Body Size: The Structure and Function of Aquatic Ecosystems

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Body Size: The Structure and Function of Aquatic Ecosystems Ecologists have long struggled to predict features of ecological systems, such as the numbers and diversity of organisms. The wide range of body sizes in ecological communities, from tiny microbes to large animals and plants, is emerging as the key to prediction. Based on the relationship of body size with key biological rates and with the physical world experienced by aquatic organisms, we may be able to understand patterns of abundance and diversity, biogeography, interactions in food webs and the impact of fishing, adding up to a potential ‘periodic table’ for ecology. Remarkable progress on the unravelling, describing and modelling of aquatic food webs, revealing the fundamental role of body size, makes a book emphasizing marine and freshwater ecosystems particularly apt. Here, the importance of body size is examined at a range of scales, yielding broad perspectives that will be of interest to professional ecologists, from students to senior researchers. A L A N G . H I L D R E W is Professor of Ecology in the School of Biological and Chemical Sciences at Queen Mary, University of London. D A V I D G . R A F F A E L L I is Professor of Environmental Science at the University of York. R O N N I E D M O N D S - B R O W N is a Senior Lecturer in Environmental Sciences at the University of Hertfordshire.

Body Size The Structure and Function of Aquatic Ecosystems Edited by ALAN G. HILDREW School of Biological and Chemical Sciences, Queen Mary, University of London, UK

DAVID G. RAFFAELLI Environment Department, University of York, UK

RONNI EDMONDS-BROWN Division of Geography and Environmental Sciences, University of Hertfordshire, UK

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521861724 © British Ecological Society 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 eBook (EBL) ISBN-13 978-0-511-29508-9 ISBN-10 0-511-29508-1 eBook (EBL) ISBN-13 ISBN-10

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ISBN-13 ISBN-10

paperback 978-0-521-67967-1 paperback 0-521-67967-2

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Contents

List of contributors Preface

page vii ix

1 The metabolic theory of ecology and the role of body size in marine and freshwater ecosystems

James H. Brown, Andrew P. Allen and James F. Gillooly

1

2 Body size and suspension feeding

Stuart Humphries

16

3 Life histories and body size 4

5

6

7 8

9 10

David Atkinson and Andrew G. Hirst Relationship between biomass turnover and body size for stream communities Alexander D. Huryn and Arthur C. Benke Body size in streams: macroinvertebrate community size composition along natural and human-induced environmental gradients Colin R. Townsend and Ross M. Thompson Body size and predatory interactions in freshwaters: scaling from individuals to communities Guy Woodward and Philip Warren Body size and trophic cascades in lakes J. Iwan Jones and Erik Jeppesen Body size and scale invariance: multifractals in invertebrate communities Peter E. Schmid and Jenny M. Schmid-Araya Body size and biogeography B. J. Finlay and G. F. Esteban By wind, wings or water: body size, dispersal and range size in aquatic invertebrates Simon D. Rundle, David T. Bilton and Andrew Foggo

33

55

77

98 118

140 167

186

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CONTENTS

11 Body size and diversity in marine systems 12

13 14 15

16 17

Richard M. Warwick Interplay between individual growth and population feedbacks shapes body-size distributions Lennart Persson and Andre´ M. De Roos The consequences of body size in model microbial ecosystems Owen L. Petchey, Zachary T. Long and Peter J. Morin Body size, exploitation and conservation of marine organisms Simon Jennings and John D. Reynolds How body size mediates the role of animals in nutrient cycling in aquatic ecosystems Robert O. Hall, Jr., Benjamin J. Koch, Michael C. Marshall, Brad W. Taylor and Lusha M. Tronstad Body sizes in food chains of animal predators and parasites Joel E. Cohen Body size in aquatic ecology: important, but not the whole story Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown

Index

210

225 245 266

286 306 326 335

Contributors

Andrew P. Allen National Center for Ecological Analysis and Synthesis, Santa Barbara, CA 93101, USA. David Atkinson Population and Evolutionary Biology Research Group, School of Biological Sciences, The University of Liverpool, Biosciences Building, Crown Street, Liverpool L69 7ZB, UK. Arthur C. Benke Aquatic Biology Program, Box 870206, Department of Biological Sciences, University of Alabama, Tuscaloosa, AL 35487-0206, USA. David T. Bilton Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. James H. Brown Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA. Joel E. Cohen Laboratory of Populations, Rockefeller and Columbia Universities, 1230 York Avenue, Box 20, New York, NY 10021-6399, USA. Andre´ M. De Roos Institute of Biodiversity and Ecosystems, University of Amsterdam, P.O.B. 94084, NL-1090 GB Amsterdam, the Netherlands. Ronni Edmonds-Brown Division of Geography and Environmental Sciences, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK.

G. F. Esteban School of Biological and Chemical Sciences, Queen Mary, University of London, East Stoke, Wareham Dorset BH20 6BB, UK. B. J. Finlay School of Biological and Chemical Sciences, Queen Mary, University of London, East Stoke, Wareham Dorset BH20 6BB, UK. Andrew Foggo Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. James F. Gillooly Department of Zoology, University of Florida, Gainesville, FL 32607, USA. Robert O. Hall, Jr. Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Alan G. Hildrew School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK. Andrew G. Hirst British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK. Stuart Humphries Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK. Alexander D. Huryn Aquatic Biology Program, Box 870206, Department of

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LIST OF CONTRIBUTORS

Biological Sciences, University of Alabama, Tuscaloosa, AL 35487-0206, USA. Simon Jennings Centre for Environment, Fisheries and Aquaculture Science (CEFAS), Lowestoft Laboratory, NR33 0HT, UK. Erik Jeppesen Department of Freshwater Ecology, National Environmental Research Institute, Denmark and Department of Plant Biology, University of Aarhus, Ole Worms Alle´, Aarhus, Denmark. J. Iwan Jones Centre for Ecology and Hydrology Dorset, Dorchester DT2 8ZD, UK. Benjamin J. Koch Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Zachary T. Long Institute of Marine Sciences, University of North Carolina at Chapel Hill, 3431 Arendell Street, Morehead City, NC 28557 and Virginia Institute of Marine Science, The College of William and Mary, Gloucester Point, VA 23062. Michael C. Marshall Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Peter J. Morin Department of Ecology, Evolution & Natural Resources, 14 College Farm Rd., Cook College, Rutgers University, New Brunswick, NJ 08901, USA. Lennart Persson Department of Ecology and Environmental Science, Umea8 University, S-901 87 Umea8 , Sweden. Owen L. Petchey Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 1SA, UK. David G. Raffaelli Environment Department, University of York, Heslington, York Y010 SDD, UK.

John D. Reynolds Department of Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada. Simon D. Rundle Marine Biology and Ecology Research Centre, University of Plymouth, Plymouth PL4 8AA, UK. Peter E. Schmid School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK and Institute of Freshwater Ecology, University of Vienna, 1090 Wien, Althanstrasse 14, Austria. Jenny M. Schmid-Araya School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK. Brad W. Taylor Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Ross M. Thompson School of Biological Sciences, Building 18, Monash University, Victoria 3800, Australia. Colin R. Townsend Department of Zoology, University of Otago, 340 Great King Street, Dunedin 9054, New Zealand. Lusha M. Tronstad Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA. Philip Warren Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK. Richard M. Warwick Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth, PL1 3DH, UK. Guy Woodward School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK.

Preface

More than ten years ago, two of us (AGH and DGR) were lucky enough to edit a previous symposium of the British Ecological Society (BES) – Aquatic Ecology: Scale, Pattern and Process (Giller, Hildrew & Raffaelli, 1994). In the Introduction to that volume, we pointed out that the BES had not devoted a single previous symposium to aquatic ecosystems. Evidently we did not change the culture, since the Body Size symposium held at the University of Hertfordshire in September 2005 was only the second! Aquatic Ecology: Scale, Pattern and Process had two objectives: (i) to explore how the scale of approach affected the patterns that were detected and the processes that appeared to be important, and (ii) to compare freshwater and marine ecosystems. In Body Size: The Structure and Function of Aquatic Ecosystems, both those questions of scale and comparison among systems are very much still alive as continuing themes. Body size determines overwhelmingly the scale at which organisms perceive and navigate through their physical world, and the contrasts between freshwater and marine ecosystems remain evident. Body size is a species trait with implications beyond scale, however, and we believe that the present volume shows that more similarities than differences are evident among the diverse aquatic systems considered. Indeed, several authors argue here that fundamental ecological processes are revealed by comparing marine, freshwater and terrestrial systems. In organizing this meeting, we were well aware of the increasing interest in body size from the wider ecological community over the past 30 years, as well as the technical challenge involved in exploring body-size data. Of course, the fascination with body size has a much longer history in ecology and was prominent in the writings, for example, of Alfred Wallace (1858) and Charles Elton (1927), the latter having discussed at length its relevance to trophic interactions (see review by Warren, 2005). It was R. H. Peters’ (1983) elegant exposition of the physiological, environmental and ecological correlates of body size that re-ignited modern interest, however, and which led indirectly to an explosion in the macroecological literature over the past ten years (Blackburn & Gaston, 2003), to the metabolic theory of ecology (Brown et al., 2004) and indeed to this present volume. All of the papers presented at the Hatfield meeting connect

x

PREFACE

with one or more of these themes and in many cases attempt to integrate aspects of body-size research that were previously treated separately. A focus on aquatic systems seemed appropriate because aquatic ecologists have historically been particularly prominent in the debate. Thus, Hardy (1924) was amongst the first to point out the significance of ontogenic (sized-based) shifts in the food webs supporting fisheries, Ryther (1969) illustrated the effects of predator and prey body sizes on food-chain length and global patterns of marine productivity, whilst Hutchinson (1959) provided a classic account of body size and species coexistence. It may well be that patterns and processes related to body size are particularly important in aquatic systems, or at least are more obvious. We asked the author(s) of each paper to examine the importance and role of body size in the systems in which they work. Essentially the book builds from the level of the individual and a consideration of body size as a species trait (Humphries; Atkinson & Hirst; Huryn & Benke; Townsend & Thompson), through food webs and communities (Woodward & Warren; Jones & Jeppesen; Schmid & Schmid-Araya), to body-size related macroecological patterns in aquatic systems (Finlay & Esteban; Rundle, Bilton & Foggo; Warwick), to dynamics and patterns in whole communities and ecosystems (Persson & De Roos; Petchey, Long & Morin; Jennings & Reynolds; Hall et al.; Cohen). Jim Brown and colleagues set the scene with a ‘wet’ exposition of metabolic theory, and although we did not ask contributors explicitly to test these ideas several did. The meeting certainly generated an old-fashioned sense of community and of excitement in what people had to say, though it was just as apparent how fragmented the community is, as was reflected in the examples chosen to illustrate particular points and the literature cited by authors from different ‘stables’ and backgrounds. We hope that this book reflects just a little of this excitement and serves as a useful synthesis of this area of ecology. Finally, we wish to thank all the contributors for their efforts and remarkable efficiency, the British Ecological Society and the Freshwater Biological Association for their support, and the local organizers at the University of Hertfordshire for all their hard work. Alan Hildrew, Dave Raffaelli, Ronni Edmonds-Brown.

References Blackburn, T. M. & Gaston, K. J. (2003). Macroecology: Concepts and Consequences. Oxford: Blackwell Science. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789.

Elton, C. S. (1927). Animal Ecology. London: Sidgwick & Jackson Ltd. Giller, P. S., Hildrew, A. G. & Raffaelli, D. G. (eds.) (1994). Aquatic Ecology: Scale, Pattern and Process. The 34th Symposium of the British Ecological Society. Oxford: Blackwell Science.

PREFACE

Hardy, A. C. (1924). The herring in relation to its animate environment. Part 1. The food and feeding habits of the herring with special reference to the east coast of England. Fisheries Investigations Series II, 7(3), 1–53. Hutchinson, G. E. (1959). Homage to Santa Rosalia, or why are there so many kinds of animals? American Naturalist, 32, 571–581. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press. Ryther, J. H. (1969). Photosynthesis and fish production in the sea. Science, 166, 72–76.

Wallace, A. R. (1858). On the tendency of varieties to depart indefinitely from the orginal type. In C. R. Darwin and A. R. Wallace: On the tendency of species to form varieties, and on the perpetuation of varieties and species by natural selection. Journal of the Proceedings of the Linnean Socioty, Zoology, 20 August 1858, 3, 45–62. Warren, P. H. (2005). Wearing Elton’s wellingtons: why body size still matters in food webs. In Dynamic Food Webs: Multispecies Assemblages, Ecosystem Development, and Environmental Change, eds. P. C. de Ruiter, V. Wolters & J. C. Moore. San Diego: Academic Press.

xi

CHAPTER ONE

The metabolic theory of ecology and the role of body size in marine and freshwater ecosystems JAMES H . BROWN University of New Mexico, Albuquerque

ANDREW P . ALLEN National Center for Ecological Analysis and Synthesis, Santa Barbara

JAMES F . GILLOOLY University of Florida, Gainesville

Introduction Body size is the single most important axis of biodiversity. Organisms range in body size over about 22 orders of magnitude, from tiny bacteria such as Mycoplasma weighing 1013 g to giant Sequoia trees weighing 109 g. Such size variation is a pervasive feature of aquatic ecosystems, where the size spectrum spans at least 20 orders of magnitude, from the smallest free-living bacteria at about 1012 g to the great whales at about 108 g (e.g., Sheldon et al., 1972; Kerr & Dickie, 2001). Nearly all characteristics of organisms, from their structure and function at molecular, cellular and whole-organism levels to ecological and evolutionary dynamics, are correlated with body size (e.g., Peters, 1983; McMahon & Bonner, 1983; Calder, 1984; Schmidt-Nielsen, 1984). These relationships are almost always well described by allometric equations, power functions of the form: Y ¼ Y0 Mb

(1:1)

where Y is a measure of some attribute, Y0 is a normalization constant, M is body mass, and b is a scaling exponent (Thompson, 1917; Huxley, 1932). A longstanding puzzle has been why empirically estimated values of b are typically close to multiples of 1/4: 3/4 for whole-organism metabolic rates (Savage et al., 2004a) and rates of biomass production (Ernest et al. 2003), 1/4 for mass-specific metabolic rates and most other biological rates such as the turnover of cellular constituents (Gillooly et al., 2005a), population growth rates (Savage et al., 2004b) and rates of molecular evolution (Gillooly et al., 2005b), and 1/4 for biological times such as cell cycle time, lifespan and generation time (Gillooly et al., 2001, 2002). Recent theoretical advances in biological scaling and metabolism represent tremendous progress in solving this puzzle. The pervasive quarter-power Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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exponents are due to the fractal-like design of the networks and surfaces that supply energy and materials used by cells in biological metabolism (West et al., 1997, 1999). One additional advance has strengthened and extended this theoretical foundation. The well documented exponential effect of temperature on metabolic rate can be incorporated by adding a Boltzmann–Arrhenius factor, e E/kT, to Eq. (1.1). Whole organism metabolic rate or production, P, can then be expressed as: P ¼ P0 M3=4 eE=kT

(1:2)

where E is the activation energy, k is Boltzmann’s constant (8.62  105 eV/K), and T is absolute temperature in degrees Kelvin (Gillooly et al., 2001, 2002). Therefore, mass-specific metabolic rate, B, and most other rates can be expressed as: B ¼ P=M ¼ B0 M1=4 eE=kT

(1:3)

where B0 is another normalization constant. The addition of temperature to this model proved critical to the development of a metabolic theory of ecology (MTE) (Brown et al., 2004). MTE incorporates these fundamental effects of body size and temperature on individual metabolic rate to explain patterns and processes at different levels of biological organization: from the life histories of individuals, to the structure and dynamics of populations and communities, to the fluxes and pools of energy and materials in ecosystems. Brown et al. (2004) began to develop MTE in some detail, made many testable predictions, and evaluated some of these predictions, using data compiled from the literature for a wide variety of ecological phenomena, taxonomic and functional groups of organisms, and types of ecosystems. Here we apply the metabolic theory of ecology to focus on some important correlates and consequences of body size in marine and freshwater ecosystems. In so doing, we build on a rich tradition that extends back over a century. Many of the most eminent aquatic ecologists have contributed. Several themes have been pursued. With respect to population dynamics and species interactions, this includes work from Gause (1934), Hutchinson (1959), Brooks and Dodson (1965), Paine (1974), Leibold and Wilbur (1992) and Morin (1995, 1999). With respect to distributions of biomass, abundance and energy use across species, this includes work from Sheldon and Parsons (1967), Sheldon et al. (1972, 1977), Cyr and Peters (1996) and Kerr and Dickie (2001). With respect to food webs, this includes work from Lindeman (1942), Odum (1956), Hutchinson (1959), Carpenter and Kitchell (1988), Sprules and Bowerman (1988) and Cohen et al. (2003). Finally, with respect to nutrient relations and ecological stochiometry, this includes work from Redfield (1958), Schindler (1974), Wetzel (1984) and, more recently, Sterner and Elser (2002). Many of these themes have been addressed by the contributors to this volume.

THE METABOLIC THEORY OF ECOLOGY

MTE provides a conceptual framework for understanding the diverse effects of body size in aquatic ecosystems (see also Peters, 1983; Cyr & Pace, 1993; Cyr, 2000; Kerr & Dickie, 2001; Gillooly et al., 2002; Brown & Gillooly, 2003; Brown et al., 2004; Allen et al., 2005; Gillooly et al., 2006). MTE is based on wellestablished fundamental principles of physics, chemistry and biology, makes explicit, testable, quantitative predictions, and synthesizes the roles of individual organisms in populations, communities and ecosystems. The literature on body size and metabolism in general, and on aquatic ecosystems in particular, is too vast to summarize here. The references cited above and below are just a few of the relevant publications, but they will give the interested reader a place to start.

Background For what follows, we will assume that Eqs. (1.2) and (1.3) capture the fundamental effects of body size and temperature on metabolic rate. As the examples below will show, these equations do not account for all observed variation. They do, however, usually account for a substantial portion of the variation within and across species, taxonomic and functional groups, and in ecosystems where body size varies by orders of magnitude. Moreover, fitting Eq. (1.2) or (1.3) to data generates precise quantitative predictions that can be used as a point of departure to evaluate the many factors that may contribute to the residual variation. These include experimental and measurement error, phylogenetic and environmental constraints, influences of stoichiometry, and the effects of acclimation, acclimatization and adaptation. Since we present Eqs. (1.2) and (1.3) as assumptions, it is important to state that MTE and the underlying models for the scaling of metabolic rate and other processes with body size and temperature have received both enthusiastic support and severe criticism. We will not cite or review these issues and references here, but simply state that we are confident that most substantive criticisms have been or will be answered, and that the theory is fundamentally sound. This volume and this chapter are on the effects of body size on the structure and dynamics of aquatic ecosystems. Metabolic rate, and other rate processes controlled by metabolic rate, are strongly affected by both body size and temperature. We can ‘correct’ for variation due to environmental or body temperature by taking logarithms of both sides of Eq. (1.3) and rearranging terms to give: lnðBeE=kT Þ ¼ ð1=4Þ ln ðMÞ þ ln ðB0 Þ

(1:4) 5

where k is Boltzmann’s constant (¼ 8.62  10 eV/K) and E is the average activation of metabolic reactions (0.65 eV; see Brown et al., 2004). Equation (1.4) shows that, after correcting for temperature, ln(BeE/kT) is predicted to be a linear function of ln(M) with a slope of 1/4. Other allometric scaling relations can be similarly analyzed using equations that have different values for the

3

J. H. BROWN ET AL.

normalization constants and sometimes for the exponents, e.g. 3/4 for wholeorganism metabolic rate (Eq. (1.2)). In aquatic ecosystems, it is reasonable to assume that the body temperature of an ectotherm is equal to water temperature. Thus, coexisting species of prokaryotes, phytoplankton, protists, zooplankton, other invertebrates and fish can usually be assumed to have the same body temperature. Additionally, since daily and seasonal variations in water temperatures are relatively modest, it is often reasonable to take some average value. Correction for variation in temperature is particularly important when comparing locations or seasons that differ substantially in water temperature, and when comparing ectotherms and endotherms, which differ substantially in body temperature. In this chapter we have followed these procedures, and corrected for temperature variation when appropriate.

Individual level: metabolic rate, production and life-history traits We begin at the level of the individual organism. The first question is whether metabolic rate varies with body size as predicted by Eqs. (1.2) and (1.3). In Fig. 1.1, we present temperature-corrected data for whole-organism metabolic rates of aquatic unicellular eukaryotes, invertebrates and fish. Note that the predicted slopes of these relationships are close to 3/4. It is apparent that the observed values cluster around and do not differ significantly from these slopes. These data confirm a large literature on the body-size dependence of metabolic rates in a wide variety of aquatic organisms, from unicellular algae and protists to invertebrates and fish (e.g., Hemmingsen, 1960; Fenchel & Finlay, 1983). Note also that there is considerable variation around these relationships. It may appear to be random scatter, but further analysis would probably suggest that much of it is due to some combination of experimental error, differences in techniques, evolutionary constraints related to phylogenetic relationships,

30 In(metabolic rate *eE/kT)

4

fish invertebrates unicells

y = 0.74x + 20.89 2 r = 0.79

y = 0.73x + 19.74 2 r = 0.97

10 y = 0.70x + 18.24 r 2 = 0.97

–10

–30

0 ln(body mass)

30

Figure 1.1 The relationship between temperature-corrected metabolic rate, measured in watts, and the natural logarithm of body mass, measured in grams. Metabolic rate is temperature corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2001).

THE METABOLIC THEORY OF ECOLOGY

ln(production * eE/kT)

40 fish algae zooplankton

15

y = 0.76x + 25.04 r 2 = 0.99

–10 –40

–10 ln(body mass)

20

Figure 1.2 The relationship between temperature-corrected biomass production rate, measured in grams per individual per year, and the natural logarithm of body mass, measured in grams. Metabolic rate is temperature corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Ernest et al. (2003).

body plan, stoichiometry, as well as acclimatization, acclimation and adaptation to different environmental conditions. The metabolism of an individual organism reflects the energy and material transformations that are used for both the maintenance of existing structure and the production of new biomass. Within taxonomic and functional groups, organisms allocate a relatively constant fraction of metabolism to production (Ernest et al., 2003). In endotherms, this is typically less than 10%, but in ectotherms it tends to be of the order of 50%. Consequently, rates of wholeorganism biomass production are predicted to scale according to Eq. (1.2), with an allometric exponent of 3/4, the same as whole-organism metabolic rate. Figure 1.2 shows that the temperature-corrected rates of production for algae, zooplankton and fish cluster closely around a common allometric scaling relation with an exponent of 0.76, almost identical to the theoretically predicted value of 3/4. This implies that the relative allocation of energy and materials to biomass production is indeed similar across most organisms. It follows from the above discussion and Eq. (1.3) that the mass-specific rate of ontogenetic growth and development should scale as M1/4, and therefore that developmental time should scale as M1/4. In Fig. 1.3, we present two examples, rates of ontogenetic development of zooplankton eggs in the laboratory (panel A) and fish eggs in the field (panel B) (Gillooly et al., 2002). This is a nice model system, because the mass of the egg indicates not only the size of the hatchling, but also the quantity of resources stored in the egg and expended in metabolism during the course of development. Note that the data for fish eggs in the field give an exponent, 0.22, very close to the predicted 1/4, but there is considerable unexplained variation. This is hardly surprising, giving the inherent difficulties in measuring both development time and temperature under field conditions. The data for development rate of freshwater zooplankton eggs measured under controlled conditions in the laboratory give an allometric exponent, 0.26, essentially identical to the predicted 1/4. The regression explains 84% of the observed

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J. H. BROWN ET AL.

(a)

(b) 26 In(hatching rate *eE/kT)

26 In(hatching rate *eE/kT)

6

24 y = –0.26x + 20.37 r2 = 0.84

22

24

y = –0.22x + 22.49 r2 = 0.24 22

–20

–7.5 ln(body mass)

–10

–8

–6

–4

ln(body mass)

Figure 1.3 The relationship between temperature-corrected hatching rate, measured in 1/days, and the natural logarithm of body mass, measured in grams, for zooplankton eggs in the laboratory (panel A) and fishes in the field (panel B). Hatching rate is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2002).

variation in the temperature-corrected data. Interestingly, for ontogenetic growth rates of adult zooplankton, Gillooly et al. (2002) have shown that stoichiometry, specifically the whole-body C:P ratio, explains most of the variation that remains after accounting for the effects of body size and temperature. This supports the ‘growth-rate hypothesis’ and the large body of theoretical and empirical work in ecological stoichiometry (Elser et al., 1996; Elser et al., 2000; Sterner & Elser, 2002). The growth-rate hypothesis proposes that differences in the C:N:P ratios of organisms are due to differences in the allocation of phosphorus-rich RNA necessary for growth. For these zooplankton, living in freshwater where phosphorus may be the primary limiting nutrient, rates of metabolism and ontogenetic growth are limited by whole-body concentrations of RNA. Not only does the C:P ratio explain most of the residual variation in development rates as a function of body size in zooplankton, but it is also related to the body-size dependence of development itself. Whole-body concentrations of phosphorus-rich RNA scale inversely with body size, with an exponent of approximately 1/4 in both aquatic and terrestrial organisms (Gillooly et al., 2005a). Therefore, this example shows how a quantitative prediction from metabolic theory can be used to assess the influence of other factors, such as stoichiometry, which may account for much of the remaining variation. Since times are reciprocals of rates, metabolic theory predicts that biological times should scale with characteristic powers of 1/4. Figure 1.4 shows data for one such time, maximal lifespan, for a variety of aquatic animals ranging from zooplankton to fish. The slope of this relationship, 0.23, is very close to the theoretically predicted value of 1/4, and the fitted regression accounts for the

THE METABOLIC THEORY OF ECOLOGY

In(lifespan/e E/kT)

–10 zooplankton amphipods molluscs fish

–20

y = 0.23x – 19.74 r 2 = 0.98

–30 –20

–10

0

ln(body mass)

10

Figure 1.4 The relationship between temperature-corrected maximum lifespan, measured in days, and the natural logarithm of body mass, measured in grams, for various aquatic organisms. Lifespan is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Gillooly et al. (2001).

vast majority of variation (r2 ¼ 0.98). The enormous variation in body size across these organisms masks considerable unexplained residual variation. It is well established that even closely related animals of the same body size can differ in lifespan by at least an order of magnitude. If the first-order effect of temperature had not been removed, then there would have been even more variation, with species in cold-water environments living longer than those of similar size in warmer waters.

Population and community levels: growth, mortality and abundance There are two logical benchmarks to measure population growth rate: the maximal rate, rmax, and the rate of turnover at steady state. Data on rmax for a wide variety of organisms, from unicellular eukaryotes to invertebrates and vertebrates, have been compiled and analyzed by Savage et al. (2004b). These data give a slope of 0.23, very close to the predicted 1/4. We have extracted and plotted the subset of these data for aquatic organisms, including algae, zooplankton and fish in Fig. 1.5. The slope is a bit lower, 0.20, but the confidence intervals still include the predicted value of 1/4. We conclude that maximal population-growth rates scale similarly to mass-specific metabolic rate and follow Eq. (1.3). This is not surprising, since metabolism fuels individual production, which in turn fuels population growth, thereby determining rmax. The rate of population turnover, and hence birth and death rates, should scale similarly. Figure 1.6 shows the body-mass dependence of mortality rates of fish in the field. The fitted regression has a slope of 0.24, very close to the predicted value of 1/4. The 1/4 power scaling of natural mortality may come as a surprise to many ecologists because mortality in the field is generally thought to be controlled by extrinsic environmental conditions, such as predation, food shortage or abiotic stress, rather than to intrinsic biological traits such as metabolic rate. The majority of mortality may indeed be due to predation or

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J. H. BROWN ET AL.

