Ecology, 85(7), 2004, pp. 1771±1789 ᭧ 2004 by the Ecological Society of America TOWARD A METABOLIC THEORY OF ECOLOGY

JAMES H. BROWN,1,2,4 with JAMES F. G ILLOOLY,1 ANDREW P. A LLEN,1 VAN M. SAVAGE,2,3 AND GEOFFREY B. WEST2,3 1Department of Biology, University of New Mexico, Albuquerque, New Mexico 87131 USA 2Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 USA 3Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA

JAMES H. BROWN, MacArthur Award Recipient, 2002

Abstract. Metabolism provides a basis for using ®rst principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include: (1) life history attributes, including devel- opment rate, mortality rate, age at maturity, life span, and population growth rate; (2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity; and (3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics. Data compiled from the ecological literature strongly support the theoretical predictions. Even- tually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology. Key words: allometry; biogeochemical cycles; body size; development; ecological interactions; ecological theory; metabolism; population growth; production; stoichiometry; temperature; trophic dynamics.

4 E-mail: [email protected] 1771 1772 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

INTRODUCTION of basic principles of biology, chemistry, and physics (e.g., Peters 1983, Sterner 1990, Elser et al. 1996, The complex, spatially and temporally varying struc- 2000a, West et al. 1997, 1999a, b, 2001, Enquist et al. tures and dynamics of ecological systems are largely 1999, Gillooly et al. 2001, 2002). Together, the older consequences of biological metabolism. Wherever they conceptual and empirical foundations and the more re- occur, organisms transform energy to power their own cent theoretical advances provide the basis for a met- activities, convert materials into uniquely organic abolic theory of ecology. This theory explicitly shows forms, and thereby create a distinctive biological, how many ecological structures and dynamics can be chemical, and physical environment. explained in terms of how body size, chemical kinetics, Metabolism is the biological processing of energy and resource supply affect metabolism. Through var- and materials. Organisms take up energetic and ma- iation in the rates and biochemical pathways of me- terial resources from the environment, convert them tabolism among different kinds of organisms and en- into other forms within their bodies, allocate them to vironmental settings, metabolic theory links the per- the ®tness-enhancing processes of survival, growth, formance of individual organisms to the ecology of and reproduction, and excrete altered forms back into populations, communities, and ecosystems. the environment. Metabolism therefore determines the demands that organisms place on their environment for Metabolism and metabolic rate all resources, and simultaneously sets powerful con- Metabolism is a complex network of biochemical straints on allocation of resources to all components of reactions that are catalyzed by enzymes, allowing the ®tness. The overall rate of these processes, the meta- concentrations of substrates and products and the rates bolic rate, sets the pace of life. It determines the rates of reactions to be regulated. A chart of the chemical of almost all biological activities. reactions of metabolism shows a bewildering number Recent progress in understanding how body size, of substrates, enzymes, and pathways. Nevertheless, temperature, and stoichiometry affect biological struc- the core of metabolism consists of a small number of ture and function at the molecular, cellular, and whole- reactions that form the basis of the TCA (tricarboxylic organism levels of organization raises the prospect of acid) cycle (Morowitz et al. 2000). The vast majority developing a metabolic theory of ecology. Metabolism of organisms use the same basic biochemistry, but the is a uniquely biological process, but it obeys the phys- rates of resource uptake, transformation, and allocation ical and chemical principles that govern the transfor- vary. mations of energy and materials; most relevant are the When we speak of energy and energetics, we refer laws of mass and energy balance, and thermodynamics. to potential energy: the energy contained in photons or Much of the variation among ecosystems, including chemical bonds. Some fraction of this energy is con-

