is most most straightforward straightforward when when there there are are only only two two habitat types. When When there habitats, the habitat emigration there are are more more than than two two habitats, the fact fact that that for for aa given given habitat emigration exceeds exceeds immigration immigration does does not not necessarily necessarily imply imply that that habitat habitat contributes contributes more more to pool than based on to aa future future gene gene pool than would would be be expected expected based on its its share share Uh uh of of the the total total population. reason for population. The The reason for this this discrepancy discrepancy is is that that emigration emigration and and immigra immigration movements of tion refer refer to to the the movements of individuals individuals within within aa single single generation, generation, whereas whereas reproductive values take into account the consequences of chains of migration reproductive values take into account the consequences of chains of migration events generations. The events among among habitat habitat types types happening happening over over many many generations. The following following subsections model described 16.1 ) subsections summarize summarize some some special special cases cases of of the the model described by by Eq. Eq. ((16.1) and ((16.2), as well well as as its its extensions extensions to to include age structure structure and and explicit spatial and 1 6.2), as include age explicit spatial dimensions. dimensions.
Habitat H a b i t a t Area Area versus versus Habitat H a b i t a t Quality Quality At can be At the the first first approximation, approximation, aa spatially spatially heterogeneous heterogeneous environment environment can be characterized terms of of the area and of the characterized in in terms the area and quality quality of the habitats habitats it it consist consist of. of. A A rea reasonable way sonable way to to describe describe the the quality quality of of different different habitats habitats would would be be to to compare compare the the reproductive reproductive success success that that is is expected expected in in each each of of them them at at the the same same popula population tion density. density. Because Because the the aforementioned aforementioned model model is is formulated formulated in in terms terms of of local local population population sizes sizes rather rather than than densities, densities, fI(n) fl(n) > > h(n) f2(n) does does not not imply imply that that habitat habitat 11 is areas. If is of of higher higher quality quality if if the the habitats habitats cover cover different different areas. If spatial spatial variation variation in in density within aa habitat density within habitat is is negligible, negligible, it it is is straightforward straightforward to to reformulate reformulate the the model by where bh is area of model by setting setting fh(nh) ft,(nh)== Fh(nh1bh), Fh(nffbh), where is the the area of habitat habitat h h and and
116. 6. SOURCE-SINK SOURCE-SINK POPULATION POPULATION DYNAMICS DYNAMICS
393 393
(a) (a)
Hab. 1 f1 (n1 ) = 1 0 1 + cn1
--
Hab. 2
Hab. 3
m23 == m32 _..,m23 m32 = = 0.3 0.3 If
•
2 t3 (n3) - -1 + cn3
(b) (b) n1 = 835 f1 (n1) = 1 .07 V1 = 1 .39
~,
9
n2 = 401 f2(n2) = 1 .20 v2 = 0.75
_.. ..
44.4 44 4
144.1 "~
1 44. 1
t73 = 286 f3(n3) = 0.52 v3 = 0.23
Fig. 6.2 A three-patch habi Fig. 116.2 three-patch model model illustrating illustrating the the discrepancy discrepancy between between the the classification classification of of habitats sink and and the value. (a) tats as as source source or or sink the habitat-specific habitat-specific reproductive reproductive value. (a) Parameters Parameters of of the the model; model; cc = = 0.01 0.01.. (b) (b) Properties Properties of of the the equilibrium; equilibrium; numbers numbers next next to to arrows arrows indicate indicate the the number number of of indi individuals viduals dispersing dispersing from from one one habitat habitat to to the the other other each each generation. generation.
h(nh1bh) F ~ ( n f f b h ) is is the the net net reproductive reproductive rate rate in in habitat habitat h h as as aa function function of of the the local local pop population ulation density. density. Other Other things things being being equal, equal, habitats habitats covering covering aa larger larger area area are are likely likely to to receive receive more more immigrants, immigrants, especially especially with with passive passive dispersal. dispersal. One One way way to to implement implement such such aa relationship relationship is is to to assume assume that that aa fraction fraction 11 - JL I~ of of potential potential dispersers habi dispersers remain remain in in the the habitat habitat of of origin origin while while the the rest rest end end up up in in various various habitats tats (including (including the the habitat habitat of of origin) origin) in in proportion proportion to to their their area, area, i.e., i.e., -
m miiii = 11 -- JL i~ + + ~bi/E~bh
= JLb/Ihbh mi m i jj = = JLb;lIhbh I~bi/Ehbh
((16.6a) 1 6.6a) ((16.6b) 1 6.6b)
394 394
TADEUSZ j. KAWECKI TADEUSZ J. KAWECKI
This This model model of of dispersal dispersal was was implemented implemented to to study study the the effects effects of of habitat habitat qual quality versus versus habitat habitat area area on on adaptive adaptive evolution evolution (Kawecki (Kawecki and and Stearns, Stearns, 11993; ity 993; Kawecki, 995). More Kawecki, 11995). More realistically, realistically, the the dispersal dispersal rates rates will will be be also also affected affected by by the size and and arrangement the size arrangement of of habitat habitat patches patches and and their their connectivity connectivity (see (see later). later). For For the the sake sake of of the the argument, argument, unless unless specified specified otherwise, otherwise, most most of of the the chapter chapter assumes area. assumes that that all all habitats habitats have have the the same same area.
Asymmetric Asymmetric Dispersal Dispersal Rates, Rates, "Reverse" "Reverse" Source-Sink Source-Sink Structure, Structure, and Black Hole Sinks and Black Hole Sinks In In the the model model described described in in the the preceding preceding paragraph, paragraph, individuals individuals in in all all habi habitats tats show show the the same same propensity propensity to to disperse, disperse, and and the the source-sink source-sink structure structure results from habitat quality. individuals may results from differences differences in in habitat quality. However, However, individuals may change change their response to their propensity propensity to to disperse disperse in in response to their their habitat. habitat. Environmental Environmental factors factors such ocean current, current, wind, wind, or also lead lead to such as as river river or or ocean or gravity gravity may may also to an an asymmetry asymmetry of dispersal dispersal rates, increasing the the probability probability of of dispersing dispersing from from an an "upstream" "upstream" of rates, increasing habitat habitat to to aa "downstream" "downstream" habitat habitat and and reducing reducing the the probability probability of of dispersing dispersing in equilibrium properties in the the opposite opposite direction. direction. The The equilibrium properties of of aa set set of of populations populations connected connected by by dispersal dispersal depend depend on on both both habitat-specific habitat-specific net net reproductive reproductive rates rates {;(ni) and ~(ni) and dispersal dispersal rates rates mij' mij. Asymmetries Asymmetries of of dispersal dispersal rates rates will will thus thus have have consequences consequences for for source-sink source-sink population population dynamics. dynamics. In particular, particular, asymmetric asymmetric dispersal dispersal rates rates can can create create aa source-sink source-sink structure structure in in In the absence of differences differences in in habitat habitat quality. quality. In In aa system system of of two two habitats habitats of of the absence of equal (;(n), habitat equal size, size, characterized characterized by by the the same same/~(n), habitat 1I will will be be aa source source and and habitat habitat m12 > m2b and m21 will 2 2 aa sink sink if if m12 > m21, and vice vice versa. versa. More More generally, generally, m12 m12 > > m21 will reinforce reinforce the the source-sink source-sink structure structure if if fl(n) fl(n) > > !2(n). f2(n). Conversely, Conversely, m m12 > m21 m21 will will make make 12 > the the source-sink source-sink structure structure less less pronounced pronounced if if fl(n) fl(n) < < !2(n) f 2 ( n )~ up up to to aa point. point. If If fl(n) fl(n) < < !2(n), f2(n), but but m12 m12 exceeds exceeds m21 m21 by by aa sufficient sufficient margin, margin, the the source-sink source-sink structure habitat 11 will become aa sink. sink. In structure will will become become rreversed e v e r s e d- habitat will become In other other words, words, an upstream upstream habitat habitat of of lower lower quality quality ((but still good good enough enough to to sustain sustain aa popu popuan but still lation lation despite despite the the drain drain due due to to emigration) emigration) may may become become aa source source if if the the asym asymmetry whereas the metry of of dispersal dispersal rates rates is is sufficient, sufficient, whereas the better better downstream downstream will will act act as as (relative) sink. sink. For For specific specific models models of of such such populations, populations, see see Doebeli Doebeli ((1995) aa (relative) 1 99 5 ) and and Kawecki Kawecki and and Holt Holt (2002) (2002).. Ann extreme extreme case case of of asymmetric asymmetric dispersal dispersal iiss one-way one-way dispersal, dispersal, resulting resulting in in A what 1 997) termed black hole hole sink" what Holt Holt and and Gomulkiewicz Gomulkiewicz ((1997) termed aa ""black s i n k "- - aa habitat habitat that that receives receives immigrants immigrants but but sends sends no no emigrants emigrants back back to to the the source. source. Within Within the framework of 1 6 . 1 ) and and ((16.2), 1 6.2), the the framework of the the model model described described by by Eq. Eq. ((16.1) the existence existence of hole sinks Caswell, 11989). 98 9 ) . This of black black hole sinks implies implies that that matrix matrix A(n) is is reducible reducible ((Caswell, This means corresponding to hole means that that eliminating eliminating the the rows rows and and columns columns corresponding to the the black black hole sinks sinks would would have have no no effect effect on on the the equilibrium equilibrium population population sizes sizes and and repro reproductive ductive values values in in the the remaining remaining habitats. habitats. In In other other words, words, population population dynam dynamics ics in in the the source source habitat habitat is is unaffected unaffected by by what what happens happens in in the the sink; sink; from from the the viewpoint viewpoint of of the the source source habitat, habitat, emigration emigration to to the the sink; sink; is is not not different different from from O. For such aa mortality. value of hole sink mortality. The The reproductive reproductive value of black black hole sink habitats habitats is is 0. For such system to exist, the must be good enough sustain aa popu system to exist, the source source habitat(s) habitat(s) must be good enough to to sustain population, lation, despite despite the the drain drain imposed imposed by by emigration. emigration. Note Note that that aa black black hole hole sink sink may may still still send send some some migrants migrants to to another another black black hole hole sink, sink, as as in in the the example example given 1 999a). given by by Rousset Rousset ((1999a).
116. 6. SOURCE-SINK POPULATION DYNAMICS
395 395
Balanced Dispersal A special special case case worth worth considering considering in in the the context context of of asymmetric asymmetric dispersal dispersal A rates rates is is the the balanced balanced dispersal dispersal scenario, scenario, whereby whereby asymmetries asymmetries in in the the dispersal dispersal rate exactly exactly compensate compensate for for differences differences in in habitat habitat quality quality (Doebeli, (Doebeli, 11995; rate 995; Lebreton Lebreton et et aI., al., 2000). 2000). Under Under the the balanced balanced dispersal dispersal scenario, scenario, Vh v h -= 11 and and fh(nh)kimhi fh(~h)~,imhi == 11 for for all all habitats, habitats, i.e., i.e., there there is is no no source-sink source-sink structure. structure. Dispersal Dispersal rates rates leading leading to to aa balanced balanced dispersal dispersal situation situation are are expected expected to to be be favored Doebeli, 11995; 995; Lebreton favored when when dispersal dispersal is is cost cost free free ((Doebeli, Lebreton et et aI., al., 2000). 2000). This Fretwell and 970). This is is equivalent equivalent to to the the ideal ideal free free distribution distribution ((Fretwell and Lucas, Lucas, 11970). Reasons Reasons why why the the evolution evolution of of balanced balanced dispersal dispersal may may be be prevented, prevented, and and thus thus the source-sink source-sink population population structure structure may may persist persist over over evolutionary evolutionary time, time, are are the discussed in in Section Section 116.5. discussed 6.5.
Stage-Structured Populations Populations Age- or Stage-Structured Generalization 1 6 . 1 ) and 1 6.2) to Generalization of of the the model model described described by by Eq. Eq. ((16.1) and ((16.2) to multiple multiple age classes classes (or stages)) is, is, in in principle, principle, straightforward, straightforward, provided provided that that the the vital vital age (or stages rates ((survival and fecundity) fecundity) are are assumed to be be aa function function of of age age ((stage) and rates survival and assumed to stage) and the current current habitat habitat only only (Lebreton, Nevertheless, the the consequences consequences of of the (Lebreton, 11996). 996). Nevertheless, source-sink source-sink population population structure structure in in age-structured age-structured populations populations remain remain rather rather unexplored. unexplored. The The definition definition of of sources sources versus versus sinks sinks based based on on the the number number of of emigrants emigrants versus versus immigrants immigrants can can still still be be upheld upheld if if dispersal dispersal occurs occurs at at aa well welldefined case, e.g., defined prereproductive prereproductive stage, stage, as as is is the the case, e.g., in in perennial perennial plants plants or or corals. corals. However, However, this this definition definition does does not not seem seem appropriate appropriate if if an an individual individual can can change change its habitat habitat at at different different ages stages, and it repeatedly, as is birds its ages or or stages, and do do it repeatedly, as is the the case case in in birds and mammals. mammals. This This can can be illustrated by equivalent of of the and be illustrated by considering considering an an equivalent the balbal anced dispersal in the the previous 1 99 6 ) anced dispersal scenario scenario discussed discussed in previous paragraph. paragraph. Lebreton Lebreton ((1996) has shown shown that that under under cost-free dispersal, natural natural selection selection should should favor favor a has cost-free dispersal, a combination of age-specific dispersal rates that that would would equalize equalize the the vector vector of of combination of age-specific dispersal rates age-specific reproductive reproductive values values across habitats. However, However, in in contrast to the the age-specific across habitats. contrast to discrete generations this case case does does imply imply balanced dispersal (Lebreton ( Lebreton discrete generations case, case, this balanced dispersal et al., aI., 2000). 2000). It It is is thus thus difficult difficult to to derive derive general general predictions this model model et predictions from from this and will become complicated if, and more more work work is is needed. needed. The The problem problem will become even even more more complicated if, as is is biologically biologically realistic, realistic, survival survival and and fecundity fecundity depend depend not not only only on on the the as current habitat, habitat, but but on the habitats individual has has experienced experienced in in the past. current on the habitats an an individual the past. Nonetheless, incorporating incorporating both both age age structure structure and and habitat heterogeneity will, will, Nonetheless, habitat heterogeneity in many many cases, cases, substantially substantially improve improve the the predictive predictive power power of of managementmanagement in oriented oriented models models of of specific specific natural natural populations populations (e.g., (e.g., Doak, Doak, 1995). 1 995).
Spatially Spatially Explicit Explicit Models Models The above above discussion assumed environmental environmental variation in the the form form of of aa The discussion assumed variation in set of of discrete discrete habitats, habitats, such such that that within within aa given given habitat habitat individuals individuals become become set mixed thoroughly thoroughly and and density density is is the the same same everywhere. everywhere. This may be be aa suffisuffi mixed This may cient approximation approximation for for systems systems such such as as herbivorous herbivorous insects insects that that use use two two cient host plant plant species species occurring occurring in in the the same same area area or or in in other other cases cases where where wellwell host defined discrete habitat patches patches form form aa relatively relatively fine-grained fine-grained mosaic mosaic (e.g., ( e.g., defined discrete habitat Blondel et et al., aI., 1992). 1 992 ) . However, However, the the spatial spatial location location of of individuals individuals must must be be Blondel
TADEUSZ KAWECKI TADEUSZ I.) . KAWECKI
3396 96
explicitly considered considered if if variation variation in in environmental environmental factors factors is is continuous. continuous. This This explicitly can be be done done with with aa diffusion diffusion approximation approximation (e.g., (e.g. , Kirkpatrick Kirkpatrick and and Barton, Barton, can 1 997) or or with with an an individual-based individual-based model. model. A A spatially spatially explicit explicit approach approach will will 1997) also be be necessary necessary if if there there are are discrete discrete habitat habitat types, types, but but the the patches patches are are large large also relative to to the the dispersal dispersal distance distance (e.g., (e.g., Boughton, Boughton, 2000). 2000 ) . Such Such aa case case is is illusillus relative trated in in Fig. Fig. 16.3, 1 6 . 3 , where where high-quality high-quality habitat habitat 11 borders borders low-quality low-quality habitat habitat trated along aa sharp sharp ecotone ecotone (model (model details details in in the the figure figure legend). legend). As As expected, expected, at at 22 along equilibrium, habitat habitat 11 is is aa source source and and habitat habitat 22 aa sink, sink, but but the the spatial spatial model model equilibrium, reveals that that the the source-sink source-sink nature nature of of the the two two habitats habitats is is most most pronounced pronounced reveals close to to the the ecotone. ecotone. That That is, is, in in habitat habitat 11 the the excess excess of of births births over over deaths deaths close (fh(fih) > > 1), 1 ), and and of of thus thus emigration emigration over over immigration, immigration, is is greatest greatest just just left left of of (fh(~) the ecotone ( light solid solid line line in in Fig. Fig. 16.3). 1 6. 3 ) . The The same same holds holds for for the the excess excess of of the ecotone (light deaths over over births births (fh(~h) (fh(fih) < < 1) 1 ) on on the the other side of of the the ecotone. ecotone. As As one one moves moves deaths other side away from from the the ecotone, ecotone, the the population population density density (heavy (heavy line) line ) converges converges to to the the away local carrying carrying capacity capacity and and fh(~) fh( fih ) converges converges to to 1. 1 . Note, Note, however, however, that that the the local reproductive value value (dotted (dotted line) line) does does not not follow follow the the pattern of fh(~h) fh( fih) within within reproductive pattern of the habitats. habitats. Instead, Instead, in in the the better better habitat habitat it it declines declines somewhat somewhat as as the the ecoeco the tone is is approached, approached, indicating indicating that that the the improved improved lifetime lifetime reproductive reproductive sucsuc tone cess due due to to lower lower density density does does not not quite quite compensate compensate for for the the fact fact that that some some cess of the the offspring offspring will will end end up up in in the the poor poor habitat. habitat. This This is is thus thus another case of another case where the pattern emigration versus where the pattern based based on on births births versus versus deaths deaths and and emigration versus immi immigration does not pattern of values. gration does not agree agree with with the the pattern of reproductive reproductive values. habitats, Even if if the the environment environment consists consists of of discrete discrete patches patches of of different different habitats, Even their connectivity will differ their size, size, shape, shape, spatial spatial arrangement, arrangement, and and connectivity will often often cause cause different patches the same habitat type different dispersal rates. Such Such aa ent patches of of the same habitat type to to have have different dispersal rates. patch modeled within patch network network may may be be modeled within the the framework framework of of the the patch patch model model described earlier [Eq. 1 6 . 1 ) ] . However, described earlier [Eq. ((16.1)]. However, the the dispersal dispersal rates rates would would now now have have to to be simple model pre be defined defined on on aa patch-to-patch patch-to-patch basis. basis. Thus, Thus, in in contrast contrast to to the the simple model presented at patches of habitat type sented at the the beginning beginning of of this this section, section, patches of the the same same habitat type could could not not be be lumped lumped together. together. Instead, Instead, the the vector vector of of population population sizes sizes n(t) n(t) would would have have to to have have an an entry entry for for each each patch, patch, not not only only for for each each habitat habitat type. type. Consequently, Consequently, the the definition definition of of source source versus versus sink sink could could now now be be applied applied to to individual individual patches; patches; depending depending on on their their connectivity, connectivity, size, size, and and shape, shape, some some patches patches of of aa given given 1100 88 'S(
66
. . . ......
.......
1: 4 4
22
00 -20 -20
I
.................... habitat habitat 11 habitat habitat 22 +-- ---. ~ -1 00 110 0 -100 Spatial Spatial distance distance xx
11.6 .6 11.4 .4 11.2 .2 11 0.8 0.6 0.4 0.4 0.2 0.2 00 20 20
�
x X 2 ~. A C x
Fig. Fig. 116.3 6.3 A A spatially spatially explicit explicit source-sink source-sink model model with with two two habitat habitat patches. patches. The The population population density density n(x) n(x) (heavy (heavy line, line, left left axis), axis), net net reproductive reproductive rate rate f(n(x» f(n(x)) (light (light line), line), and and the the reproductive reproductive value value (dotted (dotted line) line) at at equilibrium equilibrium are are plotted plotted as as aa function function of of spatial spatial location location x. x. Discrete Discrete genera generations tions are are assumed, assumed, with with census census after after dispersal. dispersal. The The net net reproductive reproductive rate rate f(n(x» f(n(x)) = = Rhl(l Rh/(1 + + n(x» n(x)),, where O in where Rh Rh = l10 in habitat habitat 11 and and Rh Rh = 4 4 in in habitat habitat 2. 2. Dispersal Dispersal distances distances follow follow aa normal normal distribu distribution tion with with mean mean 00 and and acr = = 5. 5. =
=
1 6. 16.
SOURCE-SINK POPULATION POPULATION DYNAMICS DYNAMICS SOURCE-SINK
397 3 97
habitat type type may may act act as as sources sources whereas whereas others others may may act act as as sinks. sinks. Taking Taking into into habitat account such such aa spatial effect is is of of particular particular importance importance in in applied applied models models account spatial effect developed for for the the management management and and conservation conservation of of particular particular species. species. developed
1 6.3 16.3
ECOLOGICAL CONSEQUENCES CONSEQUENCES OF OF SOURCE-SINK SOURCE-SINK ECOLOGICAL DYNAMICS: THEORY THEORY DYNAMICS: In addition addition to to the the defining defining feature feature of of source-sink source-sink structure structure m - net net flow flow of of In dispersing individuals individuals from from source source to to sink habitats m - aa number number of of other other ecoeco dispersing sink habitats logical consequences consequences of of source-sink source-sink population population structure structure have been predicted predicted logical have been by mathematical mathematical models. models. These These predictions predictions are are summarized summarized in in this this section, section, by whereas Section Section 16.4 1 6.4 reviews reviews relevant relevant empirical empirical examples. examples. whereas
Species Range Range Species Immigration stable local local population in aa habitat, in which which Immigration can can maintain maintain aa stable population in habitat, in deaths exceed low density sinks ) . Unless Unless limited limited by by deaths exceed births births even even at at low density (absolute (absolute sinks). barriers ranges will will therefore therefore as as aa rule rule extend extend beyond beyond the the barriers to to dispersal, dispersal, species species ranges areas where where habitat habitat quality quality is is sufficient to sustain sustain aa population population without without immiimmi areas sufficient to gration where the local conditions conditions satisfy satisfy the the species' species' niche niche requirements; requirements; gration (i.e., (i.e., where the local Pulliam, 11988, 988, 2000). 2000). This both to to the the geographical range of the Pulliam, This applies applies both geographical range of the species and distribution on the scale scale of of local local habitat habitat variation variation (habitat species and to to its its distribution on the (habitat occupancy) In practice, will often be difficult to distinguish distinguish between between an an occupancy).. In practice, it it will often be difficult to absolute habitat that that is not quite and acts acts as as relative absolute sink sink and and aa habitat is not quite optimal optimal and relative sink, sink, but but still still satisfies satisfies the the species' species' niche niche requirements. requirements. Successful Successful reproduction reproduction may may take take place place in in absolute absolute sinks sinks and and population population density density may may be be relatively relatively high high and and stable; stable; it it may may not not be be apparent apparent that that the the population population would would deterministically deterministically go go extinct extinct without without immigration. immigration.
Population Population Size Size and and Distribution Distribution What (global) What is is the the effect effect of of source-sink source-sink population population structure structure on on the the total total (global) population population size size?? An An answer answer will will depend depend on on the the precise precise formulation formulation of of this this question. question. First, First, one one may may compare compare aa set set of of habitat habitat patches patches connected connected by by dispersal dispersal (and (and thus thus potentially potentially having having source-sink source-sink structure) structure) with with the the same same set set of of patches patches each each inhabited inhabited by by an an isolated isolated population. population. This This perspective perspective thus thus focuses focuses on on the the effect effect of of changing changing the the dispersal dispersal rate(s) rate(s) while while keeping keeping the the landscape landscape unchanged. unchanged. In 1 98 5 ) showed In aa two-patch two-patch model model with with symmetric symmetric passive passive dispersal, dispersal, Holt Holt ((1985) showed that that no no simple simple general general prediction prediction about about the the effect effect of of dispersal dispersal on on the the total total population population size size can can be be made. made. Whether Whether the the total total population population size size will will increase increase or or decrease decrease as as aa result result of of dispersal dispersal will will depend depend on on the the shape shape of of the the functions functions relating relating local local density density to to the the local local birth birth and and death death rates. rates. This This applies applies even even if if the the poorer 1 99 5 ) considered poorer habitat habitat is is an an absolute absolute sink. sink. Doebeli Doebeli ((1995) considered two two patches patches of of the the same same habitat habitat quality quality and and showed showed that that asymmetric asymmetric dispersal, dispersal, which which resulted resulted in in aa source-sink source-sink structure, structure, led led to to an an increase increase of of the the total total population population size. size. It It is is not not clear clear how how general general this this result result is is (only (only aa numerical numerical example example is is presented). presented). A A more more general general prediction prediction concerns concerns the the effect effect of of dispersal dispersal on on the the distribution distribution of of
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the the population population among among the the habitats: habitats: with with increasing increasing dispersal dispersal the the fraction fraction of of the total total population population living living in in the the source source habitats habitats tends tends to to decrease decrease (e.g., (e.g., Holt, Holt, the Pulliam, 2000; 2000; Kawecki Kawecki and and Holt, Holt, 2002 2002).) . 11985; 985; Pulliam, Second, Second, one one may may ask ask how how adding adding aa sink sink habitat habitat oorr changing changing its its size size affects affects the total total population population size size and and the the population population in in aa high-quality high-quality source source habitats, habitats, the assuming assuming that that the the dispersal dispersal pattern pattern is is unchanged. unchanged. It It is is not not surprising surprising that that replacing replacing some some good good habitat habitat with with poor poor habitat habitat will will reduce reduce the the overall overall popula population size. size. It It is is more more interesting interesting to to ask ask how how the the population population size size is is affected affected if if tion some some sink sink habitat habitat patches patches are are eliminated eliminated (converted (converted into into hostile hostile "nonhabitat" "nonhabitat" or "matrix" "matrix")) while while keeping keeping the the amount amount of of the the source source habitat habitat constant. constant. Under Under or passive passive dispersal dispersal this this will will lead lead to to aa greater greater fraction fraction of of propagules propagules perishing perishing in in the the "nonhabitat," "nonhabitat," causing causing aa reduction reduction of of the the total total population population size. size. This This is is not not necessarily the the case case if if dispersal dispersal is is active active and and thus thus the the dispersing dispersing individuals individuals necessarily avoid the the ""nonhabitat." In one one model model that that made made this this assumption assumption ((Pulliam and avoid nonhabitat." In Pulliam and Danielson, 99 1 ), the Danielson, 11991), the number number of of individuals individuals in in the the source source habitats habitats increased increased as the the area area of of sink sink habitat habitat was was reduced. The effect effect on on the the total total population population size size as reduced. The in Pulliam Pulliam and and Danielson's Danielson's model depended depended on on the the degree degree of of habitat habitat selection. selection. in With poor habitat selection selection ability, ability, the the total total population increased as as the the With poor habitat population size size increased area decreased. With area of of sink sink habitat habitat decreased. With aa better better habitat habitat selection selection ability, ability, the the total total population size peaked peaked at habitat. In population size at an an intermediate intermediate amount amount of of sink sink habitat. In contrast, contrast, an individual-based individual-based model model (Wiegand (Wiegand et et aI., al., 11999) predicted that that eliminating eliminating an 999) predicted sink habitat will lead lead to to aa reduction of the the total total population This discrep discrepsink habitat will reduction of population size. size. This ancy suggests suggests that that no no simple simple general general predictions predictions can can be be made the effect effect ancy made about about the of eliminating eliminating patches patches of of sink sink habitat habitat on on the the overall overall population population size. size. of
P o p u l a t i o n Stability S t a b i l i t y and a n d Persistence Persistence Population If If too too many many dispersing dispersing individuals individuals end end up up in in aa habitat habitat that that is is an an absolute absolute sink, sink, the entire entire population population will will go go deterministically deterministically extinct (Pulliam, 1988; Donovan 1 988; Donovan and Thompson, Thompson, 200 2001). This is of source-sink source-sink populaand 1 ) . This is the the most most obvious obvious effect effect of popula tion structure on population population persistence. as extinction extinction risk, tion structure on persistence. More More generally, generally, as risk, at at least on the the short least on short term, term, tends tends to to be be correlated correlated negatively negatively with with population population size size ((Chapter Chapter 14), 14), the the effects effects of population structure equilibrium of source-sink source-sink population structure on on equilibrium population size likely to to have have implications implications for for population population persistence. persistence. population size are are likely However, the the existence existence of sink habitats habitats may may affect population persistence persistence However, of sink affect population by affecting affecting the by the population population dynamics dynamics independently independently of of their their effects effects on on the the equilibrium population population size. size. Several Several models models (Holt, (Holt, 1984, 1 984, 1985; 1 985; McLaughlin McLaughlin equilibrium and Roughgarden, Roughgarden, 1991) 1 9 9 1 ) predict predict that that adding adding aa habitat habitat that that is is aa sink sink for for the the and prey prey can can stabilize stabilize an an otherwise otherwise unstable unstable or or neutrally neutrally stable stable predator-prey predator-prey model. The The source-sink source-sink structure structure also also tends tends to to have have aa stabilizing stabilizing effect effect on on the the model. dynamics of of aa host-parasitoid host-parasitoid model model (Holt (Holt and and Hassell, Hassell, 1993). 1 99 3 ) . Finally, Finally, dynamics Doebeli (1995), ( 1 995), generalizing generalizing results results of of Hastings Hastings (1993), ( 1 993), showed showed that that dispersal dispersal Doebeli between between two two patches patches of of the the same same quality quality tends tends to to stabilize stabilize intrinsically intrinsically chaotic chaotic population dynamics dynamics (see ( see also also Gyllenberg et al., aI., 1996). 1 996). The The stabilizing stabilizing effect effect population Gyllenberg et is is stronger stronger if if dispersal dispersal rates rates are are asymmetric asymmetric so so that that at at equilibrium equilibrium there there is is aa source-sink population population structure. structure. One One intuitive intuitive explanation explanation of of those those results results is is source-sink that that sink habitats habitats act act as a buffer, buffer, absorbing absorbing surplus surplus individuals individuals produced produced in in source habitats. habitats. This This prevents prevents the the population population from from greatly overshooting the the source greatly overshooting equilibrium density, density, thus thus reducing reducing or or averting averting aa population population crash crash due due to to equilibrium
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overcompensating overcompensating density density dependence. dependence. In In contrast, contrast, dispersal dispersal to to aa sink sink habitat habitat that that is is available available only only seasonally seasonally can can destabilize destabilize population population dynamics; dynamics; this this mechanism (Lomnicki, 11995). 995). mechanism has has been been proposed proposed to to contribute contribute to to rodent rodent cycles cycles (Lomnicki, Existence of of aa sink sink habitat habitat may may make make the the population population less less sensitive sensitive to to envir envirExistence onmental onmental fluctuations fluctuations affecting affecting birth birth and and death death rates, rates, provided provided that that the the sink sink habitat is (Holt, 11997). 997). An case of habitat is less less affected affected by by the the fluctuations fluctuations (Holt, An extreme extreme case of this this type subject to occasional catastrophes type involves involves aa source source habitat habitat subject to occasional catastrophes that that wipe wipe out out the the local local population. population.
Age Age Structure Structure In structure in In organisms organisms with with overlapping overlapping generations, generations, the the age age structure in source source and and sink sink habitats habitats may may differ differ as as aa consequence consequence of of differences differences in in local local survival. survival. More More interestingly, dispersal dispersal into into sink sink habitats habitats may may be be age age dependent. dependent. In In territorial territorial interestingly, species, young species, young individuals individuals may may be be more more likely likely to to be be excluded excluded from from breeding breeding in in optimal, optimal, source source habitats. habitats. Sink Sink habitats habitats will will then then contain contain aa disproportionately disproportionately large large fraction fraction of of young young adults. adults.
116.4 6.4 ECOLOGICAL ECOLOGICAL CONSEQUENCES CONSEQUENCES OF OF SOURCE-SINK SOURCE-SINK DYNAMICS: DYNAMICS: EMPIRICAL EMPIRICAL EVIDENCE EVIDENCE Basic Basic Source-Sink Source-Sink Structure Structure There There is is increasing increasing evidence evidence of of source-sink source-sink structure structure in in natural natural popula populations, tions, involving involving habitat habitat variation variation at at various various spatial spatial scales. scales. At At aa continental continental scale, wolf scale, it it has has been been reported reported in in reindeer, reindeer, in in which which low low recruitment recruitment due due to to wolf predation predation causes causes boreal boreal forests forests to to act act as as sink sink habitats; habitats; the the tundra tundra is is the the source source ((Bergerud, Bergerud, 11988). 9 8 8 ) . Similarly, Similarly, the the reproductive reproductive success success of of pied pied flycatchers flycatchers (Ficedula does not, on average, average, com (Ficedula hypoleuca) at at the the northern northern range range limit limit does not, on compensate pensate for for mortality mortality (although (although it it may may do do so so in in good good years) years);; these these northern northernmost populations must most populations must thus thus be be maintained maintained by by immigration immigration (Jarvinen (J~rvinen and and Vasainen, 984). In Vfisfiinen, 11984). In black-throated black-throated blue blue warbler warbler (Dendroica (Dendroica caerulescens), caerulescens), population population density density and and estimated estimated habitat habitat quality quality decline decline aass one one moves moves away away in in either Graves, 11997). 997). either direction direction from from the the Appalachian Appalachian mountains mountains ((Graves, The The source-sink source-sink structure structure at at aa more more local local spatial spatial scale scale has has been been well well charac characterized terized in in blue blue tits tits (Parus (Parus caeruleus) caeruleus) in in southern southern France, France, where where patches patches of of good good (deciduous) (deciduous) and and poor poor (sclerophyllous) (sclerophyllous) habitat habitat form form aa mosaic mosaic landscape landscape with with aa patch 992). Even patch size size on on the the order order of of 11 to to 100 100 km2 km 2 (Blondel (Blondel et et aI., al., 11992). Even though though the the breeding less than half that breeding density density in in the the sclerophyllous sclerophyllous habitat habitat is is less than half that in in the the decidu deciduous ous habitat, habitat, birds birds in in the the sclerophyllous sclerophyllous habitat habitat have have aa smaller smaller clutch clutch size size and and aa lower 996). The lower breeding breeding success success (Dias (Dias and and Blondel, Blondel, 11996). The breeding breeding performance performance in see in the the sink sink is is impaired impaired additionally additionally by by aa locally locally maladaptive maladaptive laying laying date date ((see Section 6.6) and (Dias Section 116.6) and possibly possibly by by aa smaller smaller size size of of individuals individuals breeding breeding there there (Dias and 996). Genetic and Blondel, Blondel, 11996). Genetic marker marker data data are are also also consistent consistent with with an an asymmetric asymmetric gene deciduous to gene flow flow from from the the deciduous to the the sclerophyllous sclerophyllous habitat habitat patches patches (Dias (Dias et et aI., al., 11996). 996). A A number number of of North North American American migratory migratory songbirds songbirds suffer suffer extreme extreme rates rates of of nest nest parasitism parasitism and and predation predation in in fragmented fragmented forest forest patches patches of of agricultural agricultural and suburban landscapes. and suburban landscapes. These These highly highly fragmented fragmented habitats habitats constitute constitute sinks sinks
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supported supported by by immigration immigration from from more more extensive extensive forests forests (Robinson (Robinson et et aI., al., 1995). 1995). A A similar similar source-sink source-sink structure structure related related to to habitat habitat fragmentation fragmentation has has been been observed observed in in the the reed reed warbler warbler in in The The Netherlands Netherlands (Foppen (Foppen et et aI., al., 2000) 2000).. A A source-sink structure local scale been found pot source-sink structure at at aa more more local scale has has been found in in the the checkers checkerspot clearings and butterfly butterfly (Euphydryas (Euphydryas editha), where where forest forest clearings and rocky rocky outcrops outcrops con constitute spatially separated stitute two two spatially separated habitats, habitats, each each with with aa different different host host plant plant for for the the caterpillars caterpillars (Boughton, (Boughton, 2000) 2000).. A A source-sink source-sink structure structure at at the the scale scale ooff meters meters occurs occurs iinn the the snow snow buttercup buttercup (Ranunculus adoneus), aa perennial plant confined perennial alpine-zone alpine-zone plant confined to to deep deep snow snow beds beds of of the the Rocky Rocky Mountains. Mountains. The The beginning beginning of of the the vegetative vegetative season season and and flowering flowering time snowmelt (Stanton 997). As time are are determined determined by by the the snowmelt (Stanton and and Galen, Galen, 11997). As the the pattern pattern of patches of of snow snow accumulation accumulation is is fairly fairly constant constant from from year year to to year year and and patches of old old snow snow tend tend to to melt melt from from the the edges, edges, the the relative relative timing timing of of snowmelt snowmelt at at different different localities fairly constant year to only tens localities is is fairly constant from from year to year. year. Localities Localities separated separated by by only tens of of meters may weeks apart. is correlated meters may become become clear clear of of snow snow several several weeks apart. As As seed seed size size is correlated positively with with season length, plants plants at at later-melting later-melting sites sites produce produce smaller smaller seeds seeds positively season length, (Galen 993). These establishment rate, (Galen and and Stanton, Stanton, 11993). These small small seed seed have have aa low low establishment rate, and and most seeds produced produced in most individuals individuals at at all all localities localities come come from from large large seeds in early early melting melting sites Galen, 11997). 997). The sites (Stanton (Stanton and and Galen, The source-sink source-sink population population structure structure in in this this species is least partially mediated by species is thus thus at at least partially mediated by maternal maternal effects. effects. A A source-sink source-sink structure structure dominated dominated by by asymmetry asymmetry in in dispersal dispersal rates rates imposed imposed 981, by by wind wind has has been been described described in in the the sand sand dune dune plant plant Cakile edentula edentula (Keddy, (Keddy, 11981, 11982; 982; Watkinson, 985). In Watkinson, 11985). In that that system, system, the the base base of of aa dune dune oonn the the seaward seaward side side is is the the source source habitat habitat where where most most seeds seeds are are produced. produced. However, However, because because most most seeds closer to seeds are are transported transported by by wind wind to to the the sink sink habitat habitat closer to the the dune dune crests, crests, plant plant density considerably higher density in in the the latter latter habitat habitat is is considerably higher than than in in the the source source habitat. habitat. At At the same time, time, seed seed emigration emigration from from the the source source habitat habitat reduces reduces competition competition and and the boosts 985). In boosts the the reproductive reproductive output output from from that that habitat habitat (Watkinson, (Watkinson, 11985). In this this case case the the source source and and sink sink habitats habitats are are only only separated separated by by several several meters. meters. The above review The above review of of examples examples of of source-sink source-sink structure structure in in natural natural popula populations tions is is not not meant meant to to be be exhaustive, exhaustive, and and as as the the interest interest in in this this aspect aspect of of spatial spatial ecology increases, more ecology increases, more evidence evidence will will accumulate. accumulate. Relatively Relatively unexplored unexplored remain cases of caused by remain cases of potential potential source-sink source-sink dynamics dynamics caused by biotic biotic interactions, interactions, particularly particularly the the source-sink source-sink structure structure of of parasite parasite populations populations caused caused by by varia variation Jokela, 11996). 996). tion in in host host susceptibility susceptibility (e.g., (e.g., Lively Lively and and Jokela,
Other Other Ecological Consequences Despite accumulating Despite accumulating evidence evidence for for the the ubiquity ubiquity of of source-sink source-sink structure structure in in natural populations, populations, data data directly directly addressing addressing specific specific predictions predictions concerning concerning natural its ecological consequences scarce. Addressing its ecological consequences are are scarce. Addressing these these predictions predictions directly directly would would involve involve experimental experimental intervention, intervention, e.g., e.g., changing changing the the amount amount of of source source or or sink sink habitat habitat or or altering altering the the dispersal dispersal pattern. pattern. Applying Applying this this approach approach to to natural populations also question natural populations may may not not only only be be technically technically difficult, difficult, but but also questionable able on on ethical ethical or or legal legal grounds. grounds. For For example, example, it it is is likely likely that that some some of of the the examples earlier involve involve populations examples mentioned mentioned earlier populations persisting persisting in in absolute absolute sinks, sinks, unable 98 8 ; unable to to sustain sustain aa population population without without immigration immigration (e.g., (e.g., Bergerud, Bergerud, 11988; Robinson 99 5 ) . However, Robinson eett aI., al., 11995). However, definitive definitive confirmation confirmation would would require require "clos "closing" ing" the the population, population, i.e., i.e., preventing preventing immigration immigration and and emigration. emigration.