30

In( rmax*eE/kT )

algae zooplankton fish

25

20

y = –0.20x + 21.90 r2 = 0.97 15 –30

–5

20

ln(body mass)

28

In(mortality rate *e E/kT)

8

Figure 1.5 The relationship between the temperature-corrected maximum rate of population growth (i.e. rmax), measured in 1/days, and the natural logarithm of body mass, measured in grams, for various aquatic organisms. Rmax is temperaturecorrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Savage et al. (2004b).

y = –0.24x + 25.04 r2 = 0.47

22

16 –5

7.5 ln(body mass)

20

Figure 1.6 The relationship between the temperature-corrected mortality rate of marine fishes in the field, measured in 1/years, and the natural logarithm of body mass, measured in grams. Mortality rate is temperature-corrected using the Boltzmann factor, eE/kT, following Eq. (1.2). Data and analyses from Savage et al. (2004b).

other extrinsic factors, but birth and death rates must match, and the rate of production must offset the rate of mortality for a population to persist. Population-turnover rate is another of those phenomena which is controlled by metabolic rate and, consequently, shows characteristic 1/4-power scaling. Metabolic rate determines the rate of population turnover, but what about the abundances or steady-state densities of populations in the field? Based on data for mammals, Damuth (1981) showed that population density scales as M3/4. This is what would be expected if populations of a guild or trophic level had equal rates of resource supply, R, because the steady-state population density, N, should be proportional to the rate of resource supply divided by the resource use or field metabolic rate per individual, P, so N / R/P / M0/M3/4 / M3/4. Recent compilations of data on population density as a function of mass generally support this prediction (Damuth, 1981; Belgrano et al., 2002; Li, 2002; Allen et al., 2002; Brown et al., 2004). For example, Li (2002) showed that the densities of morphospecies of phytoplankton in the North Atlantic scaled as M0.78, where M is cell carbon mass. An important community-level consequence of population density or number of individuals per area, N,

THE METABOLIC THEORY OF ECOLOGY

scaling as M3/4 and whole-organism field metabolic rate or energy use per individual, P, scaling as M3/4, is that the rate of community energy use per unit area, E, is independent of body size: E / NP / M3/4M3/4 / M0. Damuth (1981) called this the energy equivalence rule. If the abundance and energy use of populations scale predictably with body size, these relationships are of potentially great interest to ecologists. However, care should be taken in making and testing these predictions of MTE for several reasons. First, the assumption of equal rates of resource supply is difficult to evaluate. It is likely that species in different guilds, functional groups and trophic levels will have quite different resource availability. This could even be true for members of the same guild or trophic level. Second, resource supply sets only an upper bound on population density. Predation, competition and other limiting factors may cause the steady-state density to be well below this limiting bound. Third, the above two factors can cause considerable variation, as much as several orders of magnitude, in the observed densities of species populations in the field. Fourth, data are often plotted with each point representing a species, but in organisms with indeterminate growth and consequently wide variation in body size, it may be difficult to estimate the average body mass and abundance of a species. If the organisms really do use the same resources, it is more logical to estimate the upper bound by summing the numbers of individuals of all species in a body-size interval. Ackerman et al. (2004) performed such an analysis for all of the fish coexisting at a site on the Great Barrier Reef, and found the predicted M3/4 scaling – except for the smallest size classes, which probably share food resources with invertebrates. We conclude that metabolic rate powerfully constrains the abundance of organisms in species populations, functional or trophic groups, and body-size categories, but, again, care should be exercised in making and testing predictions based on metabolic theory.

Ecosystem level: flux and storage of energy and materials Through their metabolism, organisms contribute to the flows of energy and elements in ecosystems. These flows include not only the quantitatively dominant components of the carbon cycle, but also those involving critical limiting nutrients, such as phosphorus or nitrogen, that together with carbon, comprise the ‘Redfield Ratio’. Metabolic theory provides a conceptual basis for predicting, measuring and understanding the roles of different kinds of organisms in the flux and storage of elements in ecosystems. The total biomass per unit area, W, is simply the sum of the body mass of all individuals. For organisms of similar size, it can be estimated by taking the product of the population, N, and the body mass, M. Similarly, the store of each element in living biomass per unit area, S, is: S¼

i X 0

½Xi Ni Mi

(1:5)

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J. H. BROWN ET AL.

1

In(carbon turnover rate)

10

phytoplankton wetlands

–2

y = –0.21x – 2.83 r2 = 0.80 –5 –20

–10

0

ln(body mass)

10

Figure 1.7 The relationship between carbon turnover rate, measured as 1/days, and the natural logarithm of average plant mass, measured in grams. Data have not been temperaturecorrected because environmental temperatures were not reported. Analyses from Brown et al. (2004) and Allen et al. (2005).

where X is the whole-body concentration of substance X, and the subscript i denotes a species, developmental stage or body-size class, functional or trophic group, which should be analysed separately for accurate accounting. To a first approximation, the turnover rate of these materials is proportional to massspecific metabolic rate, B, so the rate of flux, F, is F¼

i X

½Yi Ni Bi

(1:6)

0

where Y is an element-specific constant required because turnover rates vary widely for different kinds of organisms, depending in part on the form in which they are stored (e.g. structural carbon in plants, and calcium and phosphorus in the shells of molluscs and the bones of vertebrates). Knowing Y, it is also then possible to use the general mass and temperature dependence of metabolic rate to estimate the turnover rate of a particular element. We illustrate the potential applications of this framework with two examples. First, we show the relationship between the rate of carbon turnover and plant size for freshwater and marine ecosystems, where the primary producers are predominantly phytoplankton, and for wetlands, where the primary producers are predominantly herbaceous plants (Fig. 1.7). These data have not been temperature corrected due to difficulties in estimating the relevant temperatures in these ecosystems, so temperature probably accounts for substantial residual variation. Nevertheless, the regression has a slope of 0.21, close to the predicted value of 1/4, fits the data well for both phytoplankton in open waters and herbaceous plants in wetlands, and accounts for about 80% of the observed variation. Furthermore, Allen et al. (2005) show that this same relationship can be extended to include terrestrial ecosystems, where the dominant plants vary in size from herbs in grasslands to trees in forests.

THE METABOLIC THEORY OF ECOLOGY

Allen et al. (2005) further show how this framework can be extended to understand the roles of different sizes and temperatures of plants in the flux and storage of carbon, and hence in the carbon cycle at scales from local ecosystems to the globe. Belgrano et al. (2002) developed another extension, showing that plant density across the spectrum of plant sizes from algae to trees and across a range of ecosystem types from oceans, freshwaters, wetlands, grasslands and forests shows the predicted M3/4 scaling. These examples show how MTE can be applied to make more explicit and quantitative links between the processing of energy and elements at the individual level to the flux, storage and turnover of these elements at the level of ecosystems. Our second example concerns the role of metabolism in trophic relationships, including the structure and dynamics of food webs. Above, we have shown how MTE can be applied to understand the M3/4 scaling and the M0 energy equivalence observed empirically within many functional groups and trophic levels. The theory can also be applied to understand the body-size structure of food webs and the flow of energy and materials between trophic levels. Brown et al. (2004) developed quantitative expressions for the ratios for consumer:producer ratios of: (i) metabolic energy flux, F1/F0; (ii) biomass, W1/W0; and (iii) abundance, N1/N0; where the subscripts 0 and 1 denote any given trophic level and the next highest level respectively. For aquatic ecosystems, we can usually assume that all organisms (except for endotherms, which should be considered separately) are operating at approximately the same temperature. Then these ratios are: for energy flux: F1 =F0 ¼ i1 N1 M1 3=4 =i0 N0 M0 3=4 ¼ 

(1:7)

where i0 and i1 are the normalization constants for the field metabolic rates of the producers and consumers organisms, respectively; for biomass: W1 =W0 ¼ N1 M1 =N0 M0 / ðM0 =M1 Þ1=4

(1:8)

and for abundance: N1 =N0 / ðM0 =M1 Þ3=4

(1:9)

The ratio for energy flow, a, which must always be 1) of biomass or abundance that are sometimes observed empirically (see also Jones & Jeppesen, this volume). Additionally, if a is known, Eqs. (1.7) and (1.8) can be applied, and the body sizes of the organisms occupying adjacent trophic levels can be used to predict the ratios of biomass and abundance. Conversely, if the body-size ratios are known, the above equations can be used to explore the contributions of body size and the production, consumption and assimilation efficiencies to the Lindeman efficiency. More generally, the above framework represents a start at synthesizing the different approaches to food webs that have traditionally been taken by ecosystem and community ecologists. The former have used dE/dt currencies to quantify rates of energy and material flow, whereas the latter have used dN/dt currencies to focus on the dynamics of consumer populations and their resources. By considering explicitly the allometry of resource use and abundance, metabolic theory shows how these currencies are inextricably related (see also Yodzis & Innes, 1992; Kerr & Dickie, 2001; Brown & Gillooly, 2003; Brown et al., 2004; Gillooly et al., 2006).

Concluding remarks Much of ecology is concerned with the exchanges of energy and materials (i.e. elements) between organisms and their environments. These exchanges determine the life histories of individual organisms, the abundances and turnover of populations, the allocation of resources among coexisting species, and the fluxes and pools of energy and materials in ecosystems. These exchanges are direct consequences of metabolism as organisms take up energy and nutrients from their environments, transform them within their bodies, and allocate them to maintenance, growth and reproduction. The metabolic rates of organisms vary predictably, or scale quantitatively, with body size and temperature. The metabolic theory of ecology uses these scaling relations to make and test

THE METABOLIC THEORY OF ECOLOGY

predictions about the effects of energy and materials on the ecology of organisms and the roles of organisms on the fluxes and storage of energy and materials in ecological systems. The theoretical predictions provide baselines from which to measure and understand the influences of additional factors that contribute to the variation in and around empirical scaling relations for organisms in different phylogenetic lineages, functional groups and environments. The conceptual framework of MTE presumably applies to all organisms and ecosystems. Marine and freshwater organisms and ecosystems are no exception. Indeed, there is a rich tradition of empirical and theoretical work in biological oceanography and limnology that relates the structure, function and biotic composition of these systems to the body sizes of the organisms present and the temperatures at which they are operating. We have presented just a few examples to show more explicitly and quantitatively how the developing MTE can be applied. Many of the contributions to this symposium volume present additional examples. But all these studies together provide only a limited sample of the kinds of work that can potentially be done, and the breadth and depth of understanding that they can potentially contribute. Through fisheries, pollution, climate change and other impacts, humans are transforming marine and freshwater ecosystems faster than they can be studied in detail. More data are available for some systems, such as temperate lakes and streams and the surface waters of temperate oceans, than for others, such as tropical lakes and streams and the abyssal depths of the oceans. The metabolic theory of ecology provides a general, quantitative conceptual framework, grounded in accepted first principles of biology, physics and chemistry, not only for understanding the basic ecology of aquatic ecosystems, but also for applying this knowledge to conservation, management and policy.

References Ackerman, J. L., Bellwood, D. R. & Brown, J. H. (2004). The contribution of small individuals to density-body size relationships: examination of energetic equivalence in reef fishes. Oecologia, 138, 568–571. Allen, A. P., Brown, J. H. & Gillooly, J. F. (2002). Global biodiversity, biochemical kinetics, and the energetic-equivalence rule. Science, 297, 1545–1548. Allen, A. P., Gillooly, J. F. & Brown, J. H. (2005). Linking the global carbon cycle to individual metabolism. Functional Ecology, 19, 202–213. Belgrano, A., Allen, A. P., Enquist, B. J. & Gillooly, J. F. (2002). Allometric scaling of maximum population density: a common rule for

marine phytoplankton and terrestrial plants. Ecology Letters, 5, 611–613. Brooks, J. L. & Dodson, S. I. (1965). Predation, body size and composition of plankton. Science, 150, 28–35. Brown, J. H. & Gillooly, J. F. (2003). Ecological food webs: high-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences, 100, 1467–1468. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789. Calder, W. A. (1984). Size, Function, and Life History. Cambridge, MA: Harvard University Press.

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Carpenter, S. R. & Kitchell, J. F. (1988). Consumer control of lake productivity. Bioscience, 38, 764–769. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences, 100, 1781–1786. Cyr, H. (2000). Individual energy use and the allometry of population density. In Scaling in Biology, eds. J. H. Brown and G. B. West. New York: Oxford University Press, pp. 267–295. Cyr, H. & Pace, M. L. (1993). Allometric theory-extrapolations from individuals to communities. Ecology, 74, 1234–1245. Cyr, H. & Peters, R. H. (1996). Biomass-size spectra and the prediction of fish biomass in lakes. Canadian Journal of Fisheries and Aquatic Sciences, 53, 994–1006. Damuth, J. (1981). Population density and body size in mammals. Nature, 290, 699–700. Elser, J. J., Dobberfuhl, D. R., MacKay, N. A. & Schampel, J. H. (1996). Organism size, life history, and N:P stoichiometry. Bioscience, 46, 674–684. Elser, J. J., Sterner, R. W., Gorokhova, E. et al. (2000). Biological stoichiometry from genes to ecosystems. Ecology Letters, 3, 540–550. Ernest, S. K. M., Enquist, B. J., Brown, J. H. et al. (2003). Thermodynamic and metabolic effects on the scaling of production and population energy use. Ecology Letters, 6, 990–995. Fenchel, T. & Finlay, B. J. (1983). Respiration rates in heterotrophic, free-living protozoa. Microbial Ecology, 9, 99–122. Gause, G. F. (1934). The Struggle for Existence. Baltimore: Williams and Wilkins. Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M. & Charnov, E. L. (2001). Effects of size and temperature on metabolic rate. Science, 293, 2248–2251. Gillooly, J. F., Charnov, E. L., West, G. B., Savage, V. M. & Brown, J. H. (2002). Effects

of size and temperature on developmental time. Nature, 417, 70–73. Gillooly, J. F., Allen, A. P., Brown, J. H. et al. (2005a). The metabolic basis of wholeorganism RNA and phosphorus content. Proceedings of the National Academy of Sciences, 102, 11923–11927. Gillooly, J. F., Allen, A. P., West, G. B. & Brown, J. H. (2005b). The rate of DNA evolution: effects of body size and temperature on the molecular clock. Proceedings of the National Academy of Sciences, 102, 140–145. Gillooly, J. F., Allen, A. P. & Brown, J. H. (2006). Food web structure and dynamics: reconciling alternative ecological currencies. In Ecological Networks: Linking Structure to Dynamics in Food Webs, eds. M. Pasqual and J. A. Dunne. Oxford: Oxford University Press. Hemmingsen, A. M. (1960). Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and Nordisk Insulin Laboratorium, 9, 6–110. Hutchinson, G. E. (1959). Homage to Santa Rosalia or why are there so many kinds of animals. American Naturalist, 93, 145–159. Huxley, J. S. (1932). Problems of Relative Growth. London: Methuen. Kerr, S. R. & Dickie, L. M. (2001). The Biomass Spectrum: A Predator-Prey Theory of Aquatic Production. New York: Columbia University Press. Leibold, M. A. & Wilbur, H. M. (1992). Interactions between food web structure and nutrients on pond organisms. Nature, 360, 341–343. Li, W. K. W. (2002). Macroecological patterns of phytoplankton in the northwestern North Atlantic Ocean. Nature, 419, 154–157. Lindeman, R. L. (1942). The trophic-dynamic aspect of ecology. Ecology, 23, 399–417. McMahon, T. A. & Bonner, J. T. (1983). On Size and Life. New York: Scientific American Books. Morin, P. J. (1995). Functional redundancy, nonadditive interactions, and supply-side

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dynamics in experimental pond communities. Ecology, 76, 133–149. Morin, P. J. (1999). Productivity, intraguild predation, and population dynamics in experimental food webs. Ecology, 80, 752–760. Odum, H. T. (1956). Efficiencies, size of organisms, and community structure. Ecology, 37, 592–597. Paine, R. T. (1974). Intertidal community structure. Experimental studies on the relationship between a dominant competitor and its principal predator. Oecologia, 15, 93–120. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press. Redfield, A. C. (1958). The biological control of chemical factors in the environment. American Scientist, 46, 205–221. Savage, V. M., Gillooly, J. F., Woodruff, W. H. et al. (2004a). The predominance of quarter-power scaling in biology. Functional Ecology, 18, 257–282. Savage, V. M., Gillooly, J. F., Brown, J. H., West, G. B. & Charnov, E. L. (2004b). Effects of body size and temperature on population growth. American Naturalist, 163, 429–441. Schindler, D. W. (1974). Eutrophication and recovery in experimental lakes: implications for lake management. Science, 184, 897–899. Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size So Important? New York: Cambridge University Press.

Sheldon, R. W. & Parsons, T. R. (1967). A continuous size spectrum for particulate matter in sea. Journal of the Fisheries Research Board of Canada, 24, 909–915. Sheldon, R. W., Prakash, A. & Sutcliffe, W. H. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Sheldon, R. W., Sutcliffe, W. H. & Paranjape, M. A. (1977). Structure of pelagic food-chain and relationship between plankton and fish production. Journal of the Fisheries Research Board of Canada, 34, 2344–2353. Sprules, W. G. & Bowerman, J. E. (1988). Omnivory and food chain length in zooplankton food webs. Ecology, 69, 418–426. Sterner, R. W. & Elser, J. J. (2002). Ecological Stoichiometry: the Biology of Elements from Molecules to the Biosphere. Princeton, NJ: Princeton University Press. Thompson, D. W. (1917). On Growth and Form. Cambridge: Cambridge University Press. West, G. B., Brown, J. H. & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126. West, G. B., Brown, J. H. & Enquist, B. J. (1999). The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science, 284, 1677–1679. Wetzel, R. G. (1984). Detrital dissolved and particulate organic carbon functions in aquatic ecosystems. Bulletin of Marine Science, 35, 503–509. Yodzis, P. & Innes, S. (1992). Body size and consumer-resource dynamics. American Naturalist, 139, 1151–1175.

15

CHAPTER TWO

Body size and suspension feeding STUART HUMPHRIES Department of Animal and Plant Sciences, University of Sheffield

Introduction Suspension-feeding animals are ubiquitous in aquatic ecosystems, and all major taxa have members for whom suspension feeding is the main foraging mode. Suspension feeders are often the chief primary consumers in aquatic systems but, because of the diverse nature of the particles they collect, they also contribute significantly via their effects as both secondary consumers and detritivores (Gili & Coma, 1998; Jørgensen, 1966). In removing particulate food from the surrounding water, suspension-feeding organisms act as mediators of energy flux between the photic zone and the deep sea, between continental waters and the benthic zone, and between local systems in freshwaters (Gili & Coma, 1998; Wildish & Kristmanson, 1997; Wotton, 1994). Their role in energy transfer means that they are key components of aquatic ecosystems, representing important pathways for energy flow, and are crucial determinants of the productivity of aquatic environments. Suspension feeders are characterized by the possession of an organ used to capture suspended particles from the water (feeding structure). The feeding structures utilized by suspension feeders are highly variable, and include appendages bearing hairs, mucus or silk nets, gill rakers and baleen plates, lophophores, tentacles, and ciliated and flagellated cells. Within a feeding structure, individual collecting elements are the first point of contact for food particles. Transport of particles (particle flux) to the feeding structure is achieved by the flow of water, provided either by active pumping or by external flow. Suspension feeders are generally categorized as belonging to one of two major groups, based on the extent to which ambient (external) water flow is utilized for feeding (LaBarbera, 1984; Vogel, 1994; Wildish & Kristmanson, 1997). Passive suspension feeders rely entirely on ambient flow to deliver food particles to their feeding structures, while active suspension feeders use energy to regulate water flow over or through their feeding structures using a biological pump (ciliary or muscular). However, further intermediate categorization is possible, with facultative-active suspension feeders able to switch between passive and active feeding, depending on ambient flow conditions. Combined passive-active suspension feeders (Wildish & Kristmanson, 1997) utilize both passive and active methods at the same time and to varying extents, while deposit-suspension feeders switch between Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

BODY SIZE AND SUSPENSION FEEDING

deposit-feeding (picking particles from the substratum) at low velocities, and suspension-feeding when deposited particles are resuspended by higher velocities. Body size is somewhat nebulous and difficult to specify when it comes to suspension feeders, as it is for other ecological aspects of body size in this volume. Whether to use volume, length, body mass or dry weight becomes problematic when members of the suspension-feeding functional group include gelatinous pelagic animals that have large physical size, but low carbon content as an adaptation to low food concentrations (Acun˜a, 2001). Analogously, suspension feeders with dense and massive shells, such as barnacles and bivalve molluscs, have a non-trivial proportion of metabolically inactive body mass. Similar arguments can be made for those suspension feeders that use external structures to capture food; examples include silk nets (Trichoptera), as well as mucus nets (polychaetes, appendicularians) and sheets (pelagic molluscs). Many benthic suspension feeders also exhibit a predominantly two-dimensional body plan. The majority of issues concerning body size, for instance in relation to scaling in aquatic versus terrestrial ecosystems (Schmidt-Nielsen, 1984; Denny, 1993; Alexander, 1998; Brown, Allen & Gillooly, this volume), clearly apply to suspension feeders. However, this chapter will focus on the organismal- and habitat-level implications of body size that are directly relevant to the process of suspension feeding.

The hydrodynamic implications of body size The effects of water velocity, viscosity and scale ( size of the object of interest) in any biological system can be understood most easily by using a parameter, the Reynolds number (Re), that describes the flow regime within or around that system. The Reynolds number is a scaling parameter that provides a measure (ratio) of the relative importance of inertial and viscous forces within a fluid, and describes the way in which fluids will behave at difference scales. The Reynolds number is given by Re ¼ ul/, where u is velocity, l is the linear length scale of interest, and  is the kinematic viscosity of the fluid. Crudely, for biological systems where size and speed are positively correlated (Vogel, 1994), low values (Re  1) indicate slow uniform (laminar) flow, while high values (Re  1000) indicate faster, more turbulent flow. More importantly, any combination of velocity, viscosity and scale that results in the same Re will result in a geometrically similar flow regime, as characterized by the ratio of inertial to viscous forces. Thus, doubling the length scale will result in a flow regime that can also be realized by doubling velocity or by halving kinematic viscosity. As a tool, Re provides us with a way to conceptualize the link between the size of an object and the flow characteristics it experiences. Few organisms are as directly dependent on these flow characteristics as suspension feeders: although modulated by behaviour and morphology, purely physical processes

17

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fundamentally determine the food-capture rate of suspension feeding animals. In this context body size can be seen as synonymous with flow regime, with Re relating as it does, a single measure of size to environmental conditions. In biological systems, small (and hence slow) organisms tend to operate under conditions where the fluid they are immersed in is dominated by viscous forces (low Re), while larger, faster organisms operate at higher Re, where inertial forces prevail (Vogel, 1994). While high Re characterizes the flows at a human scale, the behaviour of low Re flows are frequently counterintuitive. For instance, if a bacterium were suddenly to cease swimming, it would come to a halt in a distance much less that the diameter of a hydrogen atom (Berg, 1983). Lengths of suspension feeders vary over five orders of magnitude, from singlecelled protists to baleen whales, while the Reynolds number of such organisms in general ranges between Re  106 (bacteria) and Re  108 (large whales), or 14 orders of magnitude (Nachtigall, 2001). This provides a dramatic range of conditions in which suspension feeders operate, and leads to an array of adaptations to this feeding mode. Despite such large variations in body size, aerosol theory co-opted from engineering (Rubenstein & Koehl, 1977) suggests that there are only five inclusive mechanisms by which particles can encounter collecting elements: (i) direct interception, (ii) inertial impaction, (iii) gravitational deposition, (iv) diffusional deposition and (v) electrostatic attraction. Simple sieving (where particles are caught because they are larger than the gap between collecting elements) is generally added to this group, although in the process of sieving particles encounter the feeding structure via one of the five classic mechanisms. Direct interception involves streamline kinematics: particles travelling on a streamline that passes around the collecting element will come into contact with that element if they come within one particle radius. Inertial impaction relies on particles that are denser than the surrounding fluid failing to follow rapidly turning streamlines due to their inertia, while gravitational deposition relies on a particle’s mass causing it to cross streamlines and thus impact the collector. For smaller particles, diffusional deposition may be important, whereby Brownian motion of tiny (200 Fish CPUE (no. net–1 night–1)

Figure 3.4 Boxplot (median, 25, 75, 10 and 90% quartiles) of mean body weight of cladocerans (loge-transformed) for samples collected during summer, spring/autumn and winter versus the catch per net at night in multiple meshsized gill nets in 34 Danish lakes monitored one to three times (n ¼ 56–74). Fish sampling always occurred between 15 August and 15 September. Figure is from Jeppesen et al. (2004).

Shifts in the community size spectrum, and impacts on ecosystem function Differences in life history among higher taxa such as genera or families are usually interpreted as resulting from accumulated genetic differences driven by natural selection and phylogenetic history, with variation due to phenotypic plasticity being relatively small (Doughty & Reznick, 2004). However, whatever the cause of life-history variation, the environment can still select particular body sizes, and this can have substantial consequences for ecosystem structure and function (Hall et al., this volume; Huryn & Benke, this volume). Thus, the arguments used in previous sections about mortality effects on optimal adult size can be applied to collections of different-sized species. For instance, high mortality of large zooplankton species favours smaller species. In many lakes predation intensity by planktivorous fish has been shown to drive down the average size of zooplankters (e.g. Brooks & Dodson, 1965; Zaret, 1980; Jeppesen et al., 2004; Fig. 3.4). This removal of large grazers has profound effects on phytoplankton abundance, hence water clarity, and can even facilitate a switch between alternative stable ecosystem states (Moss, 1998; Jones & Jeppesen, this volume). A parallel shift in the community body-size spectrum is observed in heavily exploited marine fish communities, where landings have become increasingly dominated by smaller species (Jennings et al., 2002; Jennings & Reynolds, this volume). Again, size-selective mortality appears to cause decreases in the relative abundance of larger species as well as mean body size within species.

Life-history analysis and scaling relationships Key elements The magnitude of many biological phenomena, including life-history traits, increase with body size in a predictable way both within and across species and higher taxa (Brown & West, 2000; Brown et al., this volume). Typically, the magnitude of a trait is assumed to scale with body mass (M) according to a power

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function, trait value ¼ aMb, where a and b are constants. Thus, log (trait value) plotted against log M gives a straight line with slope b. A special case of scaling is when two traits (e.g. body mass at hatch and at maturity) have the same units and the value of one trait is directly proportional to the value of another: here, their ratio is a dimensionless constant or an invariant (Charnov, 1993), and a log-log plot of these values produces a slope of 1. Such invariants could underpin the form and shape of trade-offs that constrain life-history evolution, and if they extend across species could provide the basis of a general theory of life-history evolution, rather than a diverse array of species-specific models. Methodological issues Determining the scaling exponent A first issue is to ensure that the appropriate regression model is used, as the value of the scaling exponent is sensitive to whether the error is assumed to be confined just to the y-variable (as in a Type I regression), or is shared between the covariates (as in a Type II regression; McArdle, 2003). Thus, if there is a similar degree of error in both covariates, a Type II regression should be used.

Identifying invariant quantities in life histories A major problem is that the method generally used for identifying invariant quantities is flawed: thus, the very existence of invariant quantities will be in doubt until an alternative method is devised (Nee et al., 2005). The difficulty is that while it is true that for an invariant quantity the log-log regression of trait values will always produce a slope of 1, it is not true that a slope of 1 always implies invariance (Nee et al., 2005). The problem arises when the variable on the y-axis is a fraction of the x-variable, for instance mass at birth versus mass at maturity, so that the variables have been regressed against themselves. De Jong (2005) provides a graphical illustration of how combining data from very different invariant relationships for a variety of species into a single relationship for all species can produce the illusion of a single invariant quantity for all the species with a slope of 1, and high r2. A high r2 does not imply invariance, as the high r2 can arise when there is a wide range of values on the x-axis (Nee et al., 2005). This problem of detecting invariance may be more widespread than it first appears, as it can occur even when one variable does not appear initially to be a fraction of the other. For instance, the proposed invariant relationship between yearly clutch size b and adult mortality rate z has been shown by Nee et al. (2005) to involve correlation with itself. Specifically, if the animal produces E eggs in total over its adult lifetime of Y years, then its yearly clutch size b is E/Y and its annual mortality rate is 1/Y: therefore, b ¼ zE, a regression of ln(b) against ln(z) is expected to have a slope of 1.0, and r2 ¼ var[ln(z)]/(var[ln(z)] þ var[ln(E)]), which will be high if z has a wide range of values.

LIFE HISTORIES AND BODY SIZE

Determining the effects of selection on scaling exponents The value of applying scaling laws to predict diverse ecological phenomena depends on the reliability of the underlying laws, and whether selection can alter the scaling exponent. Of particular recent interest is a theory that can predict life history, population growth and carrying capacity, species richness and rates of biomass production (reviewed by Brown et al., 2004; Brown et al., this volume). This theory incorporates a long-established, fundamental generalization in biology that respiration (metabolic) rate (R) ¼ aM3/4 (e.g. West et al., 1997; Savage et al., 2004). An important question is to what extent the scaling exponent, b, is fixed at 3/4? If this exponent varies with environment (e.g. pelagic vs. benthic) substantially across taxa with diverse body plans and of widely separated phylogenies, then a strong role for selection on this exponent is suggested, and a possible role for life-history theory. This is exactly what was found in a recent survey of 642 published regressions of scaling of laboratory-measured routine aerobic metabolic rate during ontogeny of invertebrates (Glazier, 2005; Glazier, 2006). Fifty per cent were significantly different from 3/4, and this rose to 70% in analyses with more statistical power (N  50 or where body mass ranges 2 orders of magnitude). Further, the exponent varied systematically with habitat: the mean exponent (95% CL) of pelagic species was nearly 1 (b ¼ 0.95  0.05, N ¼ 58) and was very highly significantly different (p < 0.0000000001) from that shown by benthic species (b ¼ 0.74  0.02, N ¼ 355). This distinction was robust, occurring between pelagic and benthic members of each of four diverse phyla, and even between pelagic larvae and benthic adults within species. This case of convergent evolution suggests a strong role for natural selection. Research is needed to discover whether near-isometric scaling of metabolic rate in pelagic species is associated with, for instance, size-dependent costs of locomotion or maintaining buoyancy, or size-dependent evolutionary responses to higher levels of predation. Relationship between intraspecific and interspecific allometries Typically, allometric relationships between some traits and body size across species use data from adults only (e.g. Savage et al., 2004). If it is assumed that natural selection has optimized body size through optimal allocation of resources to growth and reproduction independently in each species, then interspecific allometries become by-products of many body-size optimizations across the species included (Kozłowski & Weiner, 1997). This can produce different slopes for intraspecific and interspecific allometries. For instance, if one species (species A) is adapted to conditions that allow faster growth and reproduction than a related species B, then all else being equal, species A will have a higher mass-specific metabolic rate because of its faster rate of growth, and is predicted by simple evolutionary models to mature at a larger size (Kozłowski & Weiner, 1997; Daan & Tinbergen, 1997; Day & Rowe, 2002). Thus, in this case the interspecific allometric relationship will be steeper than the intraspecific ones.