Perspectives their biological structures, chemical compositions, en- verted by the reactions of photosynthesis and respira- ergy and material ¯uxes, population processes, and spe- tion into biologically useful forms that are used to per- cies diversities, depends on the metabolic character- form the work of biosynthesis, membrane transport, istics of the organisms that are present. Much of the muscle contraction, nerve conduction, and so on. We variation among organisms, including their life history use the term kinetics to refer to kinetic energy, the characteristics and ecological roles, is constrained by energy of molecular motion. Kinetics affect biological their body sizes, operating temperatures, and chemical processes largely through the in¯uence of temperature compositions. These constraints of allometry, bio- on metabolic rate. chemical kinetics, and chemical stoichiometry lead to The metabolic rate is the fundamental biological rate, metabolic scaling relations that, on the one hand, can because it is the rate of energy uptake, transformation, be explained in terms of well-established principles of and allocation. For a heterotroph, the metabolic rate is biology, chemistry, and physics and, on the other hand, equal to the rate of respiration because heterotrophs can explain many emergent features of biological struc- obtain energy by oxidizing carbon compounds as de- ture and dynamics at all levels of organization. → scribed by the reaction: CH2O ϩ O2 energy ϩ CO2 ϩ H O. For an autotroph, the metabolic rate is equal THEORETICAL FOUNDATIONS 2 to the rate of photosynthesis because this same reaction Virtually all characteristics of organisms vary pre- is run in reverse using energy (i.e., photons) provided dictably with their body size, temperature, and chem- by the sun to ®x carbon (Farquhar et al. 1980). It has ical composition (e.g., Bartholomew 1981, Peters 1983, proven challenging to measure metabolic rate accu- Calder 1984, Schmidt-Nielsen 1984, Niklas 1994, Gil- rately and consistently. Ideally, it would be measured looly et al. 2001, 2002, Sterner and Elser 2002). For as heat loss by direct calorimetry, which would quan- more than a century, biologists have been investigating tify the energy dissipated in all biological activities. the mechanistic processes that underlie these relation- However, because of the ®xed stoichiometry of respi- ships. Recent theoretical advances have shown more ratory gas exchange, it is nearly as accurate and much explicitly how these biological characteristics can be more practical to measure the rate of carbon dioxide quanti®ed, related to each other, and explained in terms uptake in plants or the rate of oxygen consumption in July 2004 MACARTHUR AWARD LECTURE 1773 aerobic prokaryotes and eukaryotes (Withers 1992). free-living organism in nature, which ideally would Physiologists typically measure the basal or standard include allocation to growth and reproduction suf®cient metabolic rate, the minimal rate of an inactive organism to maintain a stable population; and perhaps also (3) in the laboratory. Basal rates are invariably less than maximal metabolic rate, the rate of energy ¯ux during the actual or ®eld metabolic rates of free-living organ- maximal sustained activity (Savage et al., in press b). isms, which must expend additional energy for for- Recently, West et al. (1997, 1999a, b) showed that aging, predator avoidance, physiological regulation, the distinctively biological quarter-power allometric and other maintenance processes, and still more energy scaling could be explained by models in which whole- for growth and reproduction. In most organisms, how- organism metabolic rate is limited by rates of uptake ever, the average daily energy expenditure or the long- of resources across surfaces and rates of distribution term sustained rate of biological activity is some fairly of materials through branching networks. The fractal- constant multiple, typically about two to three, of the like designs of these surfaces and networks cause their basal metabolic rate (Taylor et al. 1982, Schmidt-Niel- properties to scale as ¼ powers of body mass or vol- son 1984, Nagy 2001; Savage et al., in press b). ume, rather than the ⅓ powers that would be expected In addition, most organisms exhibit phenotypic plas- based on Euclidean geometric scaling (Savage et al., ticity in the expression of metabolism. They can vary in press b). the rate and pathways of metabolism to some extent to adjust for variations in resource supply, such as ¯uc- Temperature tuating quantity and quality of food resources, or in It has been known for more than a century that bio- resource demand, such as the costs of reproduction or chemical reaction rates, metabolic rates, and nearly all of maintaining homeostasis in the face of altered en- other rates of biological activity increase exponentially vironmental temperature, osmotic concentration, or el- with temperature. These kinetics are described by the emental chemical composition. For example, during Boltzmann factor or the Van't Hoff-Arrhenius relation periods of resource shortages, many organisms are able eϪE/kT (3) to lower metabolic rates and resource requirements by Perspectives reducing activity and entering some form of diapause where E is the activation energy, k is Boltzmann's con- or torpor. Even these phenotypic variations, however, stant, and T is absolute temperature in K (Boltzmann occur within constraints on metabolic rate due to three 1872, Arrhenius 1889). The Boltzmann factor speci®es primary factors: body size, temperature, and stoichi- how temperature affects the rate of reaction by chang- ometry. ing the proportion of molecules with suf®cient kinetic energy, E, which here we measure in electron volts (1 Body size eV ϭ 23.06 kcal/mol ϭ 96.49 kJ/mol). Since early in the 20th century, it has been known This relationship holds only over the temperature that almost all characteristics of organisms vary pre- range of normal activity, which for most organisms lies dictably with body size. Huxley (1932) is credited with between 0Њ and 40ЊC (Thompson 1942, Schmidt-Niel- pointing out that most size-related variation can be de- sen 1997). Normal operating temperature varies among scribed by so-called allometric equations, which are species and taxonomic or functional groups. Any given power functions of the form species usually operates over some subset of this tem- perature range, although there are exceptions. For ex- Y ϭ YMb. (1) 0 ample, most aquatic organisms do not experience tem- They relate some dependent variable, Y, such as met- peratures above 25Њ±30ЊC, endothermic birds and abolic rate, development time, population growth rate, mammals maintain relatively high and constant tem- or rate of molecular evolution, to body mass, M, peratures (36Њ±40ЊC), some ectotherms can tolerate through two coef®cients, a normalization constant, Y0, only a very narrow range of temperatures, and some and an allometric exponent, b. Most of these biological microbes from extreme environments such as hot scaling exponents have the unusual property of being springs and hydrothermal vents can live at temperatures multiples of ¼, rather than the multiples of ⅓ that would that approach or exceed 100ЊC. With some quali®ca- be expected from Euclidean geometric scaling. Thus, tions, then, the exponential form (3) describes the tem- for example, Kleiber (1932) showed that whole-organ- perature dependence of whole-organism metabolism of ism metabolic rate, I, scales as virtually all organisms, from unicellular microbes to multicellular plants and animals (Gillooly et al. 2001). I ϭ IM3/4 (2) 0 Nearly all other biological rates and times, including where I0 is a normalization constant independent of individual and population growth rates, and develop- body size. This same relation, with different values for ment times and life spans, show a similar temperature the normalization constant, describes: (1) basal meta- dependence (Gillooly et al. 2001, 2002; Savage et al., bolic rate, the minimal rate of energy expenditure nec- in press a). Interestingly, the empirically estimated ac- essary for survival under ideal conditions; (2) ®eld met- tivation energies for all of these processes are similar, abolic rate, the actual rate of energy expenditure by a and within the range of activation energies typically 1774 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