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Given direct experimental Given the the problems problems with with aa direct experimental approach, approach, monitoring monitoring the the consequences natural experiments, consequences of of ""natural experiments,"" i.e., i.e., natural natural or or anthropogenic anthropogenic changes changes in in the the environment, environment, has has aa particular particular value. value. For For example, example, the the importance importance of of aa sink habitat was demonstrated sink habitat for for population population persistence persistence was demonstrated clearly clearly in in aa source source992, an unusual sink population of checkers pot butterfly sink population of the the checkerspot butterfly E. editha. editha. In In 11992, an unusual summer popu summer frost frost killed killed all all larvae larvae in in the the source source habitat habitat (forest (forest clearings) clearings).. The The population persisted only because larvae (rocky outcrops) lation persisted only because larvae in in the the sink sink habitat habitat (rocky outcrops) sur survived (Thomas et 996; Boughton, 999) (the vived (Thomas et aI., al., 11996; Boughton, 11999) (the outcrops outcrops were were presumably presumably the the main main habitat habitat of of this this species species before before humans humans created created forest forest clearings) clearings).. A A popu population subject to lation structure structure with with the the source source populations populations subject to repeated repeated catastrophes catastrophes has (Frouz and 1 ). Another has also also been been reported reported for for aa midge midge (Frouz and Kindlmann, Kindlmann, 200 2001). Another study Luttrell et 99 9 ) suggested study ((Luttrell et aI., al., 11999) suggested that that extinction extinction of of numerous numerous local local popu populations lations of of aa cyprinid cyprinid fish fish was was due due to to disruption disruption of of dispersal dispersal between between source source and natural and sink sink habitats habitats by by artificial artificial reservoirs. reservoirs. The The problem problem with with such such ""natural experiments" experiments" is is often often the the lack lack of of replication replication and and controls. controls. An An alternative alternative approach approach involves involves spatial spatial analysis analysis of of landscape landscape ecology ecology (Chapter 2), populations can (Chapter 2), whereby whereby the the properties properties of of local local populations can be be correlated correlated not not only only with with the the local local habitat habitat conditions, conditions, but but with with the the composition composition of of the the regional regional habitat habitat matrix matrix (e.g., (e.g., the the presence presence and and size size of of nearby nearby source source and and or or sink sink patches) patches).. Foppen Foppen et et ai. al. (2000) (2000) used used this this approach approach to to show show that that the the existence existence of of sink sink habitat habitat patches patches leads leads to to aa greater greater size size and and stability stability of of reed reed warbler warbler popu populations 1 997) has lations in in source source patches. patches. Graves Graves ((1997) has shown shown that that the the proportion proportion of of year yearlings lings among among breeding breeding males males of of black-throated black-throated blue blue warbler warbler (D. caerulescens) caerulescens) is is correlated correlated negatively negatively with with habitat habitat quality, quality, indicating indicating an an effect effect of of source-sink source-sink dynamics population age dynamics on on the the population age structure. structure. The The influence influence of of source-sink source-sink dynam dynamics population size been demonstrated ics on on the the population size structure structure has has been demonstrated in in blue blue tits tits in in south southern France, where males breeding habitat are ern France, where males breeding in in the the source source habitat are larger larger than than those those breeding breeding in in the the sink sink habitat habitat (size (size measured measured as as tarsus tarsus length; length; Dias Dias and and Blondel, Blondel, 11996). 996). However, However, because because male male fledglings fledglings produced produced in in the the two two habitat habitat types types do do not (Dias and 996), the not differ differ in in tarsus tarsus length length (Dias and Blondel, Blondel, 11996), the difference difference with with respect respect to smaller individuals to breeding breeding males males must must reflect reflect the the displacement displacement of of smaller individuals from from the the source. source. As As any any approach approach based based on on correlations, correlations, this this approach approach does does not not directly directly address causation potentially confounded included in address causation and and can can be be potentially confounded by by factors factors not not included in the analysis. This problem can the analysis. This problem can be be illustrated illustrated by by results results from from the the same same study study of of blue blue tits. tits. The The population population density density in in the the sclerophyllous sclerophyllous habitat habitat in in southern southern France, France, where where it it acts acts as as aa sink, sink, is is much much lower lower than than in in the the same same habitat habitat in in Corsica, Corsica, where where it it is is aa dominant dominant habitat habitat not not affected affected by by immigration immigration (Dias (Dias and and Blondel, 996). These Blondel, 11996). These results results seem seem to to contradict contradict the the prediction prediction that that immigra immigration should boost boost the see earlier earlier discussion). tion from from aa source source should the density density in in the the sink sink ((see discussion). The The discrepancy discrepancy is is explained explained by by the the fact fact that that reproductive reproductive success success in in the the sclero sclerophyllous phyllous habitat habitat in in Corsica Corsica is is higher higher than than in in the the same same habitat habitat in in southern southern France Blondel, 11996). 996). France (Dias (Dias and and Blondel, A A powerful powerful but but rarely rarely used used approach approach to to study study consequences consequences of of the the source sourcesink setting up sink population population structure structure involves involves setting up controlled controlled experimental experimental source-sink source-sink systems systems in in the the laboratory laboratory or or in in outdoor outdoor enclosures enclosures or or "mesocosms. "mesocosms."" Davis 1 99 8 ) used Davis and and collaborators collaborators ((1998) used this this approach approach to to study study the the effect effect of of dispersal dispersal on on population population size size and and distribution distribution along along an an environmental environmental gradient. gradient. Their population cages, Their system system involved involved four four Drosophila population cages, arranged arranged along along aa series series of 10, 15, 20, and to of temperatures temperatures ((10, 15, 20, and 25°C), 25~ to simulate simulate four four habitat habitat patches patches along along
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aa thermal thermal gradient. gradient. In In one one treatment, treatment, adjacent adjacent cages cages were were connected connected with with plas plastic tubes, tubes, enabling enabling dispersal dispersal (dispersal (dispersal rate rate about about 66% per day) day) and and thus thus creating creating tic % per conditions under under which which the the source-sink source-sink structure structure was was expected. expected. This This could could be be conditions contrasted contrasted with with aa no-dispersal no-dispersal treatment, treatment, which which simulated simulated isolated isolated populations populations living living at at different different temperatures. temperatures. Three Three Drosophila species species were were tested tested separately. separately. As As predicted predicted by by source-sink source-sink models, models, in in D. melanogaster and and D. simulans per permitting mitting dispersal dispersal led led to to reduced reduced density density in in patches patches that that had had high high density density under under no no dispersal dispersal and and to to increased increased density density at at marginal marginal temperatures. temperatures. The The pattern pattern was was less less clear clear in in D. subobscura, in in which which aa reduction reduction of of density density at at the the optimal optimal temperature temperature was was not not accompanied accompanied by by aa marked marked increase increase of of population population size size at at suboptimal suboptimal temperatures. temperatures. In In all all three three species, species, dispersal dispersal led led to to maintenance maintenance of of local local populations populations in in absolute absolute sinks, sinks, i.e., i.e., at at temperatures temperatures at at which which local local popu popul Ooe for lations lations went went extinct extinct in in the the absence absence of of dispersal dispersal ((10~ for D. melanogaster and and D. simulans, 25 25~e for for D. subobscura). Although Although Davis Davis and and colleagues colleagues did did not not address address this this question question statistically, statistically, in in all all three three species species the the overall overall (global) (global) popula population size size tended tended to to be be larger larger in in the the absence absence of of dispersal. dispersal. This This study study points points to to the the tion potential potential usefulness usefulness of of experimental experimental source-sink source-sink model model systems systems to to study study eco ecological and and evolutionary evolutionary consequences consequences of of the the source-sink source-sink structure. structure. Because Because of of logical scale scale issues, issues, it it can can only only be be used used with with some, some, mostly mostly invertebrate, invertebrate, model model systems. systems. However, However, use use of of such such model model laboratory laboratory systems systems enabled enabled important important advances advances in in other areas of ecology their use other areas of ecology and and evolutionary evolutionary biology, biology, and and their use to to address address source-sink-related questions questions should should be be promoted. promoted. source-sink-related °
116.5 6.5
NATURAL SELECTION SELECTION ON ON DISPERSAL DISPERSAL AND AND EVOLUTIONARY EVOLUTIONARY NATURAL STABILITY OF SOURCE-SINK POPULATION STRUCTURE STABILITY OF SOURCE-SINK POPULATION STRUCTURE Given the expected reproductive success is lower lower in in aa sink sink than than in in a Given that that the expected reproductive success is a source habitat, one one would would expect that dispersal dispersal from from source to sink sink habitats source habitat, expect that source to habitats should be countered by natural selection. As a result, the the dispersal dispersal pattern pattern should be countered by natural selection. As a result, should evolve evolve toward toward retaining retaining more more individuals individuals in in the the source, source, up up to to the the point point should at which which differences differences in in local local density density compensate compensate for for differences differences in in habitat habitat at quality and and the the source-sink source-sink structure disappears (balanced ( balanced dispersal dispersal scenario, scenario, quality structure disappears Section 16.2). intuitive argument 1 6 .2). This This intuitive argument has has been been supported supported by formal formal analysis analysis of of a patch patch model model assuming assuming passive dispersal dispersal (Doebeli, ( Doebeli, 1995; 1 995; Lebreton Lebreton et al., aI., 2000 ); it it also also underlies underlies the the ideal ideal free distribution model model for for actively actively disperdisper 2000); free distribution sing To explain sing organisms organisms (Fretwell ( Fretwell and and Lucas, Lucas, 1970). 1 970 ) . To explain why why the the source-sink source-sink population structure structure should should persist persist over over evolutionary evolutionary time, time, one one must must find find population reasons why why the the above above prediction prediction should should not not hold. hold. These These reasons reasons are are likely likely to to reasons be be different different for for passively passively and and actively dispersing dispersing organisms. organisms.
Passive Passive Dispersal Dispersal definition, passively passively dispersing dispersing individuals individuals cannot cannot choose choose their their destindestin By definition, ation. Dispersal Dispersal to to sink sink habitats habitats in in such such organisms organisms can can be be understood understood easily easily as as ation. consequence of of aa general general propensity propensity to to disperse. disperse. The The balanced balanced dispersal dispersal aa consequence as defined defined in in Section Section 16.2) 1 6.2) from from aa scenario requires requires that that the the dispersal dispersal rate rate (mij as scenario high to to aa low-quality low-quality habitat habitat is is lower lower than than the the dispersal dispersal rate rate in in the the opposite opposite high direction (Doebeli, (Doebeli, 1995). 1 995). Such Such an an asymmetry asymmetry of of dispersal dispersal rates rates is is possible possible if if direction
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propagules propagules produced produced in in poorer poorer habitats habitats have have aa greater greater propensity propensity to to disperse, disperse, reflecting reflecting the the plasticity plasticity of of behavioral behavioral and and morphological morphological traits traits affecting affecting dispersal. dispersal. However, However, the the evolution evolution of of such such plasticity plasticity is is likely to to be be constrained, constrained, in in particular particular because because the the probability probability of of dispersing dispersing from from aa source source to to aa sink sink not not only only depends depends on on the the propensity propensity to to disperse, disperse, but but also also on on the the relative relative area area of of different different habitats habitats types types within within an an individual's individual's dispersal dispersal shadow. shadow. If If plasticity plasticity of of dispersal dispersal rates rates is is constrained, constrained, simple simple source-sink source-sink models models predict predict that that natural natural selection Feldman, 11973; 973; selection should should drive drive dispersal dispersal to to minimum minimum (e.g., (e.g., Balkau Balkau and and Feldman, Holt, 9 8 5 ) . However, Holt, 11985). However, this this tendency tendency will will be be counteracted counteracted by by advantages advantages of of dispersing dispersing within within aa given given habitat habitat type, type, such such as as avoidance avoidance of of inbreeding inbreeding and and sib sib competition competition or or assurance assurance against against temporal temporal unpredictability unpredictability of of the the environ environment see Chapter 0 ) . The ment ((see Chapter 110). The optimal optimal dispersal dispersal propensity propensity will will reflect reflect aa balance balance between between these these two two forces. forces.
Active Active Dispersal Dispersal with with Habitat Habitat Choice Choice Three Three general general reasons reasons have have been been proposed proposed to to explain explain deviations deviations from from an an ideal ideal free free distribution distribution and and dispersal dispersal into into sink sink habitats habitats in in actively actively dispersing dispersing organisms capable of (Holt, 11997). 997). First, organisms capable of habitat habitat choice choice (Holt, First, territoriality territoriality or or other other forms forms of of contest contest competition competition may may prevent prevent some some individuals individuals from from breeding breeding in in the the source source habitat. habitat. It It will will often often pay pay for for such such individuals individuals to to attempt attempt breeding breeding in floaters" in in sink sink habitats habitats rather rather than than be be nonbreeding nonbreeding ""floaters" in source source habitats habitats (Pulliam, 11988; 9 8 8 ; Pulliam 99 1 ). Thus, (Pulliam, Pulliam and and Danielson, Danielson, 11991). Thus, in in this this scenario scenario individ individuals uals breeding breeding in in aa sink sink do do the the best best of of aa bad bad job. job. Second, Second, ideal ideal free free distribu distribution tion requires requires that that individuals individuals can can assess assess not not only only the the quality quality of of different different habitats, also the among habitats. Gaining this this habitats, but but also the distribution distribution of of individuals individuals among habitats. Gaining information likely to cognitive abilities information is is likely to be be constrained constrained by by the the cognitive abilities of of the the species, species, particularly particularly if if the the environment environment is is changing changing in in time time (Remes, (Remes, 2000) 2000).. Even Even if if the the species species is is capable capable of of evaluating evaluating habitats habitats accurately, accurately, inspecting inspecting many many habitat habitat patches patches will will be be costly costly in in terms terms of of energy, energy, time, time, and and mortality. mortality. Thus, Thus, it it may may pay pay to to settle settle in in the the first first more more or or less less suitable suitable habitat habitat patch patch (van (van Baalen Baalen and and Sabelis, 9 9 3 ) . Third, Sabelis, 11993). Third, if if the the environment environment is is temporally temporally variable variable in in such such aa way way that habitat occasionally that fitness fitness in in the the sink sink habitat occasionally exceeds exceeds that that in in the the source habitat habitat and and dispersal dispersal back back from from the the sink sink to to the the source source is is possible, possible, genotypes genotypes that that choose sink choose sink habitat habitat with with aa small small but but nonzero nonzero probability probability will will have have advantage advantage over (Holt, 11997; 997; Wilson, over those those that that avoid avoid sink sink completely completely (Holt, Wilson, 2001 2001).) . In In this this scenario, dispersal Seger and scenario, dispersal into into aa sink sink habitat habitat is is thus thus aa form form of of bet bet hedging hedging ((Seger and Brockmann, 987). Brockmann, 11987).
116.6 6.6 EVOLUTIONARY EVOLUTIONARY CONSEQUENCES CONSEQUENCES OF OF SOURCE-SINK SOURCE-SINK STRUCTURE STRUCTURE From From an an evolutionary evolutionary perspective, perspective, "habitat "habitat quality," quality," which which determines determines whether whether aa habitat habitat is is aa source source or or sink, sink, reflects reflects an an interaction interaction between between the the prop properties erties of of the the habitat habitat and and the the characteristics characteristics of of the the species; species; the the latter latter can can evolve. evolve. It It is is thus thus of of interest interest to to know know how how the the relative relative performance performance of of aa population population in in source source and and sink sink habitats habitats should should change change over over evolutionary evolutionary time. time. Adaptation Adaptation to to initially initially marginal marginal sink sink habitats habitats has has important important implications implications for for the the evolution evolutionary ary dynamics dynamics of of species species distributions. distributions.
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Adaptation lack of Adaptation to to marginal marginal habitats habitats may may be be constrained constrained by by aa lack of genetic genetic variation Lewontin and and Birch, 966; Parsons, 975; Blows Blows and Hoffmann, variation ((Lewontin Birch, 11966; Parsons, 11975; and Hoffmann, 11993), 99 3 ) , which which in in turn turn may may reflect reflect biochemical, biochemical, physiological, physiological, and and develop developmental species' evolutionary evolutionary history mental constraints constraints resulting resulting from from the the species' history (Stearns, (Stearns, 11994). 994). This This factor factor is is not not specific specific to to source-sink source-sink populations populations and and is is not not dis discussed cussed here. here. Instead Instead this this section section focuses focuses on on predictions predictions concerning concerning the the effect effect of source-sink source-sink population population structure on on adaptive adaptive evolution, evolution, assuming assuming that that of genetic variation fitness in both source and sink sink habitats genetic variation for for fitness in both source and habitats exists. exists. Two Two intuitive as to to why why source-sink intuitive arguments arguments have have been been made made as source-sink dynamics dynamics make make it it difficult difficult for for aa population population to to evolve evolve improved improved performance performance in in habitats habitats that that function function as as sinks. sinks. The The first first argument argument notices notices that that sink sink habitats habitats contribute contribute relatively reproduction of relatively little little to to the the reproduction of the the entire entire population. population. Therefore, Therefore, their their contribution to contribution to the the overall overall fitness, fitness, averaged averaged over over habitats, habitats, is is relatively relatively small, and selection on small, and natural natural selection on performance performance in in sink sink habitats habitats is is relatively relatively weak. second argument stresses gene weak. The The second argument stresses gene flow flow swamping swamping locally locally adapted adapted genotypes habitats. These genotypes in in sink sink habitats. These two two arguments arguments and and the the relationship relationship between between them them are are discussed discussed in in the the following following two two subsections. subsections. The The third third sub subsection section discusses discusses the the predictions predictions of of the the theory, theory, while while the the last last subsection subsection reviews reviews the the empirical empirical evidence. evidence.
Reproductive Reproductive Value Value and and Sensitivity Sensitivity of of Fitness Fitness In In the the classic classic model model of of quantitative quantitative traits traits under under natural natural selection selection (Price, (Price, 11970; 970; Lande 98 3 ) , the Lande and and Arnold, Arnold, 11983), the expected expected direct direct response response of of aa trait trait to to selection selection is is proportional proportional to to the the strength strength of of selection, selection, measured measured as as the the deriva derivative of of fitness fitness with with respect to the the trait trait value. For aa source-sink source-sink population population at at aa tive respect to value. For density equilibrium, density equilibrium, the the dominant dominant eigenvalue eigenvalue A.k of of the the transition transition matrix matrix A(Ii A(ri)) is Caswell, 11989; 989; Charlesworth, 994). is an an appropriate appropriate measure measure of of fitness fitness ((Caswell, Charlesworth, 11994). Thus Thus the the strength strength of of selection selection on on trait trait zz can can be be partitioned partitioned according according to to its its h (nh ) in each habitat: effect effect on on the the net net reproductive reproductive rate rate ffh(~/h) in each habitat:
aA. 2: aA. a f a;- h a fh --;;; '
O}t z - ~ OfhO-~Xo bfzOh , _
((16.7) 1 6.7)
all all derivatives derivatives are are evaluated evaluated at at Ii; ri; the the arguments arguments of of ffhh are are left left out out for for trans transparency formula. From parency of of the the formula. From the the general general equation equation for for eigenvalue eigenvalue sensitivity sensitivity ((Caswell, Caswell, 11989, 989, Eq. Eg. 6 . 6 ) , one 6.6), one gets gets
OX
UhVi
O-~h= ~z. < H i ; >
Oaih
Uh
~9-~h= 2~a vimhi" z
((~6.8) 1 6. 8 )
To 1 6.2) mhi = aih1fh, To proceed proceed further, further, note note that that from from Eg. Eq. ((16.2) aih/fh , and and that that kiviaih Eiviaih = Vh (this the definition these relationships (this follows follows from from the definition of of left left eigenvector). eigenvector). Using Using these relationships 1 6. 8 ) into in 1 6. 8 ) , noting in Eg. Eq. ((16.8), noting that that < u . v > - = 11 and and substituting substituting Eg. Eq. ((16.8) into Eg. Eq. ((16.7), 1 6.7), one one arrives arrives at at
0 X _- ~_~ ul~vh~__ofh. Oz
h
fhOZ
((16.9) 1 6.9)
116. 6. SOURCE-SINK SOURCE-SINK POPULATION POPULATION DYNAMICS DYNAMICS
405 405
Thus the relative on the the reproductive i.e., local Thus the relative effect effect of of trait trait zz on reproductive rate rate ((i.e., local fitness) fitness) in in each each habitat habitat is is weighed weighed by by the the pooled pooled reproductive reproductive value value of of individuals individuals present (Rousset, 11999a; 999a; see 993; present in in that that habitat habitat (Rousset, see also also Kawecki Kawecki and and Stearns, Stearns, 11993; Holt, 996b). The Holt, 11996b). The reproductive reproductive value value tends tends to to be be smaller smaller in in sink sink habitats habitats ((Section Section 116.2), 6 .2), and and sink sink habitats habitats tend tend to to harbor harbor fewer fewer individuals individuals than than sources. The The evolution evolution of of trait trait zz will will thus thus be be affected affected more more strongly strongly by by its its impact impact on on performance performance in in source source habitats. habitats. If If increasing increasing zz has has aa positive positive effect effect on sink, but negative effect on performance performance in in the the sink, but aa negative effect on on performance performance in in the the source, toward smaller source, the the trait trait will will evolve evolve toward smaller values values unless unless the the positive positive effect effect in larger than than the sink (Holt in the the source source is is considerably considerably larger the negative negative effect effect in in the the sink (Holt and 992; Kawecki, 995; Holt, 996b). Following and Gaines, Gaines, 11992; Kawecki, 11995; Holt, 11996b). Following this this logic, logic, one one laz = would would predict predict that that the the optimal optimal trait trait value value will will satisfy satisfy a}l.. aX/c3z = 00 (Holt (Holt and and Gaines, 992). Gaines, 11992).
Gene Gene Flow Flow versus versus Local Local Selection Selection The The approach approach just just given given is is simple simple and and elegant elegant and and has has been been used used to to gener generate Gaines, 11992; 992; Houston ate interesting interesting predictions predictions (e.g., (e.g., Holt Holt and and Gaines, Houston and and McNamara, 992; Brown 992; Kawecki 993; McNamara, 11992; Brown and and Pavlovic, Pavlovic, 11992; Kawecki and and Stearns, Stearns, 11993; Kawecki, 995; Holt, 996b). It Kawecki, 11995; Holt, 11996b). It is, is, however, however, problematic problematic because because it it neglects neglects genetic populations, which genetic differentiation differentiation between between populations, which may may be be substantial substantial if if the the dispersal dispersal rate rate is is low low in in relation relation to to selection selection coefficients coefficients operating operating on on individ individual 976; Chapter ual genetic genetic loci loci (Felsenstein, (Felsenstein, 11976; Chapter 77 of of this this volume) volume).. The The importance importance of of accounting accounting for for genetic genetic differentiation differentiation can can bbee illustrated illustrated by adaptation to black hole hole sink habitat ((i.e., i.e., aa habitat habitat that by considering considering adaptation to aa black sink habitat that receives repro receives immigrants immigrants but but sends sends no no dispersers dispersers back back to to the the source) source).. As As the the reproductive see Section 6.2), the approach ductive value value in in aa black black hole hole sink sink is is 00 ((see Section 116.2), the above above approach would allele beneficial deleterious in would predict predict that that an an allele beneficial in in the the sink sink and and deleterious in the the source source should should never never be be maintained maintained in in the the population. population. In In contrast, contrast, explicit explicit genetic genetic 997; Gomulkiewicz 99 9 ) demon models (Holt and and Gomulkiewicz, 11997; Gomulkiewicz et et aI., al., 11999) demonstrate strate that, that, although although eliminated eliminated deterministically deterministically from from the the source source habitat, habitat, such such an an allele allele will will be be maintained maintained in in the the sink sink if if the the local local net net reproductive reproductive rate rate of of its its carriers carriers exceeds exceeds 11.. The The effect effect ooff aa passive passive dispersal dispersal rate rate oonn adaptive adaptive evolution evolution in in aa source-sink source-sink system system is is another another issue issue where where qualitative qualitative discrepancies discrepancies arise arise between between the the predictions explicit genetic predictions of of fitness fitness sensitivity sensitivity approach approach and and explicit genetic models. models. In In aa two-patch model with symmetric dispersal m12 = m two-patch model with aa symmetric dispersal rate rate ((m12 m21), the pooled pooled 2 1 ), the reproductive reproductive value value of of the the subpopulation subpopulation in in the the sink sink (U (u~v~) typically increases increases hVh ) typically monotonically monotonically with with increasing increasing dispersal dispersal rate rate (for (for aa numerical numerical example, example, see see Fig. 6.4) . This Fig. 116.4). This is is largely largely because because aa greater greater dispersal dispersal rate rate shifts shifts the the spatial spatial distribution Section 116.3), 6 . 3 ) , exposing distribution of of the the population population ((Section exposing aa greater greater fraction fraction of of the the total total population population to to natural natural selection selection in in the the sink. sink. The The fitness fitness sensitivity sensitivity approach that high approach would thus thus suggest that high dispersal dispersal rates are most favorable favorable and and low low dispersal dispersal rates rates least least favorable favorable for for adaptation adaptation to to aa sink sink habitat habitat (Holt (Holt and and Gaines, 992; Kawecki, 995; Holt, 996a). Gaines, 11992; Kawecki, 11995; Holt, 11996a). However, However, the the dispersal dispersal rate rate also also affects affects the the amount amount of of gene gene flow flow between between habitats, habitats, and and thus thus the the degree degree of of genetic genetic differentiation differentiation between between source source and and sink sink habitats. The approach is habitats. The fitness fitness sensitivity sensitivity approach is likely likely to to provide provide aa reasonable reasonable approximation approximation if if gene gene flow flow is is already already strong strong enough enough to to prevent prevent any any substantial substantial
TADEUSZ I.j. KAWECKI
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0.4 o'4
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=
Fig. in aa sink Fig. 11 6.4 6 . 4 The The pooled pooled reproductive reproductive value value of of individuals individuals in sink habitat, habitat, U2VZ, u21)2, as as aa function function of and habitat and (1 of dispersal dispersal rate rate and habitat quality. quality. The The model model follows follows Eq. Eq. (1 (1 6.1 6.1)) and (1 6.2) 6.2) with with two two patches patches all results and symmetric passive and symmetric passive dispersal dispersal m1 m122 = = m21; m21; fh(nh) fh(nh)== Rh/(l Rh/(1 + + nh)' nh). For For all results Rl R1 = = 4 4 is is assumed; ifferent values 2 < assumed; the the different different lines lines are are for for d different values of of R R2 indicated on on the the right. right. If If R R2 < 4, 4, habi habi2 indicated tat sink. tat 2 2 is is aa sink.
genetic genetic differentiation. differentiation. In In contrast, contrast, if if dispersal dispersal is is low, low, and and thus thus gene gene flow flow restricted, some degree degree of in restricted, some of local local adaptation adaptation may may be be possible: possible: alleles alleles beneficial beneficial in the sink but while remaining the sink but deleterious deleterious in in the the source source may may increase increase in in the the sink sink while remaining rare case, increasing result rare in in the the source. source. In In this this case, increasing the the dispersal dispersal rate rate will will first first of of all all result in swamping of pool in in greater greater swamping of the the local local gene gene pool in the the sink sink by by gene gene flow flow from from the the source. This increased dispersal dispersal on is source. This negative negative effect effect of of increased on adaptation adaptation to to the the sink sink is likely exposing aa greater likely to to outweigh outweigh any any positive positive effect effect due due to to exposing greater fraction fraction of of the the population sink habitat. This argument argument predicts population to to the the sink habitat. This predicts that, that, at at least least under under some some circumstances, dispersal rate circumstances, the the relationship relationship between between dispersal rate and and the the expected expected degree degree of of adaptation adaptation to to aa sink sink habitat habitat will will be be U-shaped U-shaped rather rather than than monotonic, monotonic, with with an an intermediate intermediate dispersal dispersal rate rate being being least least favorable. favorable. Furthermore, Furthermore, for for aa given given amount can maintain allele frequency amount of of gene gene flow, flow, selection selection can maintain greater greater allele frequency differen differentiation tiation between between the the habitats habitats at at loci loci with with larger larger effects effects (Felsenstein, (Felsenstein, 1976). 1976). For For that that reason reason the the range range of of dispersal dispersal rates rates over over which which the the conditions conditions for for adapta adaptation become more dispersal should tion to to aa sink sink become more favorable favorable with with increasing increasing dispersal should be be greater greater when when the the adaptation adaptation involves involves loci loci with with small small effects effects (Kawecki, (Kawecki, 2000). 2000). These These predictions predictions are are confirmed confirmed by by the the results results of of aa polygenic polygenic model model of of evo evolution described in 6 .5. This lution in in aa two-patch two-patch source-sink source-sink system system described in Fig. Fig. 116.5. This model model assumes habitats, mediated assumes aa fitness fitness trade-off trade-off between between the the habitats, mediated by by aa quantitative quantitative trait each with total trait determined determined by by up up to to eight eight additive additive loci loci each with two two alleles. alleles. The The total variability constant by variability range range of of the the trait trait is is kept kept constant by adjusting adjusting the the effects effects of of single single loci. results of model (symbols) compared to predic loci. The The results of the the genetic genetic model (symbols) are are compared to the the predictions of model based based on lines) . tions of an an optimality optimality model on the the fitness fitness sensitivity sensitivity approach approach ((lines). The The latter latter approach approach predicts predicts that that the the mean mean fitness fitness iinn the the sink sink habitat habitat should should increase monotonically monotonically with with the the dispersal dispersal rate rate ((lower line in in each each panel) panel).. increase lower line When optimality approach When the the trade-off trade-off is is mediated mediated by by eight eight loci, loci, the the optimality approach accur accurately model except less ately predicts predicts the the outcome outcome of of the the genetic genetic model except for for dispersal dispersal rates rates less than Fig. 116.5a). 6.5a). Only dispersal rates local populapopula than 0.05 0.05 ((Fig. Only at at such such low low dispersal rates can can the the local tions local population population in tions differentiate, differentiate, which which allows allows the the local in the the sink sink to to adapt adapt locally. local populations populations causes causes the locally. Genetic Genetic differentiation differentiation between between the the local the mean mean
116. 6.
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11 locus / locus O +---.---r---.--. o o0 0.1 0.2 0:2 0:3 014 0.5 0;5 0.3 0.4 Dispersal Dispersal rate rate m m12 m21 21 12 = m =
Fig. in aa source-sink Fig. 11 6.5 6 . 5 Results Results of of aa genetic genetic model model of of adaptive adaptive evolution evolution in source-sink system system contrasted contrasted with model is Eq. (1 6.1 ) and and (1 6.2) and with predictions predictions of of an an optimality optimality approach. approach. The The model is based based on on Eq. (16.1) (16.2) and assumes assumes aa trade-off trade-off in in relative relative fitness fitness across across habitats, habitats, mediated mediated by by aa quantitative quantitative trait trait z, which which under antagonistic antagonistic directional directional selection in the the two two habitats. This is implemented implemented by setting setting is under fh fh = = Rhwh(z)/(l RhWh(Z)/( 1 + + nh), nh), where where Rl R1 = 4 4 and and RR22 = = 2 2 and and the the relative relative fitness fitness is is Wl wl = = 11 - zz33 in in the the sink. Symmetric m1 2 = assumed. source source and and W w22 = = 11 - (1 (1 - Z)3 z) 3 in in the the sink. Symmetric dispersal dispersal rates rates ((m12 = m2l mzl)) are are assumed. In In the the genetic genetic model, model, trait trait z z is is determined determined by by one one to to eight eight freely freely recombining recombining loci loci with with equal equal and and additive additive effects, effects, and and codominance. codominance. The The phenotypic phenotypic effect effect of of each each locus locus is is inversely inversely pro proranges from portional portional to to the the number number of of loci loci so so that that z z always always ranges from 0 0 (maximum (maximum possible possible adaptation adaptation in the in the the in the source, source, zero zero fitness fitness in in the the sink) sink) to to 11 (maximum (maximum adaptation adaptation to to the the sink, sink, zero zero fitness fitness in source). obtained using using deterministic computer iterations in Kawecki source). Results Results were were obtained deterministic computer iterations (details (details in Kawecki and and Holt, Holt, 2002) 2002) until until an an evolutionary evolutionary equilibrium equilibrium was was reached; reached; initial initial allele allele frequencies frequencies at at all all loci loci have 0.5 (slightly among loci). have been been set set to to about about 0.5 (slightly different different among loci). Plots Plots show show mean mean relative relative fitnesses fitnesses (Wh) in (X) and (I-3) habitats as functions the dispersal rate and the number number of of loci (Wh) in source (X) and sink sink (0) functions of the and the loci coding in the (Z*) and and sink sink W coding for for trait trait z. z. Solid Solid lines lines show show relative relative fitnesses fitnesses in the source source Wl wl(z*) w2(z*) pre2(Z*) pre ddicted icted with approach (the same for all panels). value z* satisfies with an an optimality optimality approach (the same for all panels). The The optimal optimal trait trait value satisfies 2A/az2z < Ak = and ac32;k/az evaluated at -- 11,, aA/az 0X/c3z = = 0, 0, and < 0, 0, where where the the derivatives derivatives are are evaluated at the the equilibrium. equilibrium. =
fitnesses fitnesses in in the the two two habitats habitats to to become become less less bound bound by by the the trade-off. trade-off. As As the the number loci that decreases, and number of of loci that mediate mediate the the trade-off trade-off decreases, and thus thus the the effect effect of of each each single single locus locus increases, increases, the the range range of of dispersal dispersal rates rates permitting permitting local local adaptation adaptation in in the the sink sink increases. increases. This This causes causes the the results results of of the the genetic genetic model model to to deviate deviate increasingly increasingly from from the the predictions predictions of of the the optimality optimality approach; approach; the the minimum minimum of of the the mean mean fitness fitness in in the the sink sink habitat habitat is is shifted shifted toward toward higher higher dispersal dispersal rates rates 6.5b-1 6.5d). With locus, the (Fig. 116.5d). 6.5d). With only only aa single single locus, the fit fit is is very very poor poor (Fig. ((Figs. Figs. 116.5b-16.5d). An An additional additional factor factor that that reduces reduces the the mean mean fitness fitness in in the the one-locus one-locus model model is is the the segregational segregational load load -~ as as the the trade-off trade-off is is convex, convex, variance variance reduces reduces mean mean fitness. fitness. It It is is also also interesting interesting to to note note that that the the two-locus two-locus version version of of the the model model predicts the the same same mean mean relative relative fitness fitness in in both both habitats habitats at at high high dispersal dispersal predicts
408 408
TADEUSZ j.J. KAWECKI KAWECKI
rates r a t e s- at at equilibrium equilibrium the the two two loci loci are are fixed fixed for for the the alleles alleles with with opposite opposite effects effects and and no no genetic genetic variation variation remains. remains. Analyzing Analyzing the the properties properties of of equilib equilibria in in polygenic polygenic models models goes goes beyond beyond the the scope scope of of this this chapter, chapter, but but it it should should be be ria kept kept in in mind mind that that details details of of the the genetic genetic system system will will affect affect the the outcome outcome of of adap adaptive populations. tive evolution evolution in in source-sink source-sink populations. This This example example illustrates illustrates the the importance importance of of using using explicit explicit genetic genetic models models to to study study evolution evolution in in source-sink source-sink systems. systems. The The overall overall effect effect of of dispersal dispersal on on adap adaptive tive evolution evolution in in aa sink sink habitat habitat will will depend depend on on the the relative relative importance importance of of the the demographic effect demographic effect of of dispersal dispersal and and the the homogenizing homogenizing effect effect of of gene gene flow. flow.
