Tài liệu Body Size: The Structure and Function of Aquatic Ecosystems pptx

Body Size: The Structure and Function of Aquatic EcosystemsEcologists have long struggled to predict features of ecological systems, such asthe numbers and diversity of organisms.. Based

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Body Size: The Structure and Function of Aquatic Ecosystems

Ecologists have long struggled to predict features of ecological systems, such asthe numbers and diversity of organisms The wide range of body sizes in ecologicalcommunities, from tiny microbes to large animals and plants, is emerging as thekey to prediction Based on the relationship of body size with key biological ratesand with the physical world experienced by aquatic organisms, we may be able tounderstand patterns of abundance and diversity, biogeography, interactions in foodwebs and the impact of fishing, adding up to a potential ‘periodic table’ for ecology.Remarkable progress on the unravelling, describing and modelling of aquatic foodwebs, revealing the fundamental role of body size, makes a book emphasizingmarine and freshwater ecosystems particularly apt Here, the importance of bodysize is examined at a range of scales, yielding broad perspectives that will be ofinterest to professional ecologists, from students to senior researchers

AL A N G HI L D R E W is Professor of Ecology in the School of Biological andChemical Sciences at Queen Mary, University of London

DA V I D G RA F F A E L L I is Professor of Environmental Science at the University ofYork

RO N N I ED M O N D S- BR O W N is a Senior Lecturer in Environmental Sciences at theUniversity of Hertfordshire

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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

3 Life histories and body size

4 Relationship between biomass turnover and body size for stream

communities

5 Body size in streams: macroinvertebrate community size

composition along natural and human-induced environmental

gradients

6 Body size and predatory interactions in freshwaters: scaling from

individuals to communities

7 Body size and trophic cascades in lakes

8 Body size and scale invariance: multifractals in

invertebrate communities

Peter E Schmid and Jenny M Schmid-Araya 140

9 Body size and biogeography

10 By wind, wings or water: body size, dispersal and

range size in aquatic invertebrates

Simon D Rundle, David T Bilton and Andrew Foggo 186

11 Body size and diversity in marine systems

12 Interplay between individual growth and population feedbacks

shapes body-size distributions

13 The consequences of body size in model microbial ecosystems

Owen L Petchey, Zachary T Long and Peter J Morin 245

14 Body size, exploitation and conservation of marine organisms

15 How body size mediates the role of animals in nutrient cycling

in aquatic ecosystems

Robert O Hall, Jr., Benjamin J Koch, Michael C Marshall,

16 Body sizes in food chains of animal predators and parasites

17 Body size in aquatic ecology: important, but not the whole story

Alan G Hildrew, David G Raffaelli and Ronni Edmonds-Brown 326

C O N T E N T S

vi

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 andChemical Sciences, Queen Mary, University

of London, East Stoke, Wareham DorsetBH20 6BB, UK

B J Finlay School of Biological andChemical Sciences, Queen Mary, University

of London, East Stoke, Wareham DorsetBH20 6BB, UK

Andrew Foggo Marine Biology andEcology Research Centre, University ofPlymouth, Plymouth PL4 8AA, UK

James F Gillooly Department ofZoology, University of Florida, Gainesville,

FL 32607, USA

Robert O Hall, Jr Department ofZoology and Physiology, University ofWyoming, Laramie, WY 82071, USA.Alan G Hildrew School of Biologicaland Chemical Sciences, Queen Mary,University of London,

London E1 4NS, UK

Andrew G Hirst British AntarcticSurvey, High Cross, Madingley Road,Cambridge CB3 0ET, UK

Stuart Humphries Department ofAnimal and Plant Sciences, University

of Sheffield, Western Bank, Sheffield S102TN, UK

Alexander D Huryn Aquatic BiologyProgram, Box 870206, Department of

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, Umea88

University, S-901 87 Umea88, 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 ofBiological Sciences, Simon FraserUniversity, Burnaby, BC, V5A 1S6, Canada.Simon D Rundle Marine Biology andEcology Research Centre, University ofPlymouth, Plymouth PL4 8AA, UK

Peter E Schmid School of Biologicaland Chemical Sciences, Queen Mary,University of London, London E1 4NS, UKand Institute of Freshwater Ecology,University of Vienna, 1090 Wien,Althanstrasse 14, Austria

Jenny M Schmid-Araya School ofBiological and Chemical Sciences, QueenMary, University of London, LondonE1 4NS, UK

Brad W Taylor Department of Zoologyand Physiology, University of Wyoming,Laramie, WY 82071, USA

Ross M Thompson School of BiologicalSciences, Building 18, Monash University,Victoria 3800, Australia

Colin R Townsend Department ofZoology, University of Otago, 340 GreatKing Street, Dunedin 9054, New Zealand.Lusha M Tronstad Department ofZoology and Physiology, University ofWyoming, Laramie, WY 82071, USA.Philip Warren Department of Animaland Plant Sciences, University of Sheffield,Western Bank, Sheffield S10 2TN, UK.Richard M Warwick Plymouth MarineLaboratory, Prospect Place, The Hoe,Plymouth, PL1 3DH, UK