observed for the biochemical reactions of metabolism as primary structural materials and have high ratios of (0.60±0.70 eV, Gillooly et al. 2001). This suggests that C relative to N and P (Elser et al. 2000a). metabolism is the underlying process that governs most The elemental composition of an organism is gov- biological rates. erned by the rates of turnover within an organism and the rates of ¯ux between an organism and its environ- Stoichiometry ment. The concentrations of elements in ecosystems are therefore directly linked to the ¯uxes and turnover In its narrow sense, stoichiometry is concerned with rates of elements in the constituent organisms. There the proportions of elements in chemical reactions. In may be reciprocal limitation, so that concentrations of broader applications, such as to ecology, stoichiometry some elements, such as N in soils and P in lakes, are refers to the quantities, proportions, or ratios of ele- regulated by a balance between the rate of supply from ments in different entities, such as organisms or their abiotic and biotic sources and the rate of uptake by environments (e.g., Reiners 1986, Elser et al. 1996, organisms. On the one hand, environmental concentra- 2000a, Sterner and Elser 2002). Protoplasm, and the tions can limit metabolic rates, and thereby growth different structural and functional materials that com- rates, reproductive rates, and standing stocks of or- prise living biomass, have characteristic ratios of the ganisms. For example, plants can be limited by nitro- common elements such as H, O, C, N, P, Na, Cl, S, gen, water, iron, and phosphorus. Under controlled lab- Ca, and K. N is found primarily in proteins; P in nucleic oratory conditions, plant growth rates have been shown acids, ADP and ATP, phospholipids, and skeletal struc- to vary linearly with N concentration (Ingestad 1979). ture; Na or K in intracellular solutes, and so on. All Similarly, fertilization and irrigation experiments have organisms have internal chemical compositions that repeatedly shown that growth rates of plants in the ®eld differ from those in their environment (Lotka 1925), are limited by nitrogen or water (Field and Mooney so they must expend metabolic energy to maintain con- 1986; see review in Tilman 1988). On the other hand, centration gradients across their surfaces, to acquire sizes of pools and rates of turnover in organisms can necessary elements, and to excrete waste products. regulate environmental concentrations of elements and Fundamental stoichiometric relationships dictate the compounds, sometimes within narrow limits (Vitousek quantities of elements that are transformed in the re- 1982). This is the case for CO2 concentration in the actions of metabolism. Biochemistry and physiology atmosphere, which is regulated in part by the balance specify the quantitative relationship between the met- between photosynthesis and respiration in the bio- abolic rate and the ¯uxes of elemental materials sphere (Falkowski et al. 2000, Chapin et al. 2002), and through an organism. The metabolic rate dictates the for the concentrations of C, N, and P found in the rates at which material resources are taken up from the organic matter of oceans and lakes, which is regulated Perspectives environment, used for biological structure and func- in part by nutrient metabolism of the biota (Red®eld tion, and excreted as ``waste'' back into the environ- 1958). ment. Far from being distinct ecological currencies, as some authors have implied (e.g., Reiners 1986, Sterner ALTERNATIVE EXPRESSIONS FOR BIOLOGICAL RATES and Elser 2002), the currencies of energy and materials The joint effects of body size, M, and temperature, are inextricably linked by the chemical equations of T (in K), on individual metabolic rate, I, can be de- metabolism. These equations specify not only the mo- scribed by combining Eqs. 2 and 3 (Gillooly et al. lecular ratios of elements, but also the energy yield or 2001). This gives demand of each reaction. Ecological stoichiometry is 3/4 ϪE/kT concerned with the causes and consequences of vari- I ϭ iM0 e (4)