Source-Sink Population Population Dynamics and Evolutionary Dynamics of of Ecological Niches In In the the model model described described above above the the mean mean relative relative fitness fitness in in the the sink sink is is typi typically habitat quality. cally lower lower than than in in the the source, source, thus thus magnifying magnifying differences differences in in habitat quality. Similar by many Similar predictions predictions have have been been reached reached by many published published models. models. Alleles Alleles with with aa small source habitat small positive positive effect effect on on fitness fitness in in the the source habitat will will tend tend to to be be favored favored even sink (Holt (Holt and 992; even if if they they have have large large negative negative effects effects in in the the sink and Gaines, Gaines, 11992; Holt, 996a; Kawecki, Holt, 11996a; Kawecki, 2000) 2000).. An An allele allele beneficial beneficial in in aa black black hole hole sink sink (no (no dis dispersal persal back back to to the the source source)) may may be be eliminated eliminated deterministically deterministically even even if if neutral neutral in source (e.g., 948; Nagylaki, 975; Slatkin, Slatkin, 11995; 995; Holt in the the source (e.g., Haldane, Haldane, 11948; Nagylaki, 11975; Holt and and Gomulkiewicz, 997). Source-sink Gomulkiewicz, 11997). Source-sink populations populations are are prone prone to to accumulate accumulate mutations source (Kawecki mutations deleterious deleterious in in the the sink sink but but neutral neutral in in the the source (Kawecki et et aI., al., 11997). 997). A A quantitative quantitative trait trait affecting affecting fitness fitness may may remain remain far far from from its its local local opti optimum habitat is mum in in aa sink sink habitat habitat if if the the optimum optimum in in the the source source habitat is different different (Garcia-Ramos 997; Kirkpatrick 997). To (Garcia-Ramos and and Kirkpatrick, Kirkpatrick, 11997; Kirkpatrick and and Barton, Barton, 11997). To summarize, natural natural selection selection is is expected expected to to maintain maintain or or improve improve adaptation adaptation in in summarize, habitats, where where the the population population is is already already well well adapted, adapted, and and be be ineffective ineffective in in habitats, improving marginal habitats. improving adaptation adaptation to to marginal habitats. This This implies implies that that ecological ecological niches niches should (Holt and 992; Kawecki, should usually usually be be evolutionarily evolutionarily conserved conserved (Holt and Gaines, Gaines, 11992; Kawecki, 11995; 995; Holt, 996b). Holt, 11996b). This This conclusion conclusion has has also also been been reached reached in in models models in in which which habitat-specific habitat-specific parameters are priori differences parameters are symmetric symmetric so so there there are are no no aa priori differences in in habitat habitat quality. quality. A A symmetric symmetric model model will will usually usually have have aa symmetric symmetric evolutionary evolutionary equi equilibrium, librium, at at which which the the mean mean fitness fitness in in all all habitats habitats would would be be the the same. same. However, However, such such an an equilibrium equilibrium may may be be unstable, unstable, and and even even when when it it is is stable, stable, alternative alternative asymmetric asymmetric equilibria equilibria may may exist; exist; which which equilibrium equilibrium is is reached reached will will depend population. Such depend on on the the initial initial genetic genetic composition composition of of the the population. Such alternative alternative asymmetric model asymmetric and and symmetric symmetric equilibria equilibria exist exist in in aa symmetric symmetric two-patch two-patch model by Kirkpatrick (200 1 ) . If initially well by Ronce Ronce and and Kirkpatrick (2001). If the the population population is is initially well adapted adapted to habitat 11 and poorly adapted adapted to habitat 2, remain so to habitat and poorly to habitat 2, it it will will tend tend to to remain so or or may may even even evolve evolve toward toward even even greater greater adaptation adaptation in in habitat habitat 11 and and reduced reduced fitness fitness in 2. The happens if population is in habitat habitat 2. The reverse reverse happens if the the population is initially initially adapted adapted to to habi habitat tat 2. 2. A A symmetric symmetric equilibrium equilibrium is is only only reached reached if if the the allele allele frequencies frequencies are are initially initially intermediate intermediate so so that that the the population population is is initially initially moderately moderately well well adapted species range adapted to to both both habitats. habitats. Similarly, Similarly, in in aa model model of of aa species range evolving evolving on on an an environmental environmental gradient, gradient, source-sink source-sink population population dynamics dynamics lead lead to to evolu evolution along the tion of of aa limited limited range, range, centered centered at at the the point point along the gradient gradient to to which which the the population was initially best adapted 997). This population was initially best adapted (Kirkpatrick (Kirkpatrick and and Barton, Barton, 11997). This
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effect is augmented effect is augmented by by character character displacement displacement caused caused by by interspecific interspecific compe competition Case and tition ((Case and Taper, Taper, 2000 2000).) . At At the the population population genetic genetic level level it it implies implies that that the the source-sink source-sink population population structure structure generates generates epistasis epistasis among among fitness fitness effects effects of of different different loci, loci, such such that that aa positive positive effect effect of of aa particular particular allele allele on on perform performance background adapted ance in in aa given given habitat habitat is is augmented augmented by by aa genetic genetic background adapted to to that that habitat. Conversely, Conversely, selection selection against against an an allele with with aa habitat-specific habitat-specific delete deleterious effect becomes weaker alleles with rious effect becomes weaker as as alleles with similar similar effects effects increase increase in in fre frequency, sink habitat quency, which which may may lead lead to to aa mutational mutational erosion erosion of of fitness fitness in in aa sink habitat (Kawecki aI., 11997). 997). (Kawecki et et al., Nonetheless, Nonetheless, the the prediction prediction that that ecological ecological niches niches should should be be conserved conserved evo evolutionarily lutionarily is is not not absolute. absolute. A A number number of of evolutionary evolutionary changes changes of of ecological ecological niches niches have have been been directly directly observed, observed, including including host host shifts shifts in in herbivorous herbivorous insects insects or or repeated repeated evolution evolution of of tolerance tolerance of of plants plants to to high high concentrations concentrations of of heavy heavy metals. This raises the question about about environmental environmental factors properties of metals. This raises the question factors and and properties of the population will the organism, organism, which which make make it it more more likely likely that that aa population will adapt adapt to to aa novel habitat, novel habitat, which which is is initially initially aa sink. sink. Dispersal Dispersal rate rate and and pattern pattern are are obviously obviously of of crucial crucial importance. importance. Given Given the the tension tension between between local local adaptation adaptation and and gene gene flow, flow, one-time one-time colonization colonization of of the the novel novel habitat habitat followed followed by by complete complete isolation isolation would would seem seem most most favor favorable. persistent population locally malmal able. However, However, foundation foundation of of aa persistent population by by aa few few locally adapted exceptions like Darwin's adapted colonizers colonizers must must be be rare, spectacular exceptions Darwin's finches finches notwithstanding. notwithstanding. If If the the population population initially initially performs performs poorly, poorly, it it will will likely become extinct Gomulkiewicz and likely become extinct before before it it has has time time to to adapt adapt ((Gomulkiewicz and Holt, Holt, 11995), 99 5 ) , especially especially that that aa single single colonization colonization event event will will typically typically be be associated associated with with aa bottleneck bottleneck causing causing loss loss of of heritable heritable variation. variation. If If so, so, gene gene flow flow fol following lowing the the initial initial colonization colonization may may facilitate facilitate adaptation adaptation to to the the novel novel habi habitat Caprio and 992; tat by by replenishing replenishing genetic genetic variation variation ((Caprio and Tabashnik, Tabashnik, 11992; Gaggiotti, 996; Gaggiotti 996; Chapter 5 ) . Finally, Gaggiotti, 11996; Gaggiotti and and Smouse, Smouse, 11996; Chapter 115). Finally, com complete plete elimination elimination of of gene gene flow flow may may be be impossible. impossible. The The above above model model suggests suggests that dispersal rates favorable for adaptation to that high high dispersal rates will will often often be be more more favorable for adaptation to aa marginal than intermediate marginal habitat habitat than intermediate dispersal dispersal rates, rates, particularly particularly if if genes genes with with small see also Kawecki small effects effects are are involved involved ((see Kawecki and and Holt, Holt, 2002 2002).) . This This conclu conclusion sion is, is, however, however, contradicted contradicted by by spatially spatially explicit explicit models models of of populations populations adapting Kirkpatrick and 99 7; adapting to to an an environmental environmental gradient gradient ((Kirkpatrick and Barton, Barton, 11997; Salathe and Kawecki, high dispersal Salathe and Kawecki, unpublished unpublished results) results),, where where high dispersal rates rates are are most Garcia most unfavorable unfavorable for for adaptation adaptation to to sink sink habitats. habitats. Another Another model model ((GarciaRamos Ramos and and Rodriguez, Rodriguez, 2002 2002)) predicts predicts aa nonlinear nonlinear relationship relationship between between dis dispersal persal and and evolutionary evolutionary invasions invasions of of novel novel habitats. habitats. It It is is not not clear clear which which of of the the differences differences in in assumptions assumptions of of these these models models were were responsible responsible for for these these different different predictions. predictions. Gene Gene flow flow can can occur occur through through both both sexes, sexes, but but in in species species without without paternal paternal care, care, only only female female dispersal dispersal contributes contributes to to the the maintenance maintenance of of local local populations populations in in sink sink habitats. habitats. One One would would therefore therefore expect expect that that female-biased female-biased dispersal dispersal would would be be more more favorable favorable for for adaptation adaptation to to aa sink sink habitat habitat than than sex-independent sex-independent or or male-biased dispersal. dispersal. A A genetic genetic model model assuming assuming independent independent male male and and female female dispersal dispersal rates rates confirms confirms this this intuition, intuition, although although depending depending on on the the parameters, parameters, the the conditions conditions for for adaptation adaptation to to the the sink sink may may be be least least favor favorable able under under moderately moderately rather rather than than extremely extremely male-biased male-biased dispersal dispersal (Kawecki, (Kawecki, 2003 2003).) .
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Finally, Finally, Kawecki Kawecki and and Holt Holt (2002) (2002) considered considered the the evolutionary evolutionary effect effect of of the the reverse source-sink structure, whereby reverse source-sink structure, whereby an an environment-imposed environment-imposed asymmetry asymmetry of of dispersal rates causes habitat to dispersal rates causes an an "upstream" "upstream" poorer poorer habitat to act act as as an an effective effective source downstream" high-quality sink (Section 6.2). In source and and aa ""downstream" high-quality habitat habitat as as aa sink (Section 116.2). In their model, selection selection tended tended to source habitat their model, to be be more more effective effective in in the the source habitat even even if if it it was was of of lower lower quality quality than than the the sink sink habitat. habitat. They They concluded concluded that, that, assuming assuming sufficient sufficient genetic genetic variance, variance, over over evolutionary evolutionary time time the the population population should should adapt adapt to to the the upstream upstream habitat habitat at at the the expense expense of of reduced reduced fitness fitness in in the the downstream downstream habitat. population dynamics habitat. In In this this case, case, source-sink source-sink population dynamics would would thus thus promote promote an an evolutionary evolutionary shift shift of of the the ecological ecological niche. niche. The dispersal rates The effect effect of of factors factors other other than than dispersal rates on on adaptation adaptation to to aa sink sink habitat habitat has has not not been been investigated investigated systematically. systematically. Fitness Fitness sensitivity sensitivity analysis analysis of 1 6 . 6 ) suggested area of aa model model described described by by Eq. Eq. ((16.6) suggested that that increasing increasing the the relative relative area of makes the of the the sink sink habitat habitat makes the conditions conditions for for adaptation adaptation to to the the sink sink more more favorable, favorable, but but only only when when the the differences differences in in habitat habitat quality quality are are not not large large ((Kawecki, Kawecki, 11995). 995 ) . This This conclusion conclusion still still needs needs to to be be supported supported by by aa genetic genetic model. habitat should model. Several Several models models suggest suggest that that adaptation adaptation to to aa sink sink habitat should be be more involved compared compared to more likely likely if if few few majo majorr loci loci are are involved to many many loci loci with with small small effects e.g., Holt Gomulkiewicz, 11997; 997; Kawecki, Kawecki, 2000) effects ((e.g., Holt and and Gomulkiewicz, 2000).. Density Density dependence dependence in in the the sink sink makes makes the the conditions conditions for for adaptation adaptation to to the the sink sink habi habitat Holt, 11996a; 996a; Gomulkiewicz aI., 11999). 99 9 ) . It tat less less favorable favorable ((Holt, Gomulkiewicz et et al., It is, is, however, however, not how general Most of them were derived from not clear clear how general these these predictions predictions are. are. Most of them were derived from two-patch, turn, spatially two-patch, spatially spatially implicit implicit models. models. In In turn, spatially explicit explicit models models com combining bining source-sink source-sink population population dynamics dynamics and and evolution evolution have have been been based based on on the the diffusion diffusion equation equation and and infinitesimal infinitesimal quantitative quantitative genetic genetic approximation approximation (e.g., 997; Case (e.g., Kirkpatrick Kirkpatrick and and Barton, Barton, 11997; Case and and Taper, Taper, 2000 2000).) . Future Future model modeling should combine ing of of evolution evolution in in source-sink source-sink systems systems should combine spatially spatially explicit explicit and and genetically genetically explicit explicit approaches. approaches.
Evidence Evidence for for Maladaptation M a l a d a p t a t i o n in in Sink Sink Habitats Habitats The The average average reproductive reproductive success success in in aa sink sink habitat habitat is is poor. poor. The The difficult difficult part part is poor at is to to show show that that it it is is poor at least least partially partially because because of of gene gene flow flow from from source source habitats. habitats. This This has has been been demonstrated demonstrated convincingly convincingly in in only only aa few few cases. cases. The The best best evidence evidence for for gene gene flow flow hampering hampering adaptation adaptation in in aa sink sink habitat habitat comes 6.4. Populations comes from from the the blue blue tit tit system system described described in in Section Section 116.4. Populations in in main mainland land southern southern France France have have aa high high breeding breeding success success in in the the deciduous deciduous habitat, habitat, whereas whereas in in the the sclerophyllous sclerophyllous habitat habitat the the breeding breeding success success and and population population density density are are low. low. However, However, on on the the island island of of Corsica, Corsica, where where the the sclerophyllous sclerophyllous forest is is the the dominant dominant habitat habitat the the breeding breeding success success in in that that habitat habitat type type is is forest higher mainland, despite higher than than on on the the mainland, despite much much higher higher local local density density (Blondel (Blondel et et aI., al., 11992; 992; Dias 996). Furthermore, Dias and and Blondel, Blondel, 11996). Furthermore, the the breeding breeding success success of of the the Corsican pockets of deciduous habitat Corsican population population in in small small pockets of deciduous habitat on on the the island island is is poorer poorer than than in in the the sclerophyllous sclerophyllous habitat; habitat; i.e., i.e., the the deciduous deciduous habitat habitat tends tends to to act (Dias and 996). act as as aa sink sink (Dias and Blondel, Blondel, 11996). It It could could still still be be argued argued that that the the difference difference in in breeding breeding success success in in the the sclero sclerophyllous phyllous habitat habitat between between Corsica Corsica and and the the mainland mainland reflects reflects different different product productivity ivity of of the the sclerophyllous sclerophyllous habitat habitat on on the the island island than than on on the the mainland, mainland, rather rather than differential differential adaptation. adaptation. However, However, the the argument argument of of maladaptation maladaptation is is also also than
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supported supported by by data data on on breeding breeding phenology. phenology. The The breeding breeding phenology phenology is expected to the main main to be be synchronized synchronized with with the the availability availability of of caterpillars, caterpillars, which which are the food for food food for for the the young, young, so so that that the the peak peak demand demand of of the the brood brood for food coincides with occurs with the the peak peak of of caterpillar caterpillar availability. availability. This This peak peak of of food food availability availability occurs about about aa month month earlier earlier in in the the deciduous deciduous than than in in the the sclerophyllous sclerophyllous habitat. habitat. Rather Rather than than showing showing aa pattern pattern of of local local adaptation, adaptation, the the breeding breeding phenology phenology of birds birds on on the the mainland mainland does does not not differ differ between between habitats habitats and and is synchronized synchronized with the with caterpillar caterpillar availability availability in in the the source source (deciduous) (deciduous) habitat. habitat. The The birds birds in the sink sink (sclerophyllous) ( sclerophyllous) habitat habitat lay lay their their eggs eggs almost almost aa month month too too early and, and, as a consequence, consequence, suffer suffer additional additional reduction reduction of of breeding breeding success. success. The The reverse holds holds in in Corsica, Corsica, where where the the breeding breeding phenology phenology is is synchronized synchronized with with caterpilcaterpil lar lar availability availability in in the the sclerophyllous sclerophyllous habitat; habitat; birds birds breeding breeding in in small small pockets pockets of of deciduous deciduous habitat habitat lay lay their their eggs eggs much much too too late late (Dias (Dias and and Blondel, Blondel, 1996). 1 996). Thus Thus inin both both regions regions the the breeding breeding phenology phenology is is well well adapted adapted to to the the source source habitat habitat and and maladapted maladapted to to the the sink sink habitat. habitat. The The difference difference in in the the laying laying date date is genetic genetic (Blondel (Blondel et et al., ai., 1990), 1 990), and and itit isis unlikely unlikely that that the the lack lack of of adaptation adaptation to to the the sink sink habitat habitat isis due due to to aa lack lack of of heritable heritable variation variation for for the the laying laying date. date. The The conclusion conclusion about about maladaptation maladaptation of of the the blue blue tits tits in in the the sink sink habitats habitats is thus thus supported supported both both by by an an optimality optimality analysis analysis and and by by comparison comparison of of the the perper formance formanceof ofthe thelocal local populations populations in in patches patches of of the the same same habitat habitat located located in in difdif ferent ferentlandscapes. landscapes. AAsimilar similar oDtimalitv optimality armroach approach has has been been used used to to demonstrate demonstrate mmaladaptation a l ~' - - - d ~ a u u' u -, ~ a t "tit~ uof l , -l~clutch . ~ u t. ~ in ~size i ~ 'ifi i S ~ t u [ u l ~t i . , i1~9 g b8~8) ) aand u d rreproduc ~prudocin.~-great tits ((Pettifor et aai.,
tive tiveeffort effortand andoffspring offspringsize size of ofmosquitofish mosquitofish in in aa marginal marginal population population (Stearns (Stearns and and Sage, Sage, 1980). 1 9 8 0 ) . AA spectacular spectacular counterexample counterexample is is the the repeated repeated evolution evolution of of heavy heavy metal metal tolerance tolerance by by numerous numerous plant plant species species that that colonized colonized abandoned abandoned heavy heavy metal metal mining mining sites sites and and zinc-polluted zinc-polluted areas areas around around the the bases bases of of electrielectri city city pylons pylons (e.g., (e.g., Jain Jain and and Bradshaw, Bradshaw, 1966; 1 966; Coulaud Coulaud and and McNeilly, McNeilly, 1992; 1 992; Alhiyaly Alhiyalyetetal., ai., 1993; 1 993; Nordal Nordal et et al., ai., 1999). 1 999). Initially, Initially, these these sites sites must must have have concon stituted small small pockets pockets of of aa sink sink habitat habitat surrounded surrounded by by aa large large source source habitat. habitat. stituted However, However, the the colonizers colonizers were were in in aa short short time time able able to to adapt adapt to to the the toxic toxic envirenvir onment, onment, despite despite continuous continuous gene gene flow. flow. Genetic Genetic studies studies reveal reveal that that in in most most cases, cases,heavy heavymetal metaltolerance tolerance in in plants plants involves involves several several major major loci, loci, although although the the contribution contribution of of minor minor loci loci isis not not excluded excluded (e.g., (e.g., MacNair, MacNair, 1993; 1 993; Schat Schat et et al., ai., 1996). 1 996). This This finding finding isis consistent consistent with with the the prediction prediction that that adaptation adaptation to to aa sink sink habitat habitatwould would be be more more likely likely ifif itit involved involved few few major major genes genes rather rather than than many many genes geneswith withsmall small effects effects (see (see earlier earlier discussion). discussion). Using Using reciprocal reciprocal transplants transplants of of seeds, seeds, seedlings, seedlings, and and adults, adults, Stanton Stanton and and Galen Galen (1997; ( 1 997; see see Section Section 16.4) 1 6 .4) have have shown shown that that snow snow buttercup buttercup populations populations living livingatatearly earlyand and late late melting melting sites sites do do not not show show aa pattern pattern of of local local adaptation adaptation tototheir theirrespective respective sites. sites. They They do do not not seem seem to to be be differentiated differentiated genetically genetically with with respectto to any any fitness-related fitness-related character. character. Instead, Instead, irrespective irrespective of of the the destination destination respect habitat, seeds seedsoriginating originating from fromlate late melting melting sites sites are are 2.5 25% less likely likely to to germingermin habitat, % less ate despite despite being being only only 8% 8 % smaller. smaller. One One can can speculate speculate that that in in the the absence absence of of ate gene flow, flow, local local populations populations at at late-melting late-melting sites sites would would evolve evolve toward toward propro gene ducing ducingfewer fewer larger larger seeds, seeds, and and that that this this change change is is prevented prevented by by the the gene gene flow. flow. Research on on the the checkerspot checkerspot butterfly butterfly (see (see Section Section 16.4) 1 6.4) provides provides some some evievi Research dence dence for for alternative alternative equilibria, equilibria, similar similar to to those those predicted predicted by by Ronce Ronce and and Kirkpatrick (2001). (200 1 ) . After After the the local local populations populations in in the the original original source source habitat habitat Kirkpatrick (forestclearings) clearings) had had been been wiped wiped out out by by aa frost, frost, in in several several localities localities the the original original (forest
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source-sink source-sink structure structure was was not not recreated. recreated. Instead, Instead, the the population population density density became became much rocky outcrops), much higher higher in in the the former former sink sink habitat habitat ((rocky outcrops), whereas whereas individuals individuals attempting recolonize the poor reproductive attempting to to recolonize the former former source source habitat habitat had had poor reproductive suc success. cess. Thus, Thus, the the source-sink source-sink structure structure became became reversed. reversed. This This reversal reversal was was not not due due to consequence of phenological differences to an an evolutionary evolutionary change change but but was was aa consequence of phenological differences between between the the habitats: habitats: migrants migrants from from the the outcrops outcrops arrived arrived too too late late to to reproduce reproduce successfully clearings. Once resident population established in successfully in in the the clearings. Once aa resident population was was established in aa clearing, it 999). Nonetheless, clearing, it expanded expanded quickly quickly (Boughton, (Boughton, 11999). Nonetheless, this this example example illus illustrates trates aa potential potential for for alternative alternative source-sink source-sink equilibria. equilibria. A A promising promising approach approach to to study study evolutionary evolutionary consequences consequences of of aa source-sink source-sink population structure population structure would would be be to to set set up up laboratory laboratory source-sink source-sink systems systems and and let populations evolve let experimental experimental populations evolve in in them them for for generations. generations. This This "experi "experimental mental evolution evolution"" approach approach has has been been applied applied successfully successfully to to other other evolution evolutionary questions, concerning, 990), ary questions, concerning, e.g., e.g., reproductive reproductive isolation isolation (Rice (Rice and and Salt, Salt, 11990), life life history history (Stearns (Stearns et et aI., al., 2000), 2000), or or learning learning ability ability (Mery (Mery and and Kawecki, Kawecki, 2002 2002).) . Although Although many many studies studies involved involved experimental experimental evolution evolution in in novel novel habi habitats, tats, few few included included experimental experimental populations populations evolving evolving in in heterogeneous heterogeneous envir environments, onments, with with different different habitats habitats connected connected by by dispersal. dispersal. Several Several of of those those studies studies focused focused on on the the role role of of environmental environmental heterogeneity heterogeneity in in the the maintenance maintenance of (McDonald and of genetic genetic variation variation at at allozyme allozyme loci loci (McDonald and Ayala, Ayala, 1974; 1974; Powell Powell and and Wistrand, 978; Haley 9 8 3 ) and Wistrand, 11978; Haley and and Birley, Birley, 11983) and quantitative quantitative traits traits (MacKay, (MacKay, 11981; 9 8 1 ; Garcia-Dorado 9 9 1 ; Hawthorne, 997). In Garcia-Dorado et et aI., al., 11991; Hawthorne, 11997). In those those studies studies the the habitats contributed equally equally to soft selection). habitats contributed to the the total total reproduction reproduction ((soft selection). This This design relationship between design eliminated eliminated the the relationship between mean mean performance performance in in aa habitat habitat and and this habitat's habitat's contribution contribution to to the the total total reproduction, reproduction, which which is is an an important important this characteristics studies were characteristics of of source-sink source-sink populations. populations. Other Other studies were focused focused on on the the evolution 986; Rice 990). evolution of of habitat habitat choice choice (Bird (Bird and and Semeonoff, Semeonoff, 11986; Rice and and Salt, Salt, 11990). Only Only aa few few compared compared adaptation adaptation to to aa novel novel habitat habitat between between lines lines exposed exposed only only to to the the novel novel habitat habitat and and lines lines exposed exposed to to both both habitats habitats (Wasserman (Wasserman and and Futuyma, 9 8 1 ; Mark, 982; Verdonck, 987; Taper, 990). Because Futuyma, 11981; Mark, 11982; Verdonck, 11987; Taper, 11990). Because these these studies studies were were also also concerned concerned with with habitat habitat choice, choice, the the adults adults could could choose choose the the habitat habitat for for oviposition, oviposition, and and the the amount amount of of gene gene flow flow was was not not controlled. controlled. Verdonck 1 987) let Verdonck ((1987) let D. melanogaster melanogaster populations populations evolve evolve in in cages cages containing containing two media: aa standard two media: standard medium medium and and aa medium medium supplemented supplemented with with NaCI. NaC1. The The latter latter medium medium created created aa sink sink habitat, habitat, with with low low larval larval survival survival (although (although not not an an absolute absolute sink) sink).. Despite Despite the the asymmetric asymmetric gene gene flow, flow, the the experimental experimental popula populations tions did did evolve evolve improved improved tolerance tolerance to to NaCl, NaCI, but but to to aa lesser lesser degree degree than than con control trol populations populations bred bred exclusively exclusively to to the the NaCI-supplemented NaCl-supplemented medium. medium. Thus, Thus, in in this this case, case, asymmetric asymmetric gene gene flow flow slowed slowed down, down, but but did did not not completely completely prevent prevent adaptation to 1 990) maintained populations of adaptation to aa sink sink habitat. habitat. Taper Taper ((1990) maintained populations of the the cow cowpea weevil weevil (Callosobruchus (Callosobruchusmaculatus) maculatus) on on aa mixture mixture of of two two host host seed seed species, species, pea either either on on its its own, own, or or together together with with aa competing competing species species specializing specializing on on one one of of hosts. In the hosts. In this this latter latter treatment treatment the the competition competition pressure pressure from from the the other other the species species caused caused that that host host to to become become effectively effectively aa sink sink habitat. habitat. As As predicted, predicted, caused the competition competition with with the the specialist specialist competitor competitor caused the generalist generalist species species to to become less well host species used by become less well adapted adapted to to the the host species used by the the competitor competitor and and better better adapted host species adapted to to the the other other host species (character (character displacement) displacement).. These These studies studies suggest suggest that that the the "experimental "experimental evolution" evolution" approach approach has has aa great great potential potential to to provide insights into provide insights into evolution evolution in in heterogeneous heterogeneous environments. environments.
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SOURCE-SINK SOURCE-SINK METAPOPULATIONS METAPOPULATIONS The The concept concept of of source-sink source-sink population population structure structure emphasizes emphasizes the the effect effect of of dis dispersal population concept persal on on the the local local population population dynamics, dynamics, whereas whereas the the meta metapopulation concept has has originally originally been been motivated motivated by by local local extinctions extinctions and and colonizations colonizations (Levins, (Levins, 1968a). 1968a). Source-sink Source-sink population population structure structure results results from from differences differences in in habitat habitat qual quality, population structure ity, whereas whereas meta metapopulation structure reflects reflects patchiness patchiness of of the the environment. environment. Both Both concepts concepts are are concerned concerned with with the the role role of of dispersal, but but the the source-sink source-sink structure structure requires much much greater greater dispersal dispersal rates rates (i.e., (i.e., greater greater connectivity connectivity of of habi habitat tat patches), patches), which which would would prevent prevent habitat habitat patches patches from from remaining remaining unoccupied. unoccupied. However, many real spatially structured structured populations populations are likely to be affected by both both processes. processes. First, First, in in aa "classic" "classic" metapopulation, metapopulation, immigration may may signifi significantly cantly reduce the the local local extinction extinction rate rate (rescue (rescue effect; effect; Brown Brown and and Kodric-Brown, Kodric-Brown, 11977; 977; Chapters Chapters 44 and and 14). 14). It It may may also also boost the the local local population size size and and the the number of of propagules propagules it it produces, thus thus potentially potentially increasing the the colonization colonization rate. rate. Second, Second, some some local local populations populations (those (those in in large large habitat habitat patches, patches, or or in in the the vicinity vicinity thereof) thereof) may may show show typical typical source-sink source-sink dynamics dynamics with with negligible extinc extinction tion probability, probability, whereas whereas the the fate fate of of others others (those in in small small and and more more isolated isolated patches) patches) will will be be dominated dominated by by extiction-recolonization extiction-recolonization dynamics. dynamics. This This idea idea is is explicit explicit in in metapopulation metapopulation models models of of limits limits of of species species ranges ranges (e.g., Lennon Lennon et et aI., al., 11997; 997; Holt Holt and and Keitt, Keitt, 2000). The The concept concept of of source-sink source-sink dynamics dynamics can can also also be be extended extended to to extinction-recolonization extinction-recolonization dynamics dynamics by by allowing allowing the the extinction extinction rate rate or or the the contribution Chapter 4). contribution to to the the pool pool of of colonizers colonizers to to vary vary among among patches ((Chapter 4). Most empty empty patches patches would would then then be be colonized colonized by by individuals originating from from patches with with more more persistent and and larger larger populations populations (sources). (sources). Colonizers Colonizers from from such such source source patches patches may may maintain maintain aa significant significant level level of of patch patch occupancy occupancy in in neigh neighboring boring sink sink patch patch networks, networks, in in which which otherwise otherwise extinction extinction rate rate would exceed exceed colonization. metapopulation model, in colonization. The The mainland-island mainland-island metapopulation in which which all all colon colonizing "mainland" population, izing individuals individuals originate originate in in aa permanent permanent "mainland" population, is is an an extreme 6.2). Such extreme case, case, analogous analogous to to the the black black hole hole sink sink (Section (Section 116.2). Such source-sink source-sink extinction-colonization extinction-colonization dynamics dynamics is is implicit implicit in in most most structured structured or or spatially spatially explicit 993; Hanski, explicit metapopulation metapopulation models models (e.g., (e.g., Hanski Hanski and and Gyllenberg, Gyllenberg, 11993; 11994; 994; Chapters Chapters 44 and and 55).) . The The distinction distinction between between source-sink source-sink dynamics dynamics at at the the level level of of extinction-colonization extinction-colonization dynamics versus at at the the level level of of local population population dynamics aI., 11999). 999). dynamics disappears disappears in in individual-based individual-based models models (e.g., (e.g., Wiegand Wiegand et et al.,
116.8 6.8
CONCLUSIONS CONCLUSIONS AND A N D PROSPECTS PROSPECTS This necessarily incomplete review of ecological and and evolutionary evolutionary aspects of the the source-sink source-sink population population structure structure elucidates elucidates its its importance importance for for population population dynamics, dynamics, size, size, distribution, distribution, and and persistence, persistence, as as well well as as for for the the understanding understanding of of evolutionary evolutionary dynamics dynamics of of ecological niches niches and and species ranges. The The import importance manage ance of of source-sink source-sink dynamics dynamics for for biodiversity biodiversity conservation conservation and and pest pest management ment has has been been widely widely recognized. recognized. As As in in many many other other areas areas of of population population biology, biology, the the development development of of theory theory has has outpaced outpaced the the accumulation accumulation of of empirical empirical data. data. In In particular, particular, direct direct experi experimental data data addressing addressing ecological ecological and evolutionary evolutionary consequences consequences of
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source-sink population dynamics reason is source-sink population dynamics are are scarce. scarce. One One reason is the the fact fact that that most most research motivated concept has concentrated on birds, research motivated by by the the source-sink source-sink concept has concentrated on birds, mammals, and long-lived flowering plants. Experimental mammals, and long-lived flowering plants. Experimental manipulations manipulations of of spatial population structure spatial population structure (e.g., (e.g., preventing preventing dispersal, dispersal, changing changing the the amount amount of habitat) should should be of source source or or sink sink habitat) be more more feasible feasible in in insects insects or or mites. mites. Their Their shorter allow one those manipula shorter generation generation time time would would allow one to to see see the the effects effects of of those manipulations ideal model tions sooner. sooner. Some Some insects insects or or mites mites are are also also ideal model organisms organisms for for labora laboratory could be tory source-sink source-sink systems. systems. Such Such systems systems could be combined combined with with the the ""experimental experimental evolution" evolution" approach approach to to study study the the evolutionary evolutionary consequences consequences of of the source-sink source-sink population population structure. structure. This This approach approach should should be be promoted. promoted. the Some concept have also remained Some applied applied aspects aspects of of the the source-sink source-sink concept have also remained neg neglected. lected. In In particular, particular, the the concept concept has has important important implications implications for for epidemiology epidemiology and human population sink habitat and public public health; health; the the human population is is aa sink habitat for for numerous numerous para parasites sites and and pathogens pathogens (e.g., (e.g., the the rabies rabies virus) virus).. The The concept concept also also applies applies to to the the dynamics dynamics of of pathogens pathogens within within the the host's host's body, body, whereby whereby some some organs organs may may be be sources others sinks sinks for has medical sources and and others for the the pathogen. pathogen. This This has medical implications, implications, as as anti pathogen drugs only target antipathogen drugs will will be be ineffective ineffective if if they they only target pathogens pathogens in in sink sink organs. human diseases organs. Some Some dangerous dangerous human diseases are are caused caused by by pathogens pathogens invading invading organs organs are hole organs from from which which they they cannot cannot transmit; transmit; such such organs are thus thus black black hole sinks. sinks. Finally, Finally, our our own own population population has has aa source-sink source-sink structure, structure, with with important important economic and social consequences. economic and social consequences. To To summarize, summarize, although although much much progress progress has has been been made made since since Pulliam's Pulliam's ((1988) 1 9 8 8 ) seminal seminal paper, paper, much much work work remains remains to to be be done done before before we we can can fully fully understand evolutionary consequences understand the the ecological ecological and and evolutionary consequences of of the the source-sink source-sink population population structure. structure.
I 7
META PO PULATION M ETAPO PU LATIO N DYNAMICS DYNAMICS OF OF INFECTIOUS ASES INFECTIOUS DISE DISEASES Matt Matt J. Keeling, Ottar Ottar N. N. Bjornstad, Bjornstad, and and Bryan Bryan T. Grenfell
117.1 7. 1
INTRODUCTION INTRODUCTION John John Donne's Donne's famous famous line line "No "No man man is is an an island, island, entire entire of of itself" itself" has has deep deep resonances resonances for for the the dynamics dynamics of of parasites. parasites. This This is is particularly particularly true true for for microparasitic microparasitic infections, infections, such such as as viruses viruses and and bacteria, bacteria, for for which which each each suscep susceptible tible host host is is aa potential potential patch patch of of favourable favourable habitat. habitat. Propagules Propagules from from infected infected ""patches" patches" can others, followed parasitic multiplication multiplication and can colonize colonize others, followed by by parasitic and ""local" local" growth parasite population. scale of host popu growth of of the the parasite population. Thus, Thus, at at the the scale of the the host population, infectious infectious dynamics dynamics bears bears strong strong analogies analogies to to metapopulation metapopulation dynam dynamlation, ics. Furthermore, ics. Furthermore, host host individuals individuals are, are, more more often often than than not, not, structured structured into into populations, within local populations, within which which contact contact among among hosts hosts may may be be very very frequent frequent and and between between which which contacts contacts may may be be less frequent. frequent. In In this this way, way, the the spatiotem spatiotemporal dynamics dynamics and and persistence persistence of of parasites parasites are are determined determined at at two two scales: scales: the the infrapopulation (a local local population population scale; parasites within infrapopulation scale scale (a scale; parasites within hosts) hosts) and and the the metapopulation spatial and/or metapopulation scale scale ((spatial and/or social social aggregation aggregation of of hosts hosts).) . The The spa spatiotemporal tiotemporal dynamics dynamics of of infection infection in in human human and and domestic domestic systems systems are are of of par particular combined with ticular academic academic interest interest because because of of the the wealth wealth of of data data combined with well-described histories. well-described natural natural histories. As As aa result result of of the the dual dual spatial spatial scales scales of of regulation, regulation, an an extended extended metapopu metapopulation disease dynamics lation paradigm paradigm is is central central to to infectious infectious disease dynamics in in two two important important
Ecology, Ecology, Genetics, Genetics, and Evolution of Metapopulations
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Copyright 2004, Elsevier, Elsevier, Inc. 0-12-323448-4
MATI MATT j. I. KEELING KEELING ET ET AL. AL.
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ways. First, First, the population approach help us ways. the meta metapopulation approach can can help us understand understand disease disease dynamics dynamics at at the the different different spatial spatial scales. scales. This This topic topic is is the the main main concern concern here, here, we we use realistic dynamic models to discuss the use extensive extensive data data sets sets and and realistic dynamic models to discuss the metapopu metapopulation dynamics Second, there lation dynamics of of infectious infectious disease. disease. Second, there are are important important conceptual conceptual insights eradication by vaccination of insights about about the the eradication by vaccination of infections infections to to be be gained gained from from studies 994; Grenfell and studies of of the the persistence persistence of of metapopulations metapopulations (Nee, (Nee, 11994; Grenfell and Harwood, 997; Ovaskainen 3 ) . This Harwood, 11997; Ovaskainen and and Grenfell, Grenfell, 200 2003). This chapter chapter therefore therefore explores explores two two main main topics: topics: (i) (i) the the analogies analogies between between the the disciplines disciplines of of ecology ecology and epidemiology and (ii) how meta population and epidemiology at at the the metapopulation-level metapopulation-level and (ii) how metapopulation theory theory at at aa variety variety of of scales scales can can aid aid our our understanding understanding of of epidemiological epidemiological dynamics. dynamics. We We discuss discuss these these issues issues in in the the face face of of aa set set of of detailed detailed models models and and high-resolution disease incidence. high-resolution space-time space-time data data of of disease incidence. Metapopulation-like Metapopulation-like disease disease dynamics dynamics occur occur whenever whenever the the environment, environment, in in this this case case the the population population of of susceptibles, susceptibles, is is sufficiently sufficiently patchy patchy that that isolated isolated clumps clumps of of suitable suitable habitat habitat exist. exist. This This is is always always the the case case at at the the microscale; microscale; each each host host is is an an island island to to be be colonized colonized and and aa resource resource patch patch to to be be depleted. depleted. At At the the macro scale, hosts macroscale, hosts are are usually usually aggregated aggregated in in local local communities communities within within which which transmission transmission is is relatively relatively frequent frequent and and between between which which infection infection spreads spreads at at aa lower rate. rate. Our dominant focus population (macro)scale. lower Our dominant focus is is on on the the meta metapopulation (macro)scale. To To illus illustrate trate the the key key issues, issues, we we first first introduce introduce aa simple simple epidemic epidemic model model and and then then use use this this to to illuminate illuminate the the basic basic processes processes in in the the spatiotemporal spatiotemporal dynamics dynamics of of epidemics. epidemics. Two Two distinct distinct modeling modeling scenarios scenarios are are considered: considered: aa fully fully stochastic stochastic metapopula metapopulation (or community) tion where where the the individual individual level level processes processes within within each each habitat habitat (or community) are are modeled explicitly implicit (Levins-type modeled explicitly and and aa spatially spatially implicit (Levins-type)) metapopulation metapopulation where where habitats formulations habitats are are classified classified into into aa limited limited set set of of discrete discrete classes. classes. Both Both formulations have have associated associated benefits benefits and and allow allow different different insights insights into into the the dynamic dynamic processes processes in population processes in disease disease spread. spread. We We then then revisit revisit how how meta metapopulation processes operate operate at at vari various ous spatial spatial scales scales (individual (individual level, level, local, local, and and regional regional epidemics). epidemics). The The resultant resultant spatiotemporal dynamics dynamics are case studies, spatiotemporal are then then illustrated illustrated through through aa series series of of case studies, which diseases metapopulation which explore explore diseases metapopulation dynamics dynamics at at the the interface interface of of models models and and data. data. We We conclude conclude with with aa section section on on fruitful fruitful areas areas for for future future work. work.
117.2 7.2 THE THE SIR SIR MODEL MODEL FOR FOR EPIDEMIC EPIDEMIC DYNAMICS DYNAMICS We We focus focus here here on on microparasite microparasite infections infections (mainly (mainly viruses viruses and and bacteria), bacteria), where where direct direct reproduction reproduction of of the the pathogen pathogen in in the the host host allows allows us us to to model model dis disease ease dynamics dynamics by by dividing dividing the the host host population population between between compartments, compartments, classified classified by their infection status (Anderson 9 9 1 ) . In by their infection status (Anderson and and May, May, 11991). In contrast, contrast, macroparasitic macroparasitic helminth helminth infections, infections, where where parasite parasite burden burden matters, matters, are are much much harder harder to to model model spatially considered here), analogies have spatially (and (and not not considered here), although although strong strong analogies have been been found found between macroparasite between macroparasite and and metapopulation metapopulation dynamics dynamics (Cornell (Cornell et et ai., al., 2000) 2000).. The The most most studied studied microparasite microparasite system system iiss the the SIR SIR model, model, where where individuals individuals are susceptible (5), are susceptible (S), infected infected (I), or or recovered recovered (R). This This classification classification holds holds analo analogies metapopulation models models in gies to to the the "compartmental" "compartmental" Levins Levins metapopulation in which which patches patches are either occupied occupied or discussed in are classified classified as as either or empty empty (Chapter (Chapter 4). 4). As As discussed in the the next next section, local patch section, the the "reversibility" "reversibility" of of true true metapopulations metapopulations (such (such that that local patch populations then reestablished populations can can become become extinct, extinct, then reestablished by by colonization) colonization) is is aa closer closer match susceptible-infectious-susceptible, such match to to the the SIS SIS dynamics dynamics ((susceptible-infectious-susceptible, such that that
ETAPOPULATION DYNAMICS OF INFECTIOUS 117. 7. M METAPOPULATION DYNAMICS OF INFECTIOUS DISEASES DISEASES
4 1 77 41
recovered individuals individuals do not possess sexually recovered do not possess immunity) immunity) associated associated with with many many sexually transmitted 9 9 1 ) . In paradigm, suscep transmitted diseases diseases (Anderson (Anderson and and May, May, 11991). In the the SIR SIR paradigm, susceptible tible individuals individuals can can catch catch the the disease disease from from contact contact with with infected infected individuals; individuals; infected infected individuals individuals then then recover recover at at aa given given rate, rate, after after which which time time they they are are assumed assumed to to be be immune immune to to further further infection. infection. This This leads leads to to the the following following set set of of dif differential equations: equations: ferential
SI dS dS SI == BN - dS B N - - 13 B_--:_as dt dt - mN SI dI dI SI at = ~3-~ gI - dI dI dt = 13 N - gI dR dR dt = gI - dR dt = g I -
((17.1) 1 7. 1 )
dR
N N == S +SI ++R I + R B
d
where where B is is the the birth birth rate, rate, d is is the the natural natural death death rate, rate, 13 13is is the the transmission transmission rate rate between between infected infected and and susceptible susceptible individuals, individuals, and and g is is the the recovery recovery rate. rate. Many Many improvements variations on improvements and and variations on this this underlying underlying framework framework have have been been devel developed diseases and oped successfully successfully to to describe describe the the behavior behavior of of particular particular diseases and hosts hosts (Anderson 9 9 1 ; Grenfell 995; Hudson Hudson et (Anderson and and May, May, 11991; Grenfell and and Dobson, Dobson, 11995; et aI., al., 2002 2002).) . IInn essence, 1 7. 1 ) predicts essence, Eq. Eq. ((17.1) predicts aa stable stable equilibrium equilibrium level level of of susceptibles susceptibles and and infected, infected, which which is is reached reached through through aa series series of of damped damped epidemics. epidemics.
117.3 7.3
g
THE THE SPATIAL SPATIAL DIMENSION DIMENSION Spatial Spatial structure structure and and the the aggregation aggregation of of hosts hosts into into discrete discrete patches patches can can have have dramatic diseases (May dramatic effects effects on on the the dynamics dynamics of of infectious infectious diseases (May and and Anderson, Anderson, 11979; 979; Grenfell 99 8 ) . We Grenfell and and Bolker, Bolker, 11998). We subdivide subdivide these these effects effects into into four four main main groups, groups, which which we we consider consider with with respect respect to to the the dynamics dynamics of of one one large, large, homo homogeneously geneously mixed mixed host host population population versus versus the the dynamics dynamics of of several several smaller, smaller, more more isolated isolated ones. ones.