Guy Woodward School of Biological andChemical Sciences, Queen Mary, University

of London, London E1 4NS, UK

L I S T O F C O N T R I B U T O R S

viii

More than ten years ago, two of us (AGH and DGR) were lucky enough to edit aprevious symposium of the British Ecological Society (BES) – Aquatic Ecology: Scale,Pattern and Process (Giller, Hildrew & Raffaelli,1994) In the Introduction to thatvolume, we pointed out that the BES had not devoted a single previous sympo-sium to aquatic ecosystems Evidently we did not change the culture, since theBody Size symposium held at the University of Hertfordshire in September 2005was 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 detectedand the processes that appeared to be important, and (ii) to compare freshwaterand marine ecosystems In Body Size: The Structure and Function of Aquatic Ecosystems,both those questions of scale and comparison among systems are very much stillalive as continuing themes Body size determines overwhelmingly the scale atwhich organisms perceive and navigate through their physical world, and thecontrasts between freshwater and marine ecosystems remain evident Body size

is a species trait with implications beyond scale, however, and we believe thatthe present volume shows that more similarities than differences are evidentamong the diverse aquatic systems considered Indeed, several authors arguehere 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 inbody size from the wider ecological community over the past 30 years, as well asthe technical challenge involved in exploring body-size data Of course, thefascination with body size has a much longer history in ecology and was prom-inent 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 ofthe physiological, environmental and ecological correlates of body size thatre-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 thispresent volume All of the papers presented at the Hatfield meeting connect

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

contrib-utors 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,

P R E F A C E

x

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.

P R E F A C E xi

C H A P T E R O N E

The metabolic theory of ecology

and the role of body size in marine

and freshwater ecosystems

at about 1012g to the great whales at about 108g (e.g., Sheldon et al.,1972;Kerr & Dickie,2001) Nearly all characteristics of organisms, from their struc-ture and function at molecular, cellular and whole-organism levels to ecologicaland evolutionary dynamics, are correlated with body size (e.g., Peters, 1983;McMahon & Bonner,1983; Calder,1984; Schmidt-Nielsen,1984) These relation-ships are almost always well described by allometric equations, power functions

of the form:

where Y is a measure of some attribute, Y0is a normalization constant, M is bodymass, and b is a scaling exponent (Thompson,1917; Huxley,1932) A longstandingpuzzle has been why empirically estimated values of b are typically close tomultiples of 1/4: 3/4 for whole-organism metabolic rates (Savage et al.,2004a) andrates of biomass production (Ernest et al.2003),1/4 for mass-specific metabolicrates 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 ofmolecular evolution (Gillooly et al.,2005b), and 1/4 for biological times such as cellcycle time, lifespan and generation time (Gillooly et al.,2001,2002)

Recent theoretical advances in biological scaling and metabolism representtremendous 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

exponents are due to the fractal-like design of the networks and surfaces thatsupply energy and materials used by cells in biological metabolism (West et al.,

1997,1999) One additional advance has strengthened and extended this retical foundation The well documented exponential effect of temperature onmetabolic rate can be incorporated by adding a Boltzmann–Arrhenius factor,

theo-e E/kT, to Eq (1.1) Whole organism metabolic rate or production, P, can then beexpressed as:

where E is the activation energy, k is Boltzmann’s constant (8.62 105eV/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 beexpressed as:

where B0is another normalization constant The addition of temperature to thismodel proved critical to the development of a metabolic theory of ecology (MTE)(Brown et al.,2004) MTE incorporates these fundamental effects of body size andtemperature on individual metabolic rate to explain patterns and processes atdifferent levels of biological organization: from the life histories of individuals,

to the structure and dynamics of populations and communities, to the fluxesand pools of energy and materials in ecosystems Brown et al (2004) began todevelop MTE in some detail, made many testable predictions, and evaluatedsome of these predictions, using data compiled from the literature for a widevariety of ecological phenomena, taxonomic and functional groups of organ-isms, and types of ecosystems

Here we apply the metabolic theory of ecology to focus on some importantcorrelates 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 havebeen 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) Withrespect 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, thisincludes 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 beenaddressed by the contributors to this volume

J H B R O W N E T A L

2

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 established fundamental principles of physics, chemistry and biology, makesexplicit, testable, quantitative predictions, and synthesizes the roles of indi-vidual organisms in populations, communities and ecosystems The literature

well-on body size and metabolism in general, and well-on aquatic ecosystems in ular, is too vast to summarize here The references cited above and below arejust a few of the relevant publications, but they will give the interested reader aplace to start

partic-Background

For what follows, we will assume that Eqs (1.2) and (1.3) capture the tal effects of body size and temperature on metabolic rate As the examplesbelow will show, these equations do not account for all observed variation They

fundamen-do, however, usually account for a substantial portion of the variation withinand across species, taxonomic and functional groups, and in ecosystems wherebody size varies by orders of magnitude Moreover, fitting Eq (1.2) or (1.3) to datagenerates precise quantitative predictions that can be used as a point of depar-ture to evaluate the many factors that may contribute to the residual variation.These include experimental and measurement error, phylogenetic and environ-mental constraints, influences of stoichiometry, and the effects of acclimation,acclimatization and adaptation Since we present Eqs (1.2) and (1.3) as assump-tions, 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 havereceived both enthusiastic support and severe criticism We will not cite orreview these issues and references here, but simply state that we are confidentthat most substantive criticisms have been or will be answered, and that thetheory is fundamentally sound

This volume and this chapter are on the effects of body size on the structureand dynamics of aquatic ecosystems Metabolic rate, and other rate processescontrolled by metabolic rate, are strongly affected by both body size and temper-ature 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=kTÞ ¼ ð1=4Þ ln ðMÞ þ ln ðB0Þ (1:4)where k is Boltzmann’s constant (¼ 8.62  105eV/K) and E is the average acti-vation 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 alinear function of ln(M) with a slope of1/4 Other allometric scaling relationscan be similarly analyzed using equations that have different values for the

T H E M E T A B O L I C T H E O R Y O F E C O L O G Y 3

normalization constants and sometimes for the exponents, e.g 3/4 for

whole-organism metabolic rate (Eq (1.2)) In aquatic ecosystems, it is reasonable to

assume that the body temperature of an ectotherm is equal to water

temper-ature Thus, coexisting species of prokaryotes, phytoplankton, protists,

zoo-plankton, 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

temper-ature, and when comparing ectotherms and endotherms, which differ

substan-tially 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,

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 ).