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However, as different patterns of growth and mortality select different patterns of adult size and mass-specific metabolic rate, a variety of interspecific allometric slopes with varying amounts of scatter can result, depending on the species included in the comparison (Daan & Tinbergen, 1997). Further implications of this kind of reasoning for interspecific scaling of metabolism are discussed by Kozłowski, Konarzewski and Gawelczyk (2003). However, it may be inappropriate for ecologists to use interspecific allometries based just on adults to predict rates such as growth or mortality within ecological functional groups, as they ignore the majority of organisms – juveniles. Instead, allometric relationships should incorporate all relevant size classes of the different species in the community. Ecological applications

Estimating global patterns of mortality Here, scaling relationships and life-history analysis are applied to deducing the value of a difficult-to-measure life-history and demographic trait (mortality) from data on other life-history and demographic variables (fecundity, development period, reproductive rate). A specific example is the estimation of global rates and patterns of mortality in marine epipelagic copepods, where scaling with body size and temperature can be examined (Hirst & Kiørboe, 2002). Mortality is especially difficult to measure in the marine environment, which is physically dynamic and where planktonic populations cannot be easily followed through time. Consequently, mortality measurements in this group are relatively scarce, and confined to a narrow range of taxa, body sizes or environment types, which limit the ability to estimate the dependence of mortality on temperature and body mass. Therefore, Hirst and Kiørboe (2002) predicted mortality rates from data on fecundity rates, egg-hatch times, egg-to-adult times and sex ratios, all of which were available from more diverse sets of species, environments, body sizes and temperatures. Their initial assumptions (justified below) were that, on average, the populations were in steady-state, the mortality rate (d1) was age independent, and egg-production rate was constant for adult females irrespective of their age. With these assumptions the net reproductive rate, which is the number of offspring per female that survive until the next generation (R0), is derived from the rate of mortality, the development time (D, days ¼ time from being laid as an egg to moulting into adulthood), and the egg-production rate (m, eggs female1 d1) (Kiørboe & Sabatini, 1994): R0 ¼ ðm=ÞeD

(3:2)

Thus, for the population to be maintained, R0 has to equal S þ 1, where S is the ratio of adult males to females, as at steady-state each female must replace herself and produce the appropriate number of males given the sex ratio. The assumption of steady-state, averaged globally, must be approximately true

LIFE HISTORIES AND BODY SIZE

because copepods are neither going extinct nor taking over the world. The assumption of constant fecundity with age in copepods was made because this group has determinate growth: with no adult moults or great increase in adult body size. Equation (3.2) was then used to derive mortality-rate estimates for sac spawning species (i.e. those species that carry their eggs from laying up to the point of hatch), with the same value for mortality rates across eggs and posthatch stages. Approximately equal mortality across all stages including eggs has been demonstrated for sac spawners in the field (Ohman & Wood, 1996; Liang & Uye, 1997). Hirst and Kiørboe (2002) also altered this approach for broadcasting species (whose eggs do not remain attached to the female but rather are free) to allow for the highly vulnerable eggs of this group (see their study for details). When compared with the limited and highly variable measures of field mortality rates, the model predictions matched well with the average rates and patterns, and with adult longevity with respect to temperature and body size (Hirst & Kiørboe, 2002). The body-mass scaling of copepod mortality was compared with a general relationship for other marine organisms: pelagic invertebrates; the eggs, juveniles and adults of fish; and mammals (data from McGurk, 1986). Copepods have much flatter slopes than the general relationship (Fig. 3.5), suggesting that the smaller bodied copepods are avoiding mortality that other marine animals of a similar size are not. Copepods have especially well-developed predator sensory systems (the first antennae) and strong escape responses, which may in part account for their ability to escape mortality. Verity and Smetacek (1996) have suggested that the remarkably homogeneous body form observed across the range of free-living epipelagic copepods has resulted from strong predation pressures. Thus, life-history analysis can be applied to identify global patterns of vital rates in populations of diverse species belonging to a large taxonomic group (copepods). Copepods are the dominant metazoan grazers of marine phytoplankton, provide an important trophic link to fish, are key exporters of particulate organic carbon from the upper mixed layer of the ocean (see Kiørboe, 1998), and play a pivotal role in regenerating nutrients in the vast oligotrophic areas of ocean (Banse, 1995). Therefore, this application of life-history analysis is likely to be important for understanding oceanic ecosystem function and global biogeochemistry.

Improving predictions of global patterns of life history Gillooly et al. (2002) have produced a model of development times for animals, including egg-hatch times and egg-to-adult times, with the primary determinants being body mass and temperature. They corrected development times for mass (as development time/mass0.25) and plotted these against temperature (as Tc/(1 þ (Tc/273)), where Tc is the temperature in 8C: this term represented a

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101

100

Mortality rate (β, d–1)

48

10–1

10–2

10–3

10–4

Other pelagic invertebrates Fish eggs, juveniles and adults Marine mammals Copepods – sac spawners Copepods – broadcast eggs Copepods – broadcast post-hatch

10–5 10–8 10–7 10–6 10–5 10–4 10–3 10–2 10–1 100 101 102 103 104 105 106 107 108 Weight (W, g) 1

Figure 3.5 Mortality rates (b, d ) as a function of body dry mass (W, g ind1) for pelagic invertebrates (excluding copepods) and the eggs, juveniles and adults of fish, and marine mammals (from McGurk 1986). Regression through these data is given by a dotted line log10b ¼ 0.325log10W  2.086 (r2 ¼ 0.826, p < 0.001). Predicted relationships from Hirst and Kiørboe (2002) are given for broadcast eggs (solid line), broadcasters post-hatch and sac spawners (dashed line). For broadcasters post-hatch and sac spawners body masses are taken as adult masses, whereas for the broadcast eggs egg masses are used. All copepod data corrected to 158C using a Q10 value of 2.0. Figure adapted from Hirst and Kiørboe (2002).

correction to relate temperature to zero Kelvin, used in biochemical kinetics theory (Hochachka & Somero, 2002)). They initially suggested that these plots would produce lines with universal slopes and intercepts. Thus, egg-hatch times should share a common slope and intercept, as should egg-to-adult times. However, Gillooly et al. (2003) have since acknowledged that intercepts are non-universal, stating ‘In our model, the coefficient a allows for variation in intercepts with metabolic rate B0, and hence for differences in development times depending on which taxa, environmental conditions and developmental stages are measured’. Variability in the intercepts of development times versus temperature have been explored further by Hirst and Lo´pez-Urrutia (2006). Using marine plankton and nekton groups as a case study, with data compiled from the copepods, chaetognaths, appendicularians, cephalopods, fish, euphausiids and mysids, they found that although differences are often taxonomically based, other factors can be important too. Specifically, after allowing for temperature and mass, a significant proportion of the variability that remains in egg-hatch times can be accounted for by the vulnerability (mortality) of the eggs. Eggs that are protected in some way, such as carried by the female, laid in

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free-floating clumped masses, or attached to the substratum, have temperaturecorrected hatch times that are on average 3.3 times longer than those for unprotected free planktonic eggs at equivalent egg masses. Furthermore, not only can differences in the egg-hatch time be observed, but data on the two- to four-cell cycle times in marine invertebrate embryos also demonstrate similar separation on the basis of egg protection strategy (Strathmann, Staver & Hoffman, 2002). Differences in egg-hatch times not only occur between taxa on the basis of egg-protection strategy, but also within single taxa such as the copepods. As the sac-carried eggs of copepods are around an order of magnitude less vulnerable than are broadcast eggs (see previous section), the patterns found in this analysis qualitatively agree with expectations from an evolutionary perspective: the period of time animals spend in some life-history stages appears to be negatively related to their vulnerability. There is also clear evidence of trade-offs between different life-history attributes. The shorter hatch times in broadcasting copepods are not short enough to offset the higher mortality in the egg stage in comparison to sac spawners (i.e. for a given number of eggs laid there will be, on average, more hatchlings from sac spawners than broadcasters). Broadcasters appear to make up for this reduced survival over the egg period in other ways: although the two groups have similar amounts of energy to invest in eggs (Hirst & Bunker, 2003), broadcasters achieve a higher rate of fecundity than sac spawners by producing relatively smaller eggs (Bunker & Hirst, 2004). It is interesting that although sac-spawning copepods are not uncommon in the marine environment, the broadcasters are generally dominant, whereas in freshwater almost all pelagic copepods are sac spawners. It is suggested here that a broadcast strategy would simply be too costly on egg survival in freshwaters, where the water column is relatively shallow and benthic predation intense, so that any eggs which settled out would have poor chances of survival.

Conclusion This chapter has shown how life-history analysis can predict the evolution of body size in different environmental conditions, and can help explain the scaling of important vital rates with body mass and temperature. Like the book as a whole, this chapter illustrates the importance of body size throughout ecology, including microevolution, population dynamics, and the structure and functioning of communities. Functional relationships between organism life histories and higher levels of ecological organization, including ecosystem functioning, are becoming increasingly appreciated, and act both up and down levels of organization. The importance of community structure on life history (including adult and offspring size), is highlighted, for instance, in recent models of optimal life history that invoke selective pressures that depend on the community size spectrum (Thygesen et al., 2005), and on indirect

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(community) consequences when altering predation rates (Gardmark, Dieckmann & Lundberg, 2003). On the other hand, the importance of life-history trade-offs in determining community structure is illustrated, albeit in a terrestrial system, by the way continuously varying life histories and trade-offs can allow multiple competitors to coexist (Bonsall, Jansen & Hassell, 2004), suggesting that such trade-offs may be fundamental to understanding the structure of ecological communities.

Acknowledgements DA’s research is supported by NERC and EU Framework 6 funding; AGH is supported as part of the BAS DISCOVERY 2010 Programme. We thank two anonymous referees for helpful comments.

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CHAPTER FOUR

Relationship between biomass turnover and body size for stream communities ALEXANDER D . HURYN University of Alabama

ARTHUR C . BENKE University of Alabama

Introduction A crucial requirement for the analysis of energy flow through freshwater food webs is the accurate and precise estimation of secondary production (Benke et al., 1988). The rate of production (or biomass-turnover rate) is often expressed as either annual production-to-biomass ratios (annual P/B) or daily biomassgrowth rates (g, Appendix I). Invertebrate production and annual P/Bs have now been estimated on a taxon-specific basis for a relatively wide range of freshwater habitats, streams and rivers in particular, and often this has been done within a community context (see reviews by Benke, 1993 and Huryn & Wallace, 2000). The relationships between body size and either daily or annual P/B for freshwater invertebrates have been assessed using empirical approaches (Banse & Mosher, 1980; Plante & Downing, 1989; Morin & Bourassa, 1992; Benke, 1993; Morin & Dumont, 1994). The results of such studies provide strong evidence that annual P/B is negatively related to body size (Appendix I; Fig. 4.10). However, recent efforts showing remarkably high P/Bs for some benthic macroinvertebrates in both warm-water (e.g. Benke, 1998; reviewed by Huryn & Wallace, 2000) and cool-water streams (e.g. Nolte & Hoffman, 1992) suggest that the results of these early studies – Banse and Mosher’s (1980) still widely cited analysis, for example – greatly underestimate biomass turnover. Furthermore, because they are based on meta-analytical approaches incorporating comparison of populations taken from many different communities, these earlier studies do not allow the analysis of factors constraining patterns of P/B as a function of the body size of individual taxa within single communities. The allometric relationship between body size and bioenergetic variables has captured the interest of ecologists for some time (reviewed by Peters, 1983; Schmidt-Nielsen, 1984; Glazier, 2006). Recent studies of the role of metabolic constraints as determinants of the relationship between body size and production have advanced earlier efforts by producing a conceptual framework that explicitly links metabolic theory with ecological theory (Brown et al., 2004; Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

A. D. HURYN AND A. C. BENKE

Brown, Allen & Gillooly, this volume). This conceptual framework (i.e. the ‘metabolic theory of ecology’; Brown et al., 2004) provides a number of specific predictions about the relationship between body size and bioenergetic variables over a wide range of ecological scales. In this paper we test selected predictions that relate to the relationship between body size and P/B for stream animal populations and communities. We chose to focus on the P/B because it is a powerful variable that summarizes the dynamic relationship between growth rate, biomass and production (Appendix I).

The predictions We used detailed community-level production budgets for four streams (described below) to test a priori predictions about the relationship between body size (M, mg or mg dry mass (DM) or ash-free dry mass individual1) and population density (N, no. individuals m2), biomass (B ¼ M  N, mg m2), production (P, mg dry mass or ash-free dry mass m2 yr1), and the P/B (yr1). We chose to analyze the relationship of each of the major production variables (N, B, P) with body size because they all interact to contribute to the ultimate relationship of body size with P/B (Appendix I). As will be seen, each of the predictions described below is derived from the theoretical framework proposed by Brown et al. (2004).

Prediction 1 Density (N, number of individuals m2) will decrease as body mass increases (M, mg individual; Fig. 4.1). Some previous studies (e.g. Brown et al., 2004; Woodward et al., 2005a) have indicated that N / M0.75 when the relationship is fitted to a power curve using least-squares regression. This relationship is expected if the following conditions are met: (1) requirement for resources by individuals scales as M0.75, (2) population size increases until limited by resources (i.e. equilibrium density), and (3) total resource use will be independent of M because resources are used at equal rates by members of each size class within a given population (Brown et al., 2004).

log abundance (N, individuals m–2) log biomass (B, mg m–2) log production (P, mg m–2 yr–1) log P/B (P/B, yr–1)

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body size (M, mg individual–1)

Figure 4.1 Predicted relationships between individual body mass and areaspecific abundance, biomass, production and the P/B. The predictions follow Brown et al., 2004.

BIOMASS TURNOVER AND BODY SIZE

Prediction 2 Assuming that a population is at equilibrium density (i.e. N / M0.75), population biomass (B ¼ M  N, mg dry mass or ash-free dry mass m2) will increase with body mass, such that B / M0.25 (Fig. 4.1). This relationship is attributed to a lower rate of flow of energy and resources through the bodies of large versus small organisms (indicated by time-specific P/B, see Appendix I, Fig. 4.10) as a result of lower metabolic costs (see Prediction 3, below; Brown et al., 2004). Prediction 3 Biomass turnover rate (P/B, yr1) will decrease with increasing M, because organisms with large body sizes often have longer development times (or CPIs, Appendix I) compared with organisms with small body sizes. The decrease in P/B is proportional to M0.25 (Fig. 4.1), which is equivalent to dividing P / M0 (see Prediction 4, below) by B / M0.25. P/B / M0.25 is identical to the relationship of the empirically derived mass-specific metabolic rate with M (Brown et al., 2004). Prediction 4 Production (P ¼ B  P/B, mg dry mass or ash-free dry mass m2 yr1) will be independent of body size (Brown et al., 2004). This is because the product of B / M0.25 and P/B / M0.25 is equivalent to P / M0 (Fig. 4.1). Each of these predictions is subject to the assumptions that resource supply and temperature are constant across body-size classes. These assumptions appear to be reasonable for population and taxon-specific production statistics extracted from within single and independent stream communities rather than for data that are pooled across communities. This is an important distinction because most studies of the relationship between body size and components of production are based on the analysis of variables pooled across a diverse assemblage of communities and ecosystems (e.g. Banse & Mosher, 1980; Benke, 1993; Morin & Dumont 1994; Brown et al., 2004), yet the factors believed to constrain these variables – such as temperature and nutrient and organic carbon supply – operate within communities and ecosystems (see Cyr & Walker, 2004).

Study streams We used data from four streams for our tests of these predictions – the Ogeechee River, Georgia; Upper Ball Creek, North Carolina; and Sutton Stream and Stony Creek, New Zealand. Each stream has perennial flow and we assume that trophic resources limit community secondary production rather than physical factors such as disturbance (see assumptions related to Prediction 1). Since our data sets are based on discrete communities we are able to assume that representatives of the different body-mass classes within each system were subject to similar resource and temperature regimes. We chose these streams because the production dynamics of their communities has

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been studied in depth. What is also particularly significant, however, is the way production was estimated for each community. Special effort was made to include all taxa of macrofauna and temporary meiofauna (e.g. retained by 100 to 250 mm mesh sieves), and production calculations for each community were independent of one another. In other words, production calculations were based entirely on system-specific and taxon-specific growth rates and lifehistory studies. This is an important point because many estimates of production are based on CPIs, P/Bs, or growth rates that have been derived from other species and/or systems. This is clearly problematical for analyses that require independent data.

Ogeechee River The Ogeechee is a low-gradient coastal plain river in which the major stable habitat is submerged wood (snags). Mean daily water temperature ranges from 2.0 to 30.88C (annual mean 19.38C) and mean annual discharge is 67 m3 s1. The densities, biomass, production and annual P/B values for its snag-inhabiting community, which is composed of more than 40 invertebrate taxa, were estimated during 1982 (Benke & Parsons, 1990; Benke & Jacobi, 1994; Benke & Wallace, 1997; Benke, 1998; Benke et al., 2001; Benke, 2002). Twenty snag samples were collected at least monthly. Care was taken to obtain the full range of insect size classes by using a 100 mm mesh sieve. Individual growth studies were done for many of the small fast-growing taxa (selected Diptera and Ephemeroptera) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. The snag community is extremely productive, when compared with the shifting-sand community of the main channel. Total annual snag production during the study was 109.3 g DM m2 (snag surface area) for primary consumers, 30.8 g DM m2 for omnivores, and 7.5 g DM m2 for predators. Upper Ball Creek Upper Ball Creek is a fishless, high-gradient headwater stream in the Appalachian Mountains of western North Carolina, USA. Its catchment is heavily forested and relatively undisturbed. Annual mean daily water temperature and discharge are 8.48C and 20 L s1, respectively. Production of its macroinvertebrate community (71 taxa) was estimated for one year during 1982–1983 (Huryn & Wallace, 1986, 1987a, 1987b; Huryn, 1990). Twenty samples were taken at monthly intervals at random locations within a 400-metre reach using a Surber sampler fitted with a 232 mm mesh net or a coring device. Samples were processed using a 100 mm sieve. Individual growth studies were done for many of the small fastgrowing taxa (Chironomidae) and slow growing taxa (crayfish) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. Annual macroinvertebrate production was 5.1 and 1.9 g ash-free dry mass m2 for primary and secondary consumers, respectively.

BIOMASS TURNOVER AND BODY SIZE

Sutton Stream and Stony Creek Sutton Stream and Stony Creek are moderate-gradient headwater streams in the Lammerlaw Range of the South Island of New Zealand. The river valleys are incised and rugged with schist bedrock. Vegetation is largely exotic pasture grasses and native tussock grasses that are extensively grazed by livestock. The 400-metre study reaches selected at each site have no canopy, although there are shrubs along the stream margins. Mean daily water temperature ranged from 0.0 to 17.48C (annual mean ¼ 5.68C) in Sutton Stream, and from 0.0 to 16.48C (annual mean ¼ 6.08C) in Stony Creek. Mean annual discharge of Sutton Stream is 568 L s1; discharge of Stony Creek is 461 L s1. Sutton Stream is inhabited by introduced brown trout (Salmo trutta); Stony Creek is inhabited by native river galaxias (Galaxias eldoni). These fish species are the top predators in both systems. Production was estimated for a one year period during 1991–1992 for 37 taxa in Sutton Stream and 42 taxa in Stony Creek (Huryn, 1996a, 1996b, 1998). Samples used to estimate invertebrate production were collected from each stream approximately monthly during 1991–1992. Sixteen benthic samples were taken from random locations approximately monthly using a 900 cm2 Surber sampler fitted with a 232 mm net. Samples were processed using a 250 mm sieve. Individual growth studies were done for many of the small fastgrowing taxa (Leptophlebiidae) and slow-growing taxa (Potamopyrgus) so that accurate taxon-specific estimates of biomass turnover (annual P/B) could be obtained. Fish production was also estimated using standard methods (Huryn, 1996a, 1998). Annual primary consumer production for Sutton Stream was 11.2 g ash-free dry mass m2, secondary consumer production was 2.1 g m2, and trout production was 2.1 g m2. Primary, secondary and Galaxias production in Stony Creek were 7.7, 0.9 and 0.2 g m2 yr1, respectively. Trout predation in Sutton Stream exerted strong top-down control on prey production. In comparision, Galaxias predation in Stony Stream had minor energetic consequences for prey production (Huryn, 1998).

Tests of predictions The average individual mass for each taxon was estimated as B/N ¼ M (mg individual1) for each stream community. Two basic approaches were used. The first approach consisted of summing production statistics for taxa occurring within discrete body-size classes. M was log10 transformed and each taxon assigned to the appropriate body-size class (log10M ¼ 0.5–0.99, 1.0–1.49 . . . 6.5–7.49). The N, B and P values for each taxon in each size class were then summed as suggested by Brown et al. (2004). A P/B was then calculated for each size class using summed values. Plots of body-mass category versus log10 transformed N, B, P and P/B were then prepared and least-squares regression was used to fit a linear model to the plots. The second approach assessed the relationship

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between M and N, and M and P/B, using individual taxa rather than size classes. The purpose of this analysis was to assess the variability of the relationship between M and N, and M and P/B within independent communities. Scaling coefficients for log10 N, B, P and P/B versus log10 M were obtained from least-squares linear-regression models. Predicted scaling exponents were assumed to be statistically indistinguishable from observed exponents when they fell within two standard errors (SE) of the latter. Results The scaling exponents for N versus M (taxa summed within size classes) ranged from 0.99 to 0.59 (Fig. 4.2). All regressions were significant (p < 0.05). The scaling exponents were negative and within one (Ball Creek, Sutton Stream, Stony Creek) or two SE of the predicted exponent of 0.75 (Fig. 4.3). The scaling exponents for B versus M (summed taxa) ranged from 0.13 to 0.29 (Fig. 4.4). Only the regression for Ball Creek was significant, however (p < 0.04). Nevertheless, the relationship between B and M was similar for all streams, with positive exponents that were within one SE of the predicted exponent of 0.25 (Fig. 4.3).

Ball Creek log10N = 4.52 – 0.76 log10M (r2 = 0.95, p < 0.001)

Ogeechee River log10N = 5.35 – 0.99 log10M (r2 = 0.88, p < 0.001)

log10N (individuals/m2)

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Sutton Stream log10N = 3.91 – 0.59 log10M (r2 = 0.62, p < 0.04)

0 0 1 7 log10M (∝g)

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Figure 4.2 Log-log plots of population density (N ¼ individuals/m2) against M (summed taxa, mg/individual) for the snag-community of the Ogeechee River and benthic communities of Ball Creek, Sutton Stream and Stony Creek. The largest body-size class for Ball Creek is occupied by crayfish. The largest body-size classes for the latter two streams are occupied by invertivorous fishes. The grey line indicates the predicted slope of the relationship between log10N and log10M (N / M0.75). The black line indicates the slope derived from least-squares regression of the data.

Upper Ball

Sutton

Ogeechee

B

N

*

*

*

*

*

P P/B

*

*

*

Ogeechee

*

Upper Ball

0.30 0.20 0.10 0.00 –0.10 –0.20 –0.30 –0.40 –0.50 –0.60

*

Sutton

1.00 0.75 0.50 0.25 0.00 –0.25 –0.50 –0.75 –1.00 –1.25 –1.50

Stony

Scaling coefficient (b)

Stony

BIOMASS TURNOVER AND BODY SIZE

Figure 4.3 Summary of regression coefficients describing the slopes of the relationships between body size (M) and N, B, P/B and P for the snag-community of the Ogeechee River and benthic communities of Ball Creek, Sutton Stream and Stony Creek. The solid black lines indicate predicted slopes of the relationships (i.e. N / M0.75, B / M0.25, P/B / M0.75 and P / M0). The error bars are 1 SE.

The scaling exponents for annual P/B versus M (summed taxa) ranged from 0.24 to 0.27 (p < 0.01) for Ball Creek, Sutton Stream and Stony Creek, and were remarkably similar to the predicted exponent of 0.25 (Figs. 4.3 & 4.5). The scaling exponent for the Ogeechee River (0.50, p < 0.01), however, diverged substantially from this prediction (Figs. 4.3 & 4.5). The regression of P versus M was not significant, as predicted, for Ball Creek, Sutton Stream and Stony Creek, with scaling exponents ranging from 0.13 to 0.03 (Fig. 4.6). Each of these fell within one SE of the predicted exponent of 0 (Fig. 4.3). The scaling exponent for the Ogeechee River, however, indicated a strong negative relationship between P and M (summed taxa, Fig. 4.6) and, like the P/B values estimated for this community (Fig. 4.5), showed a significant departure from the expected exponent (Fig. 4.3). Production by the snag community of the Ogeechee River was much greater than the other streams, as indicated by the relative height of the normalization constant for the relationship between P and M (summed taxa, Fig. 4.6). This is to be expected, given the three- to four-fold greater average annual temperature of the Ogeechee River compared with the other streams (Brown et al., 2004). The scaling exponents for N versus M (individual taxa) ranged from 0.79 to 0.52 (Fig. 4.7). Those for the Ogeechee River and Ball Creek fell within one SE,

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Ball Creek log10B = 1.72 + 0.21 log10M (r2 = 0.54, p < 0.04)

Ogeechee River log10B = 2.38 + 0.13 log10M (r2 = 0.12, p = 0.402)

log10B (mg/m2)

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Stony Creek log10B = 1.77 + 0.13 log10M (r2 = 0.06, p = 0.590)

Sutton Stream log10B = 1.29 + 0.29 log10M (r2 = 0.27, p = 0.230)

0 7 0 1 log10M (∝g)

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Figure 4.4 Log-log plots of population biomass (B ¼ mg/m2) against M (mg/individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10B and log10M (B / M0.25). The black line indicates the slope derived from least-squares regression of the data.

and those for Stony Creek and Sutton Stream fell within two SE, of the predicted slope of 0.75. The scaling exponents for P/B versus M (individual taxa) ranged from 0.41 to 0.18 (Fig. 4.8). The exponents for Stony Creek and Sutton Stream fell within one SE, and the exponent for Ball Creek fell within two SE, of the predicted exponent of 0.25. Only the exponent of the Ogeechee River (0.41) departed significantly from the predicted value. Although greater variability is apparent in both the departure of the observed scaling exponents from those expected, and the relatively low r2 of the regression models, the pattern of concordance of observed-to-predicted scaling exponents among communities, using individual taxa (>37 taxa per stream), was essentially the same as that observed for the analysis using taxa summed within size classes (seven to eight size classes per stream). Discussion Annual biomass turnover rates for benthic freshwater macroinvertebrates range over four orders of magnitude, from 200 (Butler, 1982; Benke, 1998; Huryn & Wallace, 2000). Although annual P/Bs for taxa with relatively

BIOMASS TURNOVER AND BODY SIZE

Ball Creek log10P/B = 1.22 – 0.24 log10M (r2 = 0.75, p < 0.006)

log10 annual P/B

Ogeechee River log10P/B = 2.46 – 0.50 log10M (r2 = 0.89, p < 0.001)

2.7

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0

2 3 4 5 6 7 Stony Creek log10P/B = 1.31 – 0.27 log10M (r2 = 0.81, p < 0.006)

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Figure 4.5 Log-log plots of annual P/B (yr1) against M (mg/individual) for four stream communities (see Fig. 4.2 for details). The grey line indicates the predicted slope of the relationship between log10P/B and log10M (P/B / M0.25). The black line indicates the slope derived from least-squares regression of the data.

small body size (e.g. M  (λ) m–2

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Figure 8.4 Species- and particle-size frequency distribution in three stream ecosystems (Seebach (SB), Llwch (LL) and Mynach (MY)). Mean number of species per 1 m2 given over 300 sizeclasses in increments of 100 mm for the total size range 30 mm. The figure insets show the most abundant species over 300 size classes in increments of 10 mm for body sizes 3 mm. Mean particle density per 1 ml over 600 size classes in increments of 5 mm is shown superimposed in the inset as open circles (SB), triangles (LL) and squares (MY). n is the number of species in each stream community.

emphasizes the distinctness for multifractality of the BSDs in all streams (Fig. 8.6a). This result strongly contrasts to spectra, which would collapse into a narrow range of  or even into a single value for a strictly monofractal, homogeneous size distribution with a single scaling exponent. In the three streams, the multifractal spectra were characterized by similar entropy dimensions, (1) ¼ D1 with values close to 1, which predicts that the irregularities of the species-frequency distribution are even across body sizes (Figs. 8.4 & 8.6a; Table 8.3). The fraction of small-sized particles from interstitial sediments may serve as a potential food and habitat source for the benthic communities. The particle-size distribution displayed a decline in the mean number of particles with increasing particle size (inset Fig. 8.4). Scaling irregularities increased with particle size and were particularly pronounced in the SB (inset Fig. 8.4). The interstitial particle

BODY SIZE AND SCALE INVARIANCE

Table 8.3 Summary of parameters obtained by multifractal analysis of body- and particle-size distributions in the streams Seebach (SB), Llwch (LL) and Mynach (MY). a(1), a(0) and a(1) are the Lipschitz-Ho¨lder exponents with 1 SE for q ¼ 1, q ¼ 0 and q ¼ 1 respectively. r2 are the coefficients of variation of the linear regression of log partition function on log size for each a(q). Stream

SB LL MY

Body-size distribution ( 1)

r2

(0)

r2

(1)

r2

1.039  0.078 1.131  0.024 1.075  0.011

0.998 0.999 0.999

1.012  0.027 1.044  0.003 1.030  0.001

0.997 0.999 0.999

0.882  0.002 0.949  0.001 0.968  0.001

0.998 0.999 0.999

Stream

SB LL MY

Particle-size distribution 2

( 1)

r

1.389  0.096 1.244  0.047 1.289  0.033

0.995 0.996 0.999

40

(0)

r2

(1)

r2

1.138  0.004 1.087  0.002 1.098  0.002

0.999 0.999 0.999

0.792  0.003 0.842  0.003 0.767  0.002

0.996 0.996 0.997

SB

30 20 10 0

Log partition function, log µq(λ)

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q = –10

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40 MY

30 20 10 0 –10 –20

–1.0 –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 0.8 Log body-size, λ (mm)

Figure 8.5 Log partition function, log q(l), as a function of log body-size (l) for q-moments in the range between 10 and 10 at 0.5 lag increments for the streams SB, LL and MY. Linear regressions are superimposed for each q-moment (for all r2  0.95; P < 0.001). Significant linear relationships are similar for particle-size distributions not shown here.