Isolation and Isolation and Coupling: Coupling: A A Simple Simple Two-Patch Two-Patch Model Model The The most most obvious obvious aspect aspect of of spatial spatial separation separation is is the the isolation isolation of of one one or or more more local local populations. populations. The The degree degree of of isolation isolation is is controlled controlled by by the the coupling coupling between absence of between patches. patches. In In the the absence of coupling, coupling, the the dynamics dynamics in in each each patch patch are are independent, independent, and and as as the the coupling coupling increases, increases, so so does does the the correlation correlation between between them. them. We We generally generally envisage envisage coupling coupling as as the the result result of of the the movement movement of of hosts; hosts; in in such such cases cases it it is is important important to to realize realize that that the the movement movement of of both both susceptibles susceptibles and role. We and infecteds infecteds plays plays an an equal equal role. We also also note note that that two two patches patches can can be be coupled coupled directly directly due due to to the the mixing mixing of of individuals individuals in in aa third third patch patch (e.g., (e.g., people people from from two two outlying outlying towns towns might might meet, meet, and and transmit transmit infection, infection, at at aa nearby nearby large large town). town). As As we we are are concerned concerned primarily primarily with with the the spread spread of of infection infection between between human human communities, communities, we we envisage envisage coupling coupling as as the the result result of of short short duration duration commuter commuter movements. movements. For For other other host host species, species, coupling coupling could could be be generated generated by by
MATT I.]. KEELING KEELING ET ET AL. AL. MA1-F
441 1 88
the permanent permanent movement movement of of hosts hosts or or simply simply the the movement movement of of pathogens pathogens the between local local populations populations (Keeling (Keeling et et al., aI., 2001). 200 1 ) . between A key key question question for for understanding understanding the the ensuing ensuing spatial spatial dynamics dynamics is is how how to to A accurately allow allow for for the the movement movement of of infection. infection. Consider, Consider, first, first, aa metapopulametapopula accurately tion of of just just two two patches patches (Keeling (Keeling and and Rohani, Rohani, 2002). 2002). In In this this model, model, individuals individuals tion commute from from their their home home population population to to the the other other patch, patch, but but return return rapidly rapidly commute ( Sattenspiel and and Dietz, Dietz, 1995). 1 995). We label individuals individuals by by two two subscripts subscripts such such that that (Sattenspiel We label the number number of of susceptibles susceptibles currently currently in in patch patch j, j, whose whose home home is is patch patch i. i. We We Sij isis the Sii commute at at rate rate pi and return return at at rate rate also assume assume that that individuals individuals from from patch patch ii commute also Pi and Ti, independent independent of of their their infectious infectious state. state. If If we we assume assume frequency-dependent frequency-dependent % transmission (de (de Jong Jong et et al., aI., 1995; 1995; McCallum McCallum et et al., aI., 2001), 200 1 ), then then equations equations for for transmission the number number of of susceptibles susceptibles and and infecteds infecteds in in each each patch patch are are given given by by the
dSii
dt
Iii + Iji ~SiiNi i + mji - dSii + "rimij - piSii
= bmii-
dlii
Iii + Iji
dt = ~Sitmii + mji - glii - dIii + "r
- pilii ((17.2) 1 7.2)
dSij = b N i j -
at
Iij + Ijj
f3S#Nij + Njj
_ dSij - "r
+ f)iSii
dIij Iij + Ijj = f3SilNij + Njj - gIij - dIij - $iIij + piIii dt Here, equations equations for for the (R ii and have not been where ii 7= where ~ j.j. Here, the recovered recovered class class (Rii and Ri Rii)j) have not been R == N. given be calculated from the the fact If given explicitly, explicitly, as as they they can can be calculated from fact that that S + R S ++ II + N. If we distribution of individuals to ;;INij = we allow allow the the distribution of individuals to equilibrate, equilibrate, then then N Nii/Nij = T; "ri/Pi. !Pi' Now, summing over all individuals whose home home is Now, summing over all individuals whose is patch patch ii and and assuming assuming that that time relatively short time spent spent away away from from the the home home patch patch is is relatively short compared compared to to the the dis disease dynamics, we get ease dynamics, we get
dSi dSi j] - dSi dt = [(Tii1i + = b b NNi i - - I3Si ~Si[(Yiili + (Tij! (Yijlj]dSi dt dl dlii = j ] - gIi Si [(Tii1i : I3 ~3Si [o'iiIi + + (Tij! o'iilj]gli- - d dIi1i dt dt
((17.3) 1 7. 3 )
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Fig. (A) Fig. 1 1 99.2 .2 (A) Fraction Fraction of of roadside r o a d s i d e segments s e g m e n t s occupied o c c u p i e d by by S. S. latifolia latifolia aand n d (S) (B) average a v e r a g e num number ber of of S. latifolia latifolia individuals individuals within within each each occupied occupied segment s e g m e n t in in each each year year for for the the four four areas areas of of the metapopulation. the metapopulation.
when 5 % of when nearly nearly 335% of the the populations populations were were diseased, diseased, followed followed by by aa rapid rapid decline. decline. Three Three subareas subareas were were identified identified within within this this area area on on the the basis basis of of sepa separation ration by by long long runs runs of of unoccupied unoccupied segments. segments. All All three three subareas subareas showed showed aa sim sim1 990s and ilar ilar pattern pattern with with disease disease incidence incidence peaking peaking III in the the midmid-1990s and then then declining Fig. 119.4). 9.4) . declining ((Fig.
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Fig. (A) Fraction of diseased (disease F | g . 11 99.3 .3 (A) Fraction of S. latifolia latifolia populations populations that that were were diseased (disease incidence) incidence) and and (8) (B) fraction fraction of of individuals individuals that that were were diseased diseased (disease (disease prevalence) prevalence) within within each each diseased diseased popula population tion for for three three areas areas of of the the metapopulation. metapopulation.
The The fraction fraction of of individuals individuals that that were were diseased, diseased, or or "disease "disease prevalence," prevalence," within Fig. 119.3B) 9.3B) increased within each each diseased diseased population population ((Fig. increased significantly significantly overall overall (P < 5 1 , arcsin < 0.0042, 0.0042, b = = 0.00 0.0051, arcsin square square root root transformed transformed data data).) . All All areas areas showed " year interaction showed an an increase increase in in disease disease prevalence prevalence and and the the area area':year interaction
479 419
PLANT-PATHOGEN METAPOPULATION METAPOPULATION 119. 9. PLANT-PATHOGEN
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Fig. Disease incidence and disease three different different sections sections of Fig. 11 9.4 0.4 Disease incidence and disease prevalence prevalence in in three of Area Area 3. 3. Incidence Incidence is is the the fraction fraction of of roadside roadside segments segments occupied occupied by 5. S. latifolia latifolia that that contained contained at at least least one one diseased diseased plant, plant, and and prevalence prevalence describes describes the the fraction fraction of of plants plants within within each each diseased diseased segment segment that that were were diseased. diseased.
JANIS JANIS ANTONOVICS ANTONOVICS
480 480
approached (P < . 06 1 ) . The approached significance significance (P < 00.061). The increase increase was was individually individually signifi significant only (P < .0 1 1 ) . The absolute number number of dis cant only in in Area Area 1I (P < 0.0005, 0.0005, b = - 00.011). The absolute of diseased plants significantly (P (P < 0.123) eased plants per per segment segment decreased decreased significantly < 0.0037, 0.0037, b = = -0.123) and year interaction and the the area" area*year interaction was was not not significant significant (P < < 0.21 0.21).) . Within Within the the subareas subareas ooff Area Area 33 disease disease prevalence prevalence was was positively positively but but nonsignifi nonsignificantly incidence in cantly correlated correlated with with incidence in two two subareas subareas ((rr = 0.19, 0.19, 0.38; 0.38; P < < 0.51, 0.51, 0.17), 0.17), while while in in the the other other area area they they were were negatively negatively and and nearly nearly significantly significantly correlated correlated (r = 0.50, P < (r -0.50, < 0.069). 0.069).
Host Host Colonization Colonization and and Extinction Extinction A A host host colonization colonization was was identified identified as as the the presence presence of of aa population population in in aa roadside segment after year when when no plants were were seen seen in roadside segment after aa year no plants in that that segment; segment; the the host colonization measure that host colonization rate rate is is therefore therefore aa compound compound measure that includes includes recruit recruitments plants that remained vegetative ments from from the the seed seed pool, pool, recruitment recruitment of of plants that had had remained vegetative for whole year, immigration from for aa whole year, and and immigration from other other sites. sites. We We calculated calculated the the colonization colonization rates rates of of the the host host S. latifolia latifolia as as the the number number of of new new populations populations at at time time t per per existing existing population population at at time time t -- 11.. This This "per "per capita" colonization rate capita" colonization rate does does not not take take into into account account the the number number of of empty empty segments available these were 1 989: segments available for for colonization, colonization, as as these were extremely extremely numerous numerous ((1989: 645 1 , 11990-2002: 990-2002: 6 6 1 6-6694) and 6451, 6616-6694) and did did not not vary vary appreciably appreciably with with changes changes in in host per unoccupied host occupancy. occupancy. Calculations Calculations on on aa ""per unoccupied segment" segment" basis basis (i.e., (i.e., equi equivalent "c" in 969) valent to to Levins' Levins' "c" in the the canonical canonical metapopulation metapopulation model, model, Levins, Levins, 11969) did did not not change change the the results results appreciably. appreciably. We We included included both both healthy healthy and and diseased diseased populations as populations as sources sources because because the the latter latter also also produced produced seed seed (except (except in in the the very case where where there 00 % disease very rare rare case there was was 1100% disease of of females females and/or and/or males). males). Results Results (Fig. 9 .5A) showed showed that healthy populations (Fig. 119.5A) that the the colonization colonization rates rates of of healthy populations (b = 0.0041, P < declined of the declined over over the the time time period period of the study study (b - -0.0041, < 0.040) 0.040) and and that that the the rate rate of of decline decline was was not not significantly significantly different different in in the the different different areas areas ((area*year area*year interaction interaction P < < 0.44). 0.44). Host Host extinction extinction was was identified identified as as the the absence absence of of aa population population in in aa roadside roadside segment segment after after aa year year when when plants plants had had been been seen seen in in that that segment segment the the previous previous year. apparent" host year. Strictly Strictly speaking, speaking, it it is is an an ""apparent" host extinction extinction rate rate because because it it refers refers to does not preclude the to the the absence absence of of flowering flowering individuals individuals and and does not preclude the persistence persistence of individuals or bank. Generally, of the the population population as as vegetative vegetative individuals or in in the the seed seed bank. Generally, most most plants plants flower flower every every year, year, except except for for very very small small individuals. individuals. When When vegetative vegetative plants were seen, the plants were occasionally occasionally seen, the population population was was not not recorded recorded as as extinct; extinct; however, because vegetative individuals are however, plants plants may may have have been been missed missed because vegetative individuals are not not very (Fig. 119.5B) 9.5B) showed very conspicuous. conspicuous. Results Results (Fig. showed that that the the extinction extinction rates rates of of the the host period of host tended tended to to decline decline over over the the time time period of the the study, study, but but this this decline decline was was not 0 . 0 1 7, P < decline was not significant significant (b = = -0.017, < 0.076 0.076).) . The The rate rate of of decline was not not signifi significantly areas (area ':· year interaction interaction P < 1). cantly different different in in the the different different areas (area*year < 0.2 0.21).
Disease Disease Colonization Colonization and and Extinction Extinction A A disease disease colonization colonization event event was was identified identified as as the the presence presence of of the the disease disease in in aa population of disease had population of S. latifolia after after aa year year when when no no disease had been been seen seen in in that that popu population lation the the previous previous year. year. Disease Disease colonization colonization is is most most probably probably by by immigration, immigration,
119. 9.
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Fig. (A) and (B) in each each year F i g . 11 99.5 .$ (A) Colonization Colonization rate rate and (B) extinction extinction rate rate of of S. latifolia latifolia in year for for the the four four areas areas of of the the metapopulation. metapopulation. Colonization Colonization rate rate is is measured measured as as the the number number of of new new populations populations in in the in aa given given year year per per existing existing population population in the previous previous year. year. Extinction Extinction rate rate is is measured measured as as the the number of number of populations populations that that went w e n t extinct extinct in in aa given given year year as as aa fraction fraction of of the the number number of of popu populations lations in in the the previous previous year. year.
482 482
JANIS ANTONOVICS ANTONOVICS JANIS
but or aa plant but the the persistence persistence of of the the disease disease in in aa vegetative vegetative plant plant ((or plant that that was was not not flowering flowering at at the the time time of of census) census) cannot cannot be be precluded. precluded. Across Across season season soil-borne soil-borne transmission transmission and and vertical vertical transmission transmission of of the the disease disease have have never never been been observed. observed. We We calculated calculated the the colonization colonization rate rate of of the the disease disease as as the the number number of of newly newly diseased diseased populations populations at at time time t per per existing existing population population at at time time t - 1i divided divided by by the the number number of of healthy healthy populations populations available available for for colonization colonization in in an an area area (i.e., (i.e., Levins' Levins' "c" "c").). Results 9.6A) showed Results (Fig. (Fig. 119.6A) showed that that the the colonization colonization rates rates of of disease disease declined declined over over the the time time period period of of the the study study (b = = - 00.025, .025, P < < 0.029 0.029)) and and that that the the rate rate of of decline year inter decline was was not not significantly significantly different different in in the the different different areas areas (area" (area*year interaction P < < 0.44). 0.44). action Disease Disease extinction extinction was was identified identified as as the the absence absence of of disease disease in in aa population population that been diseased apparent" extinc that had had been diseased in in the the previous previous year. year. Again Again this this is is an an ""apparent" extinction because the tion rate rate because the disease disease may may have have persisted persisted in in nonflowering nonflowering individuals. individuals. Results 9.6B) showed Results (Fig. (Fig. 119.6B) showed that that the the extinction extinction rate rate of of the the disease disease did did not not (b = .46) and change change over over the the time time period period of of the the study study (b = 0.0094, 0.0094, P < < 00.46) and that that the the extinction extinction rate rate was was not not significantly significantly different different in in the the different different areas areas (area*year (area*year interaction P < < 0.20). 0.20). The The correlation correlation between between disease disease extinction extinction and and colon coloninteraction ization ization rate rate was was not not significant. significant.
Disease Transmission Disease Transmission Rates Rates Disease transmission rates calculated using Disease transmission rates were were calculated using populations populations where where disease disease had had been been present present in in two two successive successive time time intervals intervals so so as as not not to to confound confound the the estimates colonization or likelihood estimates with with disease disease colonization or extinction extinction rates. rates. Maximum Maximum likelihood methods (5) and disease transmission methods were were used used to to estimate estimate the the survival survival rate rate (S) and disease transmission 13 ) for rate ((13) for each each year year by by fitting fitting the the following following model model to to the the data data (and (and mini minirate mizing mizing the the sum sum of of squares squares of of the the log log of of predicted predicted minus minus the the log log of of observed): observed):
Yt+l = S(Yt +
x,(1 -exp(-~3Yt/Nt))
((19.1) 19.1)
where where Xt X t iiss the the number number ooff healthy healthy plants plants in in year year t, t, Yt, Yt, Yt+ Yt+l1 iiss the the number number of of diseased diseased plants plants in in year year tt and and tt + + 11,, and and Nt Nt = = Xt Xt + + Yt. Yr. Note Note that that the the param parameter eter 13 13 represents represents aa within within season season transmission transmission coefficient coefficient (assuming (assuming no no sum summer mortality) mortality) and and 5 S represents represents overwinter overwinter survival. survival. Equivalent Equivalent analyses analyses were were mer also PROC NUN 999) and also carried carried out out using using PROC NLIN in in SAS SAS (SAS (SAS Institute, Institute, 11999) and gave gave identical identical results. results. The The frequency-dependent frequency-dependent transmission transmission model model always always resulted resulted in in aa better better fit fit - I3 Yt)]; than than the the density-dependent density-dependent model model [where [where force force of of infection infection = = 11 - exp( exp(-IBYt)]; the the latter latter also also frequently frequently produced produced unrealistic unrealistic estimates estimates of of 5S (equal (equal to to or or close close to ). A to 11). A good good fit fit was was also also obtained obtained with with aa model model where where the the force force of of infection infection was exp( - I3 Y/N/Nt),, aa model was = = 11 - exp([3Yt/Nt*Nt) model form form appropriate appropriate for for vector-based vector-based trans transmission, but mission, but because because the the relative relative values values of of 5S and and 13 [3 did did not not differ differ much much between between models, we present present the the results results of of the the more more familiar familiar frequency-dependent frequency-dependent model. model. models, we There There was was aa strong strong colinearity colinearity in in the the estimates estimates of of 5 S and and 13, [3, such such that that high high estimates estimates of of 5S were were correlated correlated with with low low estimates estimates of of 13 [3 and and vice vice versa. versa. We We there therefore fore standardized standardized the the survival survival rate rate by by taking taking the the average average over over all all years years and and including this this average average in in the the model model to to estimate estimate 13. 13. Therefore, Therefore, this this estimate estimate in in including effect effect represents represents an an overall overall "cross-season" "cross-season" transmission transmission coefficient coefficient that that is is aa com compound pound of of the the survival survival rate rate of of diseased diseased plants plants and and the the within within season season transmission. transmission.
119. 9.
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484 484
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Within Fig. F i g . 11 99.7 .7 Within population population disease disease transmission transmission rates rates per per year year for for three three areas areas of of the the metapopulation metapopulation with with diseased diseased populations populations (see (see text text for for details details of of estimation)" estimation).
Results Results showed showed that that the the transmission transmission rates rates of of the the disease disease within within popula populations Fig. 119.7) 9.7) did tions ((Fig. did not not change change significantly significantly over over the the time time period period of of the the study study .015; P .44 ) . Nor area inter (b = 0 0.015; P< < 0 0.44). Nor was was there there any any evidence evidence for for aa year* year*area inter(b = action . 9 3 ) ; regressions action (P (P < < 00.93); regressions for for each each area area were were slightly slightly positive positive but but did did not approach significance, not individually individually approach significance, even even when when an an outlier outlier was was removed removed (1' < 0.56-0 0.56-0.82). (P < .82). There a s no There w was no significant significant relationship relationship between between disease disease transmission transmission rates rates within within populations populations and and disease disease colonization colonization rate rate (correlation (correlation coefficient, coefficient, r = . 8 3 ) . When outlier was removed ((1989 1 9 8 9 estimates), = - 00. . 007, 7, P P < < 0 0.83). When an an outlier was removed estimates), the the (r = . 2 9 ) but (P < . 3 6 ) . The relationship was relationship was positive positive (r = 00.29) but still still not not significant significant (P < 0 0.36). The relationship relationship between between disease disease transmission transmission rates rates within within populations populations and and dis disease extinction (P < ease extinction rate rate was was negative negative (( - 00.26) . 2 6 ) but but not not significant significant (P < 0.40) 0.40) and and was 9 8 9 estimate was essentially essentially unchanged unchanged when when the the 11989 estimate was was removed. removed. The The same same trends trends (greater (greater colonization colonization and and lower lower extinction extinction when when the the disease disease trans transmission mission rate rate was was higher) higher) were were obtained obtained when when the the analysis analysis was was carried carried out out for for each each area area individually, individually, but but these these trends trends were were not not significant. significant.
Weather Data Weather Data Prior 997, weather Prior to to 11997, weather data data at at Mountain Mountain Lake Lake Biological Biological Station Station were were gath gathered ered manually manually and and were were obtained obtained from from the the National National Climate Climate Data Data Center. Center. In In 11994, 994, aa new weather station acquisition was new weather station with with automatic automatic data data acquisition was installed installed and and run correspondence between run by by the the station. station. There There was was aa close close correspondence between weather weather data data (monthly (monthly mean mean temperature, temperature, highest highest temperature, temperature, lowest lowest temperature, temperature, and and
119. 9. PLANT-,PATHOGEN PLANT-PATHOGEN METAPOPULATION METAPOPULATION
485 485
precipitation) precipitation) during during the the 2 2 to to 33 yr yr period period when when both both types types of of data data were were being being gathered. gathered. Therefore Therefore the the two two types types of of data data were were averaged averaged during during this this overlap overlap period 9 8 8 to period and and were were used used to to span span the the period period 11988 to the the present. present. We We investigated investigated aa specific specific set set of of weather weather variables variables that that we we thought thought might might be be related related to to host host and and pathogen pathogen colonization colonization and and extinction, extinction, as as well well as as to to within within population Based on natural history history observations population disease disease transmission. transmission. Based on our our natural observations of of field summers would would decrease field experiments, experiments, we we hypothesized hypothesized that that hot hot dry dry summers decrease dis disease ease transmission transmission and and hence hence disease disease colonization. colonization. We We also also hypothesized hypothesized that that cold cold winters winters and/or and/or unusually unusually cold cold weather weather in in early early spring spring would would increase increase host host extinction extinction rates. rates. For For each each year year of of the the census, census, for for the the summer summer (June, (June, July, July, and and August), August), we we calculated calculated precipitation precipitation and and mean mean daily daily maximum maximum and and minimum minimum temperatures; temperatures; for for the the winter winter (December, (December, January, January, and and February) February) we we calculated calculated mean mean daily daily maximum maximum and and minimum minimum temperatures. temperatures. We We also also calculated calculated the the minimum minimum temperature temperature in in March, March, as as this this represents represents the the incidence incidence of of unusually unusually cold weather weather in in the the early early spring. spring. cold Over Over the the period period of of the the census, census, there there was was aa significant significant decrease decrease in in summer summer (r = 3 ) and daily daily maximum maximum temperatures temperatures (r =-0 .0.57, 57, P < < 0.03 0.033) and an an increase increase in in (r = summer summer and and winter winter minimum minimum temperatures temperatures (r = 0.76, 0.76, P < < 0.0015; 0.0015; r = = 0.56, 0.56, P< < 0.045 0.045).) . Analysis Analysis of of weather weather data data at at Mountain Mountain Lake Lake Biological Biological Station Station from 11972 to 2001 2001 showed showed aa gradual but nonsignificant nonsignificant increase in mean, mean, from 972 to gradual but increase in maximum, 1 , 0.023, 8°C maximum, and and minimum minimum summer summer temperatures temperatures (0.02 (0.021, 0.023, and and 0.01 0.018~ per per year, year, respectively) respectively);; the the decrease decrease in in summer summer maximum maximum temperatures temperatures since since was therefore therefore contrary contrary to to the the longer longer term term trend. trend. Summer Summer precipitation precipitation 11988 98 8 was did did not not change change systematically systematically with with year, year, but but was was correlated correlated negatively negatively with with maximum (r = 3 ) . No maximum summer summer temperatures temperatures (r = - 00.60, .60, P < < 0.02 0.023). No other other weather weather relationships relationships showed showed aa significant significant change change with with year. year. With were not not correlated With aa few few exceptions, exceptions, the the population population parameters parameters were correlated with with weather Host extinction was negatively winter minimum weather data. data. Host extinction was negatively correlated correlated with with winter minimum (r = temperatures .0042) , and disease colonization colonization rate but not temperatures (r = - 00.76, .76, P < < 00.0042), and disease rate ((but not transmission transmission rate) rate) was was significantly significantly negatively negatively correlated correlated with with summer summer mean mean minimum 1 ). A minimum temperature temperature (r = = - 00. .660, 0, P < < 0.03 0.031). A Bonferroni Bonferroni correction correction of of the the P< 30 correlations < 0.05 0.05 criterion criterion for for significance significance (given (given that that 30 correlations were were estimated) estimated) 1 7. Under results results in in aa value value of of P < < 0.00 0.0017. Under this this criterion criterion none none of of the the aforemen aforementioned relationships be deemed deemed significant. significant. tioned relationships would would be Examination prevalence in Examination of of the the change change in in incidence incidence and and prevalence in Area Area 33 where where incidence was was initially initially low low and and then then peaked peaked in in the the midmid-1990s Fig. 119.4) incidence 1 990s ((see see Fig. 9.4) showed showed no no obvious obvious or or even even suggestive suggestive relationship relationship with with the the weather weather variables. variables.
11 9.4 9.4
DISCUSSION DISCUSSION This This study study provides provides clear clear evidence evidence that that the the Silene-Microbotryum Silene-Microbotryummetapopu metapopulation 9 8 8 is "global sta lation that that we we have have been been studying studying since since 11988 is not not in in aa state state of of "global stability. bility."" This This result result came came very very much much aa surprise surprise with with regard regard to to our our ongoing ongoing impressions populations. Indeed, impressions of of the the populations. Indeed, analysis analysis of of the the 1155 yr yr of of data data was was stimu stimulated lated by by an an assessment assessment of of whether whether it it was was "worthwhile" "worthwhile" continuing continuing with with the the census, given needed to our census, given the the resources resources and and effort effort needed to carry carry it it out out every every year year ((our attempts several years attempts several years ago ago to to get get funding funding for for the the study study were were unsuccessful! unsuccessful!).). Year-by-year not give Year-by-year observations observations did did not give us us the the sense sense that that diseased diseased populations populations
486 4 86
JANIS JANIS ANTONOVICS ANTONOVICS
were declining declining in in frequency, frequency, as as every every year year there there were were always always reports reports of of both both were disease extinctions extinctions and and colonizations. colonizations. disease issues are are raised raised by by these these data. data. First, First, what what is is the the proximal proximal cause cause of of Several Several issues the decline? decline? In In particular, particular, is is it it driven driven by by changes changes in in the the external external environment environment the or is is it it intrinsic intrinsic to to the the disease disease dynamics? dynamics? Second, Second, if if it it is is the the latter, latter, is is the the instainsta or bility related related to to the the fact fact that that both both the the host host and and the the disease disease are are relatively relatively recent recent bility introductions into into the the United United States? States? Finally, Finally, is is the the system system moving moving toward toward introductions some eventual eventual equilibrium equilibrium with with host-pathogen host-pathogen coexistence coexistence or or will will the the outout some come be be disease disease extinction? extinction? come It is is well well known known from the crop crop literature that variation variation in in weather weather can can It from the literature that greatly influence the the prevalence prevalence of of disease. disease. However, However, in in the the weather weather data data we we greatly influence analyzed, only only 22 out out of of aa possible possible 30 30 correlations correlations were were significant. significant. While While the the analyzed, decrease in in host-extinction host-extinction rate rate with with increasing increasing winter winter minimum minimum temperatures temperatures decrease is hard hard to to interpret interpret causally, causally, the the increase increase in in disease disease colonization colonization rate rate with with is decreasing summer summer minimum minimum temperatures temperatures is is consistent consistent with with our our own own obserobser decreasing vations that is highest low temperatures temperatures and high vations that disease disease transmission transmission is highest at at low and high humidity (Alexander (Alexander et 1 99 3 ) . These These low low temperatures temperatures are are most most likely likely to humidity et aI., al., 1993). to occur night, which is also also the the period moth visitation visitation occur during during the the night, which is period of of greatest greatest moth (Altizer aI., 1998) 1 9 9 8 ) and therefore the the period period most most likely likely for the long long distance distance (Altizer et et al., and therefore for the transport of spores. transport of spores. Other unrelated to to the the weather weather may also have Other environmental environmental changes changes unrelated may also have had had an relative importance importance is is hard hard to to judge. judge. In In Area 1, elimelim an effect, effect, although although their their relative Area 1, ination of heavily diseased diseased off-road in 1995 1 995 by by extensive reland ination of several several heavily off-road sites sites in extensive relandscaping by a local lime-manufacturing may have have reduced reduced the the scaping by a local lime-manufacturing company company may available disease sources. sources. In In one one part part of Area 2, 2, road road widening widening in in 1990 1 990 elimelim available disease of Area inated five 995 it another two inated five of of six six diseased diseased sites sites and and in in 11995 it eliminated eliminated another two diseased diseased sites sites nearby. nearby. However, However, it it is is doubtful doubtful that that this this had had aa cascading cascading effect effect elsewhere elsewhere in area. The whole region also subject subject to in the the area. The whole region of of the the census census was was also to early early spring spring spraying control gypsy 9 9 8 ) . However, spraying to to control gypsy moth moth (Sharov (Sharov and and Liebhold, Liebhold, 11998). However, because the spraying in this because much much of of the spraying in this area area has has been been with with male male mating mating pheromone whose effect likely to specific to pheromone whose effect is is likely to be be specific to gypsy gypsy moths moths (and (and which which have reached epidemic levels in census area) overall impact have not not reached epidemic levels in the the census area),, the the overall impact on on moth (which are also disease probably been been small. moth pollinators pollinators (which are also disease vectors) vectors) has has probably small. An An alternative alternative explanation explanation for for the the disease disease decline decline is is that that it it is is intrinsic intrinsic to to the the dynamics of host pathogen pathogen system dynamics of the the system system as as aa whole. whole. In In aa simulation simulation of of this this host system (Antonovics 998), the (Antonovics et et aI., al., 11998), the disease disease could could only only be be sustained sustained in in little little over over 50% 50% of of the the runs. runs. We We have have not not reparameterized reparameterized or or reevaluated reevaluated this this model model based based on on more best estimates more recent recent data, data, but but it it is is nonetheless nonetheless interesting interesting that that our our ""best estimates"" based based on on values values from from the the earlier earlier part part ooff this this census census and and from from experimental experimental stud studpredicted that population. ies often often predicted that the the disease disease would would be be lost lost from from the the meta metapopulation. ies Moreover, Moreover, as as the the disease disease was was lost, lost, the the prevalence prevalence of of the the disease disease within within the the remaining remaining populations populations increased, increased, as as we we have have observed observed in in this this study. study. This This is is largely largely because because newly newly founded founded populations populations with with low low levels levels of of disease disease were were no no longer longer being being produced. produced. The The decreasing decreasing disease disease incidence, incidence, the the increasing increasing preva prevalence disease colonization lence within within populations, populations, and and the the declining declining of of disease colonization rate rate observed observed here population. here are are all all consistent consistent with with gradual gradual disease disease extinction extinction in in the the meta metapopulation. In In this this region region of of Virginia Virginia there there is is extensive extensive genetic genetic variation variation in in the the host, host, yet yet no no detectable detectable variation variation in in the the infectiousness infectiousness of of the the pathogen. pathogen. Thus Thus Antonovics Antonovics et 1 998) showed et al. al. ((1998) showed that that if if the the simulation simulation is is carried carried out out with with aa genetically genetically
119. 9. PLANT-PATHOGEN PLANT-PATHOGEN METAPOPULATION METAPOPULATION
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uniform uniform host host population population with with aa resistance resistance that that is is intermediate intermediate between between that that of of the the most most susceptible susceptible and and most most resistant resistant genotypes, genotypes, with with an an exponential exponential 13[3 = 2.00, would persist persist about 2.00, and and aa survival survival of of 0.50, 0.50, then then the the metapopulation metapopulation would about 90% 90% of of the the time. time. (Analysis (Analysis of of census census data data gave gave an an average average value value of of 13 [3 over over all all years years of of 2.89 2.89 and and an an average average survival survival of of 0.55, 0.55, remarkably remarkably close close to to values values used used in in the the ear earlier lier simulations.) simulations.) However, However, when when the the simulation simulation was was carried carried out out with with aa geneti genetically variable host host population, less frequent cally variable population, persistence persistence was was much much less frequent (ca. (ca. 40%). 40%). Introduction Introduction of of the the disease disease into into aa population population led led to to aa rapid rapid local local spread spread of of the the resistance gene populations that resistance gene and and the the generation generation of of resistant resistant populations that were were not not colon colonized ized readily readily by by the the disease. disease. Populations Populations only only become become readily readily available available for for colon colonization ization by by the the disease disease when when the the gene gene for for susceptibility susceptibility increased increased because because of of the the cost % ; Biere 995). cost of of resistance resistance (estimated (estimated to to be be about about 25 25%; Biere and and Antonovics, Antonovics, 11995). In In experimental experimental populations populations of of S. latifolia latifolia where where individuals individuals are are not not replaced replaced over over successive successive years, years, disease disease transmission transmission showed showed an an extremely extremely rapid almost zero individ rapid decline decline to to almost zero within within 2 2 yr, yr, due due to to the the fact fact that that the the only only individuals remaining resistant families uals remaining healthy healthy were were from from genetically genetically resistant families (Alexander, (Alexander, 11989; 989; Alexander 995). Disease Alexander et et aI., al., 11995). Disease prevalence prevalence also also dropped dropped rapidly rapidly in in experimental populations started resistant genotypes experimental populations started with with progeny progeny of of resistant genotypes but but not not in (Thrall and in populations populations started started with with progeny progeny of of susceptible susceptible genotypes genotypes (Thrall and Jarosz, 11994a,b). 994a,b). Moreover, Jarosz, Moreover, detailed detailed demographic demographic studies studies of of extant extant diseased diseased populations 99 0 ) . It populations have have shown shown low low transmission transmission rates rates (Alexander, (Alexander, 11990). It is is there therefore disease colonization fore possible possible that that the the decline decline in in disease colonization rates rates may may be be due due to to an an increased disease resistance resistance in increased level level of of disease in the the metapopulation metapopulation as as aa whole. whole. It It is is relevant relevant to to place place our our metapopulation metapopulation in in aa broader broader geographical geographical and and historical historical context, context, as as this this may may help help with with the the interpretation interpretation of of the the local local changes. changes. In In aa survey survey of of over over aa thousand thousand herbarium herbarium specimens specimens of of S. latifolia latifolia in in the the eastern eastern United United States, States, there there was was no no evidence evidence that that the the plant plant had had been been col collected 9 1 4 (Antonovics aI., 2003 lected south south of of the the Pennsylvania Pennsylvania line line before before 11914 (Antonovics et et al., 2003),), apart 89 6 on apart from from aa collection collection made made in in 11896 on the the Biltmore Biltmore estate estate in in North North Carolina. House was 8 95, and Carolina. Biltmore Biltmore House was opened opened in in 11895, and it it is is likely likely that that the the estate estate imported meadows. The imported seeds seeds from from New New England England for for hay hay or or for for the the meadows. The first first record Virginia was was in 924, and and it not until 93 0s that that collections record in in Virginia in 11924, it was was not until the the 11930s collections in in Virginia Virginia became became frequent. frequent. The The first first record record we we could could find find for for Giles Giles County, County, where of the the metapopulation meta population is is located, 9 3 8 . Therefore, where the the majority majority of located, was was 11938. Therefore, the the weight weight of of the the evidence evidence is is that that the the host host plant plant has has only only been been in in the the Mountain Mountain Lake 80 years. years. Lake area area for for perhaps perhaps less less than than 80 The disease is unknown. Previously, The history history of of the the disease is completely completely unknown. Previously, M. M. vio violaceum laceum had had been been noted noted on on S. caroliniana caroliniana in in Virginia Virginia and and New New York York State State and and 9 8 9 ) , but on on several several species species of of Silene Silene in in the the western western United United States States (Farr (Farr et et aI., al., 11989), but there there is is no no record record of of it it on on S. latifolia, latifolia, even even though though other other fungal fungal diseases diseases are are recorded Farr et aI., 11989). 98 9 ) . None recorded for for this this species species in in the the United United States States ((Farr et al., None of of the the herbarium herbarium specimens specimens we we examined examined were were diseased diseased so so they they did did not not help help resolve resolve the the question question of of the the disease disease origins. origins. The The current current distribution distribution of of S. latifolia latifolia and and M. M. violaceum violaceum in in the the eastern eastern United United States States was was studied studied by by A. A. M. M. Jarosz Jarosz and and E. E. Lyons Lyons (personal (personal communication) communication).. They They found found that that the the disease disease was was largely largely confined (where 116% 6% confined to to the the ridge ridge and and valley valley system system of of western western Virginia Virginia (where ooff 1102 02 populations populations were were diseased). diseased). Further Further iinn the the northeast, northeast, they they only only found found 11 diseased (in Pennsylvania) 69, except diseased population population (in Pennsylvania) out out of of 1169, except for for 33 diseased diseased populations populations on on Nantucket Nantucket Island, Island, Massachusetts. Massachusetts. Diseased Diseased plants plants have have been been
488 488
JANIS JANIS ANTONOVICS
known 9 80s (T. known from from Nantucket Nantucket Island Island since since the the early early 11980s (T. Meagher, Meagher, personal personal communication). communication). In In the the north north central central United United States, States, aa single single diseased diseased plant plant was 8 7 populations sampled. The reason for was found found out out of of 3387 populations sampled. The reason for the the absence absence of of the the disease from unknown. In disease from more more northern northern latitudes latitudes is is unknown. In field field experiments experiments along along aa latitudinal latitudinal gradient, gradient, A. A. M. M. Jarosz Jarosz and and E. E. Lyons Lyons (personal (personal communication) communication) showed showed that that northern northern populations populations were were susceptible susceptible to to disease disease in in their their local local areas, areas, but but that that they they were were also also somewhat somewhat more more resistant resistant than than plants plants derived derived from seeds of relatively susceptible susceptible parent parent from Mountain Lake from seeds of aa relatively from Mountain Lake that that was was used pollination" with used as as aa contro!' control. Artificial Artificial hand hand ""pollination" with spores spores produced produced aa higher higher incidence incidence of of disease disease than than open open visitation, visitation, suggesting suggesting aa shortage shortage of of pollinators pollinators may may limit limit disease disease transmission. transmission. Given Given that that the the host host has has moved moved into into this this part part of of Virginia Virginia only only recently recently and and that that the disease is the disease is near near the the southern southern edge edge of of the the current current range range of of S. latifolia, latifolia, yet yet is is found sporadically in plausible that found sporadically in its its former former range, range, it it is is plausible that we we may may be be seeing seeing the the movement disease "front" movement of of aa disease "front" that that is is following following the the host host as as it it colonizes colonizes new new areas. areas. The The movement movement of of this this disease disease front front may may be be driven driven by by the the evolution evolution of of more more resistant resistant populations populations in in the the wake wake of of the the disease. disease. The The spread spread of of this this disease disease in the the United United States States may may therefore therefore be be analogous analogous to to the the spread spread of of many many other other epi epiin demics. demics. In In animal animal populations, populations, "waves" "waves" of of disease disease spread spread are are often often driven driven by by the the development development of of immunity immunity in in the the wake wake of of the the epidemic, epidemic, but but aa genetic genetic component component to this this immunity immunity has has also been posited posited frequently. frequently. In In the the present present metapopula metapopulato also been tion, major driving tion, this this genetic genetic component component may may be be the the major driving force. force. However, However, the the issue issue of of whether whether the the changes changes we we are are observing observing are are due due to to climatic climatic and and management management changes or or to to intrinsic genetic and and demographic factors cannot be determined determined by by changes intrinsic genetic demographic factors cannot be descriptive or require further descriptive or simulation simulation studies studies alone, alone, but but will will require further experiments experiments and and more studies of individual populations. more directed directed field field studies of individual populations.