ation in elemental composition among organisms and where i0 is a normalization constant independent of body between organisms and their environments (Sterner and size and temperature. We can take logarithms of both sides Elser 2002). Despite the overall similarity in the chem- of this equation and rearrange terms to yield ical makeup of protoplasm, organisms vary somewhat ln( Ϫ3/4) (1/ ) ln( ). (5) in stoichiometric ratios within individuals, among in- IM ϭϪE kT ϩ i0 dividuals of a species, and especially between different Note that in Eq. 5, we have ``mass-corrected'' meta- taxonomic and functional groups. For example, in uni- bolic rate, I, by incorporating the logarithm of mass cellular organisms and small metazoans, which have raised to the ¾ power. This method facilitates quanti- high rates of biosynthesis, a signi®cant portion of total tative evaluation of the mass and temperature depen- body phosphorus is found in ribosomal RNA (Sutcliffe dence predicted by Eq. 4, by incorporating the pre- 1970, Elser et al. 2000b, Sterner and Elser 2002). Larg- dicted scalings into the analysis and into the y-axis of er vertebrate organisms, with lower rates of biosyn- bivariate plots. Eq. 5 predicts that the natural logarithm thesis, require much less RNA, but require much more of mass-corrected whole-organism metabolic rate phosphorus for skeletal structure. Vertebrates, with should be a linear function of inverse absolute tem- bones and muscles, contain proportionately more P and perature (1/kT). The slope of this relationship gives the N and less C than plants, which use cellulose and lignin activation energy of metabolism, E, and the intercept July 2004 MACARTHUR AWARD LECTURE 1775