J H B R O W N E T A L

4

body plan, stoichiometry, as well as acclimatization, acclimation and tion to different environmental conditions.

adapta-The metabolism of an individual organism reflects the energy and materialtransformations that are used for both the maintenance of existing structureand 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 inectotherms it tends to be of the order of 50% Consequently, rates of whole-organism 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.Figure1.2shows that the temperature-corrected rates of production for algae,zooplankton and fish cluster closely around a common allometric scaling rela-tion with an exponent of 0.76, almost identical to the theoretically predictedvalue of 3/4 This implies that the relative allocation of energy and materials tobiomass production is indeed similar across most organisms

It follows from the above discussion and Eq (1.3) that the mass-specific rate ofontogenetic growth and development should scale as M1/4, and therefore thatdevelopmental 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 modelsystem, 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 metabolismduring 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 considerableunexplained variation This is hardly surprising, giving the inherent difficulties inmeasuring both development time and temperature under field conditions Thedata for development rate of freshwater zooplankton eggs measured under con-trolled conditions in the laboratory give an allometric exponent,0.26, essen-tially identical to the predicted1/4 The regression explains 84% of the observed

Eq ( 1.2 ) Data and analyses from Ernest

et al ( 2003 ).

T H E M E T A B O L I C T H E O R Y O F E C O L O G Y 5

variation in the temperature-corrected data Interestingly, for ontogenetic growthrates of adult zooplankton, Gillooly et al (2002) have shown that stoichiometry,specifically the whole-body C:P ratio, explains most of the variation that remainsafter accounting for the effects of body size and temperature This supports the

‘growth-rate hypothesis’ and the large body of theoretical and empirical work inecological 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 organ-isms are due to differences in the allocation of phosphorus-rich RNA necessary forgrowth For these zooplankton, living in freshwater where phosphorus may bethe primary limiting nutrient, rates of metabolism and ontogenetic growth arelimited by whole-body concentrations of RNA Not only does the C:P ratio explainmost of the residual variation in development rates as a function of body size inzooplankton, but it is also related to the body-size dependence of developmentitself Whole-body concentrations of phosphorus-rich RNA scale inversely withbody size, with an exponent of approximately1/4 in both aquatic and terrestrialorganisms (Gillooly et al.,2005a) Therefore, this example shows how a quanti-tative prediction from metabolic theory can be used to assess the influence ofother factors, such as stoichiometry, which may account for much of the remain-ing variation

Since times are reciprocals of rates, metabolic theory predicts that biologicaltimes should scale with characteristic powers of 1/4 Figure1.4shows data forone such time, maximal lifespan, for a variety of aquatic animals ranging fromzooplankton to fish The slope of this relationship, 0.23, is very close to thetheoretically predicted value of 1/4, and the fitted regression accounts for the

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 ).

J H B R O W N E T A L

6

vast majority of variation (r2¼ 0.98) The enormous variation in body size acrossthese organisms masks considerable unexplained residual variation It is wellestablished that even closely related animals of the same body size can differ inlifespan by at least an order of magnitude If the first-order effect of temperaturehad not been removed, then there would have been even more variation, withspecies in cold-water environments living longer than those of similar size inwarmer waters.

Population and community levels: growth, mortality and abundance

There are two logical benchmarks to measure population growth rate: themaximal rate, rmax, and the rate of turnover at steady state Data on rmaxfor awide variety of organisms, from unicellular eukaryotes to invertebrates andvertebrates, have been compiled and analyzed by Savage et al (2004b) Thesedata give a slope of0.23, very close to the predicted 1/4 We have extractedand 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 con-fidence intervals still include the predicted value of 1/4 We conclude thatmaximal population-growth rates scale similarly to mass-specific metabolic rateand follow Eq (1.3) This is not surprising, since metabolism fuels individualproduction, which in turn fuels population growth, thereby determining rmax.The rate of population turnover, and hence birth and death rates, should scalesimilarly Figure1.6shows the body-mass dependence of mortality rates of fish

in the field The fitted regression has a slope of0.24, very close to the predictedvalue of 1/4 The 1/4 power scaling of natural mortality may come as asurprise to many ecologists because mortality in the field is generally thought

to be controlled by extrinsic environmental conditions, such as predation, foodshortage or abiotic stress, rather than to intrinsic biological traits such asmetabolic rate The majority of mortality may indeed be due to predation or

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 ).

T H E M E T A B O L I C T H E O R Y O F E C O L O G Y 7

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 tion of mass generally support this prediction (Damuth,1981; Belgrano et al.,

func-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,

Figure 1.5 The relationship between the temperature-corrected maximum rate of population growth (i.e r max ), measured in 1/days, and the natural logarithm of body mass, measured in grams, for various aquatic organisms R max is temperature- corrected using the Boltzmann factor,

e E/kT , following Eq ( 1.2 ) Data and analyses from Savage et al ( 2004b ).

J H B R O W N E T A L

8

scaling as M3/4 and whole-organism field metabolic rate or energy use perindividual, P, scaling as M3/4, is that the rate of community energy use per unitarea, E, is independent of body size: E/ NP / M3/4M3/4/ M0 Damuth (1981) calledthis the energy equivalence rule.