20
META M ETAPO PO PULATION PU LATIO N DYNAMICS IN IN DYNAMICS CHANGING CH ANGING ENVIRONMENTS ENVIRONMENTS:: BUTTERFLY PONSES BUTTERF kY RES RESPONSES TO H ABITAT AND AND TO HABITAT CLI MATE CHAN GE CLIM ATE C H ANGE Chris D. Thomas Thomas and Chris and Ilkka Ilkka Hanski Hanski
20.1 20. 1
INTRODUCTION INTRODUCTION A A major major criticism criticism of of the the applications applications of of metapopulation metapopulation models models in in conserconser vation has has been been that that real real metapopulations metapopulations rarely rarely conform conform to to the the assumptions assumptions vation of classic classic theory theory (Harrison, (Harrison, 1991; 1 99 1 ; Harrison Harrison and and Taylor, Taylor, 1997). 1 997). In In metapopumetapopu of lation theory, theory, it it is is usually usually assumed assumed that that the the extinction of aa particular particular local local lation extinction of population generates one more more patch patch of of empty habitat that that is is subsequently subsequently population generates one empty habitat available for for colonization colonization and and that that each each new new colonization colonization removes removes aa previously previously available empty patch patch that that is is no no longer longer available available for for colonization colonization (Chapter (Chapter 4). 4 ) . This This empty assumption is is the the basis basis of of the the stochastic stochastic quasiequilibrium quasiequilibrium between between colonizacoloniza assumption tions and and extinctions. extinctions. An An unusual unusual number number of of extinctions extinctions in in one one generation generation tions
Ecology, Genetics, and Evolution Ecology, of Metapopulations Metapopulations
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2004, Elsevier, Elsevier, Inc. Copyright 2004, 0-12-323448-4 0-12-323448-4
CHRIS D. THOMAS HAN SKI CHRIS D. THOMAS AND AND ILKKA ILKKA HANSKI
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would would likely likely be be followed followed by by an an excess excess of of colonization colonization events events in in subsequent subsequent generations, generations, and and an an unusual unusual number number of of colonization colonization events events would would likely likely be be followed by generated by followed by an an excess excess of of extinctions. extinctions. However, However, if if extinctions extinctions are are generated by habitat follow an habitat deterioration deterioration and and if if colonizations colonizations follow an improvement improvement in in environ environmental mental conditions, conditions, then then this this feedback feedback is is broken broken and and there there is is no no logical logical reason reason why population should why aa meta metapopulation should exist exist in in any any kind kind of of equilibrium equilibrium (Thomas, (Thomas, 11994a,b). 994a,b) . In case, the In this this case, the metapopulation metapopulation dynamics dynamics of of an an organism organism will will be be superimposed (or fail superimposed upon, upon, and and track track (or fail to to track), track), the the dynamic dynamic distribution distribution of of suitable suitable habitat. habitat. At glance, this At first first glance, this criticism criticism seems seems to to be be extremely extremely serious serious because because most most of population models of the the practical practical applications applications of of meta metapopulation models relate relate to to habitat habitat that populations at that is is changing, changing, in in which which context context meta metapopulations at equilibrium equilibrium might might be real issue issue is be expected expected to to be be particularly particularly rare. rare. However, However, the the real is how how fast fast species tracking changing population species are are tracking changing environments environments and and whether whether meta metapopulation models models can can provide provide insight insight into into these these processes. processes. If If tracking tracking is is fast, fast, the the prob problem lem is is in in understanding understanding and and predicting predicting how how the the environment environment is is changing; changing; if if tracking tracking is is slow, slow, there there is is additionally additionally the the problem problem of of transient transient metapopu metapopulation dynamics responding to lation dynamics responding to the the changing changing environment. environment. This This chapter chapter reviews application of population concepts concepts and reviews the the application of meta metapopulation and models models to to situations situations where environment is persistence of metapopulation where the the environment is changing changing or or the the persistence of the the metapopulation is precarious because because the species occurs close to is precarious the species occurs close to the the extinction extinction threshold threshold ((Chapter Chapter 4). 4). Butterfly populations represent Butterfly meta metapopulations represent excellent excellent systems systems with with which which to to assess assess long-term long-term and and nonequilibrium nonequilibrium dynamics dynamics because because the the quality quality of of historical historical information information on on their their distributions distributions allows allows us us to to be be confident confident whether whether popu populations expanding or declining. Box lations are are expanding or declining. Box 20. 20.11 presents presents aa brief brief history history of of butterfly metapopulation studies. butterfly metapopulation studies. In In some some cases, cases, results results of of past past mapping mapping of of distributions allow us observed changes. distributions allow us to to test test model model predictions predictions against against observed changes. Furthermore, Furthermore, knowledge knowledge of of the the often often quite quite specific specific habitat habitat requirements requirements of of many habitat networks, many butterfly butterfly species species allows allows us us to to define define habitat networks, and and changes changes in in the the structure structure of of such such networks, networks, independently independently of of the the distribution distribution of of the species. We population models models can the species. We find find that that meta metapopulation can have have great great predictive predictive power power in in nonequilibrium nonequilibrium systems systems and and that that they they can can be be particularly particularly useful useful in in enhancing enhancing our our understanding understanding of of the the responses responses of of species species to to landscape landscape and and climate climate change. change.
BOX 20.1
Brief History of Butterfly Metapopulatlon studies
Butterfly biologists developed the concept of "open" and "closed" population structures in the 1 9605 and 1 970s (Ehrlich, 1 961 , 1 965, 1 984; Ehrlich et aI., 1 975; Thomas, 1 984), following in the steps of E.B. Ford who, in the 1 9 30s and 1 9405, observed the sedentary behavior of many butterflies, confining most individuals to their natal habitat patch. The notion of fairly discrete and often small local populations paved the way to considerations of meta populations, or assemblages of such local populations. The first full-fledged butterfly metapopulation study was due to Harrison et al. (1 988), who demonstrated a mainland-island metapopulation structure in the
20. 20. METAPOPULATION METAPOPULATION DYNAMICS DYNAMICS IN IN CHANGING CHANGING ENVIRONMENTS ENVIRONMENTS
checkers pot butterfly Euphydryas edith a in California. The first study of the Glanville fritillary in Finland produced evidence for a classic metapopulation, and Hanski et aL (1 994) concluded that "the Melitaea cinxia metapopulation . . . p rovides a contrasting example to the Euphydryas editha metapopulation reported by Harrison et aL (1 988). Unlike the latter case, there is no large "mainland" population in the M. cinxia meta population, and its long-term persistence appears to depend on genuine extinction colonization dynamics." Studies of several British butterflies fou nd that a lmost all local breeding populations occur within a dispersal range of other local populations of the same species, which finding suggested, along with direct evidence of colonizations and extinctions, that metapopulation dynamics were likely to be commonplace (Thomas et aL, 1 992; Thomas and Harrison, 1 992; Thomas a nd Jones, 1 993; Thomas, 1 994a,b). From this point onward, metapopulation studies on butterflies have taken place mostly in Europe. Extinction-colonization dynamics have been researched intensively in several species, but most notably in M. cinxia (Hanski et aL, 1 994, 1 995a,b, 1 996; Kuussaari et aL, 1 998; Hanski, 1 999b; N ieminen et aI., 2004), Plebejus argus (Thomas, 1 99 1 ; Jordan o et aL, 1 992; Thomas and Harrison, 1 992; Brookes et aL, 1 99 7; Lewis et aI., 1 997; Thomas et aI., 1 999a, 2002a), Hesperia comma (Thomas et aL, 1 986, 2001 a; Thomas and Jones, 1 993; Hill et aI., 1 996; Wilson and Thomas, 2002) and Proclossiana eunomia (Baguette and Neve, 1 994; Neve et aI., 1 996a; Petit et aI., 2001 ; Sawchik et aL, 2002; Schtickzelle et aI., 2002) in Europe and E. edith a (Harrison et aL, 1 988; H arrison, 1 989; Thomas et aI., 1 996; Boughton, 1 999; McLaughlin et a I ., 2002) in North America. Studies of these and tens of other species (e.g., Warren, 1 987, 1 994; Settele et aL, 1 996; Gutierrez et aI., 1 999, 2001 ; K nutson et aI., 1 999; Mousson et aI., 1 999; Shahabuddin and Terborgh, 1 999; Baguette et aI., 2002; Bergman and Landin, 2001 ; Bulman, 2001 ; Nekola and Kraft, 2002; Wahlberg et aI., 2002a,b; Wilson et aL, 2002) have shown great variation in metapopulation structure and that dynamics a re nearly as variable within as among species. This latter conclusion u nderscores the pivotal role of landscape structure in influencing spatial dynamics. Nonetheless, these studies have confirmed that the general metapopulation notion provides valuable insight i nto the dynamics and distribution of many, although not a l l, butterfly species at the landscape level. The metapopulation approach can be applied to virtually a l l species that were formerly considered to have "closed" population structures (Thomas, 1 984). Since the mid-1 990s, the emphasis on butterfly meta population studies has been in adding further details and evaluating how robust and useful the approach is under different circumstances. Studies have examined the validity of the major assumptions and processes of metapopulation dynamics, incorporated multispecies patterns and dynamics into the common framework (Lei and Hanski, 1 997; van Nouhuys and Hanski, 1 999, 2002), investigated the evolutionary and genetic dynamics of metapopulations (Neve et aI., 1 996b, 2000; Singer and Thomas, 1 996; Brookes et aI., 1 997; Saccheri et aI., 1 998; Thomas et aI., 1 998; Barascud et aL, 1 999; Keyghobadi et aI., 1 999; Kuussaari et aL, 2000; Nieminen et aL, 200 1 ; Saccheri and Brakefield, 2002), and applied meta population a pproaches at increasingly large scales in relation to conservation and climate change, as described in the main text. Research on butterflies has played an important, and in some cases pivotal, role in the development of the science of meta population biology and i n the application of the metapopu lation approach to conservation. Many of the studies cited here and in this chapter were at least partially motivated by conservation concerns, and this pattern is likely to continue.
491 491
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CHRIS CHRIS D. D. THOMAS THOMAS AND AND ILKKA ILKKA HANSKI HAN SKI
20.2 HABITAT HABITAT FRAGMENTATION FRAGMENTATION 20.2 Habitat loss loss typically typically results results in in ffragmentation smaller and and more more scattered scattered Habitat r a g m e n t a t i o n- smaller fragments of of habitat habitat than than existed existed formerly. formerly. In In many many cases, cases, the the habitat habitat does does not not fragments immediately all all become become unsuitable, unsuitable, and and populations populations may may be be found, found, for for some some immediately time at at least, least, in in patches patches of of habitat habitat that that have have recently recently become become small, small, more more time isolated, or or both. both. At At equilibrium, equilibrium, many many of of these these patches patches would would be be expected expected to to isolated, be unoccupied unoccupied most most of of the the time time (even (even though though they they may may contain contain perfectly perfectly be suitable habitat) habitat) because because the the rate rate of of extinction extinction of of small small populations populations is is likely likely to to suitable be high high and and the the recolonization recolonization rate rate of of isolated isolated patches patches will will be be low low (Hanski, (Hanski, be 1 994, 1999b; 1 99 9b; Chapter 4 ) . However, However, during during and and immediately immediately following following aa period period 1994, Chapter 4). of fragmentation fragmentation aa species species occupying occupying the the remaining remaining fragments fragments may may show show aa of period of of decline, decline, during during which which the the rate rate of of local local extinction extinction exceeds exceeds the the rate rate of of period recolonization. In In such such situations, situations, the the potential potential contributions contributions of of metapopulametapopula recolonization. tion models models are are to to help help understand understand the the timescale timescale of of decline, decline, the the spatial spatial pattern pattern tion of decline, decline, and and whether whether aa species species will will decline decline to to aa reduced reduced metapopulation metapopulation size size of (restricted distribution) distribution) or or become become completely completely extinct extinct from from the the areas areas where where (restricted fragmentation has has taken taken place. place. Such Such insights insights can can be be extremely extremely important important fragmentation because they they may may provide provide an an understanding understanding of of why why some species continue continue because to decline decline long long after after the the damage damage to to the the environment environment has has taken taken place. place. The The to following two examples lag behind behind habitat loss. following two examples illustrate illustrate how how species species may may lag habitat loss.
Melifaea and the Speed of Metapopulation Decline Decline Melitaea cinxia cinxia and the Speed of Metapopulatton The distribution distribution of of the the Glanville Glanville fritillary, Melitaea cinxia, in northern and The Melitaea cinxia, northern and western western Europe Europe has has become become greatly greatly reduced reduced over over the the past past decades, decades, and and the the species 995; species has has gone gone regionally regionally extinct extinct in in many many areas areas (Hanski (Hanski and and Kuussaari, Kuussaari, 11995; Maes 999; van 999). It Maes and and van van Dyck, Dyck, 11999; van Swaay Swaay and and Warren, Warren, 11999). It is is apparent apparent that that habitat habitat loss loss is is the the primary primary or or even even the the only only significant significant cause cause of of the the decline. decline. 970s (Marttila In In Finland, Finland, M. cinxia went went extinct extinct in in the the mainland mainland in in the the 11970s (Marttila et 990), and land Islands Islands in et ai., al., 11990), and it it now now occurs occurs only only in in the the A Aland in Southwest Southwest Finland Finland (Hanski 995). Luckily (Hanski and and Kuussaari, Kuussaari, 11995). Luckily for for this this butterfly butterfly and and many many other other species species of of insects insects and and plants, plants, land land use use practices practices have have changed changed less less drastically drastically in land Islands in the the A Aland Islands than than in in most most other other parts parts of of northern northern Europe. Europe. Dry Dry meadows meadows with with Plantago lanceolata and and Veronica spicata, the the two two host host plants plants of land, partly of M. cinxia, still still abound abound in in A Aland, partly because because the the general general topography topography with with numerous numerous small small granite granite outcrops outcrops prevents prevents large-scale large-scale agricultural agricultural intensi intensification. fication. At At present, present, the the suitable suitable habitat habitat covers covers ca. 66 km2, km 2, which which is is 0.6% 0.6 % of of the the total total land land area area (Nieminen (Nieminen et et ai., al., 2004) 2004).. Nonetheless, Nonetheless, substantial substantial habitat habitat loss loss has land in has occurred occurred in in parts parts of of A Aland in recent recent decades, decades, as as the the following following example example shows, shows, with with adverse adverse consequences consequences for for the the occurrence occurrence of of the the butterfly. butterfly. Figure land Islands, Figure 20.1 20.1aa shows shows one one network network of of habitat habitat patches patches in in the the A ,~land Islands, with 9 92. Thanks 1 995) detailed with 42 42 patches patches in in 11992. Thanks to to Hering's Hering's ((1995) detailed analysis analysis of of old old aerial aerial photographs photographs and and interviews interviews of of local local people, people, we we know know that that 20 20 yr yr previ previously ously there there had had been been 55 55 distinct distinct patches patches in in this this network, network, and and nearly nearly three three times times more more habitat habitat for for M. cinxia. In In this this case, case, the the area area of of suitable suitable habitat habitat had had declined 1 996) used declined largely largely because because of of reduced reduced grazing grazing pressure. pressure. Hanski Hanski et et ai. al. ((1996) used the 994; Chapter ) , parameterized the incidence incidence function function model model (Hanski, (Hanski, 11994; Chapter 44), parameterized previ previously ously for for M. cinxia, cinxia, to to assess assess the the likely likely metapopulation metapopulation dynamic dynamic consequences consequences
20.
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CHRIS SKI CHRIS D. D. THOMAS THOMAS AND AND ILKKA ILKKA HAN HANSKI
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Bulman's 1 ) study, Bulman's (200 (2001) study, four four of of which which had had predicted predicted median median times times to to extinction extinction between 3 0 yr between 24 24 and and 1130 yr (the (the remaining remaining two two metapopulations metapopulations survived survived the the entire entire duration 1 ) . As duration of of the the simulations; simulations; Table Table 20. 20.1). As the the surviving surviving metapopulations metapopulations were chosen chosen to to be be in in the the most most favorable favorable landscapes landscapes within within each each region, region, it it were is unlikely unlikely that that these these meta metapopulations would be be rescued rescued by by immigrants immigrants from from is populations would other landscapes landscapes still still containing containing E. aurinia. There There appears appears to to be be aa substantial substantial other extinction debt debt in in this this species, species, which which is is likely likely to to decline decline for for many many decades decades extinction into the the future future even even if if there there are are no no further further habitat habitat losses losses (Bulman, (Bulman, 200 2001). If the the into 1 ) . If Dorset Dorset system, system, for for which which the the model model was was parameterized, parameterized, is is actually actually in in overall overall decline, even even these these projections projections are are too too optimistic. optimistic. decline, The The projected projected times times to to extinction extinction should should not not be be interpreted interpreted too too literally, literally, as as the the model model was was parameterized parameterized with with aa limited limited amount amount of of information information and and no no regional regional stochasticity stochasticity was was taken taken into into account. account. However, However, the the modeling modeling exercise exercise has helped helped reveal reveal why why this this butterfly butterfly appears appears to to be be becoming becoming extinct, extinct, region region has after after region, region, even even when when the the remaining remaining populations populations fall fall within within protected protected areas. areas. Modeling Modeling results results suggest suggest that that protection protection of of all all remaining remaining populations populations and and habi habitat tat patches patches in in some some regions regions may may not not be be enough, enough, whereas whereas the the butterfly butterfly is is pre predicted 00 dicted to to survive survive indefinitely indefinitely in in the the two two largest largest networks networks that that contain contain over over 1100 ha of of habitat. habitat. Despite the non nonequilibrium nature of of the the system, metapopulaha Despite the equilibrium nature system, aa metapopula tion approach approach has has provided provided insight insight into into the the recent recent decline decline and and has has identified identified tion minimum viable network for the the long-term long-term conservation conservation of of the the species. species. minimum viable network goals goals for
Extinction Debt D e b t and and Conservation Conservation Extinction The The concept concept of of extinction extinction debt debt is is usually usually applied applied to to communities communities and and in in the the context (Tilman et et a!., 1 994; Hanski 2002 ). context of of species species diversity diversity (Tilman al., 1994; Hanski and and Ovaskainen, Ovaskainen, 2002). Species-area are performed performed to estimate the the numbers numbers of species Species-area calculations calculations are to estimate of species that might become extinct habitat loss loss (Brooks (Brooks and and that might eventually eventually become extinct following following habitat Balmford, 1996; 1 996; Brooks a!., 1997; 1 997; Cowlishaw, 1 999). These Balmford, Brooks et et al., Cowlishaw, 1999). These calculations calculations have extinction pprocess r o c e s s- and have provided provided insight insight into into the the extinction and into into human human impacts impacts on but it an approach a on biodiversitybiodiversity - but it is is an approach without without hope, hope, as as it it does does not not provide provide a practical conservation action. action. However, practical way way forward forward for for conservation However, aa metapopulation metapopulation approach provides aa way way forward forward even the initial initial prognosis prognosis may may be be approach provides even though though the equally pessimistic. Each will have habitat requirements, requirements, which which means Each species species will have slightly slightly different different habitat means that individual species have have somewhat different habitat habitat networks even in in the the that individual species somewhat different networks even same Guti&rez et same fragmented fragmented landscape landscape (e.g., (e.g., Gutierrez et al., a!., 2001; 200 1 ; Thomas Thomas et et al., a!., 2001b). 200 1 b ) . Species will will also also differ differ in in local local population population densities densities and and dispersal dispersal abilities, abilities, Species and and hence hence local local extinction extinction and and colonization colonization rates rates will will differ. differ. Using Using aa singlesingle species species approach, approach, it it is is possible possible to to identify identify which which areas areas of of the the fragmented fragmented landscape are are likely likely to to be be most most important important for for particular particular species species and and potentially potentially landscape to assess assess whether whether aa given given species species will will eventually eventually decline decline to to extinction extinction or or become become to restricted restricted to to some some limited limited area. area. The The theory theory described described in in Chapter Chapter 44 has has the the potential to to achieve achieve this this for for species species whose whose environments environments are are highly highly fragmented. fragmented. potential If the the prognosis prognosis is is metapopulation metapopulation extinction, extinction, the the metapopulation metapopulation approach approach If can extinction threshcan be be used used (1) ( 1 ) to to identify identify which which landscapes landscapes are are closest closest to to the the extinction thresh old old and and (2) (2) to to identify identify how how extinction extinction and and colonization colonization rates rates could could be be altered, altered, via management management of of landscape landscape structure, structure, to to ensure ensure that that extinction extinction does does not not actuactu via ally ally take take place. place. In In other other words, words, the the theory theory provides provides means means of of targeting targeting conserconser-
20. 20. METAPOPULATION METAPOPULATION DYNAMICS DYNAMICS IN IN CHANGING CHANGING ENVIRONMENTS ENVIRONMENTS
497 491
vation of E. aurinia, discussed this action might be be vation action. action. In In the the case case of discussed earlier, earlier, this action might ensuring within focal focal regions have the right ensuring that that all all grasslands grasslands within regions are are grazed grazed to to have the right vegetation that management host plant and that that vegetation height, height, that management increases increases host plant densities, densities, and habitat all meas habitat areas areas are are increased increased by by the the restoration restoration of of adjacent adjacent habitat h a b i t a t- all measures ures to to reduce reduce extinction extinction rates. rates. Similarly, Similarly, increasing increasing habitat habitat quality, quality, restoring restoring new possibly providing new habitats, habitats, and and possibly providing stepping-stone stepping-stone habitats habitats to to connect connect semi semiisolated isolated patch patch networks networks could could all all increase increase colonization colonization rates. rates. By By targeting targeting these these actions actions within within the the most most favorable favorable existing existing landscapes, landscapes, rather rather than than investing investing effort species is effort where where the the species is already already doomed doomed to to extinction, extinction, real real long-term long-term success success may possible. Most may be be possible. Most conservation conservation applications applications of of metapopulation metapopulation theory theory have have stressed stressed the the need need to to increase increase habitat habitat areas areas and and minimize minimize patch patch isolation, isolation, but but often often these these particular particular suggestions suggestions are are impractical. impractical. For For example, example, changing changing the the spatial spatial locations locations of of habitat habitat patches patches is is not not usually usually an an option. option. It It is is important important to to realize, realize, however, however, that that any any actions actions that that reduce reduce extinction extinction and and increase increase colo colonization population approach" nization rates rates are are equally equally valid valid applications applications of of the the "meta "metapopulation approach" to to conservation. conservation. For For example, example, manipulation manipulation of of habitat habitat quality quality and and the the geom geometry etry of of the the landscape landscape are are equally equally legitimate legitimate means means of of altering altering extinction extinction and and colonization aI., 2001b; 200 1 b; Box Box 20.2). 20.2) . colonization rates rates (Thomas, (Thomas, 1994a; 1994a; Thomas Thomas et et al.,
BOX 20.2 Reconciling Habitat and Metapopulatlon Approaches in Butterfly Biology
Many simplifications were made during the early development of the metapopu la tion paradigm in butterfly biology. One of these relates to the emphasis on the spatial configuration (geometry) of suitable habitat in the landscape: what are the areas of habitat patches and how isolated they are from each other? Metapopulation studies appeared to pay less attention to the role of variation in habitat quality, which had pre viously been recognized as a major determinant of butterfly distributions (Thomas, 1 984). However, this perception is somewhat misleading, as even the earliest b utterfly metapopulation studies took account of habitat quality. For example habitat quality thresholds were used to define habitat patches (Harrison et aL, 1 988), and variation in habitat quality was widely recognized as the driving force behind extinction and colon ization dynamics within many metapopulations (Warren, 1 98 7; Thomas, 1 994a,b, 1 996; Hanski, 1 999b; Wahlberg et aL, 2002a). Variation in habitat quality also underlies source-sink dynam i cs w ithin butterf ly metapopulations (Thomas et aL, 1 996) and may infl uence migration among patches (Box 20.3). The pe rception that the metapopulation approach" is somehow an alternative to the "habitat approach" has nonetheless persisted. Most recently, attempts have been made to tease apart the relative importance of variation in habitat q u ality and the spatial arrangement of habitats (Dennis and Eales, 1 999; Tho m as et aI., 2001 b; Fleishman et aI., 2002). However, this is not very satisfactory because the m etapopulation and habitat approaches operate at different levels of a hierarchy. At the metapopulation level, we are primarily interested in the probability of extinction of local populations. Habitat quality habitat type and patch size all contribute to that probability The term habitat quality is itself a "black box" simplifying complex interactions among species as well as responses to the physical environment (e.g., Hochberg et aL, 1 992; Jordano et aL, 1 992). A habitat quality approach is often a useful abstraction to summarize the conse quences of multiple interactions within (usually) single landscape elements, just as a
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CHRIS CHRIS D. D. THOMAS THOMAS AND AND ILKKA ILKKA HANSKI HANSKI
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metapopulation approach is a useful abstraction to summarize the behavior of populations in many such elements. Ultimately, the issue is not whether habitat quality matters, but how we deal with it in population biology and conservation. Most butterflies whose meta population biology has been studied are habitat specialists. In all cases where a metapopulation approach is deemed appropriate, the "first cut" is between habitat (patches) and nonhabitat (matrix). This is a given. After this first cut, the question is whether vari ation in habitat quality is great enough within patches, or within the matrix (Sutcliffe and Thomas, 1 996; Ricketts� 2001 ; Keyghobadi et aI., 2002), for it to be necessary to incorporate habitat variation within the meta population level of analysis. This can only be answered in specific terms; that is, whether and how variation in habitat quality should be treated in a particular landscape and for a particular species (Hanski . et aI., 2004). The example on Hesperia comma (Sections 20.5 and 20.6) illustrates one specific case. The truly critical issue; and the one on which the relevance of the metapopulation approach rests, is whether population connectivity makes a difference to the distri bution and spatial dynamics of the species. In this context, it is unfortunate that most empirical studies continue to use a simplistic measure of connectivity distance to the nearest population (or even distance to the nearest habitat patch) - which measure �
lacks power. Instead, one should use a connectivity measure that takes into account the distances to and sizes of all neighboring . populations (Hanski, 1 999b; Moilanen and Nieminen, 2002). Such a measure of connectivity is also an integral part of the i ncidence function metapopulation model (Hanski, 1 994, 1 999b), which has been applied exten sively in the research reviewed in this chapter. '
20.3 20.3
PRECARIOUS PRECARIOUS METAPOPULATION METAPOPULATION PERSISTENCE PERSISTENCE Some Some landscapes landscapes have have ample ample habitat habitat that that ensure ensure metapopulation metapopulation persist persistence ence and and high high patch patch occupancy, occupancy, whereas whereas other other landscapes landscapes have have very very little little habi habitat tat and and no no chance chance for for metapopulation metapopulation persistence. persistence. Yet Yet other other landscapes landscapes contain contain intermediate intermediate amounts amounts of of habitat habitat that that may may permit permit periodic, periodic, but but not not permanent permanent occupancy, occupancy, in in which which case case metapopulations metapopulations may may flip flip back back and and forth forth between and absence that recolonization between presence presence and absence (provided, (provided, of of course, course, that recolonization from from outside outside is is possible possible following following extinction). extinction). It It is is easy easy to to misinterpret misinterpret the the dynam dynamics systems, especially studies cover cover too too small region and too ics of of such such systems, especially when when studies small aa region and too short long-term and short aa time time to to encompass encompass the the long-term and large-scale large-scale dynamics dynamics of of the the sys system. serious implication tem. The The most most serious implication is is that that researchers researchers might might study study aa patch patch net network work that that is is currently currently empty empty and and conclude conclude erroneously erroneously that that it it is is of of no no consequence consequence for for conservation conservation or or the the same same network network when when it it is is well well occupied occupied and and conclude conclude that that it it is is sufficient sufficient for for long-term long-term persistence. persistence. The The following following examples examples illustrate illustrate that that such such precarious precarious metapopulation metapopulation persistence persistence may may be be commonplace. commonplace.
Arida Aricia agestis agestis in in
North Wales North Wales
The tis, is The brown b r o w n argus argus butterfly, butterfly, A. ages agestis, is a a specialist specialist on on common c o m m o n rock rock rose rose Helianthemum nummularium nummularium plants plants in in north north Wales, Wales, where where the the plant plant is is
METAPOPULATION DYNAMICS IN CHANGING CHANGING ENVIRONMENTS 20. METAPOPULATION
4499 99
restricted to to limestone limestone grasslands grasslands and and crags. crags. Therefore, Therefore, both both the the plant plant and and restricted the butterfly butterfly share share aa very very patchy patchy distribution distribution in in north north Wales Wales (Fig. (Fig. 20.2). 20.2 ) . the Within aa 600-km 600-km22 area, area, habitat habitat patchiness patchiness at a t aa coarse coarse scale scale is i s determined determined by by Within the distribution distribution of of limestone limestone outcrops, outcrops, and and at at aa finer finer scale scale by by the the distribution distribution the of traditional traditional flower-rich meadows and and crags crags (Wilson (Wilson et et al., ai., 2002). 2002). of flower-rich meadows The butterfly butterfly shows shows the the usual usual metapopulation metapopulation patterns. patterns. It It is is most most likely likely The to be be present present in in Helianthemum-containing Helianthemum-containing patches patches that that are are large large and and close close to together; some colonizations colonizations and and extinctions have been been observed, observed, and and individindivid together; some extinctions have uals have have been been recorded recorded moving moving between between habitat habitat patches patches (Wilson (Wilson and and Thomas, Thomas, uals 2002; Wilson Wilson et et al., ai., 2002). 2002 ) . Peripheral Peripheral populations populations tend tend to to contain contain only only aa subsub 2002; set of of the the genetic present within core areas, areas, suggesting suggesting colonization colonization set genetic variation variation present within core by relatively small numbers numbers of of individuals (1. Wynne Wynne et et al. ai. unpublished unpublished result). result) . by relatively small individuals (I. Wilson eett aal.i . (2002) (2002) defined defined groups groups of of meadows meadows aass semi-independent semi-independent networks networks Wilson (SINs) of of habitat habitat if if they they were were separated separated from from other other such such groups groups by by 3 3 km km or or (SINs) more of of unsuitable unsuitable habitats. habitats. Because Because movements movements over over distances distances greater greater than than more
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main figure; squares squares represent semi-independent networks (SINs), (SINs), separated by 33 km or more of of unsuitable habitats from from other other networks (inset). Simulated median times to extinction extinction of SINs 25 yr (medium-sized squares), SINs are are >200 yr (large squares), squares), 25-1 25-125 squares), and 10 > 1 0 ha) hal with with heterogeneous heterogeneous vegetation including old fields, forested area, and less suitable heath. Levels of fragmentation fragmentation have not been modified by anthropogenic influences, although the invasion by American mink mink (Mustela (Mustela vison) vison) over the last 50 years may have had some impact impact on vole dynamics ((Banks Banks et aI., al., unpublished unpublished results). On treeless skerries, skerries, vole abund abundance mirrored the seasonal development development of the vegetation. Vole populations grew grew during the early summer flush of vegetation growth, growth, and voles on skerries had higher maturation maturation rates, rates, litter size, and mean densities than on larger larger islands islands during during this this period. period. However, However, skerry skerry populations populations invariably invariably declined in late summer summer when when favored plant species were were largely consumed or or wilted. These declines resulted from both higher mortality and higher emigration movement to other islands. On larger islands, populations peaked in autumn and voles responded to seasonal crowding by intraisland movements from preferred old-field and meadows habitat habitat to suboptimal heath and forests, with relatively low rates of interisland movements. Despite the proximity of the mainland (less (less than 3 km from from the outermost islands), there there was little evidence that it was the primary source of colonists for unoccupied islands and
21.. SMALL SMALLMAMMAL MAMMAL METAPOPULATIONS METAPOPULATIONS 21
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that the the archipelago was part part of an island-mainland metapopulation ((Crone Crone al., 200 2001). et ai., 1). Extinctions Extinctions and and recolonizations recolonizations ooff local local island island populations populations were were common common and affected all island size categories. categories. Extinction rates rates were were similar for large large and medium medium islands, islands, but but populations populations on on small small islands islands turned turned over over at at aa much much higher higher rate than on larger islands. Despite the high extinction extinction probability on skerries, seasonal extinction extinction was not fully deterministic. deterministic. The median period of occupancy for skerries was 2 yr. Only 1i of 113 3 large islands monitored was occupied for all 6 yr. It is suggested that two mechanisms were important for local population population extinction: demographic stochasticity caused by low population population sizes on all islands (mean population size on skerries in May was - T Tjj
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in which L L is the boundary boundary length and bb is the penalty given to boundary boundary length length (relative (relative to to other other costs). costs). The The objectives objectives in in Possingham Possingham et et al. (2000) (2000) and and Cabeza et al. (2004) (2004) are very similar; both both essentially minimize a linear combin combination of cost (area) and boundary boundary length. The difference between between the methods methods is that in the latter the conservation conservation targets targets Tj T i are are framed framed in in expected expected numbers numbers of populations, as of populations, as P Piiij values values are are based on on aa probability model model for for the the presence presence of of the species. Cabeza Cabeza et al. (2004) (2004) used the ratio ratio of reserve boundary boundary length boundary length of the reserve (L) to reserve area (L') (L') instead of the boundary (L) directly. This is because L' L' is much much less dependent dependent on the absolute absolute size of of the the system than L' is more suitable to be used in the context than L, L, which which means that that L' context of aa stepwise stepwise heuristic heuristic optimization optimization algorithm algorithm where where the the number number of of sites sites (and (and L) L) varies during during the optimization optimization process.
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Note Note that that the the methods methods of of Possingham Possingham et et ai. al. (2000) (2000) and and Cabeza Cabeza et et ai. al. (2004) (2004) both both belong belong to to problem problem category category C2. C2. This This means means that that reserve reserve aggregation aggregation is is achieved achieved in in aa qualitative qualitative manner, manner, without without any any estimate estimate of of the the species-specific species-specific effects effects of of aggregation aggregation on on spatial spatial processes processes and and persistence persistence of of populations populations per ust assumed per se. se. It It is is jjust assumed that that aggregation aggregation is is useful useful because because itit decreases decreases edge edge effects effects and and reserve reserve maintenance maintenance costs (Possingham (Possingham et et aI., al., 2000). It It follows follows that that an an important important question question is is how how much much aggregation aggregation in in the the reserve reserve network network can can you you get get with with little little or or no no increase increase in in reserve reserve cost? cost? In In the the example example of of Cabeza Cabeza et 0 % decrease et ai. al. (2004), (2004), it it was was typically typically possible possible to to achieve achieve aa 550% decrease in in L with with aa > 0). This is not not a coincidence coincidence as DP uses the the habitat habitat model model augmented augmented with with connectivity connectivity for for the the 23 23 species species for for which which connectivity connectivity No boundary length penalty was was used for the DP method method was significant. No [b [b = = 00 in in Eq. Eq. (22.6)] (22.6)] and and thus thus the the clustering clustering obtained obtained with with DP DP is is aa conse consequence of of the use of connectivity. It is encouraging encouraging that that including a component component of spatial population population dynamics into the site selection method method consistently results in clear reserve aggregation. The results of Fig. 22.2 22.2 are put put into perspective when when combined with with those those of Fig. 22.3, 22.3, which which shows shows the evolution of of reserve reserve network network area and boundary boundary length with with increasing b when when using BLMlPA BLM/PA and and BLMlprob. BLM/prob. The general trend boundary length can be obtained trend is that that a large reduction reduction in reserve boundary obtained with with
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Fig. 22.3 22.3 Behavior Behavior of of solution area and boundary boundary length length when using the boundary boundary length minimization minimization method method [Eq. [Eq. (22.3)]. Solid and dashed lines correspond to to presence-absence presence-absence and probability probability data, respectively. respectively. Lines with triangles and circles correspond correspond to to area and boundary boundary length, respectively. respectively. With With both both problem problem variants, a significant reduction reduction in reserve reserve boundary boundary length can be achieved with a minor area. Using PIA minor increase in reserve reserve network area. P/A observations observations produces more fragmented solutions than probability fragmented solutions probability data. Results Results shown are for the 5% tar target level.
aa minor minor (even (even zero) zero) increase increase in in reserve reserve area. area. If If reserve reserve aggregation aggregation can can be be obtained obtained for for free free in in terms terms of of cost cost (here (here cost cost = area), area), such such aggregation aggregation should should often often be be favored favored (but (but see see Section Section 22.6). 22.6). Very Very similar similar results results were were obtained obtained also also for targets other other than than 110% (Fig. 22.3). for 0 % (Fig. Figure Figure 22.4 22.4 compares compares different different site site selection selection methods methods in in terms terms of of the the expected expected number number of of populations populations (per species) calculated calculated using using the the effects effects of of connectivity connectivity and and assuming assuming nonselected nonselected sites sites are are lost. lost. In In this this comparison, comparison, DP DP does does best best and and averages averages about about 30% 30% higher higher in in terms terms of of populations populations than than the the simple simple multiple multiple representation representation variants. variants. Encouragingly, Encouragingly, BLMJPA BLM/PA and and BLMJprob BLM/prob with high b also do quite well, which indicates that that the qualitative clustering achieved achieved by by BLM BLM methods methods is is aa useful useful step step in in the the direction direction of of designing designing reserves reserves that that support support long-term long-term conservation conservation of of biodiversity. biodiversity. Another Another way way of of com comparing paring the the site site selection selection methods methods looks looks at at the the difference difference between between the the realized (Fig. 22.5). (using DP) and and target target representation representation (Fig. 22.5). BLM/PA BLM/PA systematically systematically fails fails to b. Best to achieve achieve the the set set target target regardless of of the the choice of of b. Best results are are achieved achieved with with BLMJprob BLM/prob with with high high b or or with with DP. DE BLM/prob BLM/prob can can produce produce an an overall overall overrepresentation overrepresentation of of the the target target even even when when evaluated evaluated using using DP. DE This This is is because because aa high high penalty penalty for for boundary boundary length length actually actually forces forces more more area area into into the the solution. When When comparing comparing solutions solutions of of the the same same size, size, DP DP still still achieves achieves highest highest expected expected numbers numbers of of populations populations (Fig. (Fig. 22.4). 22.4). Note Note that that some some overrepresentation overrepresentation in in the the solution solution does does not not mean mean that that any any site site can can be be removed removed from from the the solution with without the target target failing for at least one species. out The The effects effects of of reserve reserve aggregation aggregation are are not not equal equal for for all all the the species; species; those those species species that that show show strongest strongest effects effects of of connectivity connectivity are are likely likely to to be be affected affected most most
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Fig. 22.4 umber of 22.4 Different Different site site selection selection methods methods and and the the average average expected expected nnumber of popula populations dynamic probability tions as as aa function function of of solution solution area area calculated calculated over over all all species species using using the the dynamic probability method (evaluating the the effects of habitat loss). The dotted for the dynamic loss). The dotted line is for dynamic probability method [Eqs. are for the the boundary length minimization [Eqs. (22.4-22.6)]. (22.4-22.6)]. Solid lines are minimization problem problem [Eq. 3)] using using the and with high [Eq. (22. (22.3)] the habitat habitat model model for for probabilities probabilities and with zero zero (lower (lower line) line) and and high penalties (upper (upper line) for for boundary boundary length. Dashed lines are as the solid lines lines but for for presence-absence observations. The worst performers are problem variants with with zero 0). These penalty for boundary boundary length (b = = 0). These solutions are fragmented fragmented (see (see Fig. Fig. 22.2), which shows a comparatively populations when con nectivity effects are comparatively low expected expected number number of populations connectivity accounted accounted for. for.
adversely adversely by by fragmentation. fragmentation. In In these these particular particular data, Plebeijus argus is is both both an an important important endemic endemic race race and and also also aa species species showing showing strong strong effects effects of of con connectivity in statistical analysis. Figure 22.6 22.6 shows predicted effects of the site selection method for P. argus. When When accounting for the effects effects of connectivity (right bars), bars), the the species species is is expected expected to to be be practically practically extinct extinct from from any any solution solution ) . Thus with with significant significant scatter scatter (all (all solutions solutions with with PIA P/A data data or or with with b = = 00). Thus the the clustering clustering of of the the reserve reserve can can be be expected expected to to be be of of primary importance for for this this species. species. When When applying applying site site selection selection methods methods to to real real world world problems, problems, at at least least two two factors factors that that were were ignored ignored earlier earlier should should be be considered: considered: the the weighting weighting of of the the species species and and landscape landscape dynamics. dynamics. It It makes makes sense sense to to set set different different targets targets for for different different species species according according to to their their conservation conservation status. status. The The setting setting of of species species
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weights is likely to be partially a political decision where where local and and global conservation conservation needs needs are balanced. balanced. In this particular particular case, giving high weight to to the the two two endemic endemic races races does does not not change change the the solution significantly significantly from from the the solutions solutions produced produced by by the the dynamic dynamic probability probability method method (not shown). shown). The The reason reason is that that the endemics have somewhat specialized habitat habitat requirements requirements that that influence influence the the solution solution disproportionately. disproportionately. The The BLM BLM and and DP DP methods applied applied to to the the case study study assume assume aa worst-case worst-case scenario scenario in in the the sense sense that that they they explicitly explicitly assume assume that that habitat habitat outside outside the the
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selected reserve network network is lost. lost. In In some some cases, cases, there there may may be be more more knowledge knowledge selected reserve available about about what what can can be be expected expected to to happen happen for for nonselected nonselected habitat habitat and and available this knowledge knowledge could could be be integrated integrated into into the the reserve reserve selection selection process. process. this
222.5 2.5
USING A A STOCHASTIC STOCHASTIC METAPOPULATION METAPOPULATION MODEL MODEL USING IN SITE SITE SELECTION SELECTION IN Moilanen and Cabeza Cabeza (2002) (2002) described described how how a stochastic stochastic metapopulation metapopulation Moilanen and model can be be used used in the the site site selection selection process process in order order to to explicitly explicitly incorincor model can porate spatiotemporal spatiotemporal population population dynamics dynamics into into reserve reserve network network design design porate (category C3, C3, see Section Section 22.2). 22.2). They They ask ask the the question: question: which which subset subset of of sites S S (category do you you select select to to maximize maximize the the long-term long-term persistence persistence of of aa metapopulation metapopulation given given do that you you have have a parameterized parameterized metapopulation metapopulation model, model, unselected unselected habitat habitat is that lost, each each site site has has aa cost, cost, and and the the amount amount of of resource resource (e.g., (e.g., money) money) available available is is lost, here what what kind of results can can be expected when when applying limited? We We show here of results be expected applying this method. method. In In our example, we we use use the the incidence incidence function function model model (IFM; (IFM; see this our example, see Chapter and 5 references and of the the model). model). Chapter 4 and 5 for for references and a description description of The way of of integrating model in in simplest way integrating a stochastic stochastic metapopulation metapopulation model The simplest site selection selection is is to to use metapopulation model model to to find find the the set set of site use the the metapopulation of sites sites that that gives the lowest lowest metapopulation metapopulation extinction rate for simulations of of aa specified specified gives the extinction rate for simulations of sites that gives the metapopumetapopu length T. (Alternatively, length (Alternatively, one one could find find the set set of sites that gives the lation the longest average average lifetime.) lifetime. ) There two significant significant problems problems with with lation the longest There are are two this extinct, only rarely (or practically practically never), never), this appoach. appoach. First, if replicates replicates go extinct, only rarely a of simulation runs is needed to evaluate evaluate the extinction a very large large number number of simulation runs needed to the extinction probability population reliably, probability of of the the meta metapopulation reliably, which which will will slow slow down down optimization optimization considerably. considerably. Second, Second, the the simple simple measure measure is is unable unable to to distinguish distinguish between between solutions solutions that that are are always persistent and and between between solutions solutions that that always always lead to Moilanen and to extinction. extinction. Consequently, Consequently, Moilanen and Cabeza Cabeza (2002) (2002) used used aa measure measure of of the the persistence persistence of of the the simulation, F(S), F(S), which which can can distinguish distinguish the the quality quality of solutions solutions without without actually actually observing observing extinctions. extinctions. This This is is the the average average one-step one-step global probability of global extinction extinction probability of the the metapopulation metapopulation calculated calculated over over N N simula simulation runs: tion runs:
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in in which which Xn,t is is the the simulated simulated patch patch occupancy occupancy pattern pattern aatt time time tt in in replicate replicate simulation simulation nn and and ~(Xn,t) is is calculated calculated as as the the probability probability of of simultaneous simultaneous extinction extinction of of all all local local populations, populations,
I~(Xt) =
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where where 01+ ~t+l1 denotes denotes metapopulation metapopulation extinction extinction at at time time tt + 1, 1, Pi(t) pi(t) is is the the occupancy occupancy state state of of patch patch ii at at time time t, t, Ci(t) is is the the probability probability of of patch patch ii being being colonized, colonized, Ei Ei is is the the probability probability of of patch patch ii going going extinct extinct independently independently of of other patches (the intrinsic extinction probability), probability), and colonization from other [[11 -- Ci(t)]Ei Ci(t)]Ei isis the the extinction extinction probability probability of of patch patch ii when when considering considering the the
22. 22.