FIG. 1. Temperature and mass dependence of metabolic rate for several groups of organisms, from unicellular eukaryotes to plants and vertebrates (from Gillooly et al. 2001). (A) Relationship between mass-corrected metabolic rate, ln(IMϪ3/4), measured in watts/g3/4, and temperature, 1/kT, measured in K. The overall slope, calculated using ANCOVA, estimates the activation energy, and the intercepts estimate the normalization constants, C ϭ ln(i0), for each group. The observed slope is close to the predicted range of 0.60±0.70 eV (95% CI, 0.66±0.73 eV; SI conversion, 1 eV ϭ 96.49 kJ/mol). (B) Relationship between temperature-corrected metabolic rate, ln(IeE/kT), measured in watts, and body mass, ln(M), measured in grams. Variables are M, body size; I, individual metabolic rate; k, Boltzmann's constant; T, absolute temperature (in K). E is the activation energy. The overall slope, calculated using ANCOVA, estimates the allometric exponent, and the intercepts estimate Perspectives the normalization constants, C ϭ ln(i0), for each group. The observed slope is close to the predicted value of ¾ (95% CI, 0.69±0.73). For clarity, data from endotherms (n ϭ 142), ®sh (n ϭ 113), amphibians (n ϭ 64), reptiles (n ϭ 105), invertebrates (n ϭ 20), unicellular organisms (n ϭ 30), and plants (n ϭ 67) were binned and averaged for each taxonomic group to generate the points depicted in the plot. gives the natural logarithm of the normalization con- variation over the biologically relevant temperature stant, ln(i0). Plotted in this way (Fig. 1), it is clear that range from 0Њ to 40ЊC. data for all groups are well-®tted by a common slope, There are, of course, quantitative deviations of in- E ഠ 0.69 eV (1 eV ϭ 96.49 kJ/mol), including en- dividual data values around the regression lines and dotherms in hibernation and torpor. Excluding these from the predictions of the models. For example, there endotherms, we obtain an average value of EÅ ഠ 0.63 exists an ϳ20-fold variation in the normalization con- eV. Both of these values are within the range (0.60± stants for basal metabolism, i0, across all taxonomic 0.70 eV) commonly reported for aerobic respiration groups. The residual variation offers clues to the other (Gillooly et al. 2001). factors, in addition to body size and temperature, that Using the value of E ϭ 0.63 eV, we can ``temper- affect metabolic and ecological processes. We will ature-correct'' metabolic rates to isolate the effects of show that some of the remaining variation in ontoge- mass: netic growth rates and litter decomposition rates is re- E/kT ln(Ie ) ϭ (¾)ln(M) ϩ ln(i0). (6) lated to elemental stoichiometry. These methods of ``mass correction'' and ``temper- We use this same value of E ϭ 0.63 eV for subsequent ature correction'' will be applied repeatedly in subse- temperature corrections. Eq. 6 predicts a linear rela- quent sections of the paper to investigate other bio- tionship between the logarithm of temperature-cor- logical rates and times. Slightly different versions of rected metabolic rate and the logarithm of mass. Plot- ting the same metabolic rate data in this alternative Eqs. 5 and 6 are required for mass-speci®c metabolic way (Fig. 1), we see that that the ®tted slope (0.71) is rate and most other biological rates, which are pre- Ϫ1/4 close to the value of ¾ predicted by the theory, and dicted to scale as M , and for biological times, which 1/4 that different groups show consistent differences in in- are expected to scale as M . For simplicity, in most subsequent equations, we will use ϰ instead of ϭ and tercepts or normalization constants, ln(i0). The explanatory power of Eq. 4 is substantial, with will leave out symbols for the normalization constants. body size predicting ϳ100 000-fold variation in rates We emphasize, however, that these coef®cients are im- over the 20 orders-of-magnitude size range from the portant, because they differ in systematic ways among smallest unicellular microbes to the largest vertebrates different biological traits, taxa of organisms, and kinds and trees, and with temperature predicting ϳ30-fold of environments. 1776 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

INDIVIDUAL PERFORMANCE AND LIFE HISTORY nitude in body mass and has a slope almost exactly equal to the predicted ¾. Trees and vertebrates of the The combined effect of body size and temperature same body mass, operating at the same body temper- on whole-organism metabolic rate, I, is given in Eq. ature, produce new biomass through some combination 4. Because the mass-speci®c rate of metabolism, B,is of growth and reproduction, at very similar rates. The simply I/M, it follows that B scales as same applies to ®sh and terrestrial insects. Of course B ϰ MeϪ1/4 ϪE/kT. (7) there is residual variation, some probably related to stoichiometric resource requirements, and the remain- Other biological rates, from heart rate to development der to other taxon- or environment-speci®c factors. But rate, and even the rate of molecular evolution (J. F. the degree of commonality is impressive. Gillooly and A. P. Allen, unpublished data), also vary with mass as MϪ1/4 and with the Boltzmann factor. Bi- Ontogenetic growth ological times, t , such as turnover times for metabolic B The rate of metabolism sets the pace of life, includ- substrates and generations of individuals, are the re- ing the life history schedule. For example, time to ciprocal of rates and therefore scale as hatching of eggs in diverse animals, including zoo- 1/4 E/kT tB ϰ Me (8) plankton, insects, ®sh, amphibians, and birds, varies with size and temperature according to Eq. 8 (West et (Gillooly et al. 2002). These equations express rela- al. 2001, Gillooly et al. 2002). Fig. 3 is a plot of de- tionships that have been studied for many decades. It velopment rates as a function of temperature and mass has long been known that large organisms require more for eggs of zooplankton in the laboratory and ®sh in resources, but ¯ux them through at slower rates than the ®eld. Note that the mass-corrected rates as a func- do smaller organisms. Both overall resource require- tion of temperature have slopes corresponding to ac- ments and ¯ux rates are higher at higher temperatures. tivation energies of 0.73 and 0.68 eV (1 eV ϭ 96.49 Elephants require more food, but reproduce more slow- kJ/mol), close to the range of estimated activation en- ly and live longer than mice. Microbial activity and ergies for aerobic metabolism (Gillooly et al. 2001). rates of litter decomposition are higher in warm, trop- The temperature-corrected rates as a function of mass ical environments than cold, subarctic ones. The ad- have slopes corresponding to allometric exponents of vantage of this framework, however, is that the equa- Ϫ0.27 and Ϫ0.24, bracketing the theoretically pre- tions combine the effects of size and temperature in a dicted value of Ϫ¼. Much of the variation within these single quantitative expression. This makes possible two groups probably can be explained by stoichio- precise comparisons across organisms that differ sub- metric resource limitation. This was shown for devel- stantially in body size and operating temperature, in- opment of zooplankton from hatching to maturity, in