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Multifractal spectrum, f (α)

P. E. SCHMID AND J. M. SCHMID-ARAYA

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Figure 8.6 Multifractal spectra for the (a) species- and (b) particle-size distributions in the streams SB, LL and MY.

distribution displayed multifractal properties (over all 10  q  10; r2 > 0.99), with wider f()-spectra than those for the species-size distributions (Fig. 8.6b). The values of the entropy dimension, (1) ¼ D1, differed from 1 (Table 8.3), which implies that particle-size irregularities are unevenly distributed and concentrate in several subintervals, which was particularly evident for the SB and MY (Figs. 8.4 & 8.6b). The various scaling domains of interstitial particles are similar to those from different soil PSDs (Posadas et al., 2001). To test the similarity of the multifractal patterns between organisms and particles the Re´nyi exponents,  q, of the BSD were plotted against the  q of the PSD for each stream (Fig. 8.7). All stream ecosystems were characterized by two linear sections of the  q relationships, where the larger section defined trends for q < 0 and the shorter, steeper section of the curve defined trends for q > 0. The well-defined difference between the two curve sections strengthens the finding of multifractal patterns governing both BSD and PSDs in streams. Particularly striking is the similarity between BSD and PSDs scaling exponents in the first-order LL as shown by the closeness of the curve to a slope of unity (Fig. 8.7). Moreover, the relationship between the Re´nyi exponents of the BSD 10

Rényi exponent of body-size distribution, τq

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–20 –20 –15 –10 –5 0 5 Rényi exponent of particle-size distribution, τq

Figure 8.7 The Re´nyi exponents, (q), of the body-size versus (q) of particle-size distribution in the streams SB, LL and MY. The dotted line gives a slope of unity.

BODY SIZE AND SCALE INVARIANCE

and PSD are similar between the Oberer Seebach (SB) and Afon Mynach (MY) for larger species and particle sizes. A distinct departure occurred between the two streams for smaller, more common species and particles. Further evidence for a close link between habitat- and body-size is given by recent experiments conducted in a Japanese mountain stream. This study revealed that body sizes of invertebrates tended to decline with decreasing crevice size, thus, strongly underlining the effect of fractal habitat complexity on body-size distribution (Taniguchi & Tokeshi, 2004; see also Townsend & Thompson, this volume).

Multifractal species-area relationships The species-area relationship (SAR) is one of the most widely studied patterns in community ecology and is often expressed as a single power-law curve. However, the SAR should not be characterized by a single curve that assigns one species richness value to each sampled area, as different samples of equal area differ in species number. Therefore, the SAR should be given as the relationship between area and its mean number of species, <S>. <S> was calculated for non-overlapping but equally shaped sampling areas taken over the sampling period. In order to estimate the mean number of species in an increasing area of size l ¼ k2 (where k ¼ 1, 2, 3, . . . ! l  maximum area), 106 Monte-Carlo randomizations without replications of the data matrix were conducted for each k-set. By randomly pooling samples of the observed data sets taken at arbitrary sampling positions and/or occasions, it was possible to obtain samples incorporating invertebrate species over different developmental stages, body-size ranges and densities. The species-area curves were obtained by averaging species richness of those randomly pooled sample sites for each area of size l. Some authors have suggested that the SAR following a power-law curve holds at all spatial scales and implies self-similarity in the distribution and abundance of species (e.g. Harte et al., 1999). A problem with this monofractal assumption is that scale invariance of SARs is not maintained over all spatial scales, but that there are different scaling domains underlying SARs over different spatial scales. Thus, irregularities in the species-abundance distribution may be statistically the same across areas resulting in a spectrum of fractal subsets. To test for different scaling domains underlying the SARs of the stream communities, the method of Re´nyi’s generalized dimension (Dq) was used for the speciesabundance data. This method follows Eqs. (8.7) to (8.11) outlined in Fractal properties of size-structured communities (see above), where in the current context, pi is defined as the relative abundance of species i in an area l. The relationships between mean species richness and sampled area is displayed as a power-law function for each of the three streams (Fig. 8.8; Table 8.4). The mean values for the parameter z (Table 8.4) differed significantly between stream communities (ANCOVA: F2,41 ¼ 54.82, P < 0.001) due to a higher z-value in the LL. No differences in slopes were found between the SB and MY

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Table 8.4 Regression parameters of the power-law relationship between the mean number of species and sampled areas of size l ¼ k2 in the streams Seebach (SB), Llwch (LL) and Mynach (MY). c gives the intercept, z the slope, r2 is the variance explained by the correlation of area with mean number of species per area, F is the value of the variance ratio test, df are the degrees of freedom, P-values are given for the F-test. Bootstrap confidence limits (95%) are given in parentheses for c and z values. Stream

c (95% CL)

z (95% CL)

r2

SB

134.50 (107.90, 205.12) 34.36 (28.64, 56.89) 92.05 (87.30, 96.16)

0.233 (0.140, 0.282) 0.448 (0.338, 0.498) 0.200 (0.190, 0.214)

0.903

LL MY

Mean number of species, <S > (λ)

160

F

df

P

139.46

1,15

0.95; P < 0.001).

Rényi’s generalised dimension, Dq

All streams are characterized by a class of multifractal distributions, as the test criterion of linearity between the log-partition function and log area is fulfilled, particularly for all q-moment 2, Dq increases slightly in all ecosystems (Fig. 8.10) while the linearity criterion 1.0

SB LL MY

0.8 0.6 0.4 0.2 0.0 –10

–5

0

Moment, q

5

10

Figure 8.10 Re´nyi’s generalized dimensions (Dq) versus q-moments for the SAR of all benthic invertebrate species in three streams, the Seebach (SB), Llwch (LL) and Mynach (MY). Parameters are given in Table 8.5.

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Table 8.5 Summary of parameters obtained by multifractal analysis of species-abundance distributions across different areas in the streams Seebach (SB), Llwch (LL) and Mynach (MY). Dq are Re´nyi’s generalized dimensions given with 1SE; D0 is the capacity dimension, which equals to the slope of the species-area relationship; D1 is the entropy dimension; D2 is the correlation dimension; r2 are the coefficient of variation of the relationship between log partition function and log area for each Dq. Stream

SB LL MY

Species abundance across areas 2

D0

r

D1

r2

D2

r2

0.233  0.025 0.448  0.031 0.200  0.024

0.959 0.973 0.968

0.126  0.001 0.241  0.003 0.109  0.002

0.833 0.901 0.921

0.105  0.013 0.116  0.021 0.080  0.009

0.868 0.894 0.925

between the log-partition function and log area remains roughly fulfilled (Fig. 8.9; r2 > 0.95; P < 0.001). Excluding slight methodological differences, these results resemble those obtained for the species-abundance distribution of a tropical forest in Panama by Borda-de-A´gua et al. (2002), where Dq was not defined for q > 1. This more general class of multifractal distributions, for which not all q-moments exist, also indicates certain scale-related limitations in the application of Re´nyi’s generalized dimension for species-abundance distributions. Nevertheless, if a single fractal dimension does characterize the SAR then values of D0, D1 and D2 would be all equal. This equality would only be attained if the densities are equally represented among species. The capacity dimension, D0, is equivalent to the value for the single fractal dimension and to the exponent z of the SAR, which differs between the three streams (Table 8.5). Comparatively low values of the capacity dimensions indicate that irregularities in the abundance distribution are more concentrated in samples from smaller areas, emphasizing small-scale patchiness in streams. An entropy dimension, D1, with a value close to 1 signifies an evenly spread distribution of irregularities in species-abundance patterns across different scales. However, D1 values varied among the three stream communities, ranging from 0.11 in the MY, 0.13 in the SB, to 0.24 in the LL (Table 8.5). Therefore, higher values of D1 in the LL implied a greater evenness in the species-abundance distribution contrasting with the other stream communities. Similarly, the low values of the correlation dimension (D2) between communities illustrated uncorrelated irregularities of speciesabundance patterns within the same spatial scale range. Following Borda-de-A´gua et al. (2002), results of the generalized dimension strengthen the positive relationship between the density and spatial range of species. Considering the extremes of the distribution (e.g. q ! 10; q ! þ10), that respectively correspond to the rarer but larger and the abundant but

BODY SIZE AND SCALE INVARIANCE

smaller species, the density of the larger species declines faster with area than the abundance of smaller species. The reason for this observation is that rare species have a smaller geographic range than abundant, mostly small-sized, organisms (Schmid et al., 2002). Small aquatic invertebrates such as testate amoebae or benthic rotifers have a much wider geographic distribution than larger species, and free-living microbial eukaryotes are probably sufficiently abundant to have a global distribution (sensu Finlay, 2002; see also Finlay & Esteban, this volume).

Conclusions During the last few decades, evidence for scale invariance has appeared in several fields other than physics, and ecology is no exception. All these rather recent findings on power-law relationships and scaling in ecology, ranging from species-biomass invariance to body-size mediated patterns of community structure, are suggestive of an underlying scale-free pattern of complex systems. Biomass invariance across sites and stream systems may reflect the relative balance between resource supply and use, mediated and maintained through size-dependent resource partitioning processes of communities (Schmid et al., unpublished). The fit of species-abundance patterns to random resourceassembly, but not to neutral models, emphasizes the link between resource dependence, body size and species composition, irrespective of trophic group. This also stresses that differences between species in response to variations in resource supply and environmental heterogeneity question the core assumption of demographically identical species under Hubbell’s (2001) neutral concept. It is also evident that the dispersal probability of individuals plays a limited role in shaping patterns of observed benthic community structure at local scales. Moreover, food in the form of biofilm-enriched particles is not a limiting factor in most temperate stream ecosystems (Schmid et al., 2000), while habitat complexity has a profound influence on species composition and size structure (e.g. Jeffries, 1993; Schmid et al., 2002; Taniguchi & Tokeshi, 2004). In benthic stream systems, resource complexity is the product of physical and biological processes acting on the shape and size distribution of organic particles (Schmid et al., unpublished). The results presented here substantiate the view that the dynamics of the interstitial habitat and the various scaling domains of particles, which serve both as food and habitat, influence the size distribution of invertebrates and therefore, diversity and species composition in stream communities. Fractals are certainly the simplest method we have for quantifying a measure across a range of scales. As such, they provide the best null model against which to judge the real behaviour of natural patterns across different spatial scales, just as stochasticity is the null model against which to test spatial patterns at a single scale. Moreover, measures on aggregates such as (a) species-abundance distributions which influence SARs, (b) population densities underlying BSDs, or (c) particle densities underlying PSDs, give rise to a very different type of scaling

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known as multifractal. Thus, through the examination of multifractal measures, subtle differences in spatial and size structure can be explored. Fine-scale patterns embedded within coarser patterns apparently reflect ecological processes operating across a wide size spectrum and spatial scales, such as the resource utilization among invertebrate species in streams. The fact that multifractals can mirror compound phenomena may prove increasingly useful in the characterization, modelling and understanding of complex phenomena in ecology.

Acknowledgements This work has been supported by grants from NERC (NER/A/S/2001/00566), the Royal Society, and in parts from the Austrian Science Fund FWF: P15597-B03. We thank Dr Luı´s Borda-de-A´gua and an anonymous reviewer for valuable comments and suggestions on an early draft of this chapter.

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Kropp, J., von Bloh, W., Block, A., Klenke, Th. & Schellnhuber, H.-J. (1994). Characteristic multifractal element distributions in recent bioactive marine sediments. In Fractals and Dynamic Systems in Geosciences, ed. J. H. Kruhl. Berlin: Springer, pp. 369–375. Kunin, W. E. (1998). Extrapolating species abundance across spatial scales. Science, 281, 1513–1515. Lennon, J. J., Kunin, W. E. & Hartley, S. (2002). Fractal species distributions do not produce power-law species-area relationships. Oikos, 97, 378–386. Mandelbrot, B. B. (1974). Intermittent turbulence in self similar cascades: divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62, 331–358. Mandelbrot, B. B. (1989). Multifractal measures, especially for the geophysicist. Pure Applied Geophysics, 131, 5–42. Manrubia, S. C. & Sole´, R. V. (1996). Selforganized criticality in rainforest dynamics. Chaos, Solutions and Fractals, 7, 523–541. Margalef, R. (1996). Information and uncertainty in living systems, a view from ecology. BioSystems, 38, 141–146. Margalef, R. (1997). Our Biosphere, ed. O. Kinne. Oldendorf/Luhe, Germany: Ecology Institute. Marquet, P. A., Quin˜ones, R. A., Abades S. et al. (2005). Scaling and power-laws in ecological systems. The Journal of Experimental Biology, 208, 1749–1769. McGill, B. J. (2003). A test of the unified neutral theory of biodiversity. Nature, 422, 881–884. Milne, B. T. (1998). Motivation and beliefs of complex system approaches in ecology. Ecosystems, 1, 449–456. Nee, S., Read, A. F., Greenwood, J. J. D. & Harvey, P. H. (1991). The relationship between abundance and body size in British birds. Nature, 351, 312–313. Pascual, M., Ascioti, F. A. & Caswell, H. (1995). Intermittency in the plankton: a multifractal analysis of zooplankton biomass

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Netherlands: Backhuys Publisher, pp. 295–319. Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2000). Relation between population density and body size in stream communities. Science, 289, 1557–1560. Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2002). Scaling in stream communities. Proceedings of the Royal Society London B, 269, 2587–2594. Schmitt, F. G. & Seuront, L. (2001). Multifractal random walk in copepod behavior. Physica A, 301, 375–396. Schroeder, M. (1991). Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise. New York: W. H. Freeman and Company. Sugihara, G. (1980). Minimal community structure: an explanation of species abundance patterns. The American Naturalist, 116, 770–787. Stanley, H. E., Amaral, L. A. N., Gopikrishnan, P. et al. (2000). Scale invariance and universality: organising principles in complex systems. Physica A, 281, 60–68. Taniguchi, H. & Tokeshi, M. (2004). Effects of habitat complexity on benthic assemblages in a variable environment. Freshwater Biology, 49, 1164–1178. Tokeshi, M (1993). Species abundance patterns and community structure. Advances in Ecological Research, 24, 111–186. Tokeshi, M. (1996). Power fraction: a new explanation of relative abundance patterns in species-rich assemblages. Oikos, 75, 543–550. Tokeshi, M. (1999). Species Coexistence. Ecological and Evolutionary Perspectives. Oxford: Blackwell Science. Turcotte, D. L. (1986). Fractals and fragmentation. Journal of Geophysical Research, 91, 1921–1926. West, G. B., Brown, J. H. & Enquist, B. J. (1999). The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science, 284, 1677–1679.

CHAPTER NINE

Body size and biogeography B . J . FINLAY Natural Environment Research Council, UK

G . F . ESTEBAN Natural Environment Research Council, UK

Introduction June 9th, having received early in the morning some rain-water in a dish . . . and exposed it to the air about the third story of my house . . . I did not think I should then perceive any living creatures therein; yet viewing it attentively, I did, with admiration, observe a thousand of them in one drop of water, which were the smallest sort that I had seen hitherto. (From a letter written in 1676 by Antonie van Leeuwenhoek, who had a passion for designing and building ‘magnifying glasses’.)

Leeuwenhoek was almost certainly the first person to see protozoa and other microfauna, and the first to record their huge population sizes. He could not explain how the microbes got into the ‘dish of rainwater’, and this rather disappointing level of understanding has not changed much in 300 years. The debate is rather polarized. On one hand are those who draw attention to the possibility that a significant proportion of free-living microbial species may be geographically restricted (examples include Mann & Droop, 1996; Foissner, 1999). On the other hand are those who recognize that this is at odds with the alternative hypothesis that neutral dispersal of small organisms is driven by extraordinarily large numbers of the individuals themselves. Although the probability of an individual microbe being transported over great distance is vanishingly small, a multitude of interacting processes and events, both common and rare (hurricanes, transport in wet fur and feathers, etc.), in combination with huge population sizes, are expected to drive large-scale dispersal across all spatial scales. A fitting analogy is the purchase of lottery tickets – buying many tickets increases the probability of winning. Similarly, if a speciespopulation is big enough, some individuals will, for purely statistical reasons, be transported over great distances. Over time, therefore, the dispersal of microbes may be essentially random, with the rate and scale of dispersal determined mainly by global population size (Finlay, Monaghan & Maberly, 2002). This view is supported by the discovery of ‘signatures’ of randomness (Fig. 9.1) in the spatial distribution of soil protozoan species, and by the observation that local and global abundances of a wide range Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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Figure 9.1 Random distribution of soil protozoa – the spatial distributions of rare and abundant species of testate amoebae in a grassland soil. Each line is the regression through six data points for each species. For clarity only the six most abundant species and the six rarest species are included. The bold line represents the equality of variance and mean. The rare species may simply have been transported randomly to the site but unable to produce a population in this particular soil habitat type. Further details are in Finlay et al. (2001).

Figure 9.2 The local and global abundances of individuals in soil protozoan species are significantly correlated (p < 0.001). This analysis is based on frequency of detection (a surrogate measure of abundance per species) of 95 ciliated protozoan species in 150 soil samples from a onehectare upland grassland in Scotland, and of the same species in 606 soil samples collected worldwide. Adapted from Finlay et al. (2001).

of microbial species are correlated (Fig. 9.2). Unlike most macroscopic organisms, whose dispersal and spatial distribution are determined by historical factors such as continental drift, or physical barriers such as mountain ranges, these probably have little influence on the geographical distribution of microbes. The microbial species that thrive in a particular habitat are probably the result of habitat properties alone and, with their capacity for ubiquitous dispersal, we can assume that they thrive wherever their preferred habitat type is realized on Earth.

BODY SIZE AND BIOGEOGRAPHY

Table 9.1 The two provinces of biodiversity – adapted from Finlay, Esteban and Fenchel (2004).

Absolute abundance Rates of dispersal Rates of allopatric speciation Rates of species extinction Relative number of endemics Global number of morphospecies Proportion of global species pool found locally Cryptic persistence of species Persistence of specific morphotypes over geological time Large-scale distribution determined by historical factors e.g. continental drift

Macro-organisms

Micro-organisms

Low Low High High High High Low Variable Low

High High Low Low Low/None Low High High High

High

Low

One of the more awkward and contentious problems for supporters of the ‘restricted distribution’ of microbial species has been the difficulty in establishing the existence of microbial ‘endemics’. This problem may be insurmountable. We can be confident in the knowledge that a particular large mammal species does not exist outside of its ‘endemic range’, but it is probably impossible to demonstrate that a microbial species does not exist elsewhere in the biosphere. Moreover, if the geographical ranges of microbial ‘endemics’ cannot be established, the term ‘endemic microbial species’ is probably meaningless. The fundamental characteristics of biodiversity at the microbial and macroscopic levels (Table 9.1) are markedly different – indeed they appear to represent two distinctly different ‘provinces’ of biodiversity. That most macroscopic organisms have biogeographies is well established, but the case for ubiquitous neutral dispersal and cosmopolitan distribution driven by population abundance in free-living organisms 50% for heliozoa and >80% for chrysomonads (all recorded species were actually recorded from roughly one tenth of a cubic centimetre of sediment). It follows that, if cosmopolitan distribution is the product of high absolute abundance, populations of the larger, non-cosmopolitan organisms will have low local:global ratios. This appears to be the case – the percentage of the global species pool of aquatic insects recorded in Priest Pot is 1), indicating that both size and taxonomy influence rates (Table 15.1; Fig. 15.2b). When fish species means were considered, excretion scaled proportionally with dry mass (that is b  1; Table 15.1, Figs. 15.2c, d). These data cannot disentangle the relative contribution of phylogeny vs. size because they are not independent. However, comparing species means to individual species, we can conclude that fish scale similarly to each other. Additionally, measurements were collected by different researchers under different conditions, which may cause high variation in excretion rates among all fishes.

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Table 15.1 Reduced major axis regression estimates for nitrogen and phosphorus excretion (log10 g N or P fish1 h1) and size (log10 dry mass, g) in five groups of fish (see Fig. 15.2). Data for Mbuna Cichlidae, Carpiodes carpio, Ictiobus bubalus and Dorosoma cepedianum estimates are excretion rates from individual fish within a taxon. We also calculated the mean excretion rate and mean size of 30 fish species taken from Gido (2002); Vanni et al. (2002); Andre et al. (2003); Schaus et al. (1997b); and Koch (unpublished data) and regressed mean excretion rate on mean body size. The bootstrapped 95% confidence intervals of the exponents are in parentheses. Taxa

Nitrogen n

Mbuna* Cichlidae Carpiodesx carpio Ictiobusx bubalus Dorosomayx cepedianum Species means

Intercept Exponent

Phosphorus r2

n

Intercept Exponent

r2

40 2.04

0.759 (0.664–0.886) 0.769 37 0.975

0.886 (0.567–1.24)

10 2.96

0.789 (0.525–1.06)

0.770 10 1.39

0.733 (0.543–0.848) 0.875

16 2.27

0.983 (0.764–1.43)

0.633 16 0.803

0.568 (0.347–0.906) 0.301

93 2.13

1.14 (1.04–1.24)

0.883 93 1.40

0.921 (0.844–0.997) 0.781

30 2.41

0.953 (0.851–1.05)

0.930 30 0.916

1.07 (0.903–1.32)

x

Gido (2002) Andre et al. (2003) y Schaus et al. (1997b) *

The relative importance of taxonomy, body size and temperature in controlling nutrient excretion rates is only just beginning to be explored, and adequately testing the interactions among these factors will require richer data sets and resolved molecular phylogenies. In addition, determining the basis of taxonomic variation in excretion rates remains a challenge. Body nutrient composition and diet may both play roles. Given that ammonium excretion rates for stream invertebrates are higher for fed than unfed animals (Grimm, 1988), predators, which feed sporadically, may have more variable excretion rates over time than continuously feeding grazers and detritivores. Stoichiometric differences in animal nutrient use might also drive taxonomic variation (Elser & Urabe, 1999). Predators, with relatively N-rich diets, may have higher N excretion rates than other feeding groups. Understanding when to account for taxonomic variation and when body size alone is sufficient for studies of animal-mediated nutrient cycling is central to predict successfully the role of animals in the nutrient dynamics of aquatic ecosystems.

0.176

0.831

BODY SIZE AND NUTRIENT CYCLING

Figure 15.2 Phosphorus (a, c) and nitrogen (b, d) excretion rates (mg P or N fish1 h1) versus dry mass (g) for individual fish of several taxa (a, b) and means of 30 fish species (c, d) from the literature (Schaus et al., 1997b; Gido, 2002; Vanni et al., 2002; Andre et al., 2003; B. J. Koch, unpublished data). See Table 15.1 for regression coefficients.

Ratios of N and P Not only will the amount of N and P excreted by animals be important in ecosystem nutrient cycling, but the ratio of these nutrients may also drive microbial assemblage structure and productivity (Elser et al., 1988). Nutrient ratios in food sources, animal composition and excretion (that is, ecological stoichiometry) have received much attention in aquatic ecology (Sterner & Elser, 2002). Stoichiometric theory predicts that the N:P in excretion is a positive function of the N:P of ingested food, and a negative function of the N:P requirement of the consumer (Sterner, 1990). Data show that the link between N:P in the zooplankton body and excreted N:P is not nearly as strong as the link with the N:P of their food (Elser & Urabe, 1999); that is, most of the variance in excreted N:P is accounted for by variation in the food. Few analyses show how body size drives the N:P in excretion in animals; indeed, there is little information on animal C:N:P content solely as a function of body size (Sterner & Elser, 2002). One hypothesis might be that aquatic animals should increase their N:P content as size increases, because increased size should lead to decreased demand for P as growth rate declines (Elser et al., 1996). Given higher body N:P, big animals should have lower excreted N:P than small ones. However,

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this effect may be hidden by phylogeny and allometric constraints, as taxonomy correlates with body size because large animals are often vertebrates that have high P storage in bone apatite, and presumably a high N:P in excreta. Data on aquatic animals suggest that excreted N:P increases with body size. Wen and Peters (1994) showed that log N excretion rate (mg N/d) increased more steeply with body mass than did excreted P for zooplankton. The difference in the exponents is 0.13, which corresponds to the exponent for N:P of excretion vs. body mass. Thus the N:P of excretion increases with body mass, suggesting that mechanisms other than growth rate control the relationship of excreted N:P with body size. Data from some vertebrates also suggest increases in the N:P excreted with body size. Excretion N:P in fishes and amphibians from a Piedmont stream in Venezuela was positively related to body size, which agrees with qualitative predictions based on a decreasing body N:P with increasing body mass in vertebrates (Vanni et al., 2002). For example, bony-scaled armoured catfishes (Loricariidae) had particularly low body N:P and therefore high N:P in excretion (Vanni et al., 2002). Tadpoles (families Bufonidae and Ranidae) had low excreted N:P; because they do not have ossified bones (low skeletal demand for P). These studies, although few, suggest that not only will body size determine the rates of nutrient regeneration, but it will also determine the ratio of these nutrients, with the data so far suggesting mostly increasing N:P with body size. Mechanisms for this increase are unclear, and certainly vary across taxa. For example, vertebrates will have proportionally more bone as their size increases (Sterner & Elser, 2002), which will increase P demand (lowering P excretion) with body size.

Body size and nutrient translocation Aquatic animals can alter nutrient cycling by moving nutrients from one location to another, thus subsidizing the receiving habitat (Kitchell et al., 1979; Vanni, 2002). In some instances this nutrient movement is between habitats within an ecosystem such as, for example, benthic feeding fish that excrete nutrients in the pelagic zone (Vadeboncoeur, Vander Zanden & Lodge, 2002) or haemulid grunts that feed in seagrass beds at night and rest above coral heads during the day, where they release nutrients that stimulate coral growth (Meyer et al., 1983). In other cases, animals move nutrients between ecosystems on a daily basis; e.g. ocean-foraging river otters (Lontra canadensis) excrete nutrients in discrete locations in terrestrial habitat (Ben-David et al., 2005). Less mobile or small-sized animals may actually concentrate nutrients at high levels in localized areas (Reinertsen et al., 1986). In contrast, Pacific salmon (Onchorhynchus spp.) transport nutrients from the ocean to rivers via an annual long-distance spawning migration (Gende et al., 2002). The degree of movement will be determined in part by the speed at which animals move and the behavioural

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constraints on their home range. Both of these controls on movements should scale with body size. The distance moved by aquatic animals will depend on their body size because swimming speed scales with animal body size (Peters, 1983). For a given time travelled, a big animal can migrate further than a small one. Over large size ranges, an animal’s Reynolds number constrains movement (e.g. zooplankter versus a salmon). Small animals (e.g. rotifers) move very slowly because their short length confers a low Reynolds number, and therefore viscous forces are much higher than inertial forces. Within fishes that have high Reynolds numbers, swimming speed scales at about M0.14 (Weihs, 1977) assuming M / length2.6 (Peters, 1983). These modelled swimming speeds include both Reynolds number effects plus allometric scaling of swimming force and metabolic costs. Animals with lower Reynolds numbers have a steeper positive relationship between body mass and swimming speed, probably because of the more pronounced effects of viscous forces at small sizes. Swimming speed in diving beetles (Dytiscidae), increases as M0.36 (Nachtigall, 1977) assuming M / L2.5 (Benke et al., 1999). Thus, the decline in swimming speed for small animals probably decreases more quickly with body size than it does for fish. Behavioural constraints on home-range size and migration will also control nutrient movement by animals. Home range scales with body size in mammals at roughly M1 (Jetz et al., 2004). Home-range sizes of fishes are similar to mammals, scaling as M1.1, while insects and crustaceans are at M0.7 and molluscs at M0.55 (Alimov, 2003). Given that distance moved will scale as the squareroot of area, distance moved for fishes should then scale as approximately M0.5. This rate of increase with body size in the actual distance moved by animals is higher than that for speed alone, because home range is determined by many more attributes than is speed. These include, for example, resource requirements and interactions with conspecifics (Jetz et al., 2004). Animals that transport substantial nutrients among habitats are likely to be large, as in Pacific salmon (Gende et al., 2002), river otters (Ben-David et al., 2005), and the longdistance migratory fish, sapuara (Semaprochilodus kneri) (Winemiller & Jepsen, 2004). It is important to consider the strong effect of behaviour; the much smaller sapuara migrates long distances along rivers, and therefore transfers nutrients much further than does the coastal river otter. Coral reef fishes are large enough to travel long distances, but many stay in one spot on the reef all their lives. Thus, while large animals are more likely to move nutrients, behavioural characteristics also control this distance.