METAPOPULATION DYNAMICS DYNAMICS AND AND RESERVE RESERVE NETWORK NETWORK DESIGN DESIGN METAPOPULATION
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rescue effect. effect. Functions Functions E() EO and and C() CO will will naturally naturally be be determined determined by by the the strucstruc rescue ture of of the the metapopulation metapopulation model. model. ture Equation (22.8) (22 . 8 ) is a function function of of the the metapopulation metapopulation model model and and its its paramparam Equation T. ItIt eter distribution, distribution, the the initial initial occupancy occupancy state state of of the the metapopulation, metapopulation, S S and and T. eter is related related to, to, but but not not identical identical to, to, the the extinction extinction risk risk of of the the metapopulation metapopulation and and is F(S)�l when when the the metapopulation metapopulation goes goes extinct extinct has the the following following properties: properties: F(S)--~I has almost immediately immediately and and F(S)--*O F(S)�O when when the the metapopulation metapopulation is highly persistent. persistent. almost When the the metapopulation metapopulation goes extinct extinct in a simulation simulation at at time time t, t, F(S) F(S) is When (T -- t)/(NT), and thus thus the value of of F(S) F(S) is always greater than than the the increased by (T increased t)/(NT), and the value always greater proportion of of time time the the metapopulation metapopulation is extinct the simulations. simulations. proportion extinct in the Importantly, Eq. Eq. (22.8) (22.8) is able able to to differentiate differentiate between between two two solutions solutions that that Importantly, F(S) is smaller smaller for the solution that persist of all simulation simulation runs; runs; F(S) persist until until the the end end of for the solution that is more more persistent. persistent. Moilanen Moilanen and and Cabeza Cabeza (2002) (2002) described described an an optimization optimization is technique that that is able able to to efficiently solve solve the the nontrivial nontrivial optimization optimization problem problem technique m of finding the optimal optimal set of of sites S* S" from the search search space space of of size 2 m,, where where of finding the from the m is is the number of patches in in the the metapopulation. metapopulation. Note Note that that the the difference difference m the number of patches between a population viability viability analysis analysis (PVA, (PVA, see, see, e.g., e.g., Murphy Murphy et aI., between a spatial spatial population et al., 1 990; Coulson aI., 200 1 ) and metapopulation site selection is that PYA 1990; Coulson et et al., 2001) and metapopulation site selection that a PVA alternatives, whereas whereas metapopulation metapopulation site selection only compares compares a few alternatives, selection actually searches for an an optimal optimal solution solution within within the the given constraints. constraints. actually searches for
Important the Selection Important Factors Factors Affecting Affecting the Selection of of the the Reserve Reserve Network Network Here we apply method to to a metapopu Here we apply the the metapopulation metapopulation site site selection selection method a metapopulation of heath fritillary Melitaea diamina. lation of the the false false heath fritillary butterfly, Melitaea diamina. M. M. diamina diamina lives on on moist moist meadows, meadows, which which are are nowadays nowadays being being overgrown overgrown rapidly. rapidly. This This poses poses persistence problems problems to to the the butterfly butterfly if if no no restoration restoration work work is is done done for for main mainpersistence taining taining the the quality quality of of the the meadows. meadows. A A system system of of 125 125 habitat habitat patches patches scattered scattered in in an an area area of of 20 20 X x 30 km km in in southern southern Finland (Fig. 22.7) 22.7) was was used used to to assess assess "which "which subset subset of of sites sites should should be be maintained maintained to to maximize maximize the the long-term long-term persistence persistence of of M. diamina, diamina, given given the the cost cost of of the the sites sites and and the the available amount amount of of resources? resources?"" A A brief brief overview overview of of the the effects effects of of different different factors factors on on optimal optimal selection selection is is given: given: the the value value of of the the dispersal dispersal parameter parameter a, cx, the the available amount amount of sites. of resources resources for for setting setting the the reserves, reserves, and and the the cost cost of of the the sites. The The dispersal dispersal ability ability of of the the species species (average (average dispersal dispersal distance distance is is given given by by 1/a) 1/0~) most important important factor in the meta metapopulation model affecting is possibly the most population model the reserve network. the configuration configuration of of the the reserve network. When When dispersal dispersal distances distances are are short short (large (large a), 0~),the the best best option option is is to to protect protect sites sites that that are are close close together together (Fig. (Fig. 22.8A). 22.8A). However, However, when when the the dispersal dispersal abilities abilities of of the the species species are are not not limiting limiting and and the the individuals individuals can can reach reach any any site site in in the the system, system, the the optimal optimal solution solution does does not not consist consist of of aa compact compact cluster, cluster, but but of of aa larger larger number number of of more more scattered scattered sites sites our example, example, to assess the effects of the dispersal dispersal parameter, parameter, (Fig. 22.8B). In our we we compared compared selections selections done done with with different different values values for for the the parameter: parameter: aa small small dispersal .5 ) and dispersal range range (a (cx = - 11.5) and aa large large dispersal dispersal range range (a (el = - 0.4). 0.4). The The configuration configuration of of the the final final reserve reserve network network might might not not be be so so intuitive intuitive as as shown shown here here when when the the real real costs costs of of the the sites sites vary vary greatly. greatly. The The real real value value of of this this algorithm algorithm comes comes to to play play when when the the costs costs of of the the sites sites are are considered. considered. An An expert expert knowing knowing the the system system and and the the dynamics dynamics of of the the species species might might be be able able to to choose choose aa good good set set of of sites sites for for species species persistence. persistence. However, However, when when the the resources resources
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are limiting and varies, it it is is very very difficult difficult to to identify identify from from aa map, map, are limiting and patch patch cost cost varies, without be the the without computational computational aid, aid, which which sites sites would would be the best best ones ones given given the amount for conservation. conservation. When When some some of of the the patches patches amount of of resources resources available available for are be proportionally proportionally more are considered considered to to be more expensive expensive than than others others (patches (patches with with commercial plantations were assumed to be 10 1 0 times times more more costly costly than than commercial forest forest plantations were assumed to be
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Distance (Km) (Km) Distance Fig. 222.8 Effects of of dispersal dispersal ability ability and and patch patch cost cost on on the the reserve reserve network network configuration configuration Fig. 2 . 8 Effects when using using the the metapopulation metapopulation approach. approach. The The area area shown shown is is aa subregion subregion of of the the complete complete when patch system system for for M. M. diamina diamina (see (see Fig. Fig. 22.7A). 22.7A). Sizes Sizes of of the the circles circles are are scaled scaled according according to to the the patch ()( = = 1.5, 1 .5, patch patch cost cost == patch patch area; area; area of of the the patch. patch. Dark Dark circles circles show show the the selected selected sites. sites. (A) (A) cx area (B) o~ ()( = = 0.4, 0.4, patch patch cost cost = patch patch area; area; and and (C) (C) ~()( == 0.4, 0.4, patch patch cost cost (white (white circles) circles) == patch patch area, area, (B) patch cost cost (dashed (dashed circles)= circles) = 10x l Ox patch patch area. area. For For the the remaining remaining IFM IFM parameters, parameters, standard standard patch M.diamina parameter parameter values values were were used used (see (see Moilanen Moilanen and and Cabeza, Cabeza, 2002). 2002). M.diemine =
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Fig. 22.9 22.9 Optimal selection at different resource levels. The shown is Optimal reserve reserve selection at different resource levels. The area area shown is aa sub subregion 7B). Panels 00 (see Fig. Fig. 22. 22.7B). Panels are are based based on on 1100 region of of the the complete complete patch patch system system for for M. diamina (see replicate optimizations replicate optimizations with with parameter parameter values values sampled sampled from from the the joint joint four-parameter four-parameter confidence confidence limits The color color of of the the patch patch shows shows how how often often the the patch patch was was selected: selected: White White = = limits for for M. diamina. The never selected; Black Black = selected. (A) (B) large never selected; = always always selected. (A) Small Small resource resource (50,000). (50,000). (B) Large resource resource (1 0 50,000). so, ooo).
those those natural natural meadows meadows in in early early successional successional stages; stages; Moilanen Moilanen and and Cabeza, Cabeza, 2002), 2002), keeping keeping all all other other factors factors equal, equal, the the optimal optimal solution solution changes changes greatly greatly (compare Figs. (compare Figs. 22.8B 22.8B and and 22.8C). 22.8C). Optimal Optimal solutions solutions with with aa large large amount amount of of resources resources do do not not always always build build on on solutions solutions found found with with aa smaller smaller amount amount of of resources. resources. Figure Figure 22.9 22.9 demonstrates demonstrates the the effect effect of of increasing increasing the the amount amount of of available resources. resources. When When the the amount amount of of resources resources is is limited, limited, it it is is optimal optimal to to select select only only aa small small cluster cluster of of sites sites (Fig. (Fig. 22.9A). 22.9A). However, However, when when the the amount amount of of resources resources is is tripled, tripled, the the solution solution consists consists of of not not only only aa larger larger amount amount of of sites, sites, but but also also aa rather rather different different set set of of sites sites (Fig. (Fig. 22.9B). 22.9B). This This result result provides provides an an important important message message for for planners planners that that often often have have thought thought that that site site selection selection algorithms algorithms only only provide provide the the core core of of the the reserve reserve network, network, which which will will be be extended extended later later on, on, by by adding adding more more sites sites to to the the core core network network when when more more resources available. The resources are are available. The optimal optimal solution solution may may strongly strongly depend depend on on the the amount amount of available. An of resource resource that that is is available. An ordering ordering in in which which patches patches should should be be conserved conserved can can only only be be given given if if the the total total amount amount of of available resources resources is is known.
22.6 22.6
DISCUSSION DISCUSSION In In order order to to optimize optimize in in situ situ conservation conservation of of biodiversity, biodiversity, and and given given limited limited resources, resources, major major effort effort has has been been placed placed on on the the development development of of reserve reserve network network design problems and design problems and algorithms to to solve solve those those problems efficiently. efficiently. Unfortu Unfortunately, problems have nately, most most of of the the existing existing problems have not not been been formulated formulated in in aa way that persistence and and hence solutions cannot cannot guarantee that is is focused focused on on persistence hence solutions guarantee the the long longterm problems have term persistence persistence of of biodiversity. biodiversity. Reserve Reserve selection selection problems have mostly mostly been formulated biodiversity, measured measured by formulated so so that that the the aim aim is is to to represent represent biodiversity, by aa snapshot snapshot of More of species species presence-absence presence-absence information, information, in the the most most efficient efficient way. way. More recent reasonable targets targets for for recent reserve reserve selection selection problem problem formulations formulations set set reasonable species for sensible species viability viability (e.g., (e.g., Noss Noss et et aI., al., 2002) 2002) and allow allow for sensible spatial spatial design design aI., 2002; aI., 2003 However, the dynamics dynamics of (McDonnell et et al., 2002; Leslie et et al., 2003).) . However,
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populations populations and and landscapes landscapes have been mostly overlooked, overlooked, and and much remains to to be achieved in formulating formulating and and solving reserve network network design problems in an an ever-changing ever-changing world. world. This chapter meta)population dynamics chapter addressed addressed the effects of spatial ((meta)population dynamics on the the persistence of biodiversity in reserves designed using using different different site selection manner with with which which they consider algorithms. These algorithms differed in the manner spatial dynamics during during the optimization process. We have shown shown how how the selection of sites for the conservation of 26 butterfly species in the Creuddyn Creuddyn Peninsula may be very different different depending depending on the reserve selection method. The The methods used here range from single representation from the simplest ""single representation heuristic" to to more more complex complex methods methods that that explicitly explicitly consider consider spatiotemporal spatiotemporal population population dynamics dynamics during during optimization. optimization. For the example concerning concerning the Creuddyn Creuddyn Peninsula, Peninsula, the single represen representation tation solution solution (i.e., (i.e., aa solution solution that that includes includes the the presence presence of of the the 26 butterfly butterfly species) population dynamics species) requires only only three three sites. sites. Studies of of butterfly butterfly meta metapopulation dynamics support the the view view that that we we cannot cannot expect expect all the the 26 species to to persist in in three three sites of 500 500 X 3< 500 500 m if all the remaining suitable habitat habitat would would be lost. We can appreciate from subsequent subsequent results that that the more more realism included in the methods (e.g., (e.g., larger number number of of representations representations per per species, species, spatial consid considerations), erations), the the larger larger the the amount amount of of sites sites in in the the solution solution and and the the better better the the prospects prospects for biodiversity persistence. Nonetheless, Nonetheless, the different different factors that that need to be considered in a reserve selection procedure procedure (including spatial popu population lation dynamics) dynamics) depend depend on on the the spatial spatial scale scale under under consideration. consideration. Reserve Reserve selection algorithms have been applied at worldwide worldwide or continental continental scales. At these these scales, scales, and and with with sufficiently sufficiently large large selection selection units, aa single representation representation for for each each species species might might be be enough enough to to ensure ensure viability, viability, especially if if the the aim aim is is to to demonstrate demonstrate the the most most efficient efficient way way of of concentrating concentrating conservation conservation efforts. efforts. However, at smaller spatial scales and with with smaller selection units, spatio spatiotemporal temporal dynamics dynamics should be be considered considered when when selecting selecting reserve reserve networks. networks. Note Note that that the the scale scale where where population population dynamics dynamics need need to to be be considered considered is is species species specific, specific, and and it it depends depends mostly mostly on on the the dispersal ability of of the the species species some bird species might show metapopulation metapopulation dynamics at a continental scale, whereas population dynamics whereas meta metapopulation dynamics would would be be quite quite localized localized for for snails. snails. The The simplest simplest site site selection selection methods methods (problem (problem categories categories CO CO and and Cl, C1, see see Section 22.2) 22.2) do not not include any notion notion of the spatial configuration configuration of the reserve, although although populations populations may may be be chosen in in aa way way that that aims at at local local persistence (problem category C l ). The C1). The simplest way of including including spatial considerations to reserve selection is to use some computational computational technique to to aggregate aggregate the the reserve reserve network network (problem (problem category category C2), C2), which which implicitly implicitly improves improves biodiversity biodiversity persistence by by minimizing negative negative external external effects. effects. In the example of the Creuddyn Creuddyn Peninsula reserve, aggregation could actually be be achieved achieved with with aa very very low low cost cost in in terms terms of of increased increased area. area. In In brief, brief, we we suggest suggest that that analysis of of the the cost cost of of reserve reserve aggregation aggregation should be be done done routinely routinely as as part of the the reserve selection process, process, and at least aggregation that that can be a part obtained obtained for for free should, should, in most most cases, be taken. taken. Given Given that that the maintenance cost cost of of aa compact compact reserve reserve is is likely to to be be smaller than than that that of of aa scattered scattered reserve reserve (Possingham prudent to (Possingham et et aI., al., 2000), 2000), it it is is economically economically prudent to pay pay aa little little extra extra for for aa compact compact reserve. reserve. Nevertheless, Nevertheless, from from the the perspective perspective of of species species persistence, persistence, there there might might also be be reasons reasons to to avoid avoid reserve reserve clustering. Where Where catastrophes catastrophes
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can impact large large areas causing causing extinctions, extinctions, it may may be less risky risky to conserve each species in at least two two or three separate places rather than than clustering those 996; Lei 997). However, those sites sites (Hess, (Hess, 11996; Lei and and Hanski, 11997). However, if if reserves reserves have have to to be be selected selected far far apart apart from from each each other, other, they they should be be large large enough enough to to allow allow species species persistence persistence independently. independently. Going one step further further from from qualitative reserve network clustering clustering to to the explicit species explicit consideration of of spatial dynamics dynamics requires information information on on speciesspecific parameters parameters of of spatial population dynamics. In the example for for the 26 butterflies, this was was done done by fitting fitting for every species a statistical model for for the function the probability probability of of occurrence occurrence of of the the species. species. This This model was was made made aa function of habitat quality and and connectivity (see also Westphal Westphal and and Possingham, Possingham, 2003 2003).). The The inclusion inclusion of of connectivity connectivity in in the the model model enables enables us us to to consider consider the the conse consequences probabil quences of of changes changes in in habitat habitat spatial spatial pattern pattern on on species' species' occurrence occurrence probabilities. ities. In In practical practical terms, terms, this this means means that that habitat habitat loss loss will will have have aa negative negative effect effect in the probabilities probabilities of occurrence occurrence in the regions close to to the site of of habitat habitat loss. This This is is aa natural natural consequence consequence of of decreased decreased immigration immigration and and increased increased edge effects. Estimates of population population numbers numbers in the selected selected reserve reserve network network differ differ quite quite significantly significantly when when effects effects of of connectivity connectivity are are excludedlincluded excluded/included in in optimization. optimization. Another Another way of considering considering spatial dynamics explicitly is integrating integrating sto stochastic metapopulation metapopulation models into the reserve selection procedure. procedure. We have presented presented an an approach approach for for selecting selecting the best reserve network network that that maximizes the the persistence persistence of of aa metapopulation metapopulation for for aa given given time time frame. frame. The The extension extension of of this this approach approach for for many many species species is is challenging, challenging, but but it it is is feasible feasible technically technically (Moilanen and and Cabeza, manuscript manuscript in preparation) preparation).. One One of the limitations limitations of of the the approach approach is is the the availability availability of of information information to to estimate estimate all all model model parameters parameters for for all all the the species. species. Reserve Reserve selection selection methods methods for for problems problems CO CO and and C1 assume assume aa best-case best-case scenario in the sense that that they they implicitly assume that that there there will be no no changes changes in the the landscape landscape outside the selected reserves. In contrast, contrast, methods methods for for classes C2 C2 and and C3 C3 assume assume aa worst-case worst-case scenario scenario in in that that all all nonselected nonselected habitat habitat is is assumed assumed to to be be lost, lost, which which of of course course will will not not always always be be the the case. case. It It is is possible possible to to improve improve the the dynamic dynamic probability probability method method by by including including information information on on threats threats and and vulnerability of sites into the optimization model (Pressey et a!., al., 11994; 994; Pressey and 1 , Cabeza and Taffs, 200 2001, Cabeza and and Moilanen, Moilanen, manuscript manuscript in prepara preparaSerneels tion). At a general level, this means means that that a model of of land-use change ((Serneels and 1 ; Veldkamp 1 ) would and Lambin, Lambin, 200 2001; Veldkamp and and Lambin, Lambin, 200 2001) would be be integrated integrated into into the the reserve reserve selection selection algorithm algorithm and and that that the the best-case/worst-case best-case/worst-case scenario would would be be relaxed relaxed and and modeled modeled more more realistically. realistically. The inclusion of landscape landscape dynamics into into reserve selection is in its infancy (Possingham et a!., 993; Costello and networks al., 11993; and Polasky, 2003). 2003). Reserve networks are are not not generally generally constructed constructed instantaneously instantaneously (except (except perhaps in in some some marine marine areas). In many many regions, sites can can only be selected selected if they they become become available for for acquisition. acquisition. While While sites are slowly being assembled assembled into into a network, network, some sites may be developed and and lost to the system. To take take this into into account, account, we we can can formulate formulate the the problem problem as a dynamic dynamic programming programming problem problem and and find find optimal optimal solutions solutions using using stochastic stochastic dynamic dynamic programming programming algorithms algorithms (Possingham (Possingham et 993; Costello and et a!., al., 11993; and Polasky, Polasky, 2003 2003).) . These These algorithms algorithms only only work work at at present that can can deliver present for for small small problems problems and and we we have have yet yet to to develop develop tools tools that deliver
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adequate adequate reserve networks networks when there are landscape landscape dynamics as well as spatial spatial population population dynamics in large systems. Preliminary results results suggest that that some measure of irreplaceability (Pressey et al., aI., 11994; 994; Pressey and Taffs, 200 1) 2001) may provide good solutions to the reserve network network design problem when there is landscape landscape change (E. Meir, personal communication) communication).. IIn n conclusion, the integration of spatial population population dynamics, landscape modeling, and scheduling of conservation action into the reserve selection problem should lead to reserve network network designs and acquisition strategies that that are better at achieving the goal of long-term biodiversity persistence. Many challenges remain in the proper proper formulation formulation of reserve network network design problems and in the development development of algorithms that that deliver robust solutions solutions uncertainty and change. in the face of several sources of uncertainty
23
ANA LYSIS VIABILITY ANALYSIS FOR ANGERED FO R END EN DAN G ERED META PO PU PUL ATIONS M ETAPO LATI O N S:: A DIFFUSION A DIFFUSION A PPROXIM ATION APPROXIMATION A PPRO A C H APPROACH E.E. E.E. Holmes Holmes and and B.X. Semmens
23.1 23.1
INTRODUCTION INTRODUCTION Population viability analysis (PVA) (PVA) assesses the rate of population decline and and the risks of extinction or quasiextinction over a defined time horizon for a population of concern ((Gilpin Gilpin and Soule, Soule, 11986; 986; Boyce, 1992; Morris and Doak, 2002). Although the techniques employed to conduct PYA PVA are varied, they typically involve building quantitative models that are parameterized by demographic and environmental data. PYA 980s PVA was first used in the early 11980s (Shaffer, 98 1 ), and in the (Shaffer, 11981), the past decade it has gained broad acceptance in the conservation community as a useful tool for assessing and managing ""at-risk" at-risk" species (Beissinger, (Beissinger, 2002; Morris and Doak, 2002; Reed et aI., al., 2002). This is particularly true for demogaphic PYAs, PVAs, due due in large part to the advancements (Beissinger, 2002). The in Monte Carlo techniques and desktop computers (Beissinger, International Union for the Conservation of Nature (IUCN)'s Red List Criteria,
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probably the most widely applied set set of decision rules for determining the sta stapartially defined defined by metrics metrics that require some form form of tus of at risk species, is partially PYA 994). For instance, under one of the Red List criteria, a taxon PVA (IUCN, 11994). may be classified as endangered endangered if a "reduction of at least 50%, projected projected or suspected suspected to be met within the next ten years or three three generations" generations" is predicted. Although many PYAs PVAs are focused on single populations populations in single sites, there are often needs for spatially explicit PYAs: PVAs: many populations populations of conservation concern concern are are distributed distributed across across multiple multiple sites sites and and additionally, additionally, the the primary primary anthropogenic anthropogenic threats threats facing facing at-risk at-risk species species are are habitat habitat destruction destruction and and alter alteretal., ation, which are fundamentally spatial processes (Wilcove et aI., 11998). 998). Several software packages have been written for spatially explicit PYA, PVA, includ includ997) and RAMAS 996), Metapop (Ak"akaya, (Ak~akaya, 11997) RAMAS GIS (Boyce, 11996), ing RAMAS Metapop ALEX (Possingham and 995), and 993). These and Davies, 11995), and VORTEX VORTEX (Lacy, 11993). models models incorporate incorporate aa diversity diversity of of demographic demographic and and spatial spatial attributes attributes such such as as distance-dependent distance-dependent migration, migration, allee allee effects, effects, social social population population structure, structure, hab habitat quality and spatial spatial arrangement, and and genetic variability. The The development itat sophisticated PYA PVA software software packages such as these has made the of flexible sophisticated construction construction and and simulation simulation of of spatially spatially explicit PYA PVA models models feasible for for those those who are not not highly skilled programmers programmers and and has greatly increased the number number who and scientists capable capable of using spatially realistic PYA PVA models. of managers and As As the use of PYA PVA has grown in conservation conservation science, so have concerns that that PYAs Reed et aI., PVAs are often overextended given limited data data sets ((Reed al., 2002). 2002). Beissinger and Westpahl ((1998) 1 998) suggested that that PYA PVA should should be limited to assess assessshort time frames flames using the simplest models that that can rea reaing relative risks over short sonably sonably be be justified. justified. For For single single species species with with spatially spatially simple simple structure, structure, data data needs needs can when Beissinger and and can often often be met when and Westpahl's call call for for model model moderation moderation and simplicity more complex spaspa simplicity are are heeded. heeded. When When one is faced faced with with species species with with more tial structure, structure, a much larger larger amount of data amount of data is needed to parameterize the populations, the levels and patterns of of dispersal, dynamics of of individual local populations, and patterns and the correlations among among local populations and the spatial pattern pattern of temporal correlations populations (e.g., Rails Ralls et aI., 2002). Unfortunately, Unfortunately, collection of data needed to parameter al., 2002). of data to parameterize a spatial model is rare of conservation concern, rare for species of concern, at least in the the disconnect between param United States (Morris (Morris et aI., al., 2002), 2002), and and there is a disconnect between the parameter PYA models and and the willingness eter requirements requirements for for spatially explicit explicit PVA willingness and/or and/or ability of management agencies to to collect the types of data data needed to to appropriappropri ately apply fulfill data apply such tools. tools. Because it is usually impossible impossible to to retroactively fulfill data requirements for spatial PVA PYA and and there there will always always be cases cases where collection requirements for a spatial where collection of spatial data data is infeasible, infeasible, managers managers require require PVA PYA tools tools that that can can help help guide concon of servation of of metapopulations meta populations in the the absence absence of of large amounts amounts of of spatial data. data. servation
D iffusion A pproximation ffor or M etapopulations Diffusion Approximation Metapopulations
One problem of limited population One approach approach to to the the problem of limited population data data is to to find find a diffudiffu sion approximation approximation that that correctly models models the the long-run statistical statistical properties properties of of complex population population process. process. This This approach approach has been used successfully for for a complex single population population models models (Karlin (Karlin and and Taylor, Taylor, 1981; 1 9 8 1 ; Lande Lande and and Orzack, Orzack, 1988; 1988; Lande, 1993; 1 993; Dennis Dennis et e t al., aI., 1991; 1 99 1 ; Hill Hill et e t al., aI., 2002; 2002; see also also Morris Morris and and Doak, Doak, Lande, 2002; 2002; Lande Lande et et al., aI., 2003) 2003) and and reduces reduces the the problem problem of of parameterizing parameterizing aa large large model model with with many many parameters parameters to to the the much much simpler simpler task task of of parameterizing parameterizing a
23. VIABILITY VIABILITY ANALYSIS ANALYSIS FOR FOR ENDANGERED ENDANGERED METAPOPULATIONS METAPOPULATIONS 23.
5567 67
two-parameter diffusion diffusion model. model. One One of of the the main main practical practical implications implications of of the the two-parameter diffusion approximation approximation approach approach is that that it it is not not necessary to to know know the the multimulti diffusion tude of of parameters parameters describing describing the the local dynamics, dynamics, dispersal dispersal levels, spatial spatial patpat tude terns of of dispersal, dispersal, and and spatial spatial synchrony between between local populations populations in in order order to to terns make basic basic predictions predictions about about the the statistical statistical distribution distribution of of the the long-term long-term make metapopulation or or local population population trajectories. trajectories. The The relevant relevant two two parameters parameters metapopulation for the the diffusion diffusion approximation approximation can be estimated estimated from from a simple time time series of of for counts from the the population population process. process. counts from This diffusion approximation approximation approach to model model the the longlong This chapter chapter uses the diffusion approach to run behavior of spatially structured populations. populations. Our Our focus is on on stochastic stochastic run behavior of spatially structured meta populations characterized characterized by structured structured population population size, density-indedensity-inde metapopulations pendent local dynamics, dynamics, and, and, in keeping with with the the assumption assumption of of density indeinde pendent pendence, a metapopulation metapopulation that that is declining as a whole. whole. Local populations populations are are pendence, assumed to to have patch-specific patch-specific structured and dispersal dispersal rates, rates, assumed structured local dynamics dynamics and with spatial spatial structure among local populations populations in terms terms of of both both their their local with structure among dynamics patterns. Description Description of the long-run statistical behavbehav dynamics and and dispersal patterns. population trajectories diffusion approximation ior of the meta metapopulation trajectories using a diffusion approximation allows PYA risk metrics rate of metapopula the estimation estimation of of PVA metrics such as the long-term rate metapopulation probability of reaching tion decline and and the probability reaching different threshold threshold declines over different horizons (i.e., probabilities probabilities of extinction or quasiextinction). different time horizons quasiextinction). These methods metapopulation PVA PYA metrics are illustrated illustrated using methods for for estimating metapopulation data metapopulations in the U.S. Pacific Northwest. data from from two two chinook chinook salmon salmon metapopulations Pacific Northwest.
23.2 23.2
A STOCHASTIC M ETAPOPULATION MODEL MODEL A STOCHASTIC METAPOPULATION Our populations, and Our focus is on declining meta metapopulations, and thus thus what what has been been termed termed nonequilibrium populations. We model a collection of local populations nonequilibrium meta metapopulations. populations connected connected by dispersal where where local populations populations have density-independent density-independent local dynamics, which sinks," but population as a which may be "sources" "sources" or ""sinks," but the meta metapopulation whole is declining. Dispersal levels could be very low, resulting in basically independent local populations, populations, or extremely high, resulting resulting in essentially one independent population. population. From a practical standpoint, standpoint, this approach approach is most appropriate appropriate when dispersal is not % per year localized dispersal not insignificant insignificant (e.g., above 22% or 0 . 1 % global dispersal), otherwise 0.1% otherwise parameterization parameterization of the model requires requires inordinately inordinately long time series. Data from this type of metapopulation metapopulation would would be characterized by fluctuating local population population trajectories, but actual extinc extinctions would be unusual until the meta population has very few individuals. Our metapopulation model assumes no density dependence nor carrying capacities within the indi individual local populations. populations. Such a model is only appropriate in cases where the population is declining and all local populations are well below their carrying capacities. Our example using data on chinook salmon illustrates a situation that that is is likely likely to to be be well well modeled modeled as as this this type type of of metapopulation. metapopulation. The following following section gives a rather parameter-intensive mathematical mathematical description of a stochastic, declining metapopulation. However, the reader should keep in mind that this model will not be parameterized. parameterized. Rather the asymptotic behavior of of this this model's trajectories will will be derived and that that informa information tion will will be be used used to to develop develop aa diffusion diffusion approximation approximation of of the the process. process. Time Time series series data data will will then then be be used used to to parameterize parameterize the the diffusion diffusion approximation. approximation.
E.E. E.E. HOLMES HOLMES AND AND B.X. B.X. SEMMENS SEMMENS
568 568
The Model Model The Consider Consider an an individual individual local local population population i with with stochastic stochastic yearly yearly growth growth and and stochastic stochastic dispersal dispersal to to and and from from other other local local populations. populations. Such Such aa local local popula populaNi(t), could be described described as follows: follows" tion's numbers in year t, Ni(t),
Ni(t)t) = - growth g r o w t h -- dispersal out out + + dispersal dispersal in Ni(
== Ni(t Ni(t - l1)ezi( - l1)) )ezi( tt +
--
di(t - l1)Ni(t - l1 )ez )ezi(;(tt - l1)) di(t )Ni(t -
E o taj jii( (tt - -- l1 )d ) djj ((tt -�
jrl- i r
.1) (23.1) (23
Nj ((tt - - l1)ezi(t-l) )ezAt- l ) 11 )) N
where where Zi(t) zi(t) iiss the the stochastic stochastic growth growth rate rate ooff local local population population i iinn year year t and and is is random variable variable with with some unspecified unspecified statistical statistical distribution distribution with with mean a random J.1i ~i and and variance variance ITT. cr2. The The J.1i ~i term term will will be be referred referred to to as as the the local local population's population's growth rate; rate; it will not be observed, observed, as the local population population is sub subintrinsic growth ject to to immigration immigration and and emigration. emigration. Some fraction fraction of individuals, individuals, di(t), di(t), ject leaves local local population population i at at year year t and and disperses disperses to to other other local populations, populations, and dispersal dispersal into into local population population i occurs occurs from from other other local populations. populations. and The fraction fraction of dispersers dispersers from from local population population j that that go to to local local population population The i in in year year t is is a;i(t) otji(t ) and and can can vary vary depending depending on on the the destination, destination, i, thus thus allow allowfor spatially spatially structured structured dispersal. dispersal. The The dispersal dispersal parameters, parameters, di(t) di(t) and and ing for ;i(t) , are otji(t), are assumed assumed to to be be temporally temporally random random variables variables from from some some unspecified unspecified a statistical distribution. distribution. statistical
The Model Model in in Matrix M a t r i x Form Form The The model for the the entire entire metapopulation can be written using a random The model for metapopulation can written using random transition dispersal and transition matrix, matrix, A(t), which which encapsulates encapsulates both both dispersal and local growth: growth:
+ 1)1 )
N l ((tt + Nj
N2 N 2 ((tt ++ 1) 1)
+
N3 N 3 ((tt +
1 1))
N mlj
(t)
N2 (t) N2 A(t) X = A(t) 3< N3 N3 (t)
(23.2)
=
NNkk ((tt ++ 1) 1)
Nk (t) (t)
where where
( l - dj ) ezl F(i-dl)eZl
a 3 1 d3eZ3 c131d3ez3 ... ( 1 -- d2)ez2 d2 ) ez2 a112dleZ1 2d l ezl a32d3eZ3 ot (1 c132d3ez3 ... A ( t) = = p cx13dleZ1 ( 1. - d3 a 1 3dj A(t) . .ezl. . .ca23d2eZ2 ~23d2e.z2 . . . .(1-d3)ez3 . .)ez3. . ... a l kd l ezl L_~lkdleZl
a21d2eZ2 c121d2ez2
a2kd2eZ2 ~2kd2ez2
a3kd3eZ3 Ot3kd3ez3
...
akj dkeZk ~ CikldkeZk ~ak2dkeZk I ak3dkeZk ~ c~k3dkeZk
(23.3) (23 . 3 )
( 1 - dk ) ezk (1-dk)ezk]
The '(t)' ' (t)' on on the the d's, cx's, a's, and and z's have have been left off off to to remove remove clutter. clutter. There There may may The be be any any level level or or spatial spatial pattern p attern of of temporal temporal correlation correlation among among the the intrinsic intrinsic local local growth rates, zi's, z;'s, dispersal dispersal rates, rates, d;'s, and dispersal dispersal patterns, patterns, c~ii's. a/so growth rates, di's, and In the the matrix matrix model, model, each each row row represents represents I1 unit unit of of habitat. habitat. Local Local populations populations In with with multiple multiple units units of of habitat habitat appear appear as as multiple multiple rows rows with with very very high high dispersal dispersal
23. FOR ENDANGERED 23. VIABILITY VIABILITYANALYSIS ANALYSIS FOR ENDANGERED METAPOPULATIONS METAPOPULATIONS
569 569
between between the the units units of of habitat habitat in in that local local population. population. The The habitat habitat units units within within aa local population population could vary vary in in quality (i.e., (i.e., habitat within within aa local population population need need not not be be uniform) uniform) and and different different local local populations populations certainly certainly differ differ in in the the num num' S are ber ber of of habitat habitat units units they they contain. contain. The The d;'s di's and and elj; OLji'S a r e assumed assumed to to be be drawn drawn from from some distribution distribution that that can be different for each local population population or local popu population lation pair. pair. Although Although the the d;'s, di's, elji oLji and and z/s zi's are are temporally temporally random random variables, variables, they they are are assumed to to be be stationary, stationary, i.e., i.e., that that there there is is no no overall overall change change in in the the mean mean values over over time. time. For For the the purposes of of this this chapter, chapter, it it will will be be assumed that that the the d;'s, di's, ' elj; S, and aji's, and z;'s zi's are are all strictly strictly postitive, postitive, which means that that all local populations populations are are connected connected to to each each other other to to some (although (although possibly possibly very very low) degree degree and that that mean mean yearly yearly geometric geometric growth growth rates, rates, exp(J.L;)'s, exp(p~i)'s, while while possibly very very small small are are not not zero. zero. These These assumptions assumptions imply imply that that the the A(t) describe describe an an ergodic ergodic set set of of matrices matrices ((Caswell, Caswell, 200 1 ). The 2001). The assumption of of strict strict positivity positivity is is not not strictly strictly necessary. necessary. It It is is possible possible for for A(t) A(t) to to describe describe an an ergodic ergodic set set if if some some elements elements of of A A are are zero; zero; it it depends on on the the pattern pattern of of zeros zeros within within A A [ef. [cf. Caswell (2001 (2001)) for for aa discussion discussion of the the conditions under under which which matrices matrices are are ergodic]. ergodic]. The The model model is is very very general, general, allowing allowing some some sites sites to to be be dispersal dispersal sources sources and and others others to to be be dispersal dispersal targets, targets, allowing allowing any any spatial spatial pattern pattern of of dispersal dispersal or or spa spatially tially correlated correlated local local growth growth rates, rates, allowing allowing any any pattern pattern of of temporal temporal correl correlation ation amongst amongst local growth growth rates, and and allowing allowing any combination combination or or pattern pattern of habitat habitat sizes sizes of of local local sites. sites.