Perspectives cluding species in different taxonomic or functional which residuals around the regression were positively groups or diverse environments. When such compari- correlated with body phosphorus concentration (Gil- sons are made, the commonalities of life and their eco- looly et al. 2002), as expected from the relationships logical manifestations are revealed. between growth rate and RNA concentrations (Sutcliffe 1970, Elser et al. 2000b). Individual biomass production Organisms devote some fraction of their metabolism Survival and mortality to catabolism and activities associated with mainte- Ecologists have traditionally viewed survival times nance, and the remainder to anabolism and activities and their inverse, mortality rates, as being highly var- associated with production of new biomass for growth iable and consequences of extrinsic environmental con- and reproduction. Empirically, rates of whole-organism ditions, such as predation, disease, and resource com- and mass-speci®c biomass production, P and P/M, re- petition, rather than intrinsic properties of individual spectively, scale similarly to whole-organism and mass- organisms (e.g., Charnov 1993, Kozlowski and Weiner speci®c rates, so P ϰ M 3/4eϪE/kT and P/M ϰ MϪ1/4eϪE/kT. 1997, Stearns et al. 2000). However, because most pop- This supports the theoretical conjecture that some con- ulations are neither continuously increasing nor de- stant fraction of metabolism tends to be allocated to creasing, mortality rates must very nearly equal fecun- production. It follows that, to the extent organisms have dity rates, and fecundity is fueled by biomass produc- similar metabolic rates after adjusting for body size tion. Metabolic theory therefore predicts that Eq. 7 and temperature, they should also have similar rates of should account for much of the variation in ®eld mor- production. This prediction is con®rmed by plotting tality rates, Z. Mortality rates of free-living marine ®sh maximal rates of temperature-corrected whole-organ- stocks support this prediction (Fig. 4; see also Peterson ism production against body mass for a wide variety and Wroblewski 1984). The slope of the size-corrected of aerobic eukaryotes, including plants and animals, relationship between mortality rate and temperature ectotherms and endotherms (Fig. 2). Note that all val- gives an activation energy of 0.47 eV, which is some- ues cluster closely around the same allometric rela- what lower than the predicted range of 0.60±0.70 eV. tionship, which extends over nearly 20 orders of mag- The slope of temperature-corrected mortality rate as a July 2004 MACARTHUR AWARD LECTURE 1777 Perspectives FIG. 2. Mass dependence (mass measured in grams) of temperature-corrected maximal rates of whole-organism biomass production (PeE/kT, measured in grams per individual per year) for a wide variety of organisms, from unicellular eukaryotes to plants and mammals (from Ernest et al. 2003). Data, which span Ͼ20 orders of magnitude in body size, have been temperature corrected using Eq. 6. The allometric exponent, indicated by the slope, is close to the predicted value of ¾ (95% CI, 0.75±0.76). function of body mass, Ϫ0.24, is almost identical to ture and function at cellular to whole-organism levels the predicted exponent of Ϫ¼ (Savage et al., in press of organization. Many of these constraints are related a). directly to metabolism. The average rate of turnover We offer two complementary, non-mutually exclu- of an element (i.e., the inverse of residence time) is sive hypotheses for the body size and temperature de- equal to the whole-organism ¯ux divided by the whole- pendence of ®eld mortality rates. First, the cumulative organism pool or storage. The ¯uxes (per individual effects of metabolism with age may affect the ability rates of uptake and loss) of most elements vary with of individual organisms to resist ecological causes of body size in direct proportion to whole-organism met- death, whether they be biotic or abiotic in origin. Stud- abolic rate, as F ϰ M 3/4 (e.g., Peters 1983). Pools of ies of aging have led to a theory of senescence that the commonest constituents of protoplasm, including attributes aging and eventual death to cumulative dam- carbon, hydrogen, oxygen, and water, usually scale lin- age at the molecular and cellular levels by the free early with body mass, i.e., as S ϰ M1. So, for these radicals produced as byproducts of aerobic metabolism common elements, turnover rate, on average, scales as (Gerschman et al. 1954, Hartman 1956, Cadenas and F/S ϰ M 3/4/M1 ϭ MϪ1/4. However, this is not true of all Packer 1999). Second, the size and temperature de- element pools, especially those that have some special pendence of ®eld mortality rates suggest that Eq. 5 function in metabolism. Metabolism of eukaryotes characterizes rates of ecological interactions that lead takes place primarily in organelles: chloroplasts, mi- to death, including competition, predation, parasitism, tochondria, and ribosomes, which are, respectively, the and disease. As we will show, the rates of these inter- sites of photosynthesis, respiration, and protein syn- actions do indeed show the predicted temperature de- thesis. These organelles are effectively invariant units; pendence. their structure and function are nearly identical across taxa and environments. The reaction rate per organelle Stoichiometry is independent of body size (but not temperature), so At the individual level, energy and materials are the rate of whole-organism metabolism depends on the linked by the chemical equations of metabolism, by the total numbers of organelles. Consequently, numbers of composition of organelles and other constituents of these organelles per individual scale as M 3/4, and con- protoplasm, and by fundamental constraints on struc- centrations or densities of the organelles scale as MϪ1/4 1778 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