Consequences of size-varying nutrient cycling Variation in body-size distributions Because excretion rates typically increase less than proportionally with animal body size, variation in size distributions can partially control animal-driven

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nutrient mineralization and storage in ecosystems. Here we ask to what degree does variation in animal size distribution regulate nutrient mineralization? Researchers have described a wide variety of biomass-size distributions (also called size spectra) for aquatic animal assemblages, including flat or smooth, uni-, bi- and poly-modal, and step or asymptotic functions. Size distributions can vary considerably in space and time within and among aquatic habitats (Hanson, Prepas & Mackay, 1989; Stead et al., 2005), complicating generalizations (see Warwick, this volume). The diversity of methods in body-size estimations (for example, Morin & Nadon, 1991; Ramsay et al., 1997; Baca & Threlkeld, 2000) and analytical techniques, such as different sieve or size classes, further complicate size-spectra summaries (Cyr & Pace, 1993; Robson, Barmuta & Fairweather, 2005). However, when only the invertebrate portions of published aquatic assemblage spectra are included (that is, smaller and larger portions excluded), clearer patterns of shape categories emerge. Most size spectra have biomass peaks that are skewed left, meaning larger animals generally account for most of the total biomass, even though they may be outnumbered by smaller ones. Size distributions in lakes vary as a function of habitat. Studies that include multiple habitat types within the same lake suggest that pelagic and littoral assemblages tend to have bimodal distributions of invertebrates (Hanson et al., 1989; Cyr & Pace, 1993; Rasmussen, 1993) and polymodal distributions when fishes are included (Gaedke, 1992), whereas profundal (and sublittoral) distributions tend to be unimodal (Hanson et al., 1989). The magnitude and locations of biomass peaks and troughs also vary among habitats within lakes; littoral habitats have peaks at larger body sizes. For example, the two biomass maxima for littoral habitats tended to occur between 1–4 mg and 64–256 mg wet mass (Rasmussen, 1993), whereas the two peak densities of pelagic zooplankton occurred between 0.044–0.125 mg and 2.0–11.3 mg dry mass for small and large animals, respectively (Cyr & Pace, 1993). Streams generally have unimodal biomass size distributions (Cattaneo, 1993; Bourassa & Morin, 1995; Mercier et al., 1999; Schmid, Tokeshi & Schmid-Araya, 2002). Body-size maxima, as equivalent to a spherical diameter, were between 2–4 mm in streams (Cattaneo, 1993), and the average individual biomass increased slightly with increasing trophic status from 24–40 mg dry mass in oligotrophic to urban eutrophic streams, respectively (Bourassa & Morin, 1995). Overall, although unimodality is robust across many streams, total biomass can vary by an order of magnitude (for example, Bourassa & Morin, 1995) suggesting possible dramatic differences in animal driven nutrient fluxes within a stream system. Estimating nutrient flux from biomass size distributions Animal assemblages with different size distributions should have different nutrient supply rates to ecosystems, all else being equal. To illustrate this

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Figure 15.3 (a–c) Representative animal size spectra from three littoral ecosystems: (a) Lake Brome, (b) Lake Waterloo, (c) Lake Bromont (Rasmussen, 1993). Total biomass (mg dry mass m2) has been normalized to 1000 mg dry mass m2 for the three communities. Size classes are Log2 (mg dry mass). (d–f) Modelled P fluxes (mg P m2 h1) supplied by excretion for the three assemblages, assuming a negative relationship between mass-specific excretion rate and body size. Total nutrient flux varies nearly two-fold for the three communities (60, 115 and 104 mg P m2 h1 for panels d, e and f, respectively) and the shapes of nutrient flux distributions changed relative to size spectra.

point we used data-capturing software to extract published size spectra from plots. We gathered three representative aquatic animal size spectra: a bimodal distribution with proportionally more large individuals (Fig. 15.3a), a strongly peaked bimodal distribution (Fig. 15.3b) and a unimodal distribution (Fig. 15.3c, Rasmussen, 1993). We assumed dry mass was 25% of wet mass (Feller & Warwick, 1988) and normalized the literature spectra data to have equivalent total biomasses (1000 mg dry mass m2) while preserving the same distribution shape in the original data sets. For each of these three animal assemblages, we then calculated the P flux supplied by excretion for each size class (Figs. 15.3d–f ), using a negative relationship between mass-specific excretion rate and body size (mg P mg dry mass1 h1 ¼ 0.0954[dry mass](0.541); Wen & Peters, 1994). While this analysis accounts for variation in animal excretion rate due to body size, it does not incorporate the effects of potentially different temperatures or taxonomic composition among animal assemblages. Nevertheless, despite total biomass being the same for the three communities, total nutrient flux (cumulative area of rectangles) from each of the three animal communities is not equivalent, varying by almost a factor of two in this example (60, 115 and 104 mg P m2 h1 for Figs. 15.3d, e & f, respectively). Furthermore, the shapes of the

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nutrient flux distributions differ from their respective biomass size spectra. For example, although larger animals comprise most of the total biomass in Fig. 15.3a, small- and medium-sized animals supply the bulk of the nutrient flux from this assemblage (Fig. 15.3d). Thus the size spectra of animal communities have important consequences on the supply and cycling of nutrients, and those size classes that contribute most to total assemblage nutrient flux are not necessarily the most biomass-rich size classes in the assemblage. Predator control of prey body size and nutrient cycling The well-known impact of predators on prey size structure may alter nutrient cycling in aquatic ecosystems. Fish predators can decrease average size of prey by eating large zooplankton (for example, Brooks & Dodson, 1965; Li, Wetterer & Hairston, 1985) and large benthic invertebrates in lakes (Blumenshine, Lodge & Hodgson, 2000). Alternatively, planktonic invertebrate predators, such as Chaoborus, select small zooplankton (for example, Dodson, 1974), increasing average prey body size. In streams, predatory invertebrates, fish and mammals tend to consume the largest individuals of their prey (Quinn & Kinnison, 1999; Allan, 2001; Woodward & Warren, this volume). In addition to changes in size structure via consumptive effects, the presence of predators can alter prey-size distribution simply through non-consumptive effects, such as chemical cues (for example, Tollrian, 1995; Peckarsky et al., 2002) and excretion (Ramcharan, France & McQueen, 1996). Simultaneous to their effects on body size, predators can also affect prey physiology by increasing the allocation of nutrients to structural cells, (for example, Lively, 1986; Vanni, 1987; Crowl & Covich, 1990; Stibor, 1992; Barry, 1994; Arendt & Wilson, 2000; Dahl & Peckarsky, 2002), which may change the composition of consumer-mineralized nutrients. Altered size structure of the prey assemblage may change nutrient cycling, because mass-specific excretion rate decreases with increasing animal size. Additionally, body size affects the nutrient ratios at which animals excrete. Changes in excretion N:P can alter the supply of the nutrient that limits primary producers. Elser et al. (1988) suggest that phytoplankton communities are more likely P-limited when the zooplankton assemblage includes large-bodied individuals and N-limited when the zooplankton assemblage is mainly small-bodied individuals. Understanding how changes in the size structure of prey can affect nutrient cycling is not straightforward, because predators can simultaneously alter prey abundance and biomass, and regenerate nutrients by consuming prey. Bartell (1981) modelled P cycling under differing levels of predation using previously published data on zooplankton size and biomass in lakes, and a mass-specific excretion model for zooplankton. Nutrient fluxes from zooplankton did not always increase when the assemblage switched from large-bodied to the

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small-bodied individuals that have greater mass-specific excretion rates. In fact, P fluxes either remained similar, increased or decreased when lakes were altered from low to high planktivore abundance, depending on changes in total zooplankton biomass. However, nutrients may be more available in lakes with abundant zooplanktivorous fish, because smaller zooplankton turn P over faster than larger-bodied zooplankton (Henry, 1985). In addition to zooplankton, fish can also be an important source of nutrients to primary producers. Some studies have reported that the nutrient flux from zooplankton is much larger than fluxes from fish (Ramcharan et al., 1996), while others found the reverse (Vanni & Findlay, 1990; Carpenter et al., 1992). Boers, Vanballegooijen & Uunk (1991) showed that the main P source switched from zooplankton to fish as planktivore biomass increased. Regardless of which animal supplies more nutrients, their body size can affect nutrient cycling. To illustrate how size structure can change nutrient supply and demand we use lakes with low and high planktivorous fish abundance. In lakes with low planktivore abundance, both large and small zooplankton may be present (Fig. 15.4a), but the assemblage is mainly composed of small zooplankton when planktivores are abundant (solid line, Fig. 15.4c). Compensatory increases in the number of small zooplankton may result when fish are present (dashed line, Fig. 15.4c); however, most studies show an overall decrease in total zooplankton biomass (for example, Vanni & Findlay, 1990). When the density of planktivorous fish is low (that is, both large and small zooplankton are present), zooplankton excrete at a range of N:P ratios (grey line is N; black line is P; Figure 15.4b); however, zooplankton excrete at a lower N:P ratio when planktivorous fish are abundant (causing N to be potentially limiting). Based on modelling by Bartell (1981), changes in zooplankton size structure may either increase, decrease or not change lake nutrient fluxes (Fig. 15.4d), depending on compensatory changes in assemblage biomass. In contrast to planktivorous fish, planktonic-invertebrate predators selectively consume small zooplankton, resulting in a large-bodied prey assemblage excreting at a high N:P ratio. Depending on biomass, prey nutrient fluxes could change in either direction but may cause P to be limiting. The effect of predators on zooplankton body size in temperate lakes is well known; however, to our knowledge no studies have investigated how shifts in body size of stream invertebrates could alter nutrient cycling. Because stream predators selectively consume large-bodied prey, similar to planktivores feeding on zooplankton, we suggest that a decline in N:P mineralization and an increase in mineralization rates may hold for streams. However, even with the advances in methods to estimate pools and fluxes of nutrients in streams, the effects of predators on prey body size and nutrient cycling has not been investigated, even though in certain cases stream invertebrates can be an important source of ammonium (Grimm, 1988; Hall et al., 2003; Koch, 2005).

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Figure 15.4 Harvesting and predators can alter the size structure of their prey, which can change nutrient cycling. (a) In an assemblage with low harvesting or planktivore density (plankton-eating fish), large animals persist but the small animals are most abundant. (b) Nitrogen (grey line) and phosphorus (black line) mass-specific excretion rates are inversely related to body size, thus smaller animals excrete at a lower N:P than larger animals. (c) When harvesting or planktivore density is high, only small animals will be abundant, which may cause compensatory increases in density (dashed line). (d) Nutrient cycling by the small-bodied assemblage may result in compensatory increases, decreases or no change in nitrogen and phosphorus supply by animals, but nutrient ratios will probably be altered.

The effect of harvesting-induced changes in animal size structure on nutrient cycling Harvesting by humans affects the size structure of aquatic animal assemblages, and these altered size distributions may affect the rates and types of nutrients mineralized by animals (Jennings & Reynolds, this volume; Persson & De Roos, this volume). Similar to many other animals, humans selectively harvest large individuals and species (Pauly et al., 1998; Jackson et al., 2001; Roy et al., 2003; Allan et al., 2005). Size-selective harvesting can substantially change species composition and food-web structure (for example, removal of predators), leading to fishing down the food web – a process by which larger species, often predators, with slower growth rates are successively removed from the assemblage, leaving smaller species with faster growth rates (and thus higher massspecific nutrient excretion) that occupy lower trophic levels (Pauly et al., 1998; Welcomme, 1999). In addition, size-selective harvesting can decrease body size indirectly, by causing earlier maturation at smaller sizes via rapid evolutionary

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change or increased resource availability that accelerates growth and decreases time to maturity of the remaining individuals (Trippel, 1995). Taken together, human harvesting generally decreases or eliminates the biomass of large animals from an ecosystem (Myers & Worm, 2003; Allan et al., 2005; Ward & Myers, 2005). There are several mechanisms by which harvest-induced changes in animal body size may alter the role of aquatic animals in mineralizing nutrients. Foremost, size-selective harvesting results in the loss of large-bodied individuals and species with high excretion rates per individual, but low mass-specific excretion. There are also important differences in the ratios at which limiting nutrients, such as N and P, are released by animals of different size (Wen & Peters, 1994; Schindler & Eby, 1997; Sterner & Elser, 2002; Vanni et al., 2002). As a result, the removal of large individuals may disproportionately reduce the amount of N relative to P supplied by animal assemblages (Fig. 15.4a, b), assuming there is no compensatory increase in abundances of smaller individuals or species (solid line; Fig. 15.4c). If there are compensatory increases in abundance of smaller individuals or species (dashed line; Fig. 15.4c) with higher massspecific mineralization rates, then the total supply of nutrients by the assemblage experiencing harvesting may equal or surpass the amount supplied by the assemblage before harvesting (Fig. 15.4d). In addition, because home-range size and migration distance increases with body size (Brown, 1995; Alimov, 2003; Jetz et al., 2004), reduced body size due to harvesting could also decrease the spatial scale over which nutrients are distributed by animals. This impact has been realized; harvesting of large, migratory salmon may have decreased marine nutrient loads to inland rivers, potentially lowering their productivity (Thomas et al., 2003). Moreover, the larger animals, which are often the first and most intensely harvested, generally have longer lifespans and more stable population cycles than the smaller, short-lived species that are less frequently harvested. Therefore, the removal of large, long-lived animals could increase the fluctuations of nutrients mineralized by animal populations. Overharvesting of large animals is a hallmark of all aquatic environments (Myers & Worm, 2003; Allan et al., 2005). However, surprisingly little is known about how the removal of larger animals alters the type or supply rate of nutrients mineralized by animal assemblages and, more importantly, whether such changes in nutrients are large enough to alter ecosystem-level processes. In the Baltic sea, Hjerne and Hansson (2002) estimated the removal of N and P in fish biomass by harvesting to be 1.4–7% of the total nutrient load, although the nutrient loss due to decreased mineralization by fish was not quantified. Although information is available on how predators can mediate nutrient mineralization rates by altering the size-structure of their prey, the process and long-term effects of harvesting by humans are likely to be very different. Humans typically remove the biomass of the largest animals, rarely switch

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prey until populations are severely reduced or regulatory restrictions are imposed, and harvest at maximal rates, which are often supported by external factors such as economic subsidies. In freshwater, species removals for biomanipulation (Horppila, 1998; Tarvainen, Sarvala & Helminen, 2002), and declines in introduced species, affect nutrient fluxes (Kraft, 1993); however, few studies have documented the direct effects of size-selective harvesting on nutrient fluxes. One reason is the mismatch in the data that are available on nutrient mineralization rates and harvesting rates of aquatic animals between marine and freshwater ecosystems. There are comparatively better data on catch size and body size of marine animals (Pauly et al., 1998; Myers & Worm, 2003; Ward & Myers, 2005) than freshwater animals (Allan et al., 2005), whereas there are more empirical data on nutrient regeneration rates for freshwater animals (Sterner & Elser, 2002). In marine systems, it may be useful to apply bioenergetic models to estimate the amount and type of nutrients lost from these systems as a result of having removed 80% of the large predatory fish biomass (Myers & Worm, 2003). Predicting the effects of harvesting-induced changes in body size on nutrient cycling is a new challenge that could improve our understanding of the role of animals in ecosystem functioning, and provide urgently needed guidance for managing and restoring these systems.

The next steps? Given that animals can often be important regenerators, storers and transporters of nutrients in ecosystems (Kitchell et al., 1979; Gende et al., 2002; Vanni, 2002; Koch, 2005), body size may be the single most important trait of the animals themselves in controlling these processes. There are plenty of avenues in which to explore further the role of body size in conjunction with other animal attributes (for example, phylogeny), and ecosystem processes. Below we give some of these examples. 1.

2.

3.

Taxonomic identity probably determines a large fraction of variation in excretion rates, and taxonomy covaries with body size. To what degree does size alone determine nutrient excretion rates? Can we integrate size and phylogeny to improve predictions of nutrient excretion rate? Body size allows us to examine how traits of animals impact ecosystem processes, but we cannot forget that the attributes of the ecosystems themselves will, in part, determine the impact. For example, plant nutrient demand, disturbance and hydrologic flushing rates are certainly important. How important is animal assemblage structure relative to physical controls and plant/microbial demand for nutrients? We can only speculate as to the potential role of many fisheries on changes to nutrient cycling. Some are well known (for example, salmon), but most are unknown (for example, groundfish stocks). These human-induced

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changes present an opportunity to examine how changes in aquatic animal assemblages affect ecosystem processes and may provide the means to compare the relative importance of direct versus indirect effects of assemblage and size structure on nutrient cycling.

Acknowledgements Mike Vanni, Emidio Andre, Keith Gido and Maynard Schaus kindly provided tables of their published data for analysis. Two anonymous reviewers provided useful comments on an earlier draft of this manuscript. Financial support was provided by National Science Foundation; Environmental Protection Agency; and the Juneau Pacific Northwest Research Station, USDA Forest Service.

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Stead, T. K., Schmid-Araya, J. M., Schmid, P. E. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Sterner, R. W. (1990). The ratio of nitrogen to phosphorus resupplied by herbivores – zooplankton and the algal competitive arena. American Naturalist, 136, 209–229. Sterner, R. W. & Elser, J. J. (2002). Ecological Stoichiometry. Princeton: Princeton University Press. Stibor, H. (1992). Predator induced life-history shifts in a fresh-water cladoceran. Oecologia, 92, 162–165. Tarvainen, M., Sarvala, J. & Helminen, H. (2002). The role of phosphorus release by roach Rutilus rutilus (L.) in the water quality changes of a biomanipulated lake. Freshwater Biology, 47, 2325–2336. Teal, J. M. (1962). Energy flow in the salt marsh ecosystem of Georgia. Ecology, 43, 614–649. Thomas, S. A., Royer, T. V., Minshall, G. W. & Snyder, E. (2003). Assessing the role of marine derived nutrients in Idaho streams. In Nutrients in Salmonid Ecosystems: Sustaining Productivity and Biodiversity, ed. J. G. Stockner. Bethesda, Maryland: American Fisheries Society, pp. 41–55. Tollrian, R. (1995). Predator-induced morphological defenses: costs, life history shifts, and maternal effects in Daphnia pulex. Ecology, 76, 1691–1705. Trippel, E. A. (1995). Age at maturity as a stress indicator in fisheries. Bioscience, 45, 759–771. Vadeboncoeur, Y., Vander Zanden, M. J. & Lodge, D. M. (2002). Putting the lake back together: reintegrating benthic pathways into lake food web models. Bioscience, 52, 44–54. Vanni, M. J. (1987). Effects of nutrients and zooplankton size on the structure of a phytoplankton community. Ecology, 68, 624–635.

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Welcomme, R. L. (1999). A review of a model for qualitative evaluation of exploitation levels in multi-species fisheries. Fisheries Management and Ecology, 6, 1–19. Wen, Y. H. & Peters, R. H. (1994). Empirical models of phosphorus and nitrogenexcretion rates by zooplankton. Limnology and Oceanography, 39, 1669–1679. Winemiller, K. & Jepsen, D. B. (2004). Migratory neotropical fish subsidize food webs of oligotrophic blackwater rivers. In Food Webs at the Landscape Level, ed. G. A. Polis, M. E. Power and G. R. Huxel. Chicago: University of Chicago Press, pp. 115–132. Wootton, J. T. (1994). Predicting direct and indirect effects: an integrated approach using experiments and path analysis. Ecology, 75, 151–165. Zhuang, S. (2005). The influence of body size and water temperature on metabolism and energy budget in Laternula marilina Reeve. Aquaculture Research, 36, 768–775.

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CHAPTER SIXTEEN

Body sizes in food chains of animal predators and parasites JOEL E . COHEN Rockefeller and Columbia Universities, New York

Introduction Food chains in which animal predators are bigger than their animal prey are called predator chains; those in which the consumers are smaller are called parasite chains (Elton, 1927; Hutchinson, 1959, p. 147). The purpose of this chapter is to display and test empirically some consequences, for predator chains and parasite chains, of assuming that the average mass of a consumer species (predator or parasite) is related to the average mass of its animal resource species (prey or host) by a power law with an exponent less than 1. In 1858, as part of his development of the theory of evolution, Wallace (1858, p. 54) noted that animal predators are generally larger and less numerous than their prey. Among the many echoes of Wallace’s remark, Elton (1927) observed anecdotally that animal predators weigh more than their prey in terrestrial food chains, Hutchinson (1959) analyzed some of the theoretical consequences of predators weighing more than their prey, and Sheldon, Prakash and Sutcliffe (1972) and others posited that marine animal predators outweigh their marine animal prey (see also Humphries, this volume; Woodward & Warren, this volume). Only recently have body sizes been studied empirically in parasite chains (Memmott, Martinez & Cohen, 2000; Leaper & Huxham, 2002) and parasitoid chains (Cohen et al., 2005). The study of parasitoid chains (e.g. Rott & Godfray, 2000; Memmott et al., 2000) appears not to have been considered by Elton (1927) and Hutchinson (1959). Predator and parasite chains are not the only possibilities observed in nature. Other relations between mass and feeding arise from social hunting and metaphoetesis. Among animals that hunt socially (such as wolves and army ants), the aggregate mass of the hunting group may be a more appropriate index of size than the mass of an individual predator. In animals where mass or feeding habit or both change dramatically with the stage of the life cycle (as in many insects and fishes), it is misleading to represent the masses of all stages by a typical adult Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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mass (Hutchinson, 1959; Cohen et al., 2005). Hutchinson (1959) called a change in diet with changing stage of the life cycle metaphoetesis. When Christine Mu¨ller measured the body lengths of individual aphid hosts and of their parasitoid wasp consumers (Cohen et al., 2005, raw data available online), one nymphal aphid Capitophorus carduinis parasitized by a male wasp Aphidius matricariae was longer than the wasp when the wasp emerged from its aphid host, while another nymphal aphid Capitophorus carduinis parasitized by a male wasp Aphidius matricariae was shorter than the wasp when the wasp emerged from its aphid host. Both aphids were found on the same plant species Cirsium palustre. Even controlling for the life stage of the aphid, for the sex of the parasitoid wasp, and for the plant, the ordering of body sizes may differ from one consumer–resource pair of individuals to another. This single instance is illustrative of the variability in the relationship of host and parasitoid body length found in many comparable observations. In most real food webs, predator chains and parasite chains are tightly interwoven because animal predators of almost all sizes support viruses, bacteria and other microscopic and macroscopic parasites. The analysis here of the typical patterns of predator chains and parasite chains makes no claim to cover all kinds of food chains. The relation between the average masses of animal predator species and the average masses of animal prey species has been approximated empirically as a power law (Schoener, 1968; Peters, 1983, p. 277; Ve´zina, 1985; Warren & Lawton, 1987). The power law also applies to individual body masses of aphids and parasitoid wasps (Cohen et al., 2005), but the theoretical implications parallel to those derived here for species-average masses remain to be studied. The analysis below predicts, first, that in predator chains, there is an upper limit to the mass of possible predators and prey; and that this upper limit is independent of the number of trophic links in the chain and independent of the mass of the smallest prey. Conversely, in parasite chains, there is a lower limit to the mass of the smallest host and parasite; this limit is independent of the number of trophic links in the chain and independent of the mass of the largest host. A second consequence is that, in a predator chain, the ratio of predator mass to prey mass decreases according to a power law, with an exponent one less than that for predators and prey masses, as the trophic level and the mass of the prey increase. (In a single food chain in which no species occurs more than once, the trophic level of a species may be unambiguously defined as the number of links between it and the basal species in the chain; thus the basal species has trophic level 0, its consumer has trophic level 1, and the top species in a chain of n trophic links and n þ 1 species has trophic level n.) Conversely, in a parasite chain, the ratio of parasite mass to host mass increases as the trophic level of the host increases (and the mass of the host decreases).

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This theoretical and exploratory analysis of body sizes and feeding is part of a larger picture that includes numerical abundance (Cohen, Jonsson & Carpenter, 2003).

Theory Maximal and minimal body masses Consider a food chain based on an animal (prey or host) of mass M0. Let M1 ¼ f (M0) be the typical (e.g. geometric mean) mass of a consumer (predator or parasite) of that prey, ignoring variation in the mass of consumers that eat prey of a given mass. Let M2 ¼ f (M1) ¼ f ( f (M0)) ¼ f 2(M0) be the typical mass of a consumer that eats the consumer of typical mass M1. The notation M2 ¼ f 2(M0) indicates that M2 results from applying two iterations of f to M0; f 2(M0) does not denote the square of f (M0), which would be written [ f (M0)]2. Similarly, f nþ 1(M0) ¼ f ( f n(M0)) is the typical mass of a consumer n þ 1 trophic links above the basal animal of mass M0. When the typical mass Y of predators on animal prey of mass X is a power function Y ¼ f ðXÞ ¼ AXB ; A > 0;

(16:1) b

then by induction (letting ^ denote exponentiation so that a^b means a ) ! n1 X n n n Bn ^ m f ðM0 Þ ¼ M0  ½A B  ¼ M0B  Að1B Þ=ð1BÞ : (16:2) m¼0

The equality on the left of Eq. (16.2) is valid for any B. The equality on the right of n1 P m B ¼ ð1  Bn Þ=ð1  BÞ. Were the Eq. (16.2) is valid when B 6¼ 1, since then m¼0

consumer’s mass directly proportional to the resource’s mass according to Y ¼ AX, i.e. were B ¼ 1, then the mass of the consumer species would change by a factor of A with each additional link in the food chain and then f n(M0) ¼ AnM0. Were B ¼ 0, the mass of consumers would be constant and equal to A, regardless of their position in a food chain. Assume henceforth that 0 < B < 1, in addition to the previous assumption that A > 0. Then according to Eq. (16.1), consumer and resource would have equal body mass X ¼ f(X) when X ¼ A1/(1  B), and this mass is strictly positive. This positivity guarantees that the intersection of the power law Eq. (16.1) with the diagonal line where Y ¼ X lies in the positive quadrant. In this model, a chain is a predator chain or a parasite chain according to whether M0 < A1/(1  B) or M0 > A1/(1  B). With increasing trophic level, the masses of successive consumers approach the finite limit A1/(1  B) > 0 (Fig. 16.1a) because the assumption 0 < B < 1 implies Bn # 0 as n"1 and hence lim f n ðM0 Þ ¼ A1=ð1BÞ : n"1

(16:3)

BODY SIZES IN FOOD CHAINS

The limit Eq. (16.3) is a maximum if each consumer has a bigger mass than its resource, as assumed in a predator chain. The limit Eq. (16.3) is a minimum if each consumer has a smaller mass than its resource, as assumed in a parasite chain. The predicted maximal mass of a top predator is independent both of the number of links leading up to that predator and of the mass M0 of the basal animal prey in the food chain. The predicted minimal mass of a parasite is independent both of the trophic level of that parasite and of the mass M0 of the basal animal host in the food chain. The limit A1/(1  B) is very sensitive to the values estimated for A and B. As B"1, 1/(1  B) A "1. The values of A and B of course are not known exactly. They are usually estimated by a least-squares fit of the coefficients of the linear relation y ¼ a þ bx where y ¼ log10 Y and x ¼ log10 X. The parameters are connected by A ¼ 10a but B ¼ b. For a given value of A, the closer B is to 1, the slower the approach to the limiting size as one proceeds along a food chain from successive resource to successive consumer (Mark Huxham, personal communication, 9 September 1995). So the limit A1/(1  B) may not be closely approached in reality when there are other limitations on food chain length. According to this model of species-average body mass in food chains, in very long chains, the predators are mostly big, close in mass to the limiting maximum, and the parasites are mostly small, close in mass to the limiting minimum (Fig. 16.1a). The removal from a predator chain of top predators shifts the size distribution of species-average body masses from one concentrated near the upper maximum to a more widely spaced distribution across the lower portions of the possible range of average body masses. This prediction could be compared with quantitative data on the body size distributions of North American vertebrate species before and after the major extinction of the megafauna and with quantitative data on the body size distributions of marine fauna before and after widespread industrial fishing. This allometric model of species-average body masses has an implication for predator–parasite cycles. Assume that Mt þ 1 ¼ AMtB along a predator chain of n links, t ¼ 0, . . ., n  1, that the top predator is the starting point for a parasite chain of n links, i.e. V0 ¼ Mn > a1/(1  b) and Vtþ 1 ¼ aVtb, t ¼ 0, . . ., n  1, with a > 0, 0 < b < 1 along the parasite chain. Then it turns out that M0 can be less than, equal to, or greater than Vn. More generally, dropping the assumption that the predator chain and the parasite chain are of equal lengths, it is still possible for M0 to be less than, equal to, or greater than Vn, as long as each chain is sufficiently long. The case where Vn ¼ M0, i.e. where the basal prey of the predator chain weighs the same as the top parasite of the parasite chain, is illustrated numerically in Fig. 16.1b. In this case, if the basal prey and the top parasite were the same

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(a) 100 predator food chain 10 consumer weight

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0.1 parasite food chain 0.01

0.001 0.001

0.01

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100

Figure 16.1 (a) Theoretical progression of body masses along a predator chain and a parasite chain. Arrows go from resource to consumer. Body masses are on logarithmic scales. The power-law relation Eq. (16.1) appears as a straight dashed line with slope B; here, B ¼ 1/2 for both predator chain (A ¼ 10) and parasite chain (A ¼ 0.1). On the solid diagonal line, consumer mass equals resource mass. Predator chains appear above the diagonal; parasite chains appear below the diagonal. In the predator chain, an arbitrary small basal prey mass is chosen (in this example, M0 ¼ 0.001) and the corresponding predator mass M1 is found by moving upward to the upper dash line. This predator is the prey of the predator at the next trophic level of the chain. The mass M1 is located on the abscissa by moving horizontally right to the diagonal line. Then vertical upward motion to the upper dashed straight line gives the mass M2 of the predator two links above the basal prey. Alternating horizontal right and vertical upward motions intersect the power function (upper dashed straight line) at the masses of successively higher predators in the predator chain. All such trajectories converge where the upper dashed line and the diagonal line intersect. In the parasite chain, an arbitrary large basal host mass is chosen (in this example, M0 ¼ 100) and the corresponding parasite mass M1 is found by moving down to the diagonal line. This parasite is the host of the parasite at the next trophic level of the chain. The mass M1 is located on the abscissa by moving horizontally left to the diagonal line. Then moving down to the lower dashed straight line gives the mass M2 of the parasite two links above the basal host. All such trajectories converge where the lower dashed line and the diagonal line intersect. (b) Theoretical masses of species in a predator chain (open bars) and in a parasite chain (filled bars) where the top predator is the basal host, and the top parasite has the same mass as the basal prey. In the predator chain, Mnþ1 ¼ 10 Mn0.5 and the upper limit of mass is 100. In the parasite chain, Vnþ1 ¼ Vn0.5 and the lower limit of mass is 1. M0 ¼ V10 ¼ 1.004503 and M10 ¼ V0 ¼ 99.55172.