If the abundance and energy use of populations scale predictably with bodysize, these relationships are of potentially great interest to ecologists However,care should be taken in making and testing these predictions of MTE for severalreasons First, the assumption of equal rates of resource supply is difficult toevaluate It is likely that species in different guilds, functional groups and trophiclevels will have quite different resource availability This could even be true formembers of the same guild or trophic level Second, resource supply sets only anupper bound on population density Predation, competition and other limitingfactors 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 severalorders of magnitude, in the observed densities of species populations in the field.Fourth, data are often plotted with each point representing a species, but inorganisms with indeterminate growth and consequently wide variation in bodysize, it may be difficult to estimate the average body mass and abundance of aspecies If the organisms really do use the same resources, it is more logical toestimate 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 ofthe fish coexisting at a site on the Great Barrier Reef, and found the predicted

M3/4scaling – except for the smallest size classes, which probably share foodresources with invertebrates We conclude that metabolic rate powerfullyconstrains the abundance of organisms in species populations, functional or tro-phic groups, and body-size categories, but, again, care should be exercised inmaking 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 andelements in ecosystems These flows include not only the quantitatively domi-nant components of the carbon cycle, but also those involving critical limitingnutrients, such as phosphorus or nitrogen, that together with carbon, comprisethe ‘Redfield Ratio’ Metabolic theory provides a conceptual basis for predicting,measuring and understanding the roles of different kinds of organisms in the fluxand storage of elements in ecosystems The total biomass per unit area, W, issimply the sum of the body mass of all individuals For organisms of similar size, itcan 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:

S¼Xi

T H E M E T A B O L I C T H E O R Y O F E C O L O G Y 9

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

mass-specific metabolic rate, B, so the rate of flux, F, is

F¼Xi

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

tem-perature corrected due to difficulties in estimating the relevant temtem-peratures in

these ecosystems, so temperature probably accounts for substantial residual

variation Nevertheless, the regression has a slope of0.21, close to the

pre-dicted value of1/4, 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

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 temperature- corrected because environmental temperatures were not reported Analyses from Brown et al ( 2004 ) and Allen et al ( 2005 ).

J H B R O W N E T A L

10

Allen et al (2005) further show how this framework can be extended tounderstand the roles of different sizes and temperatures of plants in the fluxand storage of carbon, and hence in the carbon cycle at scales from localecosystems to the globe Belgrano et al (2002) developed another extension,showing that plant density across the spectrum of plant sizes from algae to treesand across a range of ecosystem types from oceans, freshwaters, wetlands,grasslands and forests shows the predicted M3/4 scaling These examplesshow how MTE can be applied to make more explicit and quantitative linksbetween the processing of energy and elements at the individual level to theflux, 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 howMTE can be applied to understand the M3/4scaling and the M0energy equi-valence observed empirically within many functional groups and trophic levels.The theory can also be applied to understand the body-size structure of foodwebs and the flow of energy and materials between trophic levels Brown et al.(2004) developed quantitative expressions for the ratios for consumer:producerratios 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 nexthighest level respectively For aquatic ecosystems, we can usually assume thatall organisms (except for endotherms, which should be considered separately)are operating at approximately the same temperature Then these ratios are:

for energy flux:

F1=F0¼ i1N1M13=4=i0N0M03=4¼  (1:7)where i0and i1are the normalization constants for the field metabolic rates ofthe producers and consumers organisms, respectively;

for biomass:

W1=W0¼ N1M1=N0M0/ ðM0=M1Þ1=4 (1:8)and for abundance:

The ratio for energy flow, a, which must always be <1, is the traditionalLindeman efficiency that has been the subject of so much discussion and inves-tigation in ecology It is apparent from inspection of the above equations thatthe M3/4scaling of production is an important factor affecting a If the body-massratio of producer to consumer is large, and contributions to this symposiumsuggest that it is often in the range of 100–500 in aquatic ecosystems (see also

Humphries, this volume;Woodward & Warren, this volume;Cohen, this ume), then a large component of the energy dissipated between trophic levelswill be due simply to the allometry of production rates In addition to body size

vol-T H E M E vol-T A B O L I C vol-T H E O R Y O F E C O L O G Y 11

and abundance, other factors contributing to a are: (i) the fraction of themetabolism at level 0 that is allocated to biomass production, or productionefficiency, which appears to be approximately 50% across a wide variety ofectothermic organisms; (ii) the fraction of the individuals or biomass produced

by trophic level 0 that is consumed by trophic level 1, i.e the consumptionefficiency; and (iii) the fraction of the energy content of this consumed resourcethat is actually absorbed and transformed in the metabolism of organisms atlevel 1, i.e the assimilation efficiency, which has been measured for the diets ofmany kinds of consumers

The above framework can be applied to understand quantitatively howLindeman efficiencies, rates of energy and material flow, biomasses and abun-dances vary within and between ecosystems as a consequence of the body sizes

of the organisms at different trophic levels For example, Brown et al (2004)derive explicitly the conditions required to have the inverted ecological pyra-mids (i.e ratios >1) of biomass or abundance that are sometimes observedempirically (see also Jones & Jeppesen, this volume) Additionally, if a isknown, Eqs (1.7) and (1.8) can be applied, and the body sizes of the organismsoccupying adjacent trophic levels can be used to predict the ratios of biomassand abundance Conversely, if the body-size ratios are known, the above equa-tions 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 thedifferent approaches to food webs that have traditionally been taken by ecosys-tem and community ecologists The former have used dE/dt currencies to quan-tify rates of energy and material flow, whereas the latter have used dN/dtcurrencies to focus on the dynamics of consumer populations and their re-sources By considering explicitly the allometry of resource use and abundance,metabolic theory shows how these currencies are inextricably related (see alsoYodzis & 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 deter-mine the life histories of individual organisms, the abundances and turnover ofpopulations, the allocation of resources among coexisting species, and thefluxes and pools of energy and materials in ecosystems These exchanges aredirect consequences of metabolism as organisms take up energy and nutrientsfrom their environments, transform them within their bodies, and allocatethem to maintenance, growth and reproduction The metabolic rates of organ-isms vary predictably, or scale quantitatively, with body size and temperature.The metabolic theory of ecology uses these scaling relations to make and test