FIG. 3. Temperature (measured in K) and mass (measured in grams) dependence of developmental rates for eggs of zooplankton in the laboratory (data from Gillooly and Dodson 2000) and ®sh in the ®eld (data from Pauly and Pullin 1988). Hatching time data have been converted to rates (1/time) and plotted as functions of temperature (upper panels, where the rate is measured in g1/4/day) and mass (lower panels, where the rate is measured as 1/day), as described in the section Perspectives Ontogenetic growth. The activation energy and allometric exponent, as indicated by the slopes in the upper and lower panels, respectively, are similar to the predicted values of 0.60±0.70 eV (95% CIs from left to right, 0.68±0.78 eV and 0.62±0.73) and Ϫ¼ (95% con®dence intervals, from left to right, Ϫ0.24 to Ϫ0.29 and Ϫ0.16 to Ϫ0.29).

FIG. 4. Temperature (measured in K) and mass (measured in grams) dependence of ®sh mortality rates in the ®eld (data from Pauly 1980). (A) Relationship between mass-corrected mortality rate, ln(ZM1/4, measured in grams1/4 per year), and temperature, 1/kT (measured in K). The activation energy, indicated by the slope, is lower than the predicted range of 0.60± 0.70 eV (95% CI, Ϫ0.37 to Ϫ0.54). (B) Relationship between temperature-corrected mortality rate, ln(ZeE/kT, measured as 1/year), and body mass, ln(M), measured in grams. The allometric exponent, indicated by the slope, is close to the predicted value of Ϫ¼ (95% CI, Ϫ0.20 to Ϫ0.27). July 2004 MACARTHUR AWARD LECTURE 1779

FIG. 5. Temperature (in K) and mass (measured in grams) dependence of maximal rates of population growth, rmax, for a wide variety of organisms (A and B, respectively; data sources are listed in Savage et al., in press a). Data are plotted as 1/4 in Figs. 3 and 4; rmax is measured in g per day in (A) and as 1/day in (B). There are fewer data points in (B) because there are multiple temperature points for a species of a given mass. The activation energy and allometric exponent, indicated by the slopes in (A) and (B), respectively, are close to the predicted values of 0.60±0.70 eV (95% CI, 0.56±0.80) and Ϫ¼ (95% CI, Ϫ0.21 to Ϫ0.25), respectively.

(Niklas and Enquist 2001, West et al. 2002; J. F. Gil- unequivocal law of population ecology (Turchin 2001). looly and A. P. Allen, unpublished data). This has been The maximal rate of exponential increase, rmax, is pre- shown to be true for mitochondria (West et al. 2002), dicted to scale according to Eq. 7. This follows from Perspectives chloroplasts (Niklas and Enquist 2001), and RNA (Foss the fact that reproduction is fueled by metabolism, and and Forbes 1997). Thus, element pools associated with that mass-speci®c production rates and mortality rates organelles such as these should scale with body size follow Eq. 7. In fact, metabolic rates of microbes are as S ϰ M 3/4, and turnover rates of these pools should often determined by measuring maximal population 3/4 3/4 0 be independent of body size (F/S ϰ M /M ϭ M ). production Ptot or maximal population growth rates,