BODY SIZES IN FOOD CHAINS

(b)

100 90 80

predator chain

body weight

70 60 50 40 30 20 parasite chain

10 0 0

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2 3 4 5 6 7 8 9 trophic level in predator chain

10

Figure 16.1 (cont.)

species, the predator chain and the parasite chain would be linked in a predator– prey cycle. On the linear scale of mass used in Fig. 16.1b, after the first few trophic levels in both the predator chain and the parasite chain, the consumers are near in mass to the limiting mass.

Predicted value of the exponent The exponent B may be computed exactly for simple models of the distribution of the pairs (x, y), where x ¼ log10 X and y ¼ log10 Y are log prey (or host) mass and log predator (or parasite) mass, respectively. Suppose xmin is the log10 minimal observed species average mass and xmax is the log10 maximal species average mass. The previous theory predicts that xmax ¼ log10(A1/(1  B)) but the following calculations hold whether or not that prediction is true. The slope of any linear relation between y and x will be unaffected if both x and y are replaced by the identical linear transformation of x and y, so no generality is lost by assuming that xmin ¼ 0 and xmax ¼ 1. Then each trophic link from resource to consumer may be represented by a dot in a square in the (x, y) plane with lower left corner at the origin (0, 0) and upper right corner at (1, 1). The diagonal of the square is the locus of points where consumer body mass equals resource body mass. Suppose that trophic links are uniformly and independently distributed over this square, and that all links above the diagonal are in predator chains and all links below the diagonal are in parasite chains. Then, in a predator chain, for a given x (between 0 and 1), the expected y is halfway between the diagonal and the upper horizontal edge of the square, that is, E(y|x) ¼ x þ (1/2)(1  x) ¼ 1/2 þ x/2. Thus the slope of average y as a linear function

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of x is predicted to be B ¼ 1/2. Similarly, in a parasite chain, for a given x (between 0 and 1), the expected y is halfway between the diagonal and the lower horizontal edge of the square, that is, E(y|x) ¼ x/2. The slope of average y as a linear function of x is again predicted to be B ¼ 1/2. In the part of this model that pertains to a predator chain, the assumption that each trophic link is uniformly and independently distributed in the triangle above the diagonal follows from the cascade model (Cohen, Briand & Newman, 1990) in the continuous limit (possibly with additional assumptions) of many species of predators and prey. The cascade model assumes that all species are ordered by something interpreted here as body mass, and that each consumer species consumes with equal probability and independently every species smaller than it. (The cascade model does not attempt to describe parasite chains because it was intended to account for food-web data that ignored parasites.) The continuous limit of the joint distribution of prey-to-predator links posited in the cascade model is (possibly with additional assumptions) a twodimensional distribution of trophic links that is uniform in the upper triangle above the diagonal from (0, 0) to (1, 1) in the unit square in the plane where x ¼ log10 X and y ¼ log10 Y, as supposed in the previous paragraph. For parasite chains, to derive a distribution of trophic links in the (x, y) plane that is uniform over the triangle below the diagonal, as supposed above, all that is required is to reverse the ordering by body size in the argument just given for predator chains. When the pairs (x, y) are not distributed uniformly but lie in a band parallel to the diagonal, the predicted slope B will move from 1/2 toward 1. Such a band parallel to the diagonal would arise if there were a nearly constant ratio of average body mass between consumer (predator or parasite) and resource. When the pairs (x, y) lie in a band parallel to the x axis (because most predator species are roughly the same size, or most parasite species are roughly the same size), the predicted slope B will move from 1/2 toward 0.

Ratios and differences of consumer mass and resource mass Let R ¼ Y/X ¼ AXB 1 be the ratio of consumer mass to resource mass in a single trophic link. Then R is a decreasing power-law function of X. The exponent B  1 is negative because B < 1. A regression of log R on log X is predicted to have a slope exactly one less than the slope of a regression of log Y on log X, for the same set of data. The ratio R decreases (towards a limit of 1) with increasing trophic level of the prey in predator chains. In parasite chains, because body masses decrease with increasing trophic level, the ratio R increases towards a limit of 1 with increasing trophic level of the host. The difference in masses behaves in a more complex way than the ratio of masses, as the following analysis shows. Let D ¼ Y  X ¼ (R  1)X be the difference between the consumer mass Y and the resource mass X in a single

BODY SIZES IN FOOD CHAINS

trophic link. (In predator chains, D > 0. In parasite chains, D < 0.) Because dD/dX ¼ RB  1, the difference D increases with increasing resource mass X if and only if R > 1/B. The smaller B is, the bigger R must be for D to increase with X. As B < 1, a necessary condition for D to increase with X is that R > 1, and this happens only in predator chains. Thus, in predator chains, the difference D in mass between consumer and resource may increase with increasing trophic position (if initially R > 1/B); but once R  1/B, the difference D will thereafter decrease (towards a limit of 0) with increasing trophic position. By contrast, in parasite chains, where R < 1 and B < 1, it follows that RB  1 < 0 always; hence with increasing trophic level (and therefore decreasing body mass), D is always increasing (from negative values towards a limit of 0), that is, host mass minus parasite mass is always positive and decreases towards a limit of 0.

Data The data presented here deal only with food webs (cross-linked food chains), rather than with isolated food chains. The theory is relevant to these food webs in so far as food chains are a first approximation to more complex food webs. First, two examples of data on the masses of animal predators and their animal prey in a particular community will be analyzed. Then some data will be examined from literature surveys of pooled communities of specified habitat types (terrestrial and coastal). A recent database of the masses of consumers and resources (Brose et al., 2005) has been analyzed by Brose et al. (2006).

Studies of a well-defined community Menge et al. (1986) described the food web and the masses of the animals of a tropical Panamanian rocky intertidal community. From 31 data points (Fig. 16.2a), hand-read in part from their published graphs, linear regression of log10 masses yielded a ¼ 2.2334 (with 95% confidence interval (1.80, 2.67)), and b ¼ 0.4819 (with 95% confidence interval (0.19, 1.15)). The geometric mean mass Y (kg) of animal predators on animal prey of mass X would be estimated from these data as Y ¼ 0.1712X0.4819 and the upper limit in mass A1/(1  B) for the largest predator would be nearly 20.4 kg. The largest observed predator in the data weighed just under 2 kg. The 95% confidence interval for B includes both 0 and 1. If the data satisfy the assumptions of the underlying regression model well enough to justify the conclusion that the asserted confidence interval really has probability 95%, then these data do not specify an allometric relation with sufficient precision to have the predictive upper limit falsified by any finite maximal predator mass. A simple sensitivity calculation, referred to below as ‘the 10% sensitivity range,’ confirms a wide range of uncertainty in the upper limit. If the regression intercept log A and the regression slope B are both replaced by 90% of their estimated values, the maximal predator mass A1/(1  B) is 3.5 kg. If the regression

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(a) 3.5 3 log10 weight (g) of predator

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2.5 2 1.5 1 0.5 0 –0.5 –1 –1

–0.5

0

0.5

1

1.5

2

log10 weight (g) of prey

Figure 16.2 (a) Predator masses and prey masses in trophic links of a tropical rocky intertidal food web described by Menge et al. (1986). The solid diagonal line indicates where predator and prey masses are equal; all but one of the trophic links fall above this line. The upper dashed line is the regression line: log10(predator mass, g) ¼ 2.2334 þ 0.4819 log10(prey mass, g). The regression line is obtained by ordinary least squares using the log-transformed masses; the standard error of the slope coefficient is 0.3268. The data are read from Menge et al. (1986); the analysis and figure are original. (b, c) Prey and predator body mass (kg) in Tuesday Lake in (b) 1984 and (c) 1986, one marker for every trophic link in the unlumped food web. Cannibalistic links are excluded. Dotted line indicates equal prey and predator body mass. The links are coded according to the prey: circles ¼ phytoplankton, squares ¼ zooplankton, stars ¼ fish. For 1984, the regression coefficients were a ¼ 1.5598, b ¼ 0.8445, with correlation r ¼ 0.7859 and 263 trophic links (Jonsson et al., 2005, p. 34). For 1986, the regression coefficients were a ¼ 1.4108 and b ¼ 0.5928, with correlation r ¼ 0.6094 and 233 trophic links. (d) Regression lines from (b, solid diamonds) and (c, open squares) plotted over the approximate range from the mass of the smallest observed organism to the mass where predator and prey are equal. Figure 16.2b is reprinted from Cohen et al. (2003) with permission from the National Academy of Sciences. Figure 16.2c is reprinted from Jonsson et al. (2005), copyright 2005 by T. Jonsson, J. E. Cohen, S. R. Carpenter. Figure 16.2d is original.

intercept log A and the regression slope B are both replaced by 110% of their estimated values, the maximal predator mass is 169.2 kg. Combining 90% of log A with 110% of B and vice versa yields a narrower range of uncertainty from 19.0–21.8 kg. When a plausible range of the predicted maximal size is as large as the 10% sensitivity range, from 3.5–169.2 kg, only order-of-magnitude agreement between predictions and observations should be expected, at best. If seals or sea lions are occasionally part of the rocky intertidal community, the average body mass of those consumers could be compared with the limit

BODY SIZES IN FOOD CHAINS

(b)

10−2

predator body mass (kg)

10−4 10−6 10−8 10−10 10−12 10−14 −14 10

10−12

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10−4

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10−2 10−4 10−6 10−8 10−10 10−12 10−14 −14 10

10−12

10−10 10−8 10−6 10−4 prey body mass (kg)

10−2

100

Figure 16.2 (cont.)

predicted here. For example, adult Gala´pagos fur seal females Arctocephalus galapagoensis average about 28 kg in body mass (Horning & Trillmich, 1997). Gala´pagos fur seal bulls average about 70 kg in body mass (http://www.tamug. tamu.edu/labb/Galapagos/GFSwork/GFS_work.htm, accessed 27 August 2005). Cohen et al. (2003), Reuman and Cohen (2004), Jonsson, Cohen and Carpenter (2005), Reuman and Cohen (2005), and Cohen and Carpenter (2005) analyzed the community food web, the numerical abundance and the average body size of species in the pelagic community of a small lake, Tuesday Lake, in Michigan. The raw data on the food web, average body mass and numerical abundance by

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(d) 15 10 predator body mass (log10 kg)

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5 0 –5 –10 –15 –10 –14

–9

–4 1 prey body mass (log10 kg)

6

11

Figure 16.2 (cont.)

species are given by Jonsson et al. (2005). Tuesday Lake was intensively sampled during the summers of 1984 and 1986. During the summer of 1985, the three resident species of fishes were largely removed and replaced by a fourth fish species, which consumed the remaining individuals of the original three fish species. In addition to the complete turnover of the fish species present in Tuesday Lake between 1984 and 1986, the other species in the lake also changed dramatically between 1984 and 1986 (Jonsson et al., 2005, p. 23). Almost all predators had larger average body mass than their prey in 1984 (Fig. 16.2b) and 1986 (Fig. 16.2c). The calculated upper limit in 1984 exceeds 10.7  109 kg, far in excess of the largest average species mass observed in 1984, namely, 1.29  103 kg, or 1.29 g. The upper limit in 1986, 0.34  103 kg, or 0.34 g, was exceeded by the average body mass, 1.95  101 kg, of the largest species, the introduced fish Micropterus salmoides. The average body mass of this fish also exceeded the upper limit of the 10% sensitivity range. The allometric model of the relationship between predator and prey mass was probably less adequate in 1986 than in 1984: the correlation (on log-log scales) between predator and prey masses dropped notably from 1984 to 1986. Following the complete manipulation of the fish fauna in 1985, the pelagic community may have been observed in 1986 during a transient response to the manipulation. The regression lines before and after the manipulation appear in Fig. 16.2d. While the predator–prey pairs of Cohen et al. (1993) could reasonably be seen as uniformly distributed in the upper triangle of the square in the (x, y) plane, these trophic links were pooled from a variety of different communities. The

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predator–prey pairs from Tuesday Lake (Figs. 16.2b, c) and some other individual communities indicate that the pairs (x, y) may sometimes lie in a band parallel to the diagonal (Reuman & Cohen, 2004, p. 857). The non-parasite data from Ythan estuary (Leaper & Huxham, 2002, p. 447) seem to be intermediate between lying in an upper triangle and lying in a band parallel to the diagonal; they are distributed in a wedge shape.

Studies that pool multiple communities Numerous studies have collected masses of organisms in defined taxonomic groups from scattered published sources and identified trophic links based on reports of feeding habits, without reference to whether the organisms would be likely to occur within a single habitat at any single time (e.g. Schoener, 1968; Peters, 1983; Ve´zina, 1985; Hansen, Bjı´rnsen & Hansen, 1994). Other studies have combined community studies and literature surveys (e.g. Warren & Lawton, 1987; Cohen et al., 1993; Jonsson & Ebenman, 1998a; Brose et al., 2006). Cohen et al. (1993) presented two independently collected sets of data on the sizes of animal predators and prey in multiple community food webs. Data set A gave average adult masses of predators and prey in 354 trophic links from 18 community food webs. Data set B gave lengths of prey and predators in 478 trophic links from 30 webs of a compendium of sink, source and community webs. In roughly 90% of the trophic links reported in food webs from terrestrial, coastal, freshwater and marine habitats, the body mass of an animal predator exceeded that of its animal prey. Figure 16.3a compares the estimated regression lines of 109 trophic links from coastal webs in data set A, ten trophic links from coastal webs in data set B, and 31 trophic links from Menge et al. (1986). All three regression slopes are less than 1/2. The predicted largest predator from coastal data sets A and B would weigh, respectively, 0.4 kg (10% sensitivity range 0.2–0.8 kg) and 54.0 kg (10% sensitivity range 11.6–293 kg). Figure 16.3b compares the estimated regression lines of 48 trophic links from terrestrial webs in data set A, 162 trophic links from terrestrial webs in data set B, and a line hand-fitted to graphed terrestrial data from Ve´zina (1985). All three regression slopes are greater than 1/2. The predicted largest predator from terrestrial data set A would weigh 23.8 kg (10% sensitivity range 3.6–247 kg). Because the slope for data set B is so close to 1, the predicted maximal predator mass is meaningless. For the estimates from Ve´zina’s data, the largest predator would weigh 168 kg (10% sensitivity range 13.5–4660 kg). For comparison, the heaviest terrestrial vertebrate predator in Ve´zina’s data is the East African lion (Panthera leo), which weighs 160 kg. The eight empirical regression lines of log predator weight as a function of log prey weight plotted in Figs. 16.2 and 16.3 have slopes ranging from 0.1463 to 0.9443, with median value 0.5489, not far from the predicted value of 1/2.

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(a) 6

log10 weight (g) of predator

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4

coastal B

2 Menge 1986

coastal A

0 –2 –4 –6 –6

–4

–2 0 2 log10 weight (g) of prey

4

6

Figure 16.3 (a) Regression lines of predator masses and prey masses in trophic links in three sets of coastal food webs. The regression line for Menge et al. (1986) is taken from Fig. 16.2a. The regression lines for coastal A and coastal B are computed from the statistics of Cohen et al. (1993, p. 71, Table 2). Lengths reported in data set B were converted to masses, assuming spherical geometry, by log10(mass) ¼ log10(p/6) þ 3 log10(length). Although the regression lines for coastal A and coastal B extend to the right of the diagonal line where predator and prey masses are equal, roughly 90% of the data points fell above and to the left of the diagonal. The coastal A regression line is: log10(predator mass, g) ¼ 2.2114 þ 0.1463 log10(prey mass, g). The coastal B regression line is: log10(predator mass, g) ¼ 3.1985 þ 0.3241 log10(prey mass, g). (b) Regression lines of predator masses and prey masses in trophic links in three sets of terrestrial food webs. Procedures of Fig. 16.3a apply here. The terrestrial A regression line is: log10(predator mass, g) ¼ 2.1105 þ 0.5177 log10(prey mass, g). The terrestrial B regression line is: log10(predator mass, g) ¼ 1.9924 þ 0.9443 log10(prey mass, g). Ve´zina (1985) gave numerically only a range of masses for predators and no masses for their prey. Here a single straight line was fitted by hand to Ve´zina’s graph of the data for insectivores, piscivores and carnivores, and the hand-fitted straight line for the data of Ve´zina (1985) is: log10(predator mass, g) ¼ 2.19 þ 0.58 log10(prey mass, g).

Jonsson and Ebenman (1998a) computed the ratio of predator mass to prey mass for all trophic links for which both masses were known using 768 consumer species (697 trophic species) in 52 community food webs. Their finding that, for most food webs, the higher the trophic level of the predator, the smaller the predator–prey mass ratio, agrees with the theory developed here for isolated food chains if higher trophic level correlates closely with higher body mass. It will be desirable to re-examine this asserted pattern using the data of Brose et al. (2005). Data on parasite and parasitoid food webs and body sizes appear to be scarce. Memmott et al. (2000) reported a source food web of a broom community that

BODY SIZES IN FOOD CHAINS

(b) 8 terrestrial B log10 weight (g) of predator

6 4

Vezina 1985

2 0 terrestrial A

–2 –4 –6 –6

–4

–2 0 2 log10 weight (g) of prey

4

6

Figure 16.3 (cont.)

contained one plant species, 19 herbivores, 66 parasitoids, 60 predators, five omnivores and three pathogens. They plotted log consumer-species length as a function of log resource-species length with separate symbols for parasitoids, pathogens and predators (their Fig. 7) but they did not report estimates of allometric relations nor list the length data, though they did provide the foodweb data. According to Leaper and Huxham (2002), the web reported by Memmott et al. (2000) was the first and until 2002 the only published food web to present body masses for both parasites (in fact, they were parasitoids) and other consumers. Leaper and Huxham (2002) calculated but did not publish body masses of 160 of the 171 taxa in the food web of the Ythan estuary: 113 average adult body weights and mean weights for the given life-history stage of the remaining 47 taxa. They reported Pearson’s r2 for log10 consumer and log10 resource body masses for six versions of the web: including non-parasites only, parasites only, and all taxa; and for each group of taxa, with and without distinguishing life stages according to their trophic relations. No regression coefficients of log10 consumer body mass on log10 resource body mass were given. The correlations were positive in all cases and were statistically significantly different from zero at the 0.001 level except for parasites only, disregarding differences among life stages.

Discussion Hutchinson (1959, p. 147) examined ‘the order of magnitude of the diversity that a single food chain can introduce into a community’. It is worthwhile to revisit his influential calculations in the light of data and theory available since he wrote. Hutchinson assumed that ‘in general 20 per cent of the energy passing

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through one [species] can enter the next [species] in the chain’ and that ‘each predator has twice the mass (or 1.26 the linear dimensions) of its prey, which is a very low estimate of the size difference between links . . .’ This assumption may be represented in the model Eq. (16.1) by putting A ¼ 2 and B ¼ 1. This model led Hutchinson (1959, p. 147) to envisage the ‘ultimate predator’ at trophic level 49, with an individual body size ‘vastly greater than the volume of the world ocean’. Hutchinson then implicitly assumed that the numerical abundance N, or population size, of each animal species in a predator food chain equals the total energy available divided by the typical body size M, which is tantamount to assuming that the energy consumption of each animal species is directly proportional to its typical body size M. With each increase in the trophic level of species in a predator chain, according to Hutchinson’s assumptions, 20% as much energy has to be divided among the organisms each twice as big. The population size therefore is reduced by a factor of 0.2/2 ¼ 0.1, i.e. decreases by 90%. Consequently, Hutchinson concluded, the population size or numerical abundance N4 of the fifth animal species will be 10 4 times the population size N0 of the first. In this hypothetical world, food chains cannot be very long. Hutchinson’s assumptions imply an allometric relation between numerical abundance (or population size) and average body mass. Along a trophic link from any species 1 to any species 2, Hutchinson assumes that M2 ¼ 2M1 (mass doubles) while N2 ¼ (1/10)N1 (numerical abundance falls by 90%). The slope of the allometric relation between numerical abundance and body mass is then: D log10 ðNÞ=D log10 ðMÞ ¼ ½log10 ðN2 Þ  log10 ðN1 Þ=½log10 ðM2 Þ  log10 ðM1 Þ ¼  log10 ð10Þ= log10 ð2Þ ¼ 3:32:

(16:4)

Each step in Hutchinson’s argument has been re-examined. Pauly and Christensen (1995) estimated a mean trophic transfer efficiency of 10% (half Hutchinson’s estimate of 20%). Rather than doubling with each trophic link, animal body size in a predator chain is more likely to be described by Eq. (16.2) with A > 0, 0 < B < 1, neglecting the substantial variability in the size of predators on prey of a given size. Animal metabolic energy requirements increase approximately in proportion to M3/4 rather than to M (Kleiber, 1961). In Tuesday Lake, Michigan, the regression of log10(N) on log10(M) had slope 08413 (with 99% confidence interval 098, 071) in 1984 and slope 07461 (with 99% confidence interval 091, 059) in 1986 (Reuman & Cohen, 2004). These slopes are far from the slope of 332 that follows from Hutchinson’s assumptions. Cohen and Carpenter (2005) showed that the statistical assumptions underlying linear regression were justified for Tuesday Lake data in regressions of log10(N) on log10(M) but not vice versa. If animal population size were constrained by available energy alone, as Hutchinson supposed, and if the food chain were isolated from all other food chains to or from which energy might be diverted, then, in principle, a better

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formula than Hutchinson’s for the ratio of the population size or numerical abundance Nn at trophic level n to the numerical abundance N0 of the basal animal in a predator chain would appear (for the moment) to be: Nn =N0 ¼ ðM0 =Mn Þ3=4 ð0:1Þn

(16:5)

and the slope of the relation between numerical abundance and body mass is predicted by these assumptions to be: D log10 ðNÞ=D log10 ðMÞ ¼ ½log10 ðNnþ1 Þ  log10 ðNn Þ=½log10 ðMnþ1 Þ  log10 ðMn Þ ¼ 3=4 þ 1= log10 ðMnþ1 =Mn Þ:

(16:6)

For large n, M0/Mn approaches a constant (less than 1) and the ratio Eq. (16.5) declines by a factor of 0.1 with each increase in trophic level. Apparently by coincidence, this is exactly the behaviour Hutchinson calculated. That is the good news. The rest of the news is bad, and gets worse. For small n, Eq. (16.5) predicts a slower-than-exponential decline, unlike Hutchinson’s calculation. For large n, Mnþ 1/Mn ! 1 so log10(Mnþ 1/Mn) ! 0 and the right side of Eq. (16.6) diverges to infinity, clearly an unrealistic prediction. Evidently the assumptions stated just before Eq. (16.5) do not hold in the real world. One weak assumption is that the predator chain is energetically isolated from all other food chains. In addition, the population sizes of species, especially species with small body sizes, are often not limited by energy (Blackburn, Lawton & Pimm, 1993; Blackburn & Lawton, 1994). While large-bodied animal species are usually rare, small-bodied animal species commonly have a wide range of population sizes, from abundant to rare. Overall, Hutchinson’s argument that a predator chain (and by his off-hand extension, a parasite chain) ‘clearly . . . of itself cannot give any great diversity’ founders in the face of more recent facts and models. For three collections of data from coastal communities, 0 < b < 1/2, while for three collections of data from terrestrial communities, 1/2 < b < 1. Is this difference true in general? If confirmed by data of better quality from more communities, then a kilogram of resource supports a predator of larger body mass in a terrestrial community than in a coastal community. Why is this? The starting hypothesis here is that the mass of the consumer (predator or parasite) is related to the mass of the animal resource (prey or host) by a power law with exponent less than 1. This hypothesis is at best an approximation to reality, on both empirical and theoretical grounds (Cohen et al., 1993). Empirically, large predators sometimes eat prey of a wide range of masses while small predators eat prey with a narrower range of masses (as in Figs. 1 and 2 of Cohen et al., 1993). However, in Tuesday Lake, observed trophic links appear to fall in a band above and parallel to the diagonal line where predator mass equals prey mass, rather than in a triangular region in the (x, y) plane (Reuman & Cohen, 2004). Approximating both such relations by a power-law

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function ignores the apparent differences between them in how the variance in predator mass changes with the mass of the prey. The only direct evidence on how well a power-law relation describes body masses in parasite chains is Fig. 1 of Leaper and Huxham (2002, p. 447). Their scatter plots for parasites only in the Ythan estuary provide weak support for the usefulness of a power-law approximation. For log parasite size and log host size of parasites only, without trophospecies r2 ¼ 0.015 was not significant, and with trophospecies r2 ¼ 0.125 was statistically significant but still small. An approximate power law with exponent less than 1 has been derived theoretically from models of food-web structure, species abundance distributions, and the distribution of biomass across species mass categories (Cohen, 1991, pp. 5–8). Cohen et al. (1993) suggested that the logarithm of animal species masses may be approximately normally distributed, and that E(y|x) is the mean of a normal distribution censored below x (i.e. retaining only that portion of the normal distribution to the right of x). Unpublished numerical calculations show that, under this model, E(y|x) is a convex nonlinear function (always with slope less than 1) of x, rather than a strictly linear function as expected by the powerlaw relation Eq. (16.1). With the observed distribution of body mass reported by Cohen et al. (1993, p. 73, their Table 4), the power law approximates reasonably the convex nonlinear function in the range of animal body masses from 106 g to 10þ6 g. Terrestrial vertebrate predators far larger than contemporary top carnivores lived in the past (Burness, Diamond & Flannery, 2001). It would be interesting to determine whether predator and prey masses during the Cretaceous and late Pleistocene are consistent with a power law Eq. (16.1); if so, whether the coefficients A and B had different values from those estimated here; and if so, whether the maximum predator mass at that time could be predicted from the predator–prey body mass relations then in effect. Jonsson and Ebenman (1998b) suggested that the decrease they observed (Jonsson & Ebenman, 1998a) in the ratio of predator mass to prey mass with increasing trophic level in predator chains has significant consequences for stability in dynamic models of food chains. This suggestion could be extended to parasite chains, and merits further analysis and testing. The derivation of maximal body mass from the phenomenology of body sizes in trophic links is only one among many possible approaches. Other constraints on maximal body mass include mechanical or design constraints, energetics of food supply and metabolism, land area (for terrestrial consumers), natural selection of life histories and the processes of development (e.g. Bonner, 1988; Yoshimura & Shields, 1995; Burness, Diamond & Flannery, 2001; Gomer, 2001). It remains to be demonstrated whether, and if so how, these approaches are compatible. To summarize, food chains in which animal predators are bigger than their animal prey are called predator chains. Food chains in which the consumers are

BODY SIZES IN FOOD CHAINS

smaller than their animal prey are called parasite chains. If the mass of the consumer (predator or parasite) is related to the mass of the animal resource (prey or host) by a power law with exponent less than 1, then, in predator chains, there is an upper limit to the mass of the largest predator and prey, and in parasite chains, there is a lower limit to the mass of the smallest host and parasite. These limits are independent of the number of trophic links in the chain and independent of the mass of the basal animal species. In a predator chain that obeys this allometric relation of predator and prey masses, the ratio of predator mass to prey mass decreases as the trophic level and mass of the prey increase. In a parasite chain that obeys this allometric relation of predator and prey masses, the ratio of parasite mass to host mass increases as the trophic level of the host increases and the mass of the host decreases. In the data on predator chains here, predator masses generally exceed prey masses. The regression of the logarithm of predator mass on the logarithm of prey mass has slope b less than 1 in all cases. While it is possible to calculate maximal predator sizes from these regressions, estimates of maximal predator size are highly sensitive to uncertainty in the parameters of the regression lines. For three collections of data from coastal communities, 0 < b < 1/2, while for three collections of data from terrestrial communities, 1/2 < b < 1. A model of the joint distribution of consumer and resource body masses predicts a slope of 1/2 for both predator and parasite chains, and specifies conditions under which the slope should deviate up or down from 1/2. The theory developed here pertains to isolated chains, but all the data are drawn from webs with interconnecting chains. An ideal test of the theory would describe the full frequency distribution of body sizes of each species in a more or less isolated chain, if such can be found in nature. It would also be useful to extend the theory from isolated chains to more complex food webs and to analyze the consequences in the variability of body sizes of both resources and consumers.