J H B R O W N E T A L

12

predictions about the effects of energy and materials on the ecology of isms and the roles of organisms on the fluxes and storage of energy and mater-ials in ecological systems The theoretical predictions provide baselines fromwhich to measure and understand the influences of additional factors thatcontribute to the variation in and around empirical scaling relations for organ-isms in different phylogenetic lineages, functional groups and environments.The conceptual framework of MTE presumably applies to all organisms andecosystems Marine and freshwater organisms and ecosystems are no exception.Indeed, there is a rich tradition of empirical and theoretical work in biologicaloceanography and limnology that relates the structure, function and bioticcomposition of these systems to the body sizes of the organisms present andthe temperatures at which they are operating We have presented just a fewexamples to show more explicitly and quantitatively how the developing MTEcan be applied Many of the contributions to this symposium volume presentadditional examples.

organ-But all these studies together provide only a limited sample of the kinds of workthat can potentially be done, and the breadth and depth of understanding thatthey can potentially contribute Through fisheries, pollution, climate change andother impacts, humans are transforming marine and freshwater ecosystemsfaster 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 theoceans The metabolic theory of ecology provides a general, quantitative concep-tual framework, grounded in accepted first principles of biology, physics andchemistry, not only for understanding the basic ecology of aquatic ecosystems,but also for applying this knowledge to conservation, management and policy.References

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con-T H E M E con-T A B O L I C con-T H E O R Y O F E C O L O G Y 15

1997; Wotton, 1994) Their role in energy transfer means that they are keycomponents of aquatic ecosystems, representing important pathways for energyflow, and are crucial determinants of the productivity of aquatic environments.Suspension feeders are characterized by the possession of an organ used tocapture suspended particles from the water (feeding structure) The feeding struc-tures utilized by suspension feeders are highly variable, and include appendagesbearing hairs, mucus or silk nets, gill rakers and baleen plates, lophophores,tentacles, and ciliated and flagellated cells Within a feeding structure, indivi-dual 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 aregenerally categorized as belonging to one of two major groups, based on theextent to which ambient (external) water flow is utilized for feeding (LaBarbera,

1984; Vogel,1994; Wildish & Kristmanson,1997) Passive suspension feeders relyentirely on ambient flow to deliver food particles to their feeding structures,while active suspension feeders use energy to regulate water flow over or throughtheir feeding structures using a biological pump (ciliary or muscular) However,further intermediate categorization is possible, with facultative-active suspen-sion feeders able to switch between passive and active feeding, depending onambient flow conditions Combined passive-active suspension feeders (Wildish

& Kristmanson,1997) utilize both passive and active methods at the same timeand 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

deposit-feeding (picking particles from the substratum) at low velocities, andsuspension-feeding when deposited particles are resuspended by higher velocities.Body size is somewhat nebulous and difficult to specify when it comes tosuspension feeders, as it is for other ecological aspects of body size in thisvolume Whether to use volume, length, body mass or dry weight becomesproblematic when members of the suspension-feeding functional group includegelatinous pelagic animals that have large physical size, but low carbon content

as an adaptation to low food concentrations (Acun˜a, 2001) Analogously, pension feeders with dense and massive shells, such as barnacles and bivalvemolluscs, have a non-trivial proportion of metabolically inactive body mass.Similar arguments can be made for those suspension feeders that use externalstructures to capture food; examples include silk nets (Trichoptera), as well asmucus nets (polychaetes, appendicularians) and sheets (pelagic molluscs).Many benthic suspension feeders also exhibit a predominantly two-dimensionalbody plan

sus-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 suspen-sion feeders However, this chapter will focus on the organismal- and habitat-levelimplications of body size that are directly relevant to the process of suspensionfeeding

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, theReynolds number (Re), that describes the flow regime within or around thatsystem The Reynolds number is a scaling parameter that provides a measure(ratio) of the relative importance of inertial and viscous forces within a fluid, anddescribes the way in which fluids will behave at difference scales The Reynoldsnumber is given by Re¼ ul/, where u is velocity, l is the linear length scale ofinterest, and  is the kinematic viscosity of the fluid Crudely, for biologicalsystems 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 ofvelocity, viscosity and scale that results in the same Re will result in a geometric-ally similar flow regime, as characterized by the ratio of inertial to viscousforces Thus, doubling the length scale will result in a flow regime that canalso be realized by doubling velocity or by halving kinematic viscosity

As a tool, Re provides us with a way to conceptualize the link between thesize 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

B O D Y S I Z E A N D S U S P E N S I O N F E E D I N G 17

fundamentally determine the food-capture rate of suspension feeding animals.