Using Using Random Random Theory Theory to to Understand Understand the the Model's Model's Statistical Statistical Behavior Behavior Together, Together, Eqs. Eqs. (2) (2) and and (3) (3) describe describe aa quite quite generic generic model model of of aa declining declining meta population with metapopulation with density-independent density-independent local local dynamics. dynamics. From From aa viability viability analysis Can one analysis perspective, perspective, one one might might ask ask the the question: question: ""Can one predict predict the the viability viability of what are of the the total metapopulation? metapopulation?"" In In more precise precise terms, this is is asking asking what are the the statistical properties of the meta population trajectories con metapopulation trajectories of this type of connected 3 ) ] ? Clearly, nected collection collection of of local populations populations [of [of the the form form in in Eqs. (2) (2) and and ((3)]? Clearly, the the matrix matrix A(t) A(t) has has aa large large number number of of parameters parameters that that would be be difficult, difficult, if if not not impossible, population of impossible, to to estimate estimate for for any any given given meta metapopulation of conservation conservation concern. concern. However, However, using using random random theory, theory, it it can can be be shown shown that that the the long-term long-term dynamics dynamics can can be be described described by by only only two two parameters parameters and and that that it it is is unnecessary unnecessary to to know know the the multitude multitude of of other other parameters parameters for for the the purpose purpose of of projecting projecting long-run long-run dynamics. dynamics. To To use use this this random random theory, theory, we we first first need need to to recognize recognize that that this this stochastic stochastic metapopulation model falls into into the class of random random processes that that involve meta population model products random matrices, products of of ergodic ergodic random matrices, in in this this case case products products of of A(t), A(t), which which can can be local population population sizes sizes forward: be seen seen by by using using Eq. Eq. (2) (2) to to project project the the vector vector of of local forward:
N(1) A(0)N(0) N( l ) = A(O)N(O) N(2) = A(O)A( A(0)A(1)N(0) N(2) l )N(O)
(23.4) (23.4)
o o o
N( )A(2) . . . A(t )N(O) N(t)t) = - A(0)A(1 A(0)A(1)A(2)... A(t - l1)N(0) where in Eq. where N(t) N(t) is is the the column column vector vector of of Ni Ni values values at at time time tt in Eq. (2). (2). Products Products of of random random ergodic ergodic matrices matrices have have aa well-established well-established theoretical theoretical foundation foundation and and certain well-studied well-studied asymptotic asymptotic statistical statistical properties. properties. A brief brief review review of of have certain two two of of the the key key results results from from this this theory theory is is provided provided in in Box Box 23.1 23.1 and and aa simulated simulated
570 $10
E.E. HOLMES AND B.X. E.E. HOLMES AND B.X. SEMMENS SEMMENS
BOX 23.1
Key Results from Random Theory
Two of the fundamental results from the theory of products of random matrices are reviewed and interpreted in the context of our metapopulation model. The reader is referred to chapter 1 4. 3 in Caswell (200 1 ) and Tuljapurkar (1 990) for other reviews interpreted in the context of demographic, single population models. The Metapopulatlon and Local Populations Decline at the Same Rate
One of the basic results from Furstenberg and Kesten's "Products of Random Matrices" (1 960) is that the product of ergodic random matrices asymptotically goes to an equilibrium. Say that Xt is an ergodic random "k x kIf matrix and that V (also a k x k matrix) denotes the product of n of the X matrices: X" XbX3, Xn. Then Furstenberg and Kersten's results say that V goes to an equilibrium state such that •
lim ! log k
t-'"
t
lEa
ki Vii
=
.
a constant which is the same for all a
•
(B1 )
We can use this result to show that the long-run exponential growth rate of the metapopulation and the local populations will be the same. N(t) = A( O) A( 1 ) A( 2). . . A( t - 1 ) N ( O )
Let V
=
A( 0) A( 1 ) A( 2 ) . . .A( t
Then log Nj( t)
=
log
a nd log M( t) = log Thus from Eq. (B1 ), lim ! log t
... "
t
1)
2: Vii + log N,{ O ) i
2: 2: Vii i i
2: Vii i
-
our metapopulation model
=
+
log M( O )
lim ! log /--4>'
t
2: 2: Vii i i
=
a constant
=
11m
The Distribution of Local Population and Metapopulatlon Sizes Is Distributed Lognormally
One of the most powerful results, for our purposes at least, concerns the statistical distribution of the metapopulation and local trajectories. This tells us what distribution of sizes we would see if we ran our model over and over again and allows us to make population viability analyses for metapopulations since we have a prediction about the likelihood of different metapopulation futures. Random theory (Furstenberg and Kersten, 1 960; Tuljapurkar and Orzack, 1 980) shows that any sum of the N,(t),s, such as the total metapopulation (all i's), a single local population (one i), or any other subset, goes to the same distribution: (82)
where the sum of local populations is denoted in matrix terms as cON(t) and c is a column vector with O's and 1 's to show which local populations to sum together.
23. 23. VIABILITY VIABILITYANALYSIS ANALYSIS FOR FOR ENDANGERED ENDANGERED METAPOPULATIONS METAPOPULATIONS
511 571
Example These results are simple to see with simu lations. An example of a linear chain of 1 0 local populations connected via 2% yearly dispersal to their nearest neighbors and 0.2% to nonnearest neighbors is shown. The local dynamics were eZ; where Zi is a nor mally distributed random variable, Normal(lJ.i, The local g rowth rates, IJ./s, for local populations 1 to 1 0 were, respectively, 0.97, 1 .00, 0.96, 0.83, 0.88, 1 .00, 1 .00, 0.89, 0.99, and 0.81 . Figure 2 3 . 1 A shows that the long-run g rowth rate of the local population a nd metapopulations is equal to the same constant. Fig u re 2 3 . 1 B shows that the distribution of metapopulation size after 1 00 yr is Normal(1 00IJ.m, 1 OO(J�). The expected distribution was specified using the maxi m u m likelihood (ML) estimates for 11m and (J� [Eq . (9)] from a single 1 000-yr time series of metapopulation counts. The M L estimate for (J� relies on a n assumption of normality for t 1 , although strictly speaking normality only holds for t large. However, it does quite well as can be seen in Fig. 2 3 . 1 B.
> 1150, and the the normality normality assumption was was generally generally violated violated except except again again at at large large t.t. This This means that that when when dispersal is is very very low, low, diffusion diffusion population would be more approximate approximations for this meta metapopulation approximate than for meta populations with higher dispersal. metapopulations 23.2 illustrates results from from one particular model. Repeating Repeating this Figure 23.2 process for for aa number of of different different models models indicated indicated some some general general behaviors. behaviors. The higher the dispersal levels, the more trajectories behaved behaved like a diffusion diffusion process. process. Global Global dispersal levels of of at least 2 to 5 % were were generally generally high high enough enough to to result in in diffusion-like diffusion-like behavior behavior within within aa short short time time frame. Note Note that that local localized dispersal has the effect of of lowering lowering the effective effective dispersal rates. The The higher higher the populations in the amount amount of of temporal temporal covariance covariance between between local populations in terms terms of of their their yearly growth growth rates, the more the trajectories behaved behaved like a diffusion diffusion process. The simulations simulations were were done done with with the local population population sizes within within the equilib equilibrium set of population distributions of local population distributions ~ indeed the theory theory is predicated predicated on the local populations populations being near equilibrium. equilibrium. For metapopulations metapopulations with with 2 to 55% % dispersal, dispersal, the the local local populations populations equilibrated equilibrated fairly fairly quickly quickly starting starting from from all all populations with with equal numbers. numbers. However, However, at very very low low dispersal, dispersal, equili equililocal populations bration bration took took thousands thousands of of time time steps. steps. This This suggests suggests that that the assumption assumption of of equilibrium equilibrium should should be be viewed viewed cautiously cautiously for for metapopulations metapopulations that that have have very very low low dispersal dispersal rates rates between between local local populations. populations. =
0 . 1 % d i dispersal spersal 0.1%
0
11% % ddispersal ispersal
0
-0.01 -0.01
-0.01 -0.01
-0.02 -0.02
-0.02 -0.02
-0.02 -0.02
~ --0.03 0.03
-0.03 -0.03
-0.03 -0.03
-0.04 -0.04
-0.04 -0.04
-0.05 -0.05
-0.05 -0.05 00
2: "-
-~ if % 0
0 0
50 50
100 100
150 150
200 200
0.05 0.05 0.04 0.04
0.03 0.03
0.03 0.03
0.03 0.03
0.02 0.02
0.02 0.02
0.02 0.02
100 100
150 150
200 200
0.01 0
50 50
100 100
150 150
200 200
0.01 0.01
2
2
11.5 .5
1.5 1.5
1
1
0.5 0.5
0.5 05
0.5
0
0
1.5 1.5
'" "
�
100 100
0.05 0.05
2I
o c
50 50
-0.05 ' -0.05 200 00 200
0.04 0.04
50 50
0
50 50
100 100
150 150
200 200
' "~--
-0.04 -0.04 ' 150 150
0.05 0.05
0
�
-0.01 -0.01
_
0.04 0.04
0.01
...
_
5% 5 % ddispersal ispersal
0
0
50 50
100 100
150 150
200 200
00
'
'
50 50
100 100
150 150
200 200
50 50
100 100
150 150
200 200
- - pp=o.o5 1I- o.05 1I
0 0
50 50
100 100
150 150
200 200
t
Fig. Illustration the performance the Fig. 23.2 23.2 Illustration of of the performance of of aa diffusion diffusion approximation approximation for for modeling modeling the behavior with 50 50 local populations 1 , 11,, or 5% behavior of a metapopulation metapopulation with populations and and uniform uniform 0. 0.1, 5% yearly ddispersal. ispersal. The iffusion approximation frame when The ddiffusion approximation performs performs well well for for aa given given time time frame when JLm(t) /t)logM(t)/M(O) and I~m(t) = = (1 (1/t)logM(t)/M(0) and O"ii,(t) Cr2m(t)= = (l ( l /it) t ) var var [logM(t)/M(O)] [IogM(t)/M(O)] are are constants constants over over that that time time frame frame and when when log M(t)/M(O) is normal. normal.
23. ANALYSIS FOR FOR ENDANGERED 23. VIABILITY VIABILITYANALYSIS ENDANGERED METAPOPULATIONS METAPOPULATIONS
23.4 23.4
515 575
ESTIMATING ESTIMATING THE THE PARAMETERS PARAMETERS Maximum Maximum likelihood likelihood estimates estimates of of fL i~m and a;' Cr2mcan can be be calculated calculated using using the the dif difm and Denote the series as fusion approximation fusion approximation for for log log M(t). M(t). Denote the observed observed time time series as M M = = M(O), M(0), M(1),), M(2), M ( 2 ) ,.. . .., , M(n). If If we we approximate approximate log log M(t) M(t) as as aa diffusion diffusion process, process, the the M(l 1 M ) is likelihood likelihood function function L(fL L(la,m m,, a;' o'2]M) is given by by the the product product of of the the probability probability M(t + function function distributions distributions for for the the transitions transitions from from log log M(t) M(t) to to log log M(t + 11),), which which is 1, over Eq. (7) with Eq. (7) with 'T~ = = 1, over tt = = 0, 0, 1, 1, 2, 2 , ... .. ,. , n. n. Thus Thus the the log log likelihood likelihood function function is is log
L(bl,m,, a� (r2 I[ M) M) = = - ((nn / 2) (2~rcr2m) L(fLm 2) log (21Ta�)
�
11 n - 2cr2�m ~ [10g(M(i) /M(i - 1 ) ) 2a ii=1 [log(M(i)/M(i - 1))
-
-
2
fLml ~m] 2
(23.8) (23.8)
Maximum likelihood estimates Maximum likelihood estimates are are obtained obtained by by solving solving for for fL tXm and a;', (r2m,which which m and maximize Eqn. (8), (8), maximize A = fLm ~m --
_
( ) 1 � [ 1 ( M( i ) ) ] fLm -;; i� M( i 1 ) 1 M( n ) log ;; -~ \ MM(O) (O) ]
A2 a6"2= og m ni=l log -
Mi;
_
1/ -
-
A
2
(23.9 (23.9))
Note n rather than than n. Note that that the the unbiased unbiased estimator estimator for for a;' Cr2mdivide by by ((n - 11)) rather n. The The estimates of variance from and a;' ~2 are are analogous analogous to to the the estimates of mean mean and and variance from n n sam samfl~mm and ples ples from from aa normal normal distribution, distribution, and and confidence confidence intervals intervals on on fL ~m and a;' cr2 are are m and analogous: analogous:
(~m -- G/2,n- 1X/' ~r2mIn, ~m q- G/2,n- 1V' ~2 In ) (nor m^21 X2,n -1 ,norm^2 i X 2 _ e~,n-1 )
(23.10) (23. 10)
where where tm G,qq iiss the the critical critical value value ooff aa tt distribution distribution aatt P = = ex ~ and and q degrees degrees of of freedom and and X�,q • the critical value value of of a x • 2 distribution distribution at at P = = ex cx and and q freedom is the 1991 ) for degrees of freedom. See al. ((1991) degrees of freedom. See Dennis Dennis et et al. for aa more more in-depth in-depth discussion discussion of of maximum maximum likelihood likelihood estimates estimates for for diffusion diffusion processes. processes. Following Following Dennis Dennis et et al.'s al.'s monograph, monograph, parameter parameter estimation estimation based based on on the the diffusion diffusion approxi approximation mation has has been been widely widely used used for for the the analysis analysis of of single single population population trajectories. trajectories. For For aa discussion discussion of of parameter parameter estimation estimation that that is is not not based based on on the the diffusion diffusion approximation, 1985). approximation, the the reader reader is is referred referred to to Heyde Heyde and and Cohen Cohen ((1985). Maximum Maximum likelihood likelihood estimates estimates assume assume that that the the metapopulation metapopulation has has reached reached aa stochastic stochastic equilibrium equilibrium and and thus thus that that the the diffusion diffusion approximation approximation is is reasonable. reasonable. When When exploring exploring these these methods methods using using simulations, simulations, it it is is important important to equilibrate, after simulation with to allow allow the the system system to to equilibrate, after starting starting the the simulation with something something peculiar like all local populations at the the same size. Equilibruim Equilibruim can can be moni monipeculiar populations at tored tored by by waiting waiting for for the the variance variance of of (log(NAt)) (log(Ni(t)) - 10g[mean(Nj(t))]) log[mean(Ni(t))]) to to stabilize. stabilize. In In simulations simulations done done for for this this chapter, chapter, the the distribution distribution stabilized stabilized relatively relatively quickly dispersal is quickly when when dispersal dispersal was was nonzero. nonzero. If If dispersal is zero, zero, however, however, the the distri distribution ) - 10g[mean(N;(t) )] ) bution never never stabilizes stabilizes and and the the variance variance of of (log(N;(t) (log(Ni(t))log[mean(Ni(t))]) increases wants to to increases continually. continually. For For an an actual actual metapopulation, metapopulation, for for which one wants
576 576
E.E. E.E. HOLMES HOLMES AND B.X. B.X. SEMMENS SEMMENS
conduct conduct aa PYA, PVA, it it is is also also critical critical to to test test the the appropriateness appropriateness of of the the diffusion diffusion approximation for for one's one's time time series series data. data. Dennis Dennis et et al. al. ((1991) and Morris Morris and and approximation 1 99 1 ) and Doak Doak (2002) (2002) reviewed reviewed how how to to do do this, this, which which is is based based on on diagnostic diagnostic proced procedures for for evaluating evaluating the the appropriateness appropriateness of of linear linear models. models. ures Parameter Bias Parameter Bias
The The estimators estimators are are unbiased unbiased maximum maximum likelihood likelihood estimators estimators for for the the diffu diffusion approximation, approximation, X(t). X(t). It It is is important important to to understand understand whether whether and and how how these these sion estimates population estimates are are biased biased when when working working with with short short time time series series of of meta metapopulation trajectories, trajectories, M(t), as as opposed opposed to to an an actual actual diffusion diffusion process. process. In In particular, particular, iT;' 82 is is certain certain to to be be biased biased to to some some degree, degree, as as it it reli.:s relics on on the the diffusion diffusion approximation approximation holding holding for for T~ = 1i in in log log M(t + 'T)/M(t), ~)/M(t), regardless regardless of of the the length length of of the the time time series series used used for for estimation. estimation. This This is is not not the the case case for for ,J.,m, Igm,which which is is also also an an unbiased unbiased predictor predictor for for M(t) given given aa long long time time series series (Heyde (Heyde and and Cohen, Cohen, 1985). 1985). To To numerically numerically explore explore parameter parameter bias bias from from short short time time series, series, simulations simulations were were used used to to look look at at the the difference difference between between ,J.,m lkm and and iT;' 82 from from aa 20-yr 20-yr time time series series versus versus their their true true values values JLm ~m and and a;'. Cr2m.An An example example metapopulation metapopulation of of 50 50 local local sites sites was was simulated simulated with with global global dispersal dispersal and and correlated correlated local local growth growth rates, rates, Zi(t), zi(t), drawn drawn yearly yearly from from aa normal normal distribution distribution with with mean mean = = JL ~i,i, variance variance = = , &, and and covariance "' between covariance of of 0.2 0.2*& between any any two two local local growth growth rates rates Two Two versions versions of of the the simulation simulation were were run: run: one one to to model model uniform uniform site site quality quality (spatially (spatially uniform uniform JLi 13,,i = -- -0.05) - - 0 . 0 5 ) and and one one to to model model highly highly variable variable site site quality quality (spatially (spatially variable variable JL;'s). IXi's). To To explore explore biases biases over over aa range range of of different different dispersal dispersal and and variability variability levels, levels, models models were . 1 and % per were run run with with dispersal dispersal between between 00.1 and 55% per year year and and local local variability, variability, , &, between 0.1 These parameters parameters translated translated to population level level rates, rates, between 0.1 and and 0.5. 0.5. These to meta metapopulation in the to --00.05 metapopulation level level variability, variability, a;', in tXm, in the range range of of 0.01 0.01 to . 0 5 and and metapopulation (r2m,in JLm, the to 0.08. For each each dispersal dispersal and local variability variability pair, pair, 1000 1 000 the range range of of 0.001 0.001 to 0.08. For and local replicate metapopulation trajectories were simulated, each each with an initial replicate metapopulation trajectories were simulated, with an initial distridistri bution of local local population sizes selected selected randomly randomly from from the the equilibrium equilibrium set. bution of population sizes The ,J.,m and over the the dispersal and local vari The mean mean difference difference between between }~m and JLm ~m over dispersal and local variability parameter space space was was very very low, both uniform uniform and variable ability parameter low, -
o o m
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11 55 1100 115 5 20 20 25 25 30 30 35 35 40 40 45 45
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i! I
20 25 20 25 30 35 30 35 Unit on on X, A Rank of of Influence Influence of of Habitat Habitat Unit Rank
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Fig. 3.1 Fig. 223.7 Relationship between between the the influence influence of of aa given given habitat habitat unit unit on on the the metapopulation metapopulation k" Relationship and the the average average density density in in that that habitat habitat unit. unit. One One hundred hundred 77 •x 77 metapopulations meta populations with with spatially spatially and variable rates (some targets) were variable dispersal dispersal rates (some sites sites dispersal dispersal sinks sinks and and others others targets) were generated generated randomly randomly in in each of of three three classes: classes: (1) (1 ) spatially spatially uniform uniform growth growth rates and global global dispersal, dispersal, (2) (2) spatially spatially variable variable each rates and growth with neighborhood neighborhood dispersal, dispersal, and and (3) (3) spatially spatially variable variable growth with directional directional growth rates rates with growth rates rates with neighborhood dispersal dispersal to to the the SS and and EE two two neighbors neighbors only. only. The The xx axis axis shows shows the the rank rank in in terms terms of of neighborhood cfA/dj.L, and and the the yy axis axis shows shows aa box box plot plot of of the the distribution distribution of of density density ranks ranks for for sites sites with with aa given given clk/d~, cfA/dj.L rank across all 100 1 00 models models in in each each class. class. Thus Thus the the box box plot plot at at xx == 11 shows shows the the distribution distribution dk/dp, rank across all of ranks ranks for for the the sites sites with with the the highest highest dX/dl~ cfA/dj.L in in each each model. model. The The line line in in each each box box shows shows the the median median of density rank rank for for the the sites sites with with aa given given dX/d~ cfA/dj.L rank, rank, the the box box encloses encloses 50% 50% of of the the ranks, ranks, and and the the density whiskers whiskers show show the the range range from from all all 100 1 00 randomly randomly generated generated models. models.
23. FOR ENDANGERED 23. VIABILITY VIABILITYANALYSIS ANALYSIS FOR ENDANGERED METAPOPULATIONS METAPOPULATIONS
593
One One application application of this would would be to estimate where where negative impacts would would lead lead to to the the greatest greatest decrease decrease in in 'A, k, thus thus suggesting suggesting where where protection protection in in most most critical. critical. It would would also suggest suggest where where local improvements would would be most effect effective for a given increase in the local growth rate. rate. However, in actual manage management ment situations situations where where improvements improvements are are being being sited, sited, one one is is generally generally trying trying to to maximize bang per maximize the the ""bang per buck," d'A/d$ dkJd$ = d'A/dlLj dkj/dl~j X • dlL/d$. dl~Jd$. The The cost, cost, d$, as, is is the the actual monetary monetary cost or some combination combination of monetary, logistical, logistical, and and polit political ical costs costs and and dlL/d$ dlxJd$ is is the the cost cost of of aa unit unit improvement improvement to to aa unit unit of of habitat habitat j. j. Thus Thus d'A/dlL dkj/dl~ is is one one part part of of the the equation, equation, and and the the other other part, part, the the cost cost of of aa unit unit improvement in different different habitats, would would have to come from from a specific analy analysis of the costs and estimated estimated effects of of management management actions on different different local populations. populations. =
Example Example Using the the Snake Snake River River ESU
The The overall level of salmon salmon dispersal dispersal between between and and among among stocks stocks within within this ESU is known known to be fairly low low and and spatially localized (Mathews (Mathews and and Waples, 11991; Quinn, 11993). addition, there there is high variability in the the Waples, 99 1 ; Quinn, 99 3 ) . In addition, habitat habitat quality between between stocks, stocks, with with some stocks relatively relatively pristine and and pro protected tected within within wilderness wilderness areas, areas, whereas whereas others others are are exposed exposed to to high high and and mul multiple tiple impacts impacts (such (such as as stream stream degradation degradation and and disturbance, disturbance, pollution, pollution, in-stream in-stream harvest, harvest, and and irrigation irrigation impacts). Figure 23.8 23.8 (top) shows shows the the distribution distribution of of average average normed normed redds redds per per mile mile for for 50 50 Snake Snake river river spring! spring/ summer 9 80 and 995, the redds summer chinook chinook stocks. stocks. For For each year between between 11980 and 11995, reddsper-mile count count for for each stock stock was was divided by the the maximum maximum count count among among the the 50 stocks stocks in in that that year. year. The The average average over over the the 1166 yr yr was was then then used used as as an an estimate estimate of of the average normed normed redds redds per mile. The The long-tailed distribution distribution is the expectation expectation from from theory theory given given low low dispersal dispersal and and high high variability variability in in stock stock habitat habitat quality. Estimation of the average normed normed redds redds per per mile was was repeated repeated using a var variety of different different time periods. Regardless of the time period period or or number number of of years used used for for averaging, averaging, six six stocks stocks consistently consistently appeared appeared among among the the top top five five stocks stocks with Johnson Cr., with the the highest highest density density of of redds: redds: Johnson Cr., Poverty Poverty Cr., Cr., and and Secesh Secesh R. R. in in the subbasin, the south south fork fork of of the the Salmon Salmon R., R., the the Lostine Lostine R. R. in in the the Grande Grande Ronde Ronde subbasin, Marsh Marsh Cr. Cr. in in the the middle middle fork fork of of the the Salmon Salmon R., and and the the Imnaha Imnaha R. R. Perhaps Perhaps not not surprisingly, surprisingly, all all of of these these are are in in relatively relatively low low impacted impacted regions regions of of the the ESU. ESU. At At aa subbasin level, south fork fork of level, the the overall overall highest highest redd redd density density was was in the the south of the the Salmon river where where summer-run summer-run chinook chinook primarily occur occur (Fig. 23.8, 23.8, bottom). bottom). The The other other regions regions are are primarily primarily spring-run spring-run chinook. chinook. The The south south fork fork of of the the Salmon river is relatively pristine and and few hatchery hatchery fish have been released into into this this subbasin; subbasin; the the stocks stocks presumably have have experienced experienced relatively relatively low low inter interbreeding breeding with with hatchery-reared hatchery-reared stocks. In In addition, addition, the the later later run run timing timing may may somehow somehow be be associated associated with with less less straying, straying, lower lower harvest, harvest, or or lower lower hydropower hydropower impacts. This This analysis analysis predicts predicts that that the the 'Ak of of the the Snake river river spring/summer spring/summer chinook chinook ESU would would be most most sensitive to to changes changes to to the the summer-run summer-run stocks stocks in the the south south fork fork of of the the Salmon Salmon river river and and to to the the spring-run spring-run stocks, stocks, the the Lostine Lostine R., Imnaha Imnaha River, River, and and Marsh Marsh Creek Creek and and should should be be protected protected preferentially preferentially from from impacts. imag impacts. This This can can be be counterintuitive counterintuitive in in some situations. situations. For example, example, imagine ine making choices about about where where to to allow allow aa limited limited catch-and-release catch-and-release sport sport
E.E. E.E. HOLMES HOLMES AND AND B.X. B.X. SEMMENS SEMMENS
5594 94
Snake River sprlsum chinook
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.8
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Fig. 23.8 23.8 Distribution Distribution of of densities densities of of redds redds in in the the Snake Snake river river spring/summer spring/summer chinook chinook ESU ESU at at aa stock stock and and subbasin subbasin level. level. The The average average normed normed redds redds densities densities (top) (top) are are shown shown for for the the 50 50 stocks with 980-1 995 data (the with 11980-1995 (the years were chosen chosen to maximum maximum the number number of of stocks with data). 6 yr data). For For each each stock stock the the normed normed redd redd density density was was averaged averaged over over the the 116 yr to to get get an an estimate estimate of the normed average density. In the lower plot, relative average densities over all stocks within within different different basins basins are are shown shown (with (with the the number number of of stocks stocks in in each each basin basin shown shown above above the the bars). bars). The The basin designations are GR, Grande Ronde; I, Imnaha; SFS, SFS,south fork salmon; MFS, MFS, middle fork salmon; salmon; US, US, upper upper salmon; salmon; C, C, Clearwater. Clearwater. Redds Redds due due to to hatchery hatchery fish fish released released into into stocks stocks were were removed removed before before doing doing these these analyses, analyses, as as the the density density will will be be artificially artificially high high simply simply due due to to hatch hatchery could not ery fish fish releases. releases. This This correction correction could not be be done done for for the the upper upper salmon salmon or or Clearwater Clearwater regions regions because the fraction of of spawners that are hatchery strays were were unknown; however, the hatch hatchery ery releases releases are are very very high high in in these these basins basins and and thus thus the the corrected corrected relative relative densities densities would would be be much much lower lower than than shown. shown.
fishery. Sites with the highest density would seem to be the prime prime candidates, whereas the analysis of d"AldJL dk/d~t indicates just the opposite. opposite. In terms of deter determining where to direct improvements, the d"A/dJL dk/d~ suggests that these pristine sites are where a given dJL d~ would produce the greatest metapopulation metapopulation "A; k; however, the regions dk/d~ is the highest highest are not not necessarily the regions where where d"A/dJL regions where f.J., i~ is improved improved most easily. Indeed a given given unit of improvement improvement regions may be more difficult in pristine sites. Choosing Choosing where to direct stock improvements improvements requires consideration consideration of the cost and difficulty of a given df.J., d~ for different stocks in combination combination with the estimate of the sensitivity of "A to to local local changes. changes.
VIABILITYANALYSIS ANALYSIS FOR ENDANGERED METAPOPULATIONS 23. VIABILITY FOR ENDANGERED
23. 11 23.11
595 595
POPULATION IN PRACTICE POPULATION VIABILITY VIABILITY ANALYSIS ANALYSIS IN PRACTICE The The purpose purpose of of this this chapter chapter is is to to present present aa theoretical theoretical framework framework for for metapopulation metapopulation PYA PVA using using time time series series data data and and diffusion diffusion approximations. approximations. These These methods populations. The methods are are then then illustrated illustrated using using data data from from two two salmon salmon meta metapopulations. The salmon salmon analyses analyses are are intended intended as as an an example example of of how how to to calculate calculate the the diffusion diffusion parameters parameters and and metrics. metrics. An An actual actual PYA PVA must must grapple grapple with with other other important important issues issues that that are are outside outside the the scope scope of of this this chapter, chapter, but but which which anyone anyone contemplat contemplating ing an an actual actual PYA PVA must must be be aware. aware. Morris Morris and and Doak (2002) (2002) gave gave aa review review of of the the criticisms criticisms and and caveats caveats surrounding surrounding the the use use of of PYA PVA and and outlined outlined general general recom recommendations mendations and and cautions when when conducting conducting aa PYA. PVA. In In the the context context of of diffusion diffusion approximation approximation methods methods in in particular, particular, Holmes (2004) (2004) outlined outlined an an approach approach using using matrix matrix models models to to conduct conduct sensitivity sensitivity analyses analyses in in order order to to choose choose among among different parameterization methods different parameterization methods and and metrics metrics for for aa specific specific PYA PVA application. application. One One of of the the issues issues that that is is especially especially pertinent pertinent for for our our chapter chapter is is the the issue issue of of variability variability in in estimated estimated risk risk metrics. metrics. A A number number of of recent recent PYA PVA cross-validations cross-validations using using actual actual data data on on aa large large number number of of different different populations populations have have shown shown that that careful careful PYA PVA analyses analyses give give unbiased unbiased risk risk estimates estimates (Brook (Brook et et aI., al., 2000; 2000; Holmes Holmes and and Fagan, Fagan, 2002; 2002; Fagan Fagan et et aI., al., 2003). 2003). Although Although this this is is very very encouraging, encouraging, aa dif difficult ficult issue issue is is the the high high inherent variability variability associated associated with with estimated estimated probabil probabilities ities (such (such as as probability probability of of extinction), extinction), even even though though they they may may be be unbiased unbiased (Ludwig, 996, 11999; 999; Fieberg (Ludwig, 11996, Fieberg and and Ellner, Ellner, 2000; 2000; Holmes, Holmes, 2001 2001;; Ellner Ellner et et aI., al., 2002). 2002). How How to to properly properly use use risk risk metrics metrics that that have have high high variability variability is is currently currently being don't use being debated debated within within the the field field with with arguments arguments ranging ranging from from ""don't use them" them" (Ludwig, 996, 11999; 999; Fieberg use to (Ludwig, 11996, Fieberg and and Ellner, Ellner, 2000), 2000), to to ""use to estimate estimate risks risks within within collections collections of of populations" populations" (Fagan (Fagan et et aI., al., 2001 2001;; Holmes Holmes and and Fagan, Fagan, 2002), 2002), to to ""use use where Coulson et aI., 2001 where data data are are extensive extensive and and high high quality" quality" ((Coulson et al., 2001),), to to "PYA "PVA metrics metrics based based on on data, data, even even if if variable, variable, are are better better than than the the alternatives" alternatives" (Brook (Brook et et aI., al., 2002). 2002). An An encouraging encouraging aspect aspect of of diffusion diffusion approximation approximation methods methods is is that that cross-validations cross-validations using using real real time time series series data data have have indicated indicated that that the the uncertainty uncertainty in the estimated metrics appears to be characterized properly (Holmes and Fagan, Fagan, 2002). 2002). Nonetheless, Nonetheless, how how to to use use and and present present metrics metrics with with high high variability, variability, albeit albeit well well characterized, characterized, is not not an easy easy question question to answer. answer. Presentation Presentation of of 1100(1-0~)% 00( 1 - a ) % is is an an oft-used oft-used approach, approach, but but experience experience in in the the forum forum of of salmon salmon recovery recovery planning planning in in the the Pacific Pacific Northwest Northwest has has shown shown that that it it is is easy easy to to misin misinterpret % confidence terpret confidence confidence intervals. intervals. For For example, example, it it is is easy easy to to interpret interpret 95 95% confidence .0 as intervals intervals for for A ~ that that overlap 11.0 as an an indication indication that that data data are are equivocal as as to to whether whether the the population population is is declining or or increasing, whereas there there may may be be consid considerable erable data data support support for for aa declining declining population. Graphic Graphic presentations presentations of of data data support support for for different different risk risk levels levels have have been been more more compelling compelling and and informative, informative, although although translating translating levels levels of of data data support support into into numbers that that policy policy makers makers can use use to to take take uncertainty uncertainty into into account account in in policy decisions has been been challenging. challenging.
23. 2 3 . 1122
DISCUSSION DISCUSSION This This chapter chapter focused focused on on the the calculation calculation of of metapopulation metapopulation PYA PVA metrics; metrics; how however, ever, there there are are other other more more general general PYA PVA insights insights from from an an examination examination of of stochastic stochastic meta populations and and of this specific metapopulations of this specific class class of of declining declining density-independent density-independent
596 .$96
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metapopulations. pop metapopulations. First, by definition the the trajectory trajectory of a stochastic stochastic meta metapoppopulation trajectory ulation is is subject subject to to random random processes processes and and thus thus the the meta metapopulation trajectory observed in any one snippet of time is unlikely to to capture capture the long-term dynamics. The shorter the time frame, the farther farther the observed trend trend is likely to be from the long-term trend. trend. Thus the trends trends in any two two adjacent adjacent time periods periods are unlikely to to be identical, and and the difference indicates not not necessarily a change in the underlying rate of decline, but but can be due simply to chance. The The variability of of observed observed rates rates of of decline decline can can be be estimated estimated from from the the level level of of the the variability variability driving the long-term dynamics, and and thus thus statistical tests performed performed to to deter determine the likelihood that apparent change in trend that an apparent trend occurred due to to the stochastic nature of the process rather rather than than an an underlying change in conditions. conditions. Second, the local populations populations within within a metapopulation metapopulation are linked and experi experience the same long-term growth growth rates, regardless of of the underlying difference difference in local population "). population conditions conditions (i.e., whether they are "sources" "sources" or "sinks "sinks"). However, However, measured measured over over aa short short time time period, period, there there will will bbee differences differences iinn the the observed local population population trends due to chance chance and local conditions. conditions. This means that that over a given time period, local populations populations will appear to be declining at different different rates, but this is not an indication the long-term trends trends and not not necessarily related to to local conditions conditions being better or or worse worse than than other other areas. areas. That That the the long-term long-term trends trends of of the the individual individual local local populations populations are are the the same as the metapopulation metapopulation has a direct impact on PYA PVA for for local populations populations within within a metapopulation. The rate of decline observed among among the different local populations populations will differ, as will the apparent apparent level of variability in the local time series. Thus Thus if an individual viability analysis is done done using parameters parameters estimated from from local population population time series alone, it will appear that that there is tremendous tremendous variability among among the local populations populations risk levels when in fact their long-term risks are similar. When When looking looking at the long-term risks, use of metapopulation metapopulation level parameters parameters leads to better estimates of the long-term local population population risks. Short-term risks, however, are still strongly influenced by local conditions. conditions. Clearly estimates of both both short-term and long-term risks are are needed needed to to capture capture the the whole whole viability viability picture picture for for aa metapopulation. metapopulation. Although populations modeled here Although local populations populations within within the type of meta metapopulations will be eventually repopulated repopulated by dispersal if they undergo undergo extreme declines, the resulting loss of genetic diversity leads to to a gradual gradual erosion of the genetic health of of the the metapopulation. metapopulation. Indeed this this has happened for for salmon salmon species species throughout throughout the the Pacific Pacific Northwest. Northwest. Recovery planning planning for endangered endangered and threatened threatened species typically requires determining where to put put the most most effort. effort. Rarely is it the case that that maximal effort effort can be applied everywhere. Using the stochastic stochastic metapopulation metapopulation model, a sensitivity analysis was used to look for for local characteristics characteristics that that predict where where local changes would produce produce the biggest change in the metapopulation metapopulation growth growth rate. Interestingly, local density (not absolute numbers) numbers) was a strong predictor of where a unit change in local growth growth rates led to to the largest metapopulation metapopulation growth growth rate. This relationship relationship was observed even in simula simulations tions with dispersal sources and and targets targets and and strongly strongly directional directional dispersal, although although it will break break down down when when dispersal is strictly unidirectional. unidirectional. Determining which local populations populations are best best suited for restoration restoration efforts also requires assessing assessing the the feasibility, cost, cost, and and acceptance of restoration restoration efforts. Indeed Indeed when when it it comes comes to to actually actually implementing implementing recovery recovery actions, actions, optimizing optimizing
23. FOR ENDANGERED ETAPOPULATIONS 23. VIABILITY VIABILITYANALYSIS ANALYSIS FOR ENDANGERED M METAPOPULATIONS
597 591
the efficiency of effort effort in terms affecting recovery requires solving a complex complex function of biological, economic, economic, and political information. information. However, under underfunction standing the population population dynamics of the species of concern concern and gaining insight regarding regarding how the demography demography of the species will respond respond to alternative management management actions are fundamental fundamental and primary components components of this conser conservation equation. equation.