Acknowledgements I am grateful for helpful, critical comments on previous drafts from John Tyler Bonner, Benni Hansen, Mark Huxham, Tomas Jonsson, Mark Laska, Robert H. Peters, Dave Raffaelli, Thomas W. Schoener, Alain Ve´zina and two reviewers; the support of US National Science Foundation grants BSR92-07293, DEB 9981552 and DMS-0443803; the assistance of Priscilla K. Rogerson; and the hospitality of Mr and Mrs William T. Golden during this work.

References Blackburn, T. M. & Lawton, J. H. (1994). Population abundance and body size in animal assemblages. Philosophical Transactions of the Royal Society of London Series B, 343, 33–39.

Blackburn, T. M., Lawton, J. H. & Pimm, S. L. (1993). Non-metabolic explanations for the relationship between body size and animal abundance. Journal of Animal Ecology, 62, 694–702.

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Bonner, J. T. (1988). The Evolution of Complexity. Princeton, NJ: Princeton University Press. Brose, U., Cushing, L., Berlow, E. L. et al. (2005). Body sizes of consumers and their resources. Ecology, 86, 2545. Brose, U., Jonsson, T., Berlow, E. L. et al. (2006). Consumer-resource body-size relationships in natural food webs. Ecology, 87, 2411–2417. Burness, G. P., Diamond, J. & Flannery, T. (2001). Dinosaurs, dragons, and dwarfs: the evolution of maximal body size. Proceedings of the National Academy of Sciences, 98, 14518–14523. Cohen, J. E. (1991). Food webs as a focus for unifying ecological theory. Ecology International (International Association for Ecology Bulletin), 19, 1–13. Cohen, J. E. & Carpenter, S. R. (2005). Species’ average body mass and numerical abundance in a community food web: statistical questions in estimating the relationship. In Dynamic Food Webs: Multispecies Assemblages, Ecosystem Development and Environmental Change – A Volume of Theoretical Ecology, ed. P. C. de Ruiter, V. Wolters & J. C. Moore. Amsterdam: Elsevier, pp. 137–156. Cohen, J. E., Briand, F. & Newman, C. M. (1990). Community Food Webs: Data and Theory. Biomathematics Vol. 20. Heidelberg, Berlin, New York: Springer-Verlag. Cohen, J. E., Pimm, S. L., Yodzis, P. & Saldan˜a, J. (1993). Body sizes of animal predators and animal prey in food webs. Journal of Animal Ecology, 62, 67–78. Cohen, J. E., Jonsson, T. & Carpenter, S. R. (2003). Ecological community description using the food web, species abundance, and body size. Proceedings of the National Academy of Sciences, 100, 1781–1786. Cohen, J. E., Jonsson, T., Mu¨ller, C. B., Godfray, H. C. J. & Savage, V. M. (2005). Body sizes of hosts and parasitoids in individual feeding relationships. Proceedings of the National Academy of Sciences, 102, 684–689.

Elton, C. (1927). Animal Ecology. (New impression with additional notes 1935.) New York: Macmillan. Gomer, R. H. (2001). Not being the wrong size. Nature Reviews Molecular Cell Biology, 2, 48–54. Hansen, B., Bjı´rnsen, P. K. & Hansen, P. J. (1994). The size ratio between planktonic predators and their prey. Limnology and Oceanography, 39, 395–403. Horning, M. & Trillmich F. (1997). Development of hemoglobin, hematocrit and erythrocyte values in Gala´pagos fur seals. Marine Mammal Science, 13, 100–113. Hutchinson, G. E. (1959). Homage to Santa Rosalia or why are there so many kinds of animals? American Naturalist, 93, 145–159. Jonsson, T. & Ebenman, B. (1998a). Trophic links and the relationship between predator and prey body sizes in food webs. Chapter 2 in T. Jonsson, Food Webs and the Distribution of Body Sizes. Linko¨ping Studies in Science and Technology, Dissertation 535, Linko¨ping, Sweden, pp. 63–81. Jonsson, T. & Ebenman, B. (1998b). Effects of predator-prey body size ratios on the stability of food chains. Journal of Theoretical Biology, 193, 407–417. Jonsson, T., Cohen, J. E. & Carpenter, S. R. (2005). Food webs, body size and species abundance in ecological community description. In Food Webs: From Connectivity to Energetics, Advances in Ecological Research Vol. 36, ed. H. Caswell. San Diego: Elsevier, pp. 1–84. Kleiber, M. (1961). The Fire of Life: An Introduction to Animal Energetics. New York: John Wiley. Leaper, R. & Huxham, M. (2002). Size constraints in a real food web: predator, parasite and prey body-size relationships. Oikos, 99, 443–456. Memmott, J., Martinez, N. D. & Cohen, J. E. (2000). Predators, parasitoids and pathogens: species richness, trophic generality and body sizes in a natural food web. Journal of Animal Ecology, 69, 1–15.

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Menge, B. A., Lubchenco, J., Gaines, S. D. & Ashkenas, L. R. (1986). A test of the Menge-Sutherland model of community organization in a tropical rocky intertidal food web. Oecologia (Berlin), 71, 75–89. Pauly, D. & Christensen, V. (1995). Primary production required to sustain global fisheries. Nature, 374, 255–257. Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge: Cambridge University Press. Reuman, D. C. & Cohen, J. E. (2004). Trophic links’ length and slope in the Tuesday Lake food web with species’ body mass and numerical abundance. Journal of Animal Ecology, 73, 852–866. Reuman, D. C. & Cohen, J. E. (2005). Estimating relative energy fluxes using the food web, species abundance, and body size. In Food Webs: From Connectivity to Energetics, Advances in Ecological Research Vol. 36, ed. H. Caswell. San Diego: Elsevier, pp. 137–182. Rott, A. S. & Godfray, H. C. J. (2000). The structure of a leafminer-parasitoid community. Journal of Animal Ecology, 69, 274–289. Schoener, T. W. (1968). Size of feeding territories among birds. Ecology, 49, 123–141.

Sheldon, R. W., Prakash, A. & Sutcliffe, W. H., Jr. (1972). The size distribution of particles in the ocean. Limnology and Oceanography, 17, 327–340. Ve´zina, A. F. (1985). Empirical relationships between predator and prey size among terrestrial vertebrate predators. Oecologia (Berlin), 67, 555–565. Wallace, A. R. (1858). On the tendency of varieties to depart indefinitely from the original type. In C. R. Darwin & A. R. Wallace, On the tendency of species to form varieties; and on the perpetuation of varieties and species by natural means of selection. Journal of the Proceedings of the Linnean Society, Zoology, 20 Aug. 1858, 3, 45–62. Online: http://pages.britishlibrary.net/charles. darwin3/jpls.html#natsel Warren, P. H. & Lawton, J. H. (1987). Invertebrate predator-prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure? Oecologia (Berlin), 74, 231–235. Yoshimura, J. & Shields, W. M. (1995). Probabilistic optimization of body size: a discrepancy between genetic and phenotypic optima. Evolution, 49, 375–378.

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CHAPTER SEVENTEEN

Body size in aquatic ecology: important, but not the whole story ALAN G . HILDREW School of Biological and Chemical Sciences, Queen Mary, University of London

DAVI D G . RAFFAELLI Environment Department, University of York

RONNI EDMONDS - BROWN Division of Geography and Environmental Sciences, University of Hertfordshire

Introduction Ecologists have long been aware of regularities and patterns in the body size of organisms in populations and communities, observations that go back at least to Alfred Wallace and continue through the works of Elton, Thienemann, Hutchinson, MacArthur and many others. The classical contribution of R. H. Peters (1983) codified such patterns through the concept of body-size allometry, of metabolic rate and other features, and led on to many of the phenomena now included under macroecology (Blackburn & Gaston, 2003). Brown and colleagues (Brown et al., 2004; Brown, Allen & Gillooly, this volume), in particular, added new advances in scaling theory and, incorporating the exponential effect of temperature on metabolic rate, sought to explain a wide variety of patterns and processes in ecology at levels of organization from individuals to ecosystems. The focus on aquatic systems at the Hatfield symposium, and in this resultant volume, is justified because body-size patterns may be more important, or at least more obvious, in aquatic ecosystems. Woodward and Warren (this volume) offer three possible reasons. First, the most important primary producers in water are small and, along with small heterotrophic micro-organisms and small detritus particles, are gathered from suspension by larger consumers. Second, they point out that conventional predators, larger in turn than their prey, seem particularly prominent in aquatic systems where there may be fewer parasite food chains (see Cohen, this volume). A third, methodological reason for a particular emphasis on body size by aquatic ecologists, may be the relative ease of automated counting of particles and organisms in suspension across a wide range of scales. Perhaps with particular reference to methodology, it is noteworthy that terrestrial and aquatic ecologists have also generally taken different perspectives on body size. Thus, in describing assemblages, aquatic Body Size: The Structure and Function of Aquatic Ecosystems, eds. Alan G. Hildrew, David G. Raffaelli and Ronni Edmonds-Brown. Published by Cambridge University Press. # British Ecological Society 2007.

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ecologists often present their data as a continuous size spectrum of individuals, irrespective of taxonomic affinities, whereas terrestrial ecologists generally view the species as the individual datum, and usually as a fixed entity – mean adult body mass. The ways these two research communities present and subsequently interpret their data affect their understanding of how aquatic and terrestrial systems work (Raffaelli, Solan & Webb, 2005). To these speculations we might add that aquatic systems show one feature for which there is no obvious parallel in the terrestrial world: a viscous medium that greatly shapes how organisms function and behave. This unique attribute of aquatic systems has understandably been a major focus for aquatic ecology and has accordingly produced a perspective that is quite different from that of terrestrial ecologists. As the chapters in this book testify, body size has clearly remained a major research focus for the ecological community, from ecophysiology to the ecosystem. In part this is because body size sets real mechanical limits on what organisms can do (e.g. limits to the dimensions of prey that can be physically ingested), and in part because body size is a super-parameter, which does well at capturing a range of associated physiological and ecological traits, but is much more easily measured (or found in books) than those traits themselves. A few of the authors herein have set out explicitly to test such data against the predictions of the metabolic theory of ecology (Brown et al., 2004), with varying degrees of success, while others chose ostensibly different theoretical backgrounds against which to consider patterns and dynamics related to body size.

Body size and metabolic theory We consider first the few chapters that explicitly mention explorations of metabolic theory, or at least consider metabolic theory against patterns in the different fields of literature. With respect to life history, Atkinson and Hirst (this volume) consider whether selection can alter the scaling exponent (b) relating metabolic rate to body size, the core of metabolic theory. They ask to what extent is b fixed at 3/4? They cite Glazier’s (2005) survey of 642 metabolic rates during ontogeny, around half of which deviated from 3/4 and, interestingly, with higher values (mean 0.95) in pelagic compared to benthic (mean 0.74) species, perhaps due to the increased costs of buoyancy or avoiding predation in pelagic species. Huryn and Benke (this volume) consider biomass turnover and body size in stream benthic invertebrates, analyzing the relationships between body size (M) and population density, biomass (B), production (P) and P/B. They found an encouraging degree of fit with theory for three temperate streams, with the relationship between P/B and body size (as mass) having a scaling exponent varying between 0.24 and 0.27, bracketing the predicted value of 0.25. Huryn and Benke (this volume) consider this precise fit ‘extraordinary when considering the large ecological differences between the streams’, forested or grassland, with or without fish, etc. The ‘snag’ community

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(organisms sedentary on woody debris in the channel) of the warm water Ogeechee River (Georgia, USA) was inconsistent with the theory (scaling exponent of M and P/B, 0.50), though this discrepancy could be accounted for in various ways. Thus, for Huryn and Benke’s data on stream benthos, metabolic theory does fairly well. Several other authors found encouraging, though patchy, fits of pattern with metabolic theory in different contexts (Petchey, Long & Morin, this volume; Humphries, this volume; Hall et al., this volume; Jennings & Reynolds, this volume), leaving us with the intellectually awkward task of judging whether the theory survives because we can explain the discrepancies, or if the theory falls in general. The problems of testing theory in this way are several and were vigorously debated at the meeting, and there seem to be three major issues involved. First, testing has essentially been a post-hoc exercise in which data gathered for completely different purposes are used to challenge the theory, always a tricky process. Second, different measures of body size were used in the present collection of chapters: mass or weight (dry, ash-free, wet, whole-body or elemental), volume or equivalent spherical diameter, individual, average or adult body size. Different measures will be appropriate for different research questions and in many cases a clear rationale for selecting a particular measure of body size is presented. For other studies, however, including many macroecological investigations, the data used are simply those at hand, often adult body sizes, which can be extracted from field guides or species survey lists. If patterns that emerge from the analyses of such data are interpreted in the context of theory that assumes other expressions of body size, such as individual biomass, then the value of the research is compromised. One solution to this potential problem is to make available a much greater variety of body-size measurements for a broad range of systems within a public domain database, so that analyses can be tailored more closely to theory. Third, body-size data and relationships are presented in a variety of forms within the present volume. Several chapters reported bi- or tri-variate relationships, with body size as the explanatory variable, often seeking to allow comparisons with theory (mainly as judged by slopes of regression lines). However, testing for deviation from theoretical relationships opens up a can of worms. For instance, the choice of regression models (least squares, geometric mean, bisector regressions and others) is important because each estimates a different value for the slope. Similarly, it is not good enough to assume that, because a slope through the observed data is not significantly different from the theoretical prediction, the data are consistent with theory. An alternative explanation is that there is not enough power (essentially the number of data points) in the analysis to falsify the model, and formal power analyses should be carried out to check this, although this is rarely done. More suitable statistical procedures to demonstrate negligible trends in data are now available (Dixon & Pechmann,

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

2005), and these authors also provide a good discussion of the difference between a failure to reject a null hypothesis and verifying that null hypothesis. In addition, for claimed invariant relationships, where a slope of zero is predicted by theory, it is incredibly difficult to distinguish such invariance in a data set from a non- (and therefore meaningless) relationship. Finally, different representations of the data could well generate quite different perspectives on the significance of body size in ecology. Within taxonomic collections (e.g. a family of water beetles or harpacticoid copepods), bivariate plots of body size against abundance provide reasonable representations of relationships. As the taxonomic grouping becomes coarser (e.g. freshwater benthos or marine benthic invertebrates), regression techniques begin to fail to provide an adequate model of the data. At the whole system level, a constraint space (e.g. Brown, 1995) or biomass spectrum (e.g. Stead et al., 2005) might be more appropriate, although formally quantifying such pattern and exploring deviations from theoretical prediction is fraught with difficulty (Leaper & Raffaelli, 1999).

Other empirical, theoretical and conceptual backgrounds Most chapters in this book do refer to metabolic theory, but perhaps wisely do not attempt explicit tests, instead setting their findings in the context of a variety of other areas of theory and concept. For instance, Humphries (this volume) considers suspension feeding, a mode of feeding virtually restricted to aquatic systems, in relation to body size and the physics of water and flow. Body size is crucial for aquatic organisms because it determines flow regime and thus, for suspension feeders, food supply. We are particularly struck by Humphries’ remark that body size is particularly ‘nebulous and difficult to specify’ for suspension feeding organisms, because they stretch to the very limits the relationship between the various measures of size that ecologists can use. Consider for instance gelatinous pelagic filter feeders, of large physical dimensions but very low body mass; benthic filter feeders with large and heavy, but metabolically inactive, shells; and organisms that build extensive nets and mucus sheets to capture food at a rate beyond that expected from their body size alone. Perhaps for this reason there is still no clear relationship between body size and food-particle size for suspension feeders, in contrast to the situation for conventional predators. Townsend and Thompson, Atkinson and Hirst, and Huryn and Benke (all this volume) all deal with body size as a species trait in relation, respectively, to the habitat templet hypothesis, life-history theory and metabolic theory. Townsend and Thompson (this volume) consider body size against the habitat templet hypothesis of Southwood (1977), and allied predictions specifically developed for streams by Townsend and Hildrew (1994), and referring to traits in relation to disturbance, productivity, land use, predation and others. They conclude that

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clear patterns of macroinvertebrate body size are ‘sometimes apparent but rarely account for a large proportion of variation along the (environmental) dimension of interest’. They attribute this result to the complexity of multiple stressors in natural systems and to the inclusion of mixtures of organisms with different ‘solutions’ (including body size) to particular environmental conditions. We also wonder whether in such systems, population and community dynamics will often be transient and thus the ‘snapshot’ patterns often weak. Disturbance is one obvious cause of fluctuations, though others are feasible, and we return to this notion below. Jennings and Reynolds (this volume) relate body size to the pressures of commercial fishing and to fisheries management (see also Atkinson & Hirst, this volume). The effects of fishing on the population size structure of exploited species have been stark and, apart from the well-known phenomenon of ‘fishing down the food chain’ in overexploited systems, Jennings and Reynolds (this volume) have managed to use theory and data to predict that the abundance of large fish (16–66 kg body weight) in the North Sea may now be a remarkable 99.2% lower than before exploitation. Jennings and Reynolds’ paper is wide ranging, and also deals with community-level phenomena such as trophic structure and biomass size spectra, and they point out the practical applications of food-web theory in the adoption of ecosystem and community-level management of fisheries and the oceans. In terms of trophic structure, they highlight the absence of clear trophic steps (trophic levels) in most aquatic (as opposed to terrestrial) ecosystems, and the prevalence of life-cycle omnivory and size-based predation, all arguments for a size-based analysis of the ecosystem impacts of exploitation. Two other chapters focus on body size in relation to species interactions, food-webs and food web theory. Woodward and Warren (this volume) provide much evidence for the importance of body size in determining feeding links, food-web structure and life-cycle omnivory. Communities of freshwater benthic invertebrates evidently provide some of the clearest evidence of all of the primacy of body size in natural food webs, thus chiming with Jennings and Reynolds’ (this volume) conclusions. They analyze explicitly the limits, both upper and lower, to the size disparity observed between predator and prey – i.e. both upper and lower size refugia exist – and show the effect of basing estimates of size disparity on individuals and on species averages. If species averages are taken (i.e. the average size of the predator and the average size of the prey) it turns out that the predator is about ten times greater than the prey, whereas if individual links are considered (i.e. the size of the particular predator and its actual prey) the mean size disparity is about 100. Jones and Jeppesen (this volume) consider further the role of body size in relation to trophic structure, and in their case to the occurrence of alternative regimes and in particular of trophic cascades, many examples of which seem to be ‘wet’ (Strong, 1992). In the

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

sense that trophic cascades are characterized by clear trophic levels, there seems a disparity between the view that cascades are prevalent and the rejection by Jennings and Reynolds (this volume) of integer trophic levels for most aquatic ecosystems, as well as Woodward and Warren’s (this volume) findings for simple freshwater benthic communities. Jones and Jeppesen (this volume) argue that cascades are common where there is a large size disparity between predator and prey, such that ‘prey’ are so small that they are fed on unselectively by the consumers, and where small productive producers turn over very rapidly and can sustain a large biomass of long-lived predators. These features may be more decisive than body size per se in determining the occurrence of cascades. Several chapters took a biogeographical or macroecological approach. These include Finlay and Esteban; Rundle, Bilton and Foggo; Warwick; and Schmid and Schmid-Araya (all this volume). Finlay and Esteban (this volume) consider the biogeography of organisms in relation to their notion of a ‘biogeographical divide’, a body size below which species, by consequence of their enormous population abundances (thus linking this concept to macroecological theory), are cosmopolitan, but above which they are not. This body-size transition seems to be in the range 1–10 mm. For macro-organisms, Rundle et al. provide evidence of a positive relationship between range size and body size in actively dispersing dragonflies. For passively dispersing freshwater organisms, they find that those within the body-size transition of Finlay and Esteban, such as small crustaceans, do indeed have a biogeography and are not cosmopolitan. For passively dispersing marine and freshwater organisms, range size increases with body size, perhaps related to the covariance between body size and propagule output, and hence dispersal probability. It might be that microbial species below about 1 mm tend to be cosmopolitan, but that above this body size, geographical range again increases, as the ability to disperse actively goes up with body size in active dispersers, and the likelihood of dispersal goes up with propagule output (and therefore with body size) in passive dispersers. It seems clear that data on range size for aquatic organisms lag well behind those for terrestrial organisms, which may explain the general paucity of (biogeographical) macroecological relationships for aquatic organisms. Warwick (this volume) deals with a macroecological pattern for which there is a long history of research in aquatic ecosystems, the species–body size spectrum. He reports a regularly bimodal spectrum for the marine benthos, apparently contrasting with a unimodal one for freshwater. In the marine benthos the small mode consists of meiofauna and the large mode the macrofauna, with few intermediate species. Warwick attributes this pattern not to local ecological interactions or habitat architecture, as originally advocated by Schwinghamer (1981), but to the evolutionary history of the marine benthos. The trough of species in the spectrum equates to the size of the planktonic, larval forms of the larger macroinvertebrate benthos. These cannot be benthic because the smaller

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meiofaunal species would predate on or compete with them (many meiofaunal predators take relatively large prey, often larger than themselves). According to Warwick, this general regional pattern of species–body size then produces the local patterns observed. In contrast, Schmid and Schmid-Araya (this volume) analyze such community patterns in relation to fractal geometry, potentially the most fundamental of all the approaches in this volume since fractals may underly the scaling of metabolic rate with body size itself. Schmid and SchmidAraya did not find a self-similar pattern of body size across all scales, however, referring to the changes in scale as ‘multifractal’. Interestingly, Warwick (this volume) also rejected a single fractal scaling for the marine benthos. Other chapters took experimental or modelling approaches. In their experiments using model ecosystems of protists, Petchey, Long and Morin (this volume) demonstrated the effects of body size at three levels of organization: the population, community and ecosystem. The results were encouraging, but there were discrepancies with allometric theory and we can conclude that the effects of body size on ecological processes are modified by trophic complexity (connectedness) and species richness. Persson and De Roos (this volume) also looked at model systems, but focused on individual variation using physiologically structured population models. They stress the within-species variation, much of it ontogenetic, in food intake, growth and body size that is so characteristic of most metazoans. This variation generates intrinsic dynamics and divergent body-size distributions, not wholly predictable by metabolic theory for instance. Systems with strong cohorts that are constantly changing are non-equilibrial systems that can approach alternate states. In short, they emphasize population and community dynamics rather than the structure and pattern that was addressed by many of the other authors. These models are remarkably powerful, and explain effects apparent in many fish populations, but we can only join Persson and De Roos (this volume) in concluding that ‘a major challenge . . . is to develop approaches that allow the analysis of more complex configurations in terms of the numbers of species present’. When even simple real food webs may contain tens or hundreds of species, this is a challenge indeed. Several authors referred to the ecosystem consequences of body size, including CO2 production (Petchey et al., this volume) and nutrient cycling, though this aspect was most explicitly addressed by Hall et al. (this volume). The latter address the extent to which animals affect nutrient cycling directly, through ingestion, egestion, production and excretion, and how body size controls such effects. Partially as expected, nutrient excretion rates scaled allometrically, with an exponent less than 1. Ammonium excretion of stream invertebrates from 18 taxonomic orders scaled at 0.85 with body mass, though there is an interesting degree of variation, apparently related to taxonomy and thus also potentially to the measure of body size used for different taxa. For instance, why are there differences in the scaling of the excretion of P, but not N, between two species of

BODY SIZE: IMPORTANT, BUT NOT THE WHOLE STORY

zebra mussel (Dreissena), and why does excretion of N and P in Dreissena scale so disproportionately with body size (b ¼ 1.38)? There are some fascinating insights in this chapter into how body size could feed back onto ecosystem processes. For instance, they note that the removal of large, migratory salmon has reduced nutrient subsidies to many rivers and their catchments, and that the harvesting of large fish will similarly feed back onto nutrient regeneration rates. Joel Cohen (this volume) closed our symposium with a consideration of the consequences, in both predator and parasite food chains, of the average body mass of a consumer being related to the average mass of the species consumed by a power law with an exponent less than 1. We were struck by Cohen’s finding that ‘one kilogram of resource supports a predator of larger body mass in a terrestrial community than in a (marine) coastal community’, though it is not at all obvious why this should be so. This and other intriguing outcomes of his analyses only serve to highlight the need for more data on body size in natural systems.

Concluding remarks We finish with some speculations. Body-size allometry, and its extension to the metabolic theory of ecology, does pretty well at predicting some, but not all, of the patterns and processes dealt with in this book, and hence provides our chapter title. Whilst appealing to issues of scale may these days seem like the resort of the scoundrel, it is obvious that patterns appear and disappear as spatial and temporal resolution changes and analyses include more and more heterogeneous groups of species at different trophic levels. Further, the appropriate measure of body size is difficult to specify a priori, and we are struck by nature’s ingenuity in creating ways of cheating the scaling and limitations of body size, allowing organisms to ‘punch above their weight’ in obtaining food, and in the process making the ecologist’s task more difficult. Examples include filterers that build large external feeding structures and Cohen’s (this volume) cases of social hunting that enables predators to feed on prey much larger than themselves. Perhaps even the very large marine filter feeders are only possible because they can exploit whole aggregations of prey, effectively a ‘superindividual’, with a combined body size much larger than the single krill ‘particle’. The greatest challenge to a size-based approach to food webs lies with the enormous terrestrial primary producers, trees, the largest of all organisms but which lie at the base of land-based food webs, though their biomass is mainly metabolically inactive (Cousins et al., 2005). Transient dynamics and temporal fluctuation are referred to in several papers, and clearly point to the notion that patterns based on energetic rules and allometry may be obscured at the scale at which it is possible to observe them. It seems likely that the processes underlying metabolic theory provide an envelope or a constraint outside which natural systems may not sustainably lie,

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but that heterogeneity, fluctuations and non-equilibrial processes mean that systems obey such rules only in an approximate way. Energy subsidies among neighbouring systems can be considered in a similar way to transient dynamics. Thus, subsidies to top predators can produce ‘apparent’ cascades in shallow lakes (Jones & Jeppesen, this volume) and might have produced the discrepancies with metabolic theory in the highly productive snag communities of filter feeding organisms in the Ogeechee River observed by Huryn and Benke (this volume). In short, our title captures the discussions and conclusions at the symposium about the role of body size – it is important, but not the whole story.

References Blackburn, T. M. & Gaston, K. J. (2003). Macroecology: Concepts and Consequences. Oxford: Blackwell Science. Brown, J. H. (1995). Macroecology. Chicago:University of Chicago Press. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage. V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789. Cousins, S. H., Bracewell, K. V. & Attree, K. (2005). Measuring the ability of food to fuel work in ecosystems. In Dynamic Food Webs, ed. Ruiter et al. London: Academic Press, pp. 248–257. Dixon, P. M. & Pechmann, J. H. K. (2005). A statistical test to show neglible trend. Ecology, 86, 1751–1756. Leaper, R. & Raffaelli, D. G. (1999). Defining the body size-abundance constraint space: data from a real web. Ecology Letters, 2, 191–199. Peters, R. H. (1983). The Ecological Implications of Body Size. New York: Cambridge University Press.

Raffaelli, D., Solan, M. & Webb, T. J. (2005). Do marine and terrestrial ecologists do it differently? Marine Ecology Progress Series, 304, 271–307. Schwinghamer, P. (1981). Characteristic size distributions of integral benthic communities. Canadian Journal of Fisheries and Aquatic Sciences, 38, 1255–1263. Stead, T. K., Schmid-Araya, J. M., Schmid, P. & Hildrew, A. G. (2005). The distribution of body size in a stream community: one system, many patterns. Journal of Animal Ecology, 74, 475–487. Strong, D. R. (1992). Are trophic cascades all wet? – differentiation and donor-control in speciose ecosytems. Ecology, 73, 747–754. Southwood, T. R. E. (1977). The habitat, the templet for ecological strategies. Journal of Animal Ecology, 46, 337–365. Townsend, C. R. & Hildrew, A. G. (1994). Species traits in relation to a habitat templet for river systems. Freshwater Biology, 31, 265–275.