In this context body size can be seen as synonymous with flow regime, with Rerelating as it does, a single measure of size to environmental conditions

In biological systems, small (and hence slow) organisms tend to operate underconditions where the fluid they are immersed in is dominated by viscous forces(low Re), while larger, faster organisms operate at higher Re, where inertialforces prevail (Vogel,1994) While high Re characterizes the flows at a humanscale, the behaviour of low Re flows are frequently counterintuitive Forinstance, if a bacterium were suddenly to cease swimming, it would come to ahalt 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 single-celled protists to baleen whales, while the Reynolds number of such organisms

in general ranges between Re 106(bacteria) and Re 108(large whales), or 14orders of magnitude (Nachtigall,2001) This provides a dramatic range of con-ditions in which suspension feeders operate, and leads to an array of adapta-tions to this feeding mode

Despite such large variations in body size, aerosol theory co-opted from neering (Rubenstein & Koehl,1977) suggests that there are only five inclusivemechanisms by which particles can encounter collecting elements: (i) directinterception, (ii) inertial impaction, (iii) gravitational deposition, (iv) diffusionaldeposition and (v) electrostatic attraction Simple sieving (where particles arecaught because they are larger than the gap between collecting elements) isgenerally added to this group, although in the process of sieving particles encoun-ter the feeding structure via one of the five classic mechanisms Direct intercep-tion involves streamline kinematics: particles travelling on a streamline thatpasses around the collecting element will come into contact with that element

engi-if they come within one particle radius Inertial impaction relies on particles thatare denser than the surrounding fluid failing to follow rapidly turning stream-lines due to their inertia, while gravitational deposition relies on a particle’s masscausing it to cross streamlines and thus impact the collector For smaller particles,diffusional deposition may be important, whereby Brownian motion of tiny(<1 mm) particles causes them to cross streamlines and impact the collectingelement Finally, electrostatic attraction may act to draw some particles towardscollecting elements in non-electrolyte fluids

The obvious restrictions imposed by only five inclusive mechanisms for ticle capture suggest that evolutionary convergence in feeding methods may

par-be inevitable Differences do exist, however, in the importance of the differentmechanisms to particular organisms, a factor itself determined by morphology,particle type and availability, and to some extent by body size What is now clear

is that these particle-encounter mechanisms comprise an ‘envelope of the sible’, and are common to almost all suspension feeders (Rubenstein & Koehl,

pos-1977; LaBarbera,1984; Shimeta & Jumars,1991; Vanderploeg,1994)

S H U M P H R I E S

18

Body size changes during ontogeny and evolution

The flow regime that an organism experiences is critical to a number of logical processes (Palumbi, 1986; Vogel, 1994; Rex, Montebon & Yap, 1995).Given that the body size of suspension feeders determines the flow regimearound them, and considering the extent of growth in aquatic organisms,ontological shifts between regimes are common Physical limits to growth andpatterns of modularity (the way in which clones group together) are important

physio-in many groups with physio-indetermphysio-inate growth, where size of feedphysio-ing surfaces istraded against the risk of mechanical failure and respiratory costs of increasedtissue volume Feeding itself is highly dependent on flow, and hence size of thecollecting elements within a feeding structure

Although it has been commonly assumed that the Re of collecting elements(based on element diameter) is much less than unity, there is mounting evidencethat a large fraction of suspension feeders may operate in a 1 Re  100 regime(intermediate-Re), where neither viscosity nor inertia truly dominates (Shimeta &Jumars,1991; Table2.1& Fig.2.1a) The physics of fluid flow in this regime isunderdeveloped, and little experimental work has been carried out to investigatethe implications of this flow regime for the large number of suspension-feedinganimals whose collecting elements are thought to operate in this intermediate-Rerange The few studies in this area have already shown some surprising shifts inthe way feeding appendages operate with a transition to intermediate-Re (Koehl,

1983; Cheer & Koehl,1987; Koehl,1993,1996,2000,2001)

It has been shown that hair-bearing appendages used for functions such assuspension feeding, swimming, flying and olfaction, operate in fundamentallydifferent ways depending on Re (based on the gap between hairs: Koehl, 1983;Cheer & Koehl,1987; Koehl1993,1996,2000,2001) At very low Re these append-ages act as paddles, pushing water in front of them, whilst at Re near unity theyfunction more like leaky sieves with water passing easily between the hairs(Fig 2.1b) The strong implications for suspension feeders are reinforced whenthe relationship between Re of the hair-gaps and body size is considered Reynoldsnumber in this instance is related to body size via both appendage size and speed

of movement (proportional to limb length and body size) However, there iscurrently a lack of evidence for ontological transitions within species, as com-pared with between-species differences This difference is probably a consequence

of ‘leakiness’ having a low sensitivity to changes in size at very low Re (Koehl,1995).Limits to maximum body size

The density of water is around 800 times greater than air, which (in addition toreducing sinking rates and hence promoting the existence of suspension feed-ing per se) provides substantial physical support not available to terrestrialorganisms As a result, both maximum body size and appendage elaboration

in suspension feeders are somewhat less restricted by constraints related to

B O D Y S I Z E A N D S U S P E N S I O N F E E D I N G 19

Table 2.1 Partial list of suspension feeders likely to feed at intermediate-Re, based on estimates

of flow local to feeding structures, and measurements of collecting-element diameter taken from the literature Unless indicated, species are those identified from published drawings and photographs by Shimeta and Jumars ( 1991 ): 1 Humphries unpublished; 2 Johnson ( 1993 );

3 Hentschel ( 1996 ); 4 Loo et al ( 1996 ); 5 Anthony ( 1997 ); 6 Shimeta and Koehl ( 1997 ); 7 Allen ( 1998 ); 8 Jesling ( 2002 ).