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682 682
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INDEX INDEX
A A
effects, 200 variance, 1160 60 alternative stable equilibria, 112 2 strategies, 141 strategies, American mink (Mustela vison), 520, 522 population population size size and extinction risk, 527 Ochotona princeps), 1100, 00, American pika ((Ochotona 1132, 32, 503, 5 17 517 75 ancestral process, 1175 ancient lineages in a metapopulation, 88 metapopulation, 1188 androdioecy, 245 anther smut, 473-4 473-4 anthropogenic threats, 566 assignment test, 371 assortative mating coefficient, 82 coefficient, 377, 3382
abundance distribution, 36 distribution, 1136 adaptation, 8 , 223 adaptation, 118, in subdivided 65 subdivided populations, populations, 1165 to local conditions, conditions, 295 to marginal habitats, habitats, 409 to sink habitats, habitats, 406, 409-10 409-10 adaptive landscapes, 118, 8 , 280 plasticity, 263 additive additive genetic effects, 264 genetic variance, 203, 205-6, 13, 205-6, 208, 2213, 264, 348-9 348-9 age at maturity, 246 at reproduction, reproduction, 246 age-structure, 252, 399 age-structured population, 02 population, 1102 aggregation, 62, 64 A land Islands, 74, 492, 500-1, 506 Aland 500-1,506 Allee effect, 113, 3 , 87, 90, 346, 346, 458 alleles average effects of, 208 allelic diversity, 349
B B
badger, 28 Bateson-Dobzhansky-Muller model, 279, 296 Bay checkerspot butterfly, butterfly, see Euphydryas editha Bayesian approach, 1184 84 approach, 86 approach, hierarchical, 378, 383, 3386 approach, 84 approach, potential potential problems, 3384
683 683
684 684
Continued) Bayesian ((Continued) inference, 374 model choice, 380 BDM model, 279, 296 296 multilocus generalization of, 281 bet-hedging strategy, 243 Bicyclus anynana, 359 biodiversity, 541 black hole sink habitat, 158 adaptation adaptation to, 405 Cynomys black-tailed prairie prairie dog ((Cynomys 1 7, 5 19 ludovicianus), 5 517, 519 boundary length minimization problem, 556-7 556-7 breeder's equation, 203 breeding dispersal, 528 phenology, 4 11 411 value, 201 , 208 201,208 bubonic plague, 435, 438-40 438-40 Burramys parvus, 532
C C Carlina vulgaris, 246 carrying capacity, 389 Centaurea jacea, 459 chaotic fluctuations, 346 childhood diseases, 428 chinook salmon meta population, 567 metapopulation, clade disparity, 289 Clarkia concinna, concinna, 458 classic meta population metapopulation dynamics, 506 model, 9 theory, 12, 83 small mammal, 5 17 517 climate change, 507-9 507-9 coalescence approach, 7, 368 approach, 117, in metapopulations, 186 in panmictic populations, 1175 75 79 in two-sex diploid populations, 1179 times, 1176 76 coalescent inference inference analytical methods, 1182 82 computational method, 1183 83 iin n metapopulations, 1196 96 76 interval, 1176 77 standard model, 1177 coalescent predictions in meta populations, 1194 94 metapopulations, coalescent process, 1175, 75, 1178 78 at a multisite genetic locus, 1178 78
INDEX making inferences with the, 1182 82 simulations, 193 standard, 1175-6, 75-6, 1192 92 theory, 1174 74 coevolution in a metacommunity, 270 of dispersal and habitat specialization, 326 of phenotype and context, 259-60 259-60 coevolving species, 270 coexistence, 146-7, 146-7, 149 of multiple species, 1134 34 collecting phase, 1189-93 8 9-93 colonization, 85, 87, 247, 367, 370, 3385, 85, 505 dataset, 1116 16 density-dependent effects on, 376 distance effects effects on, 464 events, 3382 82 evolutionary effects of, 275 rate, 92, 1130 30 related ttoo connectivity, 1115 15 colonization and extinction processes, 82 rates, rates, 78 colonization-competition trade-off, 146, 149 colonizer syndrome, 238, 25 2511 colonizing groups, composition of, 378 common lizard, 3313, 1 3, 3316, 1 6 , 3318, 1 8 , 323-5 323-5 community heritability, 271 estimate of, 272 competition, 251 competitive ability, 148, 272 interactions as forms of IGEs, 269 complementarity, 543 connectivity, 25, 1100, 00, 1102, 02, 108, 1114, 14, 527, 550, 552, 563 asymmetrical, 28 in a metacommunity, 1138 38 measure of, 1111,498 1 1, 498 of networks, 501 conservation, 8, 5 11 511 biology, 20, 338, 541 conspecific attraction, 1111,315, 1 1 , 3 1 5, 5 1 9, 529, 519, 5 3 1 , 534 531,534 context evolving, 263 kinds of, 262 variance in, 262 continuum models, 50 core-satellite distributions, 90 correlated landscape, 424 random walk, 1133
INDEX INDEX corridors, 144 coupled-map lattice, 48, 100 critical community size, size, 423, 429 CSI method, 385 cyclic populations, populations, 530
D D Daphnia, 0 1 , 360 Daphnia, 1101,360 decision theory, 127 decline long-term geometric rate of, 577 rate of, 596 declining-population declining-population paradigm, 339, 365 deleterious 62 deleterious alleles, alleles, 1162 fixation of, 353 deleterious deleterious mutations, mutations, 327, 327, 350, 353-4, 353-4, 363 accumulation accumulation of, 356 demographic rescue, 358 stochasticity, stochasticity, 84, 339-40, 339-40, 344, 346 variance, 340 density dependence, 267, 338 density-dependent density-dependent dispersal, 5 1 , 3 14, 329 dispersal, 2251,314, immigration, immigration, 533 DIC, 3381 81 diffusion diffusion coefficient, 886 6 modeling, 461 approximation approximation approach, 572 approach, practical implications, 567 direct genetic effects, 272 disease colonization colonization event, 480 colonization colonization rate of, 482 decline, 486 dynamics, global coupling, 4 19 419 effect o onn population population growth, 475 eradication, 442 extinction, 482 impact on population population extinction, extinction, 475 incidence, 476 local abundance, 476 persistence, persistence, 423 prevalence, 476, 486-7 486-7 regional abundance, 476 resistance, resistance, 350, 473, 487 spread of, 488 transmission, transmission, 356, 473, 473, 483, 487 dispersal, dispersal, see see also also migration, 230, 250, 307, 389 balanced, 395, 402 breeding, 528
685 61~$ causes of evolution, 309 condition-dependent, condition-dependent, 307, 322 cost and benefits, benefits, 234, 322 curve, curve, 460 density-dependent, 25 1 , 3 1 4-5, 329 251,314-5, directed, 5 30 530 effects of, 3397, 97, 40 4011 ES rate, 2 3 1 , 233, 249-50 231,233,249-50 evolution of, 233, 255 exploratory exploratory movement, 534 forces selecting for, for, 230 functions, 3313, 1 3 , 462, 14 462, 5514 habitat 10 habitat heterogeneity, heterogeneity, 3310 iin n meta populations, 230, 528 metapopulations, inbreeding, 3 13 313 kernel, 52, 85-6 85-6 kernel, Laplace, 379 landscape structure, 3312 12 long-distance, 462 morphs, 3 19 319 mortality due to predation, predation, 529 natal and breeding, 309 natural natural selection selection on, 402 negative density dependence, 329 one-way, 394 parental control, 323 passive, 86, 402, 402, 405 pattern, 402, 402, 409 physiological physiological and behavioral control of, 320 see see plant plant predation, 12, 323 predation, 3312, presaturation, presaturation, 308 propensity, 234, 234, 235, 403 propensity, evolution of, 234 proximate control 19 control of, 3319 rate, 248, 390, 394, 409 rate, habitat-specific, 3 11 311 rate, optimal, 253 rate, plasticity of, 403 saturation, saturation, 308 social factors, 3 14 314 species interactions, interactions, 332 state-dependent, 1 3 , 3318-21 1 8-21 state-dependent, 3313, stepping-stone, stepping-stone, 534 strategy, conditional, conditional, 253 success, 28-30, 28-30, 32 swamping effect of, 406 symmetric, 397 threshold, 30 distribution distribution cauchy, 462 gaussian, 462 negative negative exponential, exponential, 462
686 686
disturbance, disturbance, 145 effects of, 250 effect on dispersal rate evolution, 249 249 rate, 144 diversification dynamics of, 283 patterns patterns of, 298 phase, 286 time homogeneous, 289 diversity, 140, 149 dominance, 1165 65 coefficients, 62 coefficients, 1162 effects, 362 drift load, 69 load, 1169 dynamic probability method, 554, 556 problem, 550 dynamic theory of island biogeography, 6-9, 83
E E
ecological niches, 408 evolutionary dynamics of, 408 ecotone, 396 edge effects, 38, 5 566 sensitivity, 38, 39 effective colonization colonization rate, 94-5 94-5 density, 328 dispersal, dispersal, 328 extinction rate, 93, 95 isolation, 27, 28 metapopulation metapopulation size, size, 94-7, 166, 328 migration rate, 1171,215 7 1 , 215 number of habitat patches, 95, 98 population population size, size, 154, 156-7, 391 size, 1155, 55, 1175, 75, 193, 326, 370 size with source-sink structure, 1159 59 elasticity 90 elasticity ooff long-term growth rate, 5590 emigration, 3361 61 main proximate proximate cause ooff extinction, 534 probability, 330 rate, 266-7 266-7 endangered endangered species, species, 566 recovery planning for, for, 596 endogenous heterogeneity, heterogeneity, 45 environment coarse-grained, 390 spatially heterogeneous, 392 environmental deterioration, deterioration, population population responses to, 356 heterogeneity, heterogeneity, 55
INDEX INDEX stochasticity, 3 9-40, 344 stochasticity, 84-5, 3339-40, variance, 203, 340-1 340-1 epidemic epidemic theory demographic stochasticity, stochasticity, 420 traveling waves, 426 epidemics, epidemics, 67 epidemiology, 1102, 02, 4 16 416 models, 103 theory, 12 epistasis, 262 epistasis, 200-1, 200-1,262 epistatic interaction, 1164 64 equilibrium equilibrium assumption, assumption, 495 eradication eradication threshold, 442 ESU, 8 1-2, 585-6 ESU, 5581-2, 585-6 Euphydryas 30, 494-5 aurinia, aurinia, 1130, 494-5 editha, 9, 338, 400-1, 400-1,491,503, editha, 491, 503, 505, 507, 5 14 514 European nuthatch, 32-3 evolution of dispersal, 1 7, 467 dispersal, 3317, 467 dispersal, kin selection selection model, 231 dispersal, dispersal, multiple factors, 317 dispersal, dispersal, theoretical studies, studies, 230 host-parasite interactions, 468 interactions interactions among individuals, 260 life span in a meta population, 237 metapopulation, migration rate, 118, 8 , 1102, 02, 3 1 7, 467 317, species' ranges, 8-9 ranges, 118-9 evolutionary equilibrium, 408 genetic theory, 259, 262 load, 349 significant 81 significant units, units, 5581 evolutionary dynamics in metapopulations, metapopulations, 275 of reproductive systems, systems, 467 exogenous heterogeneity, heterogeneity, 45 extinction, extinction, 20, 345 caused by disease, 5 19 519 correlates of, 526 dataset, 1116 16 debt, 41, 94, 452, 494, 496, 532 effect of habitat patch size, size, 357 genetic effects effects of, 157 mechanisms of, 355, 365 probability of, 252 related 15 related to patch patch area, 1115 rate, 344, 521 rate and and emigration, 521 risk, 34, 346, 357 risk, effect of gene flow, 358, 362 risk, effect of migration, 358, 362
INDEX INDEX risk in dynamic landscapes, 40 risk, scaling with carrying capacity, 343 threshold, 34-7, 34-7, 42, 89, 94, 98-9, 98-9, 423, 465, 490, 494, 496 time, 80 vortices, 355 extinction-colonization 07-8, 1111, 1 1 , 1114 14 probabilities, 1107-8, processes, 230 rates, 83 stochasticity, 96, 98, 122, 533
F F
fadeouts, 42 4211 fecundity, 248 fence effect, 308 Microtus agrestis), 30, 5 1 7, 520 field vole ((Microtus agrestis), 1130, 517, Fisherian quantitative genetics, 201 , 223 201,223 fitness, 350 measure of, 404 sensitivity of, 404 variation, 263 fixation 69 deleterious alleles, 1169 index, 180 180 rate, 285 flour beetles, 267 foot-and-mouth epidemic, 428 forest models, 48 founder effect, 241 fractal landscape, 30-1 30-1,, 35 fragmentation, 35 effects on extinction threshold, 36 effects on species richness, 145 fragmented communities, 144 frequency dependence, 1163 63 frequency-dependent transmission, 4 18 418 Fst, 60, 1162, 62, 1173, 73 , 1187, 87, 1180, 80, 368-9 Fst, 153-4, 1160, 368-9 as an estimator of dispersal, 1173 73 fugitive 35, 1139-40, 3 9-40, 145 fugitive species, 1135,
G G
gametic disequilibrium, 371 equilibrium, 371 gene by deme interaction, 209-10 209-10 flow, 359, 3 6 1 , 405 361,405 for gene ((GFG) GFG) resistance, 468 frequency change, 1154 54 genealogies, 1174-5 74-5 genealogies, effect of metapopulation meta population structure on, 1175, 75, 1189 89
687 687
interaction and speciation, 220 genealogical approaches, 368 branching patterns, 77, 1190 90 patterns, 1177, histories, simulations of, 1183 83 genealogies, branching patterns of, 1177, 77, 1190 90 genealogy of a sample, 1176 76 generation overlap, 349 genetic architecture, architecture, 297 297 architecture of sex, 241 background, 200 basis of dispersal, 3319 19 contexts, intraindividual, 262 data to directly estimate immigration, 535 differentiation between populations, 405 differentiation between source and sink, 405 diversification, 2 81 281 diversity, 252, 349 diversity, effects of extinction and recolonization, 535 drift, 1153-4, 5 3-4, 230, 348 effects of population structure, described, 1173 73 factors, relative importance, 3338 38 load, 3361 61 load iin n subdivided populations, 1168 68 mixture coefficients, coefficients, 376 neighborhoods, 474 rescue effect, 359, 365 resemblance, 242 stock identification method, see see GSI structure structure of metapopulations, metapopulations, 1166 threats, 347 variability, 348-9 348-9 variability, habitat fragmentation, 537 variability in metapopulations, 539 variability, loss loss of, 347 variance, 348 variance among demes, 208 variance components, 203 variance partitioning, 2 16 216 variance, fragmented populations, 536 variation, 207, 207, 347, 499 variation in a sample, effect of metapopulation structure, 93 structure, 1193 variation, effect of extinction, 187 187 variation, effect of recolonization, 1187 87 variation, loss of, 350 variation, maintenance of, 412 genotype fitness, 1160, 60, 1163 63 genotype-by-environment interactions, 263 genotypic value, 205, 2 16 216
~688 8 geographical geographical information systems, systems, 43 information distributions, 508 fritillary Glanville fritillary (Melitaea cinxia), cinxia), 36, 36, 74, 74, 83, 83, butterfly (Melitaea 89-90, 92-3, 92-3, 129, 129, 146-7, 146-7, 229, 229, 233,237, 233, 237, 89-90, 3 15, 358, 358, 491-3,500-1,503, 491-3, 500-1, 503, 505 315, model, 95-6 95-6 model, global eradication eradication (extinction) of disease, 423 graph theory, 32-3 32-3 gray seal, 375 great tit, tit, 340 growth growth rate long-term, 341 stochastic, 341 stochastic, GSI, 371,373, 371, 3 73, 376-7 376-7 gynodioecious species, 239
H I-I
habitat and meta population approaches, 497 metapopulation 497 area, 392 choice, active active dispersal, 403 choice, evolution of, 412 configuration, 463 connectivity, 32, 456, 456, 459 corridors, 3312, 12, 465 deterioration, 490 fragmentation, 99, 234, 492 fragmentation and extinction thresholds, 35 fragmentation, reduced reduced species species richness, 459 heterogeneity, 140 loss, 34, 99, 364, 493, 545, 563 loss and fragmentation, 42 loss, lagged response, 37 management, 508 networks, 500 patch, 75 quality, 129, 3315, 1 5, 392, 497, 508, 5512 12 quality threshold, 497, 5512 12 selection, 11 selection, 3311 specialization, 1137, 37, 140 value of patches, 99 Halicoerus 75 Halicoerus grypus, grypus, 3375 hard selection, 60-1, 1 6 6 selection, 1160-1,166 haystack model, 5 heritability, 203 of dispersal, 3319 19 heritable variation, 262 hermaphrodites, 245 245 Hesperia 498, 507-9, 5513 13 Hesperia comma, comma, 235, 491, 491,498,
INDEX INDEX
heterogeneous heterogeneous environments, 65 landscapes, 28 landscapes, metapopulation, 95 metapopulation, patch networks, 81 81 patch SPOM, 11, 1 1 , 76 heterosis, 171,323, 1 7 1 , 323, 327, 357 heterosis, heterozygosity, 348 loss of, of, 357 heterozygous advantage, 351 351 heterozygous landscapes, 15, 73-5, 73-5, 496 highly fragmented landscapes, metapopulation biology, biology, 6 history of metapopulation adaptive landscapes, landscapes, 18, 1 8, 280, 297 holey adaptive host 480 colonization, 480 extinction, 480 occurrence, occurrence, 476 population, population, 415 host-pathogen system, simulation of, 486
I 1 1 , 332 ideal free free distribution, 3311,332 ideal population, 1155, 55, 347 IGE, 259, 264, 268, 273 effects of, 269 immigration, 254 density-dependent, 17 density-dependent, 5517 negative density-dependent, 533-4 density-dependent, 533-4 inbreeding, 245 14 avoidance, 3314 coefficient, 206, 2 1 3 , 3351,538 5 1 , 538 213, decreasing resistance, 458 depression, 1162, 62, 3314, 14, 3317, 1 7, 350-2, 355 depression, effect effect of environmental conditions on, 352 depression, 51 depression, purging of, 3351 effect of, 457 incidence dataset, 1116 16 function model (IFM), (IFM), 33, 82, 87, 90, 1100-1, 00-1, 108, 12, 1116, 1 6 , 428, 453, 492, 108, 1112, 495, 503, 508-9, 5518, 1 8 , 521, 558 521,558 matrix, 141 indirect genetic 8 , 259, 272 genetic effects, effects, 118, in meta populations, 266 metapopulations, individual by deme interaction, interaction, 209 movement, 27, 505 individual-based individual-based model, 46-7, 98-9 infinite sites 79 sites model, 1179 integrodifference equations, 50 interacting particle systems, systems, 48 interdemic interdemic selection, selection, strength of, of, 265
689 689
INDEX INDEX
interspecific competition, competition, 65, 65, 273 273 interspecific intragenomic conflicts, conflicts, 241 241,243 intragenomic , 243 introductions of of introductions Melitaea cinxia, cinxia, 506 506 Melitaea species, 504 504 species, invasion capacity of of aa network, 89-90 invasions, 65 65 invasions, island biogeographic biogeographic theory, theory, 6-9, 6-9, 883 island 3 island model, model, 111, 74, 776, island 1 , 115-6, 5-6, 74, 6 , 1155, 55, 1168, 68, 1172, 72, 1187, 87, 2213, 1 3, 3368 68 of dispersal, dispersal, 3328 of 28 isolation bby y distance, 3370 70 iteroparity, 2238 38
K K
key patches, 1100 00 kin 231,235, competition, 2 3 1 , 235, 3316, 16, 3319 19 cooperation, 3316 16 231,255 selection, 23 1 , 255 kin-based interactions, 3317 17 Krebs effect, effect, 308
L L
Lactuca mura/is, muralis, 467 Lactuca lacunarity index, 3311 Lande's model, 79, 8811 landscape change, 5551 51 24-9, 32-3 connectivity, 24-9, dynamics, 44, 563 ecological perspective, 25 7-8, 111-2, ecology, 7-8, 1-2, 23, 102 1 02 fragmentation, evolutionary consequences of, 234 matrix, 24 mosaics, 24 structure, 34, 36, 76, 98, 101,491 1 0 1 , 491 lattice lattice model, 46, 48, 48, 68, 98 98 Leadbeater's Leadbeater's possum, 99 Levins model, 74, 74, 77, 77, 79, 81, 8 1 , 93, 101 101 rule, rule, 81, 8 1 , 100 100 Levins-type models, models, 90 90 life span, 235, 237 237 span, 235, table, table, 38 life history, history, 347 347 density-dependent, density-dependent, 251 25 1 evolution, evolution, effect of of genetic structure structure on, on, 255 255 evolution, evolution, in in metapopulations, metapopulations, 228, 228, 255-6 255-6 evolution, evolution, metapopulation metapopulation effect on, on, 228 228 strategies, strategies, 252 252
strategies, strategies, evolution evolution of, of, 246 246 strategies, strategies, evolutionarily evolutionarily stable, stable, 255 255 syndromes, syndromes, 237, 237, 250 250 theory, theory, 227, 227, 229, 229, 237 237 traits, traits, 227 227 traits, traits, evolution evolution of, of, 243, 254 life-time life-time reproductive reproductive contribution, 340 340 success, success, 396 396 likelihood 80 likelihood ratio ratio test, 373, 373, 3380 linkage 71 linkage disequilibrium, disequilibrium, 3371 Linum 68 Linum marginaie, marginale, 4468 load iin n subdivided populations, 71 populations, 1171 local adaptation, 326, 407, 457 and and regional patterns of of diversity, diversity, 142 average effects, 18 effects, 207, 209, 212, 2218 breeding value, 205-6 205-6 breeding populations, 209 breeding value in meta metapopulations, context, 261 diversity, 144-6, 148 drift load, 1171 71 dynamics, 248 extinction, 84 extinction, effect of inbreeding on, 352 extinction, evolutionary effects effects of, 275 275 extinction in the meta population metapopulation context, context, 358 mate competition, 3 17 317 population decline rate, 570 population size, 234 population population size size distribution, 570 population trends, differences in, 596 resource competition, 317 317 resource selection, 405 specialization, 501 specialization, regression, 552 552 logistic regression, long-term dynamics, 132 model, 52 Lotka-Volterra model,
M M
macroparasites, 416 416 macroparasites, mainland-island mainland-island epidemic metapopulation, 426 metapopulation model, model, 413, 4 1 3 , 531 531 metapopulation metapopulation structure, structure, 490 490 metapopulation major histocompatibility histocompatibility complex, complex, 350 350 major maladaptation, 411 411 maladaptation, habitats, 410 410 in sink habitats, actions, 587 587 management actions, harvest, 588 588 harvest, local population population level, 589 589 local river hydropower hydropower systems, systems, 588 588 river
INDEX INDEX
6690 90
Mantel test, test, partial, partial, 385 385 Mantel marginal habitats, habitats, adaptation adaptation to, to, 404 404 marginal Markov Chain, Chain, 80 80 Markov see MCMC MCMC Monte Carlo Carlo method, method, see Monte Markov process, process, 80 80 Markov mark-release-recapture, 505 505 mark-release-recapture, of seeds, seeds, 461 46 1 of techniques, 28 techniques, marsh fritillary fritillary butterfly, butterfly, see see Euphydryas Euphydryas marsh
aurinia aurinia mass effects, effects, 140 140 mass mate choice, choice, 310 310 mate maternal effects, 325 maternal and state-dependent state-dependent dispersal dispersal cues, cues, 321 321 and matrix, 313 313 matrix, population models, 12, 102 1 02 population MCMC, 117-8, 1 1 7-8, 183 183 MCMC, mean additive genetic variance, variance, within additive genetic demes, 206 genetic variance, variance, effect of drift additive genetic on, 217 217 on, allele frequency, 60 frequency, 1160 210 local average effect, 210 phenotypic values, 200 200 161 relatedness of individuals, 161 time ttoo extinction, 778, 8 , 353-4 353-4 measles, 420-1, 423, 426, 429-30, 429-30, 420-1,423,426, 432, 436 mega population, 500 megapopulation,
Melitaea Melitaea cinxia, cinxia, see see Glanville Glanville fritillary diamina, diamina, 233-4, 233-4, 559-61 metacommunity, 1133, 33, 270 diversity, diversity, 140 140 indirect effects effects in, 270 mass effects perspective, 1136 36 neutral perspective, 1136 36 patch-dynamic perspective, 1134 34 species-sorting 35 species-sorting perspective, 1135 meta population metapopulation approach, 3, 9, 111,514 1 , 514 approach, criticism of, 14-5 biology, biology, fundamental processes, 367 citations citations to, to, 66 classic, population classic, see see classic classic meta metapopulation capacity, 1 , 93, 98, 465, capacity, 35, 88-9 88-91, 465, 495, 495, 500-1 , 506, 512 500-1,506, 512 concept, concept, 243, 243, 413 413 concept, concept, plant-specific plant-specific problems, problems, 451 451 decline, decline, 492, 492, 567, 567, 570 570 diffusion diffusion approximation, approximation, 566 566 dynamic 7 dynamic connectivity, connectivity, 887 ecology, ecology, 99
effect, 467 467 effect, endangered, endangered, 565 565 evolution, 18 18 evolution, extinction, extinction, 40, 40, 78, 78, 98,~100, 98, 1 00, 311,362, 3 1 1 , 362, 364, 496 496 364, extinction time, time, 127, 127, 558 558 extinction genealogies of of samples samples from, from, 188 188 genetic structure, structure, 273 273 genetic genetics, 15 15 genetics, level management management actions, actions, 587 587 meltdown, meltdown, 363 363 stochastic, 567 567 model, stochastic, models, structured structured by the the sizes of of local populations, populations, 101 101 o birds, 8 off birds, of butterflies, butterflies, 8 of of fishes, 8 of of mammals, 8 of plants, 8 patterns, 6, 494, 499 persistence, 34, 42, 129, 498 498 processes, 5 processes, butterflies, 14 processes on population genetic structure, structure, 536 genetics, 200, 200, 205, 205, 223 quantitative genetics, site selection, 559 91, 328 size, 91,328 size distribution, 570 spatially realistic theory, 9, 111, 1 , 76, 83 stochastic theory, 94 structures, 5 theory 8, 228 trajectories, 573 viability metrics, 577, 584, 587 with very small local populations, 538 Metropolis-Hastings algorithm, 1184 84 MHC MHC loci, 350, 352 Microbotryum violaceum, violaceum, 473, 473,487 Microbotryum 487 microsatellite DNA polymorphism, 536 genotyping, genotyping, 528 528
Microtus Microtus oeconomus, oeconomus, 530 530 rossiomeridionalis, rossiomeridionalis, 532 532 migrant pool, pool, 158 158 migrant model, model, 369 369 migration, see see also also dispersal, dispersal, 153, 153, 360, 360, 505 505 migration, corridor, corridor, 360 360 cost cost of, of, 505 505 costs costs and and benefits benefits of, of, 323 323 density density dependence, dependence, 528 528 diversity, diversity, 144 144 in aa meta metapopulation context, 385 385 in population context,
691 691
IINDEX NDEX limitation, limitation, 140 load, 1170 70 process, 367 rate, 372 rate and diversity, 139 139 migrational 361,364 migrational meltdown, 3 6 1 , 364 formulation, 547 minimum set set coverage formulation, missing missing data, 1 8-20 data, 1118-20 117 years, 117 moment moment closure, closure, 58-9 58-9 moment moment equation equation approaches, approaches, 68 Moran Moran effect, 426 mosaic mosaic models, 456 movement parameters, parameters, habitat-specific, 27 multi locus multilocus properties of, 282 BDM model, properties genotype approaches, approaches, 368 genotype methods, methods, 20, 20, 370 370 multiple equilibria, equilibria, 90 multitrophic interactions, 459 multitrophic 459 mutation, 7, 1162, 62, 1179 79 mutation, 117, accumulation, accumulation, 353 and 81 and genealogical genealogical process, 1181 average fitness effects, 354 load, 68 load, 1168 number of, 1181 81 79 parameter, 1179 rate, genome-wide, 355 rate, per-genome, 354 mutational meltdown, 1170, 70, 327, mutational meltdown, 327, 354, 356, 363, 365 mutation-selection 62 mutation-selection balance, 1162 mutualistic mutualistic relationship, 459
N N
natural natural experiments, experiments, 401 selection, 62 selection, 1162 populations, 259 selection in meta metapopulations, Ne, 156, 1173, 73, 349, 354 effect of population population structure structure on, 157 network network connectivity, connectivity, 501 neutral landscape models, 32, 34 metacommunity perspective, 143 theories of community structure, 110 0 neutrality tests, 1180, 80, 1185 85 non-equilibrium non-equilibrium systems, 490 non-linear interaction, 260 non-random 55, 1163 63 non-random mating, 1155, number number of alleles, 80 alleles, 1180 of species, species, 276-7, 276-7, 292
o O Oncorhynchus species, species, 581 581 open and closed population population structures, 490 attraction, 534 opposite-sex attraction, Orkney Isles, 376 outbred vigor, vigor, 360 outbred outbreeding depression, 361-2 3 6 1-2 outbreeding overdominance, 163, 351 351 overdominance,
p P
pair approximation, approximation, 49 panmictic population, population, 175 1 75 parapatric speciation, 289 289 Pararge 10 Pararge aegeria, aegeria, 5510 parasitoid-prey system, 5 1 , 6611 51, parentage parentage assignment, 528 parental control of offspring parental control dispersal, 323 dispersal, passive propagule passive propagule dispersal, 86 patch areas, 76 connectivity, 26 connectivity, dynamics, 139, 456 homogeneous, 77 network, homogeneous, occupancies, 1114 14 occupancy models, 77 turnover, 40 values, 88, 91, 93, 1100 values, 00 pathogen pathogen colonization, colonization, 485 extinction, 485 occurrence, 476 percolation, percolation, 29 theory, 26, 331, 1 , 1100 00 threshold, threshold, 29-30, 29-30, 32 phase locking, 425 phenotypic effects of alleles, 200 of genes, 262 phenotypic plasticity, 457 457 plasticity, variance, 201 , 203, 263 201,203, variation, partitioning partitioning of, 263 philopatry, 3316 16 phylogenetic envelope, 91 envelope, 3391 147-8 pitcher plants, 145, 147-8 plant dispersal, 460-1 dispersal, molecular markers, 462 dispersal, dispersal, distance distance curve, 460 metapopulations, 449, 449, 475 475 metapopulations, interactions, 459 plant-animal interactions, plant-pathogen metapopulation, metapopulation, 471 plant-pathogen
6692 92
plant-specific problems problems with with metapopulation metapopulation plant-specific concept, 451 451 concept, plasticity, 251 251 plasticity, Plebejus argus, argus, 131, 1 3 1 , 234, 234, 491,501-4, 491, 501-4, 512, 5 12, Plebejus 556-7 552, 556-7 point speciation speciation model, 277 point pollinators, 458 458 pollinators, polymorphic polymorphic nucleotide sites, sites, number number of, 181 181 nucleotide sites, expected number number of, 177 1 77 sites, 181 sites, expected value, 181 total number number of, 181 181 sites, total polymorphism, protected, protected, 247 247 polymorphism, pool frog pool frog (Rana lessonae), 129 population biology, perspective in, 338 population population population age-structured, 395 bottleneck, 348-50 bottleneck, 348-50 connectivity, 498 density, 246, 387 246, 387 differentiation, 1 3 , 223 differentiation, 2213,223 dynamics, 250, 250, 345-6 345-6 dynamics, transient, 256 256 extinction, 337, 355 extinction, extinction, ceiling model, 343 extinction, extinction, ecological factors, factors, 339 extinction, 347 extinction, genetic factors, factors, 347 extinction extinction rate, 358 fluctuations, 340, 344 genetic methods, 3368 68 genetic processes, 1172 72 growth rate, 344, 346 history, inferences about, 82 about, 1182 mean fitness, 353 neighborhood, neighborhood, 63-4 63-4 persistence, effects of source-sink structure, structure, 398 regulation, 337-8, 390 size, effect of source-sink structure, structure, 397 stability, effects of source-sink structure, structure, 398 stage-structured, 395 structure, inferences about, 1182 82 synchrony, 329 turnover, 455, 502-3, 502-3, 524, 526 turnover, genetic effects of, of, 368 viability analysis, 113, 3, 20, 338, 565, 595 portfolio effect, 421 posterior distribution, distribution, 374 predator-prey interaction, 66 models, 54 54
INDEX
prior distribution, distribution, effect of, of, 384 3 84 prior probability of of probability coexistence, 332 332 coexistence, common origin, origin, 370 370 common extinction, 355 355 extinction, fixation, 165 fixation, fixation, effect of of population population structure structure fixation, 168 on, 168 fixation o alleles, 165-7 165-7 fixation off beneficial alleles, fixation of of additive additive alleles, alleles, 165 fixation fixation of neutral neutral mutations, mutations, 285 285 fixation fixation of of new mutations, mutations, 165-6 1 65-6 fixation Proclossiana eunomia, eunomia, 491 productivity, 142, 1 42, 248 248 productivity, index, 378 378 index, propagule-pool propagule-pool colonization, 535 model, 369-70 369-70 pattern, 38 pattern, 5538 propagules, 69 propagules, colonizing, 3369 polymorphism, 247 protected polymorphism, 247 PVA, 565-6 565-6
Q Q
quantitative genetic parameters, effect migration on, 213 213 of migration quantitative 99 quantitative genetics, 1199 quasiequilibrium, quasiequilibrium, 495 495 quasistationarity, 14, 122, 1131 31 quasistationarity, 1114, assumption, assumption, 122 quasistationary quasistationary distribution, distribution, 78-80, 78-80, 82, 97 equilibrium, 1116 16 state, 1107-8, 07-8, 124
II R
radiation adaptive, 298 duration duration of, 289, 297 297 dynamics of, 289 time to beginning of, 297 random fission model, 277 random walk, 886 6 model, 28 range boundaries, 507 expansion, 509 margins, 507 rate of expansion, 508, 5510, 1 0, 5512 12 habitat destruction, destruction, 4411 reaction norm, 252 252 reaction-diffusion, 50
IINDEX NDEX reciprocal transplant transplant experiments, 457 recolonization, 241,243, 241, 243, 245, 254, 254, 526 genetic effects of, 1157 57 recombination, 1153 53 genealogies and, 1178 78 recruitment from seed rain vs seed bank, 455 Red List List criteria, 566 regional coexistence, 146 diversity, 144, 146, 148 dynamics, 248 stochasticity, 89, 96, 1100, 00, 121, 1130, 30, 363, 5 14 514 stochasticity, migration and, 363 relatedness, 242 remnant populations, 452-3, 455-6 455-6 representativeness, 542 reproduction reproduction assurance, 241 reproductive effort, 246, 248, 250, 252 age-specific, age-specific, 238 ES, 235, 235, 248 evolution of, 235 in a meta population, 235 metapopulation, in a metapopulation, metapopulation, evolution of, 246 reproductive isolation, 2 8 1 , 284, 296 281,284, genetic architecture of, 279 genetics of, 278 threshold effect, 297 reproductive success in sink habitats, 4 10 410 reproductive value, 349, 3391,404-5 9 1 , 404-5 habitat 91 habitat specific, 3391 rescue effect, 113, 3 , 887, 7 , 90, 1101, 0 1 , 1107-8, 0 7-8, 1111-2, 1 1-2, 1115, 15, 1130, 30, 3310, 1 0, 328, 464, 5 1 8-9, 529, 518-9, 531, 534 531,534 reserve aggregation, 550, 554-5, 554-5, 562 reserve network, 541 design, 542 design, landscape dynamics, 546 design, spatial population population dynamics, 546 dispersal ability, 560 patch cost, 560 reserve selection, 541 algorithms, 542, 544 algorithms, persistence, 546 amount of resources, 61 resources, 5561 resistance, fitness costs of, 473 resource partitioning, 37 partitioning, 1137 restoration restoration efforts, 596 Reversible Jump Markov Chain Monte Carlo, 3381 81
693 693 risk metric confidence intervals for, 578 uncertainty, 578 variability of, 595 risk of extinction, extinction, 340, 344, 353, 356-7, 356-7, 359 long-term, 596 short-term, 596 RJMCMC, 81 RJMCMC, 3381
$ S
81 salmon, 5581 scattering phase, 1189, 89, 1191-3 9 1-3 scoring approaches, 543 seasonal forcing, 426 seed banks, 454, 456 456 dimorphism, 3 19 319 sowing, 451 segregating sites expected number of, 1177 77 expected value, 1181 81 segregation load, 1169 69 SEIR model, 422 selection, 153, 2 1 9, 230, 237 219, 237 among local populations, populations, 1188 balancing, 1163 63 differential, 203 directional, 221 diversifying, 200 hard, 1160-1, 60-1, 1166 66 heterogeneous, 1164 64 in meta populations, 264 metapopulations, in subdivided populations, 59 populations, 1159 individual, 266, 268, 270 interdemic, 266, 268-70 268-70 response to, 1160, 60, 200, 203, 203, 266, 404 soft, 1160-1, 6 0-1, 1166 66 spatially heterogeneous, 1159, 59, 1164, 64, 245 stabilizing, 165 strength of, 1160 60 temporal heterogeneity in, 245 uniform, 1159-60 59-60 selfing 245 semelparous organisms, 246 semi-independent patch patch network (SIN), 499-500 499-500 Senecio jacobaea, 146 settlement decision, 334 pattern, 529 success, 324-5 324-5
694 694 sex sex allocation, 238, 243, 245 inheritance, mode of, 242 ratio, 241-2 241-2 ratio, evolution, 239 ratio, evolution in a meta population, 239 metapopulation, ratio variation, 239 sex-biased dispersal, 1 3-4, 3317, 1 7, 521 dispersal, 3313-4, sexual selection, 13 selection, 3313 sexually transmitted diseases, 427 shifting 8 , 1186 86 shifting balance theory, 118, shrews, 1130, 30, 344, 347, 5 31 531 Silene alba, 360 latifolia, lati[olia, 457, 473, 487 Silene-Microbotryum population, Silene-Microbotryum meta metapopulation, 475, 485 sink, 40 absolute, 3 88 388 black-hole, 394 habitat, habitat, 388, 392, 398, 40 4011 populations, 58 populations, 136, 141, 1158 relative, 88 relative, 3388 SIR model, 4 1 6 , 427, 442 416, SIS model, 427 SIS site selection algorithms, 542 stochastic metapopulation model, 558 dispersal dispersal ability, 559 site-frequency distribution, 85 distribution, 1185 size-structured populations, 02 populations, 1102 15 small mammals, 5515 small-population 3 9 , 365 small-population paradigm, 3339, snapshot 12, 1114-5 14-5 snapshot data, 1112, social contact networks, networks, 67 context, average, 264 context, genetic variation in, 265 fence, 329 fence effect, 534 soft selection, , 1 66 selection, 160-1 160-1,166 Sorex, 344 araneus, 130, 5531 31 caecutiens, 1130, 30, 5 31 531 minutus, 1130, 30, 5 31 531 source source habitat, habitat, 388, 392 populations, 158 populations, 136, 141, 141,158 source-sink concept, applied aspects aspects of, 414 dynamics, 37, 143, 497 dynamics, ecological consequences of, 397, 399
INDEX INDEX dynamics, influence influence on population population size, size, 401 meta populations, 117, 7, 19, 3 11 metapopulations, 311 meta populations, evolutionary models of, metapopulations, 408 models, predictions of, of, 402 population 87-8, 408 population dynamics, 3387-8, populations, populations, 404, 453 potential, 337-8 7-8 relations, 39 relations, 1139 structure, 3387, 87, 398-400 398-400 structure, 13 structure, concept of, 4413 structure, ecological ecological consequences consequences of, 400 structure, effect of, 158 structure, effect on adaptive evolution, 405 structure, evolutionary consequences, consequences, 403 structure, evolutionary stability of, 402 structure, patch model of, 3389 89 structure, reverse, 394, 4 10 410 system, experimental, 401 system, polygenic model of evolution evolution in, 406 systems, 358 systems, laboratory, 412 spatial aggregation, 4 configuration, configuration, 497 correlation, correlation, 97 coupling coupling in epidemic metapopulations, metapopulations, 433 ecology, 4, 9 genetic structure, 327 locations, 76 logistic model, 64 moment equations, 46, 5 1, 9 51, 988 point process, 47 population population viability analysis, analysis, 559 reserve design, 547 synchrony, 50 spatially correlated correlated environmental environmental conditions, conditions, 96 correlated 1 8 , 527, 532-3 correlated extinction, extinction, 5518, 532-3 explicit explicit approach, 396 explicit explicit models, 47, 395 explicit models, consequences consequences for ecological processes, 471-2 471-2 explicit models, consequences consequences for genetic processes, processes, 471-2 471-2 realistic Levins model, 82, 84 realistic metapopulation theory, 9, 111, 1 , 76, 83 realistic realistic models, 234 speciation, 221, 223, 278, 296, 298 221,223, by random random drift and mutation, mutation, 300 dynamics, 296 in metapopulations, metapopulations, 275 mechanisms, 221
INDEX INDEX probability of, 278 rate rate of, 291 species extinction, 364 range, 364, 397 sorting, 1139-40, 39-40, 147 species-area species-area curves, 276-7 276-7 relationship, 6 SPOM, 111, 1, 74-75, 05-6, 1112, 12, 428 74-75, 1105-6, classification, classification, 89 deterministic approximation approximation of, 76, 82 homogeneous, 111, 1 , 76 homogeneous, homogeneous, deterministic deterministic approximation approximation of, l11l SRLM, 93-4 93-4 stable equilibria, 346 stationary state, 244 statistical genetics, 20 methods, limitations limitations of, 375 stepping-stone dispersal, dispersal, 534 model, 116 6 stochastic and seasonal forcing, 420 cellular automata, automata, 48 forcing of epidemics, epidemics, 420 logistic model, 78-9, 881, 1 , 98 logistic model, deterministic mean-field approximation approximation of, 77 meta population equilibrium, 82 metapopulation metapopulation metapopulation model, effects effects of management, 587 metapopulation, metapopulation, trajectory of, 596 patch patch occupancy models, see SPOM theory, 94 structured structured coalescent, 1187-8 87-8 meta population model, 12, 440 metapopulation populations, 86 populations, genetics of, 1186 successional 13 successional habitats, habitats, 5513 susceptible-infected-susceptible (SIS) (SIS) model, 103
T T
tagging experiments, 582 temporal variation, 97 temporally varying environmental conditions, conditions, 9966 territoriality, 3314 14 threatened species, species, recovery planning for, 596 threats to populations, populations, 365
695 695
threshold 1 , 889 9 condition, 79, 881, in connectivity, connectivity, 29 response, 3311 value, 880 0 (lag), 454-6, 454-6, 465, 494 time delay (lag), in meta population response, 494 metapopulation time to extinction, 9 1 , 344, 452, 495-6, 91, 495-6, 499, 503 most recent common ancestor, 92 ancestor, 1192 total coalescence 78 coalescence times, expected, 1178 77 total length of the genealogy, distribution, distribution, 1177 trade-off, 1137-8, 3 7-8, 146, 148-9 148-9 between competitive ability and predator predator tolerance, 148 between colonization colonization and competitive abilities, 135, 146 transient transient dynamics, 24, 93 dynamics, evolutionary importance importance of, 254 dynamics of speciation, 288 growth, 248 metapopulation metapopulation dynamics, 490 period in population population dynamics, 243-4 243-4 population population dynamics, 250 transmission transmission model density-dependent, 482 frequency-dependent, 482 transplantations, transplantations, 451 traveling waves of infection, 434 434 tree frog (Hyla 09-10, (Hyla arboreal, arborea), 106, 1109-10, 1122-4, 22-4, 128 Tribolium castaneum, 266, 271-2 271-2 trophic cascades, 43 cascades, 1143 turnover, 125, 127, 1132 32 14-5, 1117-8 1 7-8 data, 1114-5, events, events, 506 underestimate 32 underestimate of, of, 1132
U U
unstable equilibrium, 346 Urophora cardui, cardui, 129 Urtica Urtica dioica, dioica, 459 Uta stansburiana, 1 6 , 320 stansburiana, 3316,
v V
vaccination pulse, 442-4 442-4 random, random, 443 strategies, strategies, 442 Vancouver Island marmot marmot (Marmota vancouverensis), 532
INDEX INDEX
696 696
variance in average effects, effects, 2210 local average 10 on, 2217 local average effects, effect ooff drift on, 17 reproductive success, 155-7 reproductive viability analysis, 565 metric validation, simulations for, 579 of total metapopulation, 38, 569
W W
water populations, 522 water vole meta metapopulations, wavelet wavelet phase analysis, analysis, 434 white-backed woodpecker (Dendrocopos (Dendrocopos leucotos), leucotos), 8811 whooping cough, 421-2 421-2 Wright-Fisher model, 1176 76