Index

absolute abundance, microbial species 169–171 abundance and metabolic rate 8–9 consumer:producer ratios 11–12 distribution across species 2 Acartia tonsa (copepod) 24–25 acidification effects in freshwaters 112–113 adaptive dynamics evolutionarily unbeatable strategy 36 fitness definition 36 frequency and density dependence 36–37 relationship of traits to fitness 35–36 trade-offs among traits 35–36 adaptive dynamics life history model 35–36 Allee effect 236–237 allometric equations, form of 1–2 allometric scaling strategies 227–228 alternative states and body size distributions 235–239 aquatic ecosystems body size as a structuring force 98–99 individual biomass production rates 5 individual metabolic rate and body size 4–5 temperature corrections 3–4 aquatic invertebrates (dispersal and body size) 188–193, 195, 196, 198, 200, 201 active dispersers in freshwaters 188–189 active dispersers in freshwaters (case studies) 188, 193–196 dispersal in marine systems 191–193 dispersal in marine systems (case studies) 199–203 passive dispersers in freshwaters 188, 190–191 passive dispersers in freshwaters (case studies) 188, 196–199 Arctic char 236, 237 Atlantic silverside (Menidia menidia) 41 Avelia martinicensis 175 B (mass-specific metabolic rate) 2 b (scaling exponent) 1–44, 45 Bacillus cereus 247 Bacillus subtilus 247 bacteria, body size 1 barndoor skate (Dipturus laevis) 267–268

biodiversity characteristics macroscopic organisms 169 microbial species 169 biogeography and size see microbial species biological scaling relations 1–4 biomass and body size (stream communities) 56, 57, 60, 61, 62, 68–71 and diversity 246–247 consumer:producer ratios 11–12 distribution across species 2 estimates 42 biomass invariance mechanisms 146, 148–152 biomass per unit volume, consistency of 245 biomass production rates, individual organisms 5 biomass turnover (P/B) factors affecting 000 range of rates 000 biomass turnover (P/B) and body size (stream communities) 000 application of the MTE 60, 62–68 biomass 56, 57, 60, 61, 62, 68–71 biomass turnover rate (P/B) predictions and results 56, 57, 61, 62, 63, 66, 68–71 differences in temperate and subtropical streams 60, 62–68 discussion 60, 62–68 metabolic theory of ecology 55–56 population density 56, 60, 61–62, 65, 68–71 predictions 56–57, 68–71 production (P) 56, 57, 61, 63, 64, 68–71 results 60–62, 63, 64, 65, 66 secondary production rate 55–56, 68–71 study streams 57–59 tests of predictions 59–60 bluegill sunfish (Lepomis macrochirus) 39, 40 body size adaptive plasticity in Cladocera 37–39 correlation with characteristics of organisms 1–2 early writings and studies ix–x link to patterns in natural systems 98 range of variation among organisms 1 relation to metabolic rate 1–2

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body size (cont.) relationship with temperature 42 variation within species 226 body-size distribution (BSD) in communities 140 effects of shifts in 112–113 multifractal properties 155–156, 157, 158–159 body-size increase, costs and benefits in suspension feeders 19–24 body-size measurement, difficulties in suspension feeders 17 Boltzmann-Arrhenius factor 2 Boltzmann’s constant (k) 2 brown trout 236, 237 BSD see body-size distribution cannibalistic system 233–234, 235 capelin 237 carbon cycle, and metabolism of organisms 9–11 carbon:phosphorus:nitrogen ratio 9–10 carbon:phosphorus ratio influence on growth rate 6 relation to body size 6 carbon turnover and plant size 10–11 Cladocera, adaptive plasticity in body size 37–39 common skate (Dipturus batis) 267–268 community consequences of body size (microbial systems) 249–250, 252–256, 257, 258, 259, 260, 261–262 community size distributions 110–112 and food web construction 110–112 distinct multiple nodes 111–112 factors affecting size structure 112 invertebrate macrofauna 111–112 megafauna 111–112 meiofauna 111–112 vertebrate macrofauna 111–112 Condylostoma reichi 175 consumer:producer ratios abundance 11–12 biomass 11–12 metabolic energy flux 11–12 copepods body size in relation to prey size 24–25 estimation of global patterns of mortality 46–47, 48 Coregonus albula 229 cosmopolitan-biogeography transition size 171–172 general validity 180–181 cosmopolitan distribution theory (microbial species) 168, 172–180 ‘biogeography’ of microbes 180 cosmopolitan genotypes (rDNA) 178–180 diversity of cryptic protists exceeds active species 172–174 endemic species 168, 175–178, 179 habitat influence on species composition 168, 175–176 habitat selects for cryptic or active phase 172–174 local:global species ratios 176, 177 random dispersal of free-living protists 168, 174

similar species inventories irrespective of geographical distance 174 species concepts 178 undersampling problem 176–178, 179 Cyclidium glaucoma 178–179, 181 density and biomass scaling 146–148 density–body-mass scaling 144–145 with sample area 145–146, 147 density dependence (strength of compensation), response to additional mortality 270–273 determinate growth 228 diatom communities, influences on species composition 175–176 Dipturus batis (common skate) 267–268 Dipturus laevis (barndoor skate) 267–268 dispersal challenges for aquatic organisms 187–188 microbial species 169–171 dispersal ability macroecological significance 187 traits which influence 187 dispersal and body size (aquatic invertebrates) 188–193, 195, 196, 198, 200, 201 active dispersers in freshwaters 188–189 active dispersers in freshwaters (case studies) 188, 193–196 dispersal in marine systems 191–193 dispersal in marine systems (case studies) 199–203 passive dispersers in freshwaters 188, 190–191 passive dispersers in freshwaters (case studies) 188, 196–199 distribution, cosmopolitan-biogeography transition size 171–172 disturbance, effects on marine species diversity 216, 218–220, 221 diversity see species diversity Dreissena spp. (mussels) 289 Dyar’s constant 211, 212 E-state (environmental state) 231 ecological stoichiometry and nutrient relations 2 ecosystems application of MTE 9–12 biomass invariance mechanisms 146, 148–152 body-size distribution (BSD) 140 body-size scaling relationships 98 carbon turnover and plant size 10–11 consequences of body size (microbial systems) 250–251, 256–259, 260, 262–263 effects of community size spectrum 43 element turnover rate and metabolic rate 9–10 energy and materials flow in food webs 11–12 flux and storage of elements 9–12 flux and storage of energy 9–12 fractal geometry framework for patterns and relationships 141–143 influence of body size 225–226 influence of body-size attributes 140 particle-size distribution (PSD) in benthic habitats 142 power-law behaviour 140–143

INDEX

role of metabolism in trophic relationships 11–12 scale-invariance and fractal properties of SADs 141–142 scale-invariance and fractal properties of SARs 141–142 scale-invariance properties 140–143 species-abundance distribution (SAD) mechanisms 146, 148–152 storage of elements in living biomass 9–10 stressor-induced size-spectrum changes 112–113 stressor-induced species loss 112–113 egg hatch times and egg protection strategy 48–49 model 47–49 egg-to-adult times, model 47–49 endothermy and individual growth rate 228 energy availability models 273–274 energy equivalence rule 8–9 energy flux, consumer:producer ratios 11–12 energy transfer in predator–prey interactions 274 energy use across species 2 energy use of populations, and body size 8–9 environmental gradients and body size 78 biomonitoring tools 94 body size patterns 90–94 in stream ecosystems 78 environmental gradients and body size (stream studies) 78–85 agricultural and mining pollution 84–85 altitude 82–83 catchment land use 82 chemical contaminants 84–85 descriptive studies of abiotic gradients 79–81 descriptive studies of biotic gradients 81–82 descriptive studies of complex gradients 82–83 disturbance regime 79–80 experimental studies 83–85 floods 81 hydraulic stress 81 New Zealand streams database 85–88, 89, 90, 91, 92 phosphate availability 81–82 predation 82, 83–84 primary productivity 82 substrate particle size 80, 83–84 evolution fisheries-induced 40–41 of body size see life history analysis; life history theory feeding and size factors affecting variation in prey choice 101–105 individual level processes 100–105 ontogenetic dietary shifts in predators 104–105 scaling to species 105–110 size constraints on predation 100–105 fish eggs, ontogenetic development rate and body size 5–6 fish species, mortality selection for smaller size at maturity 40–41, 42

fisheries describing and predicting community responses 274–280 genetic shifts in mature size of fish 40–41 modelling effects on community size structure 274–280 shifts in fish community size spectrum 43 size-based responses to fishing 274–280 fisheries-induced evolution 40–41 fisheries management changes in size-spectra slopes 269 extinction of marine species 267–268 ‘fishing down the food web’ 268 indirect effects of fishing 269 magnitude of fishing effects 267–268 population and community effects of exploitation 266, 267–268 seabed damage by fishing gear 268, 269 significance of body size 266 size-related effects of fishing 268–269 size-related responses to exploitation 268–269 state of the world’s fisheries 267–268 flow regime (Reynolds number, Re), and body size 17–18 food availability, and body size (suspension feeders) 21, 26–28 food-chain body sizes lower limit to mass of host and parasite 307 metaphoetesis 306–307 parasite chains 306–308 parasitoid chains 306, 307 power-law relationships 306, 307 predator chains 306–308 predator–prey size relationships 306–308 social hunters 306–307 upper limit to mass of predators and prey 307 food-chain body sizes data differences between terrestrial and coastal communities 310, 314, 321–322 empirical values of the exponent 310, 314, 321–322 examination of Hutchinson’s (1959) arguments 319–321 limits to mass of host and parasite 310, 314, 321–323 limits to mass of predator and prey 310, 314, 321–323 power-law relationships 310, 314, 321–323 food-chain body sizes theory 308–313 maximal and minimal body masses 308–311 predicted value of the exponent 311–312 ratios and differences of consumer mass and resource mass 312–313 see also food webs data food-dependent development 235–239 food-dependent growth 228 food webs 2 application of MTE conceptual framework 11–12 body size structure 11–12 construction of size-based models 113–114 construction related to community size distributions 110–112 feeding loops 110

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food webs (cont.) ‘life history’ omnivory 110 masking of size-related effects 107, 108, 109–110 rates of energy and material flow 11–12 role of metabolism 11–12 species-averaging effects 105–110 structure by size rather than species 110 synthesis of approaches to 12 food webs data 313–319 studies of a well-defined community 313–317 studies that pool multiple communities 314, 317–319 fractal geometry framework for patterns in ecosystems 141–143 fractal properties of size-structured communities 152–159 Gadus morhua (North Atlantic cod) 237 Gadus morhua (northern cod) 40–41 global patterns of life history, prediction 47–49 global patterns of mortality in copepods, estimation 46–47, 48 growth and development patterns 226–229 allometric scaling strategies 227–228 classification of growth types 228 determinate growth 228 endothermy and individual growth rate 228 food-dependent growth 228 indeterminate/plastic growth 228 link between individual traits and community attributes 229 population-level feedback and dynamics 229 scaling constraints 227–228 see also ontogenetic development growth-rate hypothesis 6 habitat complexity and predator–prey interactions 129–132 and species complexity 129–132 and trophic cascades 129–132 hatching rate and body mass 5–6 Hubbell’s unified theory of biodiversity (UTB) 149–152 Hutchinson’s (1959) arguments, food chain body size and diversity 319–321 Hutchinsonian ratio 211 i-state (individual) distribution models 230–231 indeterminate/plastic growth 228 individual body size and population dynamics 229–240 alternative states and body size distributions 235–239 cannibalistic system 233–234, 235 E-state (environmental state) 231 emergent Allee effect 236–237 extensions to more complex configurations 239–240 food-dependent development 235–239 i-state (individual) distribution models 230–231 modelling framework 230–231

ontogenetic development and community structure 235–239 ontogenetic development dynamics 231–234, 235 p-state (population state) 230–231 physiologically structured population models (PSPMs) 230–231 size-dependent predation 235–239 size-structured consumer-resource system 231–233, 234 structured biomass community model 239–240 tritrophic food chains 235–239 individual organism biomass production 5 influence of body size on performance 225 metabolic rate and body size 4–5 intrinsic rate of increase (rmax), response to additional mortality 270–271 intrinsic rate of increase in a habitat (r) 34–35, 38–39 invariant quantities 44 invertebrate macrofauna 111–112 Leeuwenhoek, Antonie van 167 Lepomis gibbosus (pumpkinseed sunfish) 39, 40 Lepomis macrochirus (bluegill sunfish) 39, 40 life histories and body size 269–271 and population dynamics 269–271 and responses to exploitation 270–271 trade-offs 270–271 see also growth and development patterns life history analysis 33 biomass estimates 42 body size relationship with temperature 42 ecological applications 40–43 ecosystem function and community size spectrum 43 fisheries-induced evolution 40–41 prediction of body size variation within species 40–41, 42 shifts in community size spectrum 43 temperature-size rule (TSR) 42 life history analysis and scaling relationships ecological applications 46–49 estimation of global patterns of mortality 46–47, 48 intra- and interspecific allometries 45–46 invariant quantities 44 key elements 43–44 methodological issues 44–46 prediction of global patterns of life history 47–49 scaling exponents 43–44, 45 selection effects on scaling exponents 45 life history theory adaptive dynamics model 35–37 adaptive plasticity in life histories 37–39 fitness definition 34–35, 36 frequency and density dependence 36–37 interpretation of phenotypic variation 39 intrinsic rate of increase in a habitat (r) 34–35, 38–39 key elements 34–36 lifetime reproductive success (LRS) 34–35, 38–39

INDEX

methodological issues 36–39 optimality (optimization) model 34–35, 36–37 phenotypic plasticity 37–39 prediction of life history plasticity 37–39 reaction norms 37–39 relationship of traits to fitness 35–36 trade-offs among traits 35–36 life history traits, stream habitats 77–78 lifespan and body size 6–7 and temperature 6–7 lifetime reproductive success (LRS) 34–35, 38–39 Lindeman efficiency 11–12 local:global species ratios, size dependence 181–182 Lontra canadensis (river otter) 292–293 Loxodes rex 175 macroecological patterns acidification effects in freshwaters 112–113 aquatic ecosystems 186–187 effects of individual level processes 99–100 effects of shifts in body-size distribution 112–113 effects of species dispersal ability 187 influence of body-size relationships 186 size-spectrum changes in stressed ecosystems 112–113 stressor-induced species loss 112–113 macroscopic organisms, characteristics of biodiversity 169 marine communities describing and predicting responses to mortality 274–280 energy availability models 273–274 energy transfer in predator–prey interactions 274 modelling fishing effects on size structure 274–280 PPMR (ratio of mean predator size to mean prey size) 274 size-based features of aquatic food webs 273 size-based responses to fishing 274–280 size-based structuring 273–274 size-spectra emergence models 273–274 slope of size spectra 273–280 see also fisheries marine systems, similarities to terrestrial systems 210 marine systems species diversity benthic species adult body size distributions 212–216, 217, 218, 219 benthic species all-animal body size distributions 216–217, 219, 220 Dyar’s constant 211, 212 effects of disturbance 216, 218–220, 221 effects of pollution 216, 218–220, 221 evolutionary influences 214–216, 217, 218, 219 Hutchinsonian ratio 211 influence of feeding traits 215–216, 217, 218, 219 influence of habitat architecture 213–214, 215 influence of life history characteristics 214–216, 217, 218, 219 number of co-occurring species in a guild 211–212, 213

pelagic species size distributions 218, 220 relationship with body size 210–211 size difference between competing species 211, 212 species guilds 211–212, 213 mass-specific metabolic rate (B), equation for 2 maximal population growth rate (rmax) 7, 8 megafauna 111–112 meiofauna 111–112 Menidia menidia (Atlantic silverside) 41 metabolic energy flux, consumer:producer ratios 11–12 metabolic rate and body size in aquatic ecosystems 4–5 effect of temperature 2 factors affecting 3 relation to body size 1–2 metabolic theory of ecology (MTE) 98, 226 and body size (summary) 327–329 application to biomass turnover (P/B) and body size 60, 62–68 applications 2–3, 13 conceptual framework 3 development of 1–2 effects of body size 2–3 flow of energy and materials between trophic levels 11–12 food web structure and body size 11–12 in aquatic ecology 2–3 predictions 3 quantitative links from individual to ecosystem levels 10–11 synthesis of approaches to food webs 12 metaphoetesis 306–307 microbial species absolute abundance and dispersal 169–171 cosmopolitan-biogeography transition size 171–172 cosmopolitan distribution hypothesis 167–169 endemism question 169 general validity of geographical distribution data 180–181 geographical restriction hypothesis 167–169 neutral dispersal hypothesis 167–169 neutral theory of community structure 181–182 size dependence of local:global species ratios 181–182 size effects on biodiversity 169 size effects on dispersal and distribution 167–169 size range 170 see also cosmopolitan distribution theory microbial systems (experimental) 246–247 community consequences of body size 249–250, 252–256, 257, 258, 259, 260, 261–262 description of the experiments and data sets 248–249 discussion 259–263 ecosystem consequences of body size 250–251, 256–259, 260, 262–263 methods 247–251

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340

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microbial systems (experimental) (cont.) population consequences of body size 249, 251–252, 253, 254, 255, 259–261 results 251–259, 260 species choice 247–248 mortality rate and body mass 7–8 mortality selection in fish species, evolutionary responses 40–41, 42 MTE see metabolic theory of ecology multifractal behaviour in ecosystems 142–143 empirical applications 142 multifractal properties of PSDs in river ecosystems 156–159 multifractal SARs 159–163 multifractality of BSDs in river ecosystems 155–156, 157, 158–159 mussels (Dreissena spp.), nutrient excretion 289 Mycoplasma, body size 1 Neobursaridium gigas 175, 181 neutral theory of community structure 181–182 New Zealand streams database analysis 85–88, 89, 90, 91, 92 algal productivity effects 88, 90, 92 biomonitoring tools 94 body size patterns 90–94 disturbance effects 88, 90 factors affecting body size 88, 89, 90, 91, 92 fish 85 fish-predation effects 88, 92 land-use effects 88, 91 macroinvertebrates 85–86 methods 85–86 physicochemical conditions 86, 87 Principal Components Analysis 88, 92 results 88, 89, 90, 91, 92 statistical analyses 86 study sites 85 substrate effects 88, 90, 92 normalization constant 1–2 North Atlantic cod (Gadus morhua) 237 northern cod (Gadus morhua) 40–41 nutrient cycling in aquatic systems consequences of variation by size 293–300 direct and indirect regulation 286–287 effects of harvesting-induced changes in size structure 298–300 influence of body size 287 nutrient flux estimation from biomass size distributions 294–296 predator impact on prey size structure 296–297, 298 regulation by aquatic animals 286–287 variation in body-size distributions 293–294 nutrient excretion in aquatic systems chemical form of excreted N and P 287 fed and unfed animals 288–289, 290 influence of body size 287–292 influence of temperature 288–289, 290 rates of N and P excretion 287–290, 291 ratios of N and P excretion 291–292 taxonomic differences 289–290, 291

nutrient relations and ecological stoichiometry 2 nutrient translocation in aquatic systems and body size 292–293 and speed of movement 292–293 behavioural constraints on home range 292–293 Onchorhynchus spp. (Pacific salmon) 292–293 ontogenetic development and community structure 235–239 dynamics 231–234, 235 rate and body size 5–6 see also growth and development ontogenetic dietary shifts in predators 104–105 ontogenetic size refugia for prey species 107, 108, 109–110 ontogenetic variation in body size 226 optimality (optimization) model (of life history) 34–35 fitness definition 34–35 frequency and density dependence 36–37 intrinsic rate of natural increase (r) 34–35, 38–39 lifetime reproductive success (LRS) 34–35, 38–39 relationship of traits to fitness 35 trade-offs among traits 35, 36 P see production p-state (population state) 230–231 Pacific salmon (Onchorhynchus spp.) 292–293 Paraphysomonas 172, 181 parasite and host, lower limit to mass of 307, 310, 314, 321–323 parasite chains 306–308 parasitoid chains 306, 307 particle-size distributions (PSDs) in benthic habitats 142 multifractal properties in river ecosystems 156–159 perch (Perca fluviatilis) 234, 235, 238 phenotypic plasticity in life histories 37–39 phenotypic variation co-gradient 88 counter gradient 39, 40 interpretation 38, 39 phosphorus, as a growth-limiting nutrient 6 physiologically structured population models (PSPMs) 230–231 Plagiopyla frontata 174 Poecilia reticulata (Trinidadian guppy) 41, 42 Polarella glacialis 181 pollution, effects on marine species diversity 216, 218–220, 221 Polycentropus flavomaculata 24 population consequences of body size (microbial systems) 249, 251–252, 253, 254, 255, 259–261 population density and body size (stream communities) 56, 60, 61–62, 65, 68–71 population density at steady state, and metabolic rate 8–9 population dynamics and body size 269–271 and life histories 269–271

INDEX

and species interactions 2 intrinsic rate of increase (rmax) 270–271 responses to additional mortality 270–273 strength of compensation (density dependence) 270–273 population dynamics and individual body size 229–240 alternative states and body size distributions 235–239 cannibalistic system 233–234, 235 E-state (environmental state) 231 emergent Allee effect 236–237 extensions to more complex configurations 239–240 food-dependent development 235–239 i-state (individual) distribution models 230–231 modelling framework 230–231 ontogenetic development and community structure 235–239 ontogenetic development dynamics 231–234, 235 p-state (population state) 230–231 physiologically structured population models (PSPMs) 230–231 size-dependent predation 235–239 size-structured consumer-resource system 231–233, 234 structured biomass community model 239–240 tritrophic food chains 235–239 see also adaptive dynamics life history model population-level feedback and dynamics 229 population maximal growth rate (rmax) 7, 8 population turnover rate, and metabolic rate 7–8 Power Fraction (PF), niche-assembly model 148–152 power-law and scaling relationships in ecosystems 144–145 power-law behaviour in ecosystem features 140–143 power-law relationships food-chain body sizes 306, 307 food-chain body sizes data 310, 314, 321–323 PPMR (ratio of mean predator size to mean prey size) 274 predator chains 306–308 predator–prey interactions and trophic cascades 129–132 energy transfer 274 factors influencing variation in prey choice 101–105 feeding loops 110 individual level processes 100–105 ‘life history’ omnivory 110 networks structured by size 110 ontogenetic dietary shifts in predators 104–105 ontogenetic size refugia for prey species 107, 108, 109–110 particle capture by suspension feeders 24–26 PPMR (ratio of mean predator size to mean prey size) 274 predator impact on prey size structure 296–297, 298 scaling to species 105–110 size-dependent foraging 100–105 size-dependent predation 235–239

size relationships 24–26, 306–308 species-averaging effects in food webs 105–110 upper limits to mass of predator and prey 307, 310, 314, 321–323 production (P) (whole organism metabolic rate) and body size (stream communities) 56, 57, 61, 63, 64, 68–71 equation for 2 individual organisms 5 Proteus vulgaris 247 PSDs see particle-size distributions PSPMs (physiologically structured population models) 230–231 pumpkinseed sunfish (Lepomis gibbosus) 39, 40 quarter-power exponents (b), explanation for 1–2 r (intrinsic rate of increase in a habitat) 34–35, 38–39 rmax (intrinsic rate of increase), response to additional mortality 270–271 rmax (maximal population growth rate) 7, 8 Re see Reynolds number reaction norms 37–39 Redfield ratio 9–10 resource supply and abundance 8–9 Reynolds number (Re) 17–18, 293 collecting elements of suspension feeders 19, 20, 21 river ecosystems data collection 143–144 density and biomass scaling 146–148 density-body mass scaling 144–145 density-body mass scaling with sample area 145–146, 147 fractal properties of size-structured communities 152–159 multifractal behaviour 142–143 mulitfractal properties of BSDs 155–156, 157, 158–159 multifractal properties of PSDs 156–159 multifractal SARs 159–163 power-law and scaling relationships 144–145 scale-related patterns 142–143 river otter (Lontra canadensis) 292–293 RNA, influence on growth rate 6 roach (Rutilus rutilus) 238 SADs see species-abundance distributions sapuara (Semaprochilodus kneri) 293 SARs see species-area relationships scale-invariance of power laws 144–145 scale invariance properties of ecosystems 140–143 fractal properties of size-structured communities 152–159 scaling constraints 227–228 scaling exponent (b) 1–2, 43–44, 45 secondary production rate and biomass turnover rate 55–56, 68–71 self-similarity, fractal properties of size-structured communities 152–159 Sequoia trees, size of 1 Serratia marcescens 247

341

342

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Simulium (blackfly) larvae, feeding strategy 28 size-spectrum changes in stressed ecosystems 112–113 size-structured consumer-resource system 231–233, 234 social hunters 306–307 solid–fluid interfaces, and body size 21, 26–28 species-abundance distributions (SADs) mechanisms 146, 148–152 scale-invariance and fractal properties 141–142 species-area curves 141–142 species-area relationships (SARs) multifractal properties 159–163 scale-invariance and fractal properties 141–142 species-averaging in food webs 105–110 species complexity and habitat complexity 129–132 and trophic cascades 129–132 species diversity, and total biomass 246–247 species diversity (marine systems) benthic species adult body size distributions 212–216, 217, 218, 219 benthic species all-animal body size distributions 216–217, 219, 220 Dyar’s constants 211, 212 effects of disturbance 216, 218–220, 221 effects of pollution 216, 218–220, 221 evolutionary influences 214–216, 217, 218, 219 Hutchinsonian ratio 211 influence of feeding traits 215–216, 217, 218, 219 influence of habitat architecture 213–214, 215 influence of life history characteristics 214–216, 217, 218, 219 number of co-occurring species in a guild 211–212, 213 pelagic species size distributions 218, 220 relationship with body size 210–211 size difference between competing species 211, 212 species guilds 211–212, 213 species interactions and population dynamics 2 stoichiometry, whole body carbon:phosphorus ratio 6 stream habitats and life history traits 77–78 community size structure 78 species traits related to disturbance regimes 78 trophic roles 77 see also biomass turnover; environmental gradients streams database analysis (New Zealand) 85–88, 89, 90, 91, 92 algal productivity effects 88, 90, 92 biomonitoring tools 94 body-size patterns 90–94 disturbance effects 88, 90 factors affecting body size 88, 89, 90, 91, 92 fish 85 fish-predation effects 88, 92 land-use effects 88, 91 macroinvertebrates 85–86 methods 85–86

physicochemical conditions 86, 87 Principal Components Analysis 88, 92 results 88, 89, 90, 91, 92 statistical analyses 86 study sites 85 substrate effects 88, 90, 92 strength of compensation (density dependence), response to additional mortality 270–273 stressor-induced size-spectrum changes 112–113 stressor-induced species loss 112–113 structured biomass community model 239–240 Sugihara Fraction (SF), niche-assembly model 148–152 suspension feeders active 16–17 body size and flow regime (Reynolds number, Re) 17–18 body size and food availability 21, 26–28 body size and solid-fluid interfaces 21, 26–28 body-size measurement difficulties 17 body size relation to food particle size 24–26 collecting elements 16 colonial or clonal animals 22–23 costs and benefits of feeding structure size increase 19–24 dependence on flow characteristics 17–18 deposit-suspension feeders 16–17 development of gelatinous bodies 24 feeding structure 16 hydrodynamic implications of body size 17–18 influence on local sediment deposition 26–27 limits to maximum body size 19–24 modification of body parts into feeding structures 23–24 ontological shifts between flow regimes 19 overcoming velocity gradients 27–28 particle capture as predator–prey relationship 24–26 particle encounter mechanisms 18 passive 16–17 range of feeding adaptations 18 Re of collecting elements 19, 20, 21 role in ecosystem energy transfer 16 roles in the food web 16 transport of particles to feeding structure (particle flux) 16–17 use of external capture apparatus 24 vortex shedding rate and body size 26–27 temperature and lifespan 6–7 effect on metabolic rate 2 temperature correction 3–4 temperature-size rule (TSR) 42 terrestrial ecosystems role of body size 98–99 trophic cascades 134 Tracheloraphis caudata 174 Trichoptera (caseless caddis flies) larvae, use of external feeding structures 24 Trinidadian guppy (Poecilia reticulata) 41, 42 tritrophic food chains 235–239

INDEX

trophic cascades alternative equilibria 132–133 and biomass distribution 122 and habitat complexity 129–132 and predator–prey interactions 129–132 and species complexity 129–132 body-size disparity between predators and prey 119–122 body-size effects 133–134 body size of primary producers 127–128 conditions which lead to 119 definition 118–119 effects of herbivory 127–128 in terrestrial ecosystems 134 predation effects 118 shape of the trophic pyramid 128–131

system productivity and food web structure 122–124, 125–126 turnover rate of primary producers 127–131 trophic roles, in stream ecosystems 77 unified theory of biodiversity (UTB) 149–152 vertebrate macrofauna 111–112 vortex shedding rate, and body size 26–27 whales, body size 1 within-species variation in body size 226 Zero-Sum Multinomial (ZSM) distribution, dispersal-assembly model 148, 149–152 zooplankton eggs, ontogenetic development rate and body size 5–6

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