Lanice conchilega1Polydora ligni3Pseudopolydora kempi japonica Pseudopolydora paucibranchiata6Pygospio elegans8

Sabella pavonina Scolelepis squamata Spio filicornis 8 Echinodermata (Ophiuroids, Holothurians & Crinoids) Amphiura filiformis 4

Comaster multifidus Cucumaria miniata 1 Fluorometra serratissima 1 Oligometra serripinna Ophiopholis aculeata Ophiopteris antipodium Ophiothrix fragilis7Psolus chitinoides

Stylasterina (Hydrozoan hard corals) Stylaster californicus1

Octocorallia (soft corals & sea pens) Paracyanthus stearnsi1

Sansibia spp 1 Stylatula elongata 1 Xenia spp 1

Anthopleura elegantissima Corynactis californica 1 Metridium senile

Alveopora spongiosa1Balanophyllia elegans1Montipora digitata5Pocillopora damicornis5Porites cylindrica5

Simulium bivittatum Simulium spp 1

S H U M P H R I E S

20

Figure 2.1 Functional transitions in relation to Reynolds number (a) Generalized pattern

of particle encounter for direct interception inflections indicate a transition in encounter rate with Re (redrawn from Shimeta & Jumars, 1991 ), (b) leakiness of an array of hairs, plotted against Re Leakiness is defined as the volume of fluid passing between two

elements (hairs) in an array, divided by the volume that would flow through the space if the elements were not present Lines represent gap:element diameter ratios: squares

50:1, triangles 15:1, diamonds 5:1, circles 0.6:1 (redrawn from Koehl, 1995 ).

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physical support than in terrestrial organisms However, physical restrictions

on the size of feeding structures will start to appear as body size increases, incommon with many other mechanical devices

Energetic optimality models suggest that growth should stop at some getically optimal body size in both passive (Sebens, 1982, 1987) and activesuspension feeders (Acun˜a, 2001; Humphries, unpublished) Nonetheless, itshould be remembered that the size limit set by energy balance may never bemet in animals with determinate growth (Sebens,1987)

ener-The most obvious way to increase energetic intake from suspension feeding issimply to increase the size of the feeding structure As long as (i) positive netenergy gain is possible, and (ii) costs and gains increase at a similar rate withincreasing size of the capture apparatus, suspension feeding will be viable givenfeeding structure(s) sufficiently large to collect enough food for reproductionand/or growth However, this method of increasing energy gain will producediminishing returns if the costs of producing and maintaining a larger feedingstructure increase more rapidly than the gain provided by that structure This ismore than likely when body size is increased, as the metabolic costs of greatertissue volume tend to increase much faster than the gain from an essentiallytwo-dimensional feeding structure For instance, passive suspension feedersshould theoretically have capture rates directly proportional to the surfacearea of their capture apparatus (i.e increasing as body mass0.67) if their growth

is isometric (Sebens, 1982, 1987) In active suspension feeders, gain rate isproportional to the volume of water processed per unit time, thus leading to apredicted proportionality to cross-sectional area, ciliated surface, or other appo-site surface Concurrently, basic metabolic costs will increase with any increase

in body size, although not necessarily linearly (Fig.2.2) As far as it is possible togeneralize, metabolic costs are likely to scale as somewhere between bodymass0.67 and body mass0.75 for most animals (Peters,1983; Schmidt-Nielsen,

1984; White & Seymour,2005) In addition to any possible metabolic drawbacks,

an increase in size simply may lead to movement restrictions, or compromisefunction in some other way as for any other organism

One method of circumventing, or at least offsetting, the costs of constructing

a larger feeding apparatus and a body to support it is to find a way of increasingthe size of the feeding apparatus at a rate disproportionately more than that ofthe increase in body size (allometric scaling) For instance, colonial sea ane-mones, corals and gorgonians have a growth form that allows the surface area

of their feeding apparatus to increase at a rate proportional to their mass ratherthan their surface area as might be expected of animals whose body surface iswhere their feeding structures are situated (Sebens,1982,1987) The flat-sheet

or multiply-branched body form of these colonial or clonal animals allows theirfeeding surfaces to increase linearly with body mass as colony growth appears tooccur through the production of new polyps (of equal size to the originals),

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rather than a general increase in the size of existing polyps This method has itslimitations, however, because while it enables escape from a size limit imposed

by energetic constraints, other size limits may well be imposed, for instance, bysuitable ambient velocities, substrata, local food depletion, local competition,

or ‘self-shading’ (Sebens,1982,1987; Kim & Lasker,1998; Okamura, Harmelin &Jackson,2001)

A method available to non-colonial animals is to modify existing body parts toact as feeding structures (sometimes even to the exclusion of their originalfunction) Examples include the use of locomotory arms raised into the current

in brittle stars, and the limbs of some euphausiid shrimps By using such

Body size (mass, kg)

Body size (mass, kg)

Figure 2.2 Cost:gain curves for two suspension feeders: (a) the mussel Mytilus edulis, and (b) the sea anemone Anthopleura xanthogrammica Solid lines are gain functions, broken lines are cost functions Redrawn from Sebens ( 1987 ).

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dual-function organs, these animals might profit by increasing the size of theirfeeding apparatus for a given body size However, the above scaling argumentsstill hold for further increases in the size of feeding apparatus, and thus body size.

A particularly interesting solution to the scaling problem is the use of externalcapture apparatus, usually silk or mucus nets, by animals such as the larvae ofcaseless caddis flies (Trichoptera) and many polychaete worms, respectively.Here, the solid substratum provides support and anchor points for a net thatthe animal constructs, and the animal is thus able to increase the size of itsfeeding structure without an increase in body size The increase in filter area inrelation to body size can be very large: one species of caseless caddis fly with abody mass of less than 6 mg regularly builds nets up to 20 cm long (Petersen,Petersen & Wallace,1984) Although the costs of net construction are relativelyhigh (in Polycentropus flavomaculata, the process of silk spinning and net construc-tion raises metabolic rates by about 17% (Dudgeon,1987)), they are likely to beconsiderably less than the metabolic costs of a body large enough to hold aninternal feeding structure of similar size Furthermore, the costs of building anexternal structure are ‘capital’ costs, in that they do not require sustained invest-ment at a high level, as would equivalent volumes of metabolically active tissue.Use of an external feeding structure is also common in oceanic environments.Pelagic pteropod molluscs use large mucus nets suspended from their body tocapture planktonic food The low-turbulence environment of the open oceanallows them to construct fragile nets that are not constantly torn apart by forcesgenerated by turbulent water movement (Harbison, 1992) Many pelagic sus-pension feeders probably also utilize another mechanism for increasing gainand reducing costs that is facilitated by their low turbulence environment: thedevelopment of gelatinous bodies Pelagic tunicates appear to use metabolicallyinert gelatinous tissue to increase their body size so that they can support alarger filter without the energetic costs of increasing the volume of metabol-ically active tissue (Acun˜a, 2001) Indeed, some deep-sea species of append-icularians with bodies 75 mm long build external gelatinous ‘houses’ withdiameters of up to 1 m (Ruppert & Barnes,1994), presumably in response tothe very low seston concentrations in their environment Acun˜a’s (2001) argu-ment is based on the scaling of gain to costs in a similar way to that discussedabove, but invokes a quadratic increase in pumping costs with filter size, incomparison to a linear increase in gain as the driving force for the development

of gelatinous bodies As seen above, however, the same principle of costsincreasing more rapidly than gains is equally applicable to passive suspensionfeeders (Sebens,1987)

Particle capture as a predator–prey relationship

The existence of a positive relationship between the body size of a predator tothat of its prey (Peters,1983) is currently only an assumption for suspension

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feeders Evidence from vertebrates eating ‘small-prey’ (Peters,1983) suggests arelationship of the form Wprey¼ 0.0018Wpred1.18, where W is mass in kg, with anexponent not significantly different from unity For invertebrates, Warren andLawton (1987) describe a positive relationship between mean prey length andpredator length (L, in m) equivalent to the form Lprey¼ 5.83  104Lpred0.984.Wilson (1973) gives Lprey¼ 7.83  105

Lpred2– 6.61 105

Lpredþ 4.4  105

, forthe maximum plastic bead diameter ingested by the copepod Acartia tonsa(Fig.2.3) The latter data are also fit well by a power function with an exponent

of close to unity (Lprey¼ 5.52  105Lpred1.0397; Humphries, unpublished), but arevalid only for one species with a small size range

The general predator–prey size relationship is also characterized by ing variance in prey size as predator size increases (Peters, 1983; Warren &Lawton,1987; Cohen et al.,1993) Mechanisms for this pattern in ‘traditional’predators are thought to relate to the ability to switch to small prey when largerprey is unavailable, which becomes less feasible as predator size decreases.However, when considering suspension feeders a physical basis for the patterncan be proposed If particles with a linear dimension greater than the filter-gapsize are utilized (sieving) then the maximum prey size will be determined by thedimensions of the filter apparatus or mouth, and all particles larger than thiscritical size will be retained Thus, if sieving is utilized by a particular species, abimodal prey-size distribution is predicted (Silvester,1983; Brown et al.,2005)and maximum prey size will increase isometrically with predator size

Figure 2.3 The relationship between prey size and body size in the copepod Acartia tonsa capturing

plastic beads Maximum ingested bead size varies as L prey ¼ 05.52 

10 5 L pred1.0397, while minimum bead size is constant across the body-size range studied Redrawn from Wilson ( 1973 ).

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Minimum prey size, however, will be limited by hydrodynamic considerations(encounter rate has a minimum against particle size as diffusion falls off beforeother mechanisms increase rates; Rubenstein & Koehl,1977; Shimeta & Jumars,

1991) and the problems of dealing with extremely small particles

It is reasonable to expect tuning of the size of filtering structures and ing elements to profitable prey size (determined by energy content and distri-bution in the environment) Mean prey size (or other measure or centraltendency) may not scale isometrically as expected for maximum prey size.Unfortunately, information on predator–prey size relationships for suspensionfeeders is scarce and a general analysis has not yet been attempted

collect-Body size and food availability (body size and solid–fluid interfaces)Although large size may directly increase the size range of particles available to

an animal, body size can also influence the availability of particles through itseffects on flow regime Physical interactions involving availability and thedeposition of particles depend on body size because of the link between bodysize and flow regime When considering benthic suspension feeders, body size

in conjunction with spatial positioning can determine the availability of pended particles Hydrodynamic studies have highlighted the influence ofsurface roughness on flow (Nowell & Church, 1979; Nowell & Jumars, 1984;Eckman,1990; Abelson & Denny,1997), and this has been observed to relatedirectly to animal size and positioning (Pawlik, Butman & Starczak, 1991;Friedrichs, Graf & Springer,2000; Cardinale, Palmer & Collins,2002)

sus-Any structure extending into the flow from the substratum will perturb thelocal flow pattern, and the formation and shedding of vortices from benthicsuspension feeders can lead to differential deposition of particles downstream(Vogel,1994; Abelson & Denny,1997; Turner,2000) In this case, the size of thestructure or animal determines Re and thus a characteristic wavelength for vortexshedding Vortices are shed at a rate determined by the Strouhal number (St), adimensionless frequency, dependent on the shape and Re of the object (Vogel,

1994), and interact most strongly with the substratum downstream at a istic distance related to shedding rate (Fig.2.4) Positive feedback may then occur

character-as increcharacter-ased deposition leads to increcharacter-ased feeding rates and hence growth ofdownstream animals (Turner,2000) A further consequence is that growth itselfwill alter the vortex shedding rate An additional study (Abelson, Miloh & Loya,

1993) suggests that body morphology can determine the availability of foodparticles As morphology in this instance is characterized by a slenderness ratio(height/diameter) body size per se may also play an important part, particularly if

an animal’s slenderness ratio changes through ontogeny because of the change in

Re associated with its linear dimension parallel to the flow

Since body size can influence sediment deposition in the local area, it will alsohave strong effects on the importance of benthic suspension feeders as ecosystem

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