The extent to which whole-body stoichiometry is rmax. determined by these pools, and thus varies with body The Ϫ¼ mass dependence of rmax has been well doc- size, will depend on their sizes relative to other pools. umented empirically (Slobodkin 1962, Blueweiss et al. For example, whole-body phosphorus concentrations 1978), but what about the temperature dependence? should decline with increasing body size in growing Fig. 5 shows that Eq. 5 describes tightly constrained unicellular organisms because they contain relatively variation in rmax across a wide variety of organisms, high concentrations of phosphorus in RNA relative to from unicellular eukaryotes to mammals. The com- phosphorus in other pools. However, whole-body phos- monality is impressive, especially because these or- phorus concentrations in most multicellular organisms ganisms have very different modes of reproduction and should vary little with body size because most phos- occur in a wide variety of environments (Savage et al., phorus is found in other pools that do not scale with in press a). body size (J. F. Gillooly and A. P. Allen, unpublished This ®nding suggests that some interpretations of data). Similar reasoning should apply to the concen- differences in life history and resulting population pro- trations of nitrogen in plants, because a signi®cant frac- cesses should be reexamined. For example, differences tion is found in chloroplasts. between populations in life history, including the clas- sical r and K strategies, have often been viewed as POPULATION AND COMMUNITY DYNAMICS adaptations to particular environmental conditions. We can extend this framework to population and Metabolic theory shows that smaller organisms, and community levels of ecological organization. Many those operating at higher temperatures, tend to have features of population dynamics and community or- higher rmax values than larger, colder organisms, simply ganization are due to effects of body size, temperature, as a consequence of allometric and kinetic constraints. and stoichiometry on the performance of individual We hasten to add, however, that this does not neces- organisms. sarily mean that size- and temperature-related differ- ences between populations in life histories are not Population growth rates and rmax adaptive. Organisms can respond to selection resulting Population dynamics can be complex and unpre- from different environments by changing body size. dictable, but the potential for exponential growth that For example, strong selection, perhaps for high repro- underlies these ¯uctuations has been called the one ductive rates in the absence of predators, apparently 1780 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

causes rapid dwar®ng of elephants and other large mammals on islands (e.g., Lister 1989, Roth 1990, Brown 1995). Some organisms can also change tem- perature adaptively. For example, many terrestrial ec- tothermic animals exhibit some kind of behavioral ther- moregulation: they seek out warm microenvironments to elevate body temperatures and increase rates of pro- duction for growth and reproduction. Population density It is straightforward to solve the equation for pop- ulation growth rate for the steady state when the num- ber of individuals, N, is not changing (dN/dt ϭ 0) The equilibrium number of individuals or carrying capacity, K, is predicted to vary as K ϰ [R]MeϪ3/4 E/kT (9) FIG. 6. Mass dependence of population density in terres- linearly with the supply rate or concentration of the trial mammals (data sources are listed in Ernest et al. [2003], limiting resource [R], as a power function of body including data from Damuth [1987]). Density was measured as no. individuals/km2, and mass was measured in grams. Data mass, and exponentially with temperature (Savage et were analyzed without temperature correction because mam- al., in press a). The qualitative effects of resource sup- mals have very similar body temperatures. The slope of this ply and body size are not surprising: more individuals relationship gives an allometric exponent close to the pre- with increased resource or decreased size. The effect dicted value of Ϫ¾ (95% CI, Ϫ0.72 to Ϫ0.82). There is con- siderable variation in the densities of mammals of similar of temperature, however, may not be so intuitive. In- size, which is not surprising since the data are for all kinds creasing the temperature actually reduces the carrying of mammals from throughout the world. So, for example, capacity, because the same supply of energy supports some of the residual variation is related to trophic level: car- a smaller number of individuals, each ¯uxing energy nivores with lower rates of resource supply tend to have lower and materials at a higher rate. This prediction of an population densities than herbivores. inverse Boltzmann relationship between equilibrium abundance and environmental temperature for ecto- issue is the unit of analysis. The theory predicts how therms is supported by the analysis of Allen et al. many individuals of a given size can be supported, but (2002). the data are often compiled by species. For example, Perspectives If resource supply rate [R] and temperature T are Damuth (1981, 1987; see also Carbone and Gittleman held constant, then population density should vary in- 2002) showed empirically that population densities of versely with body size, as MϪ3/4. This is the basis for species of terrestrial mammals from all over the world deriving a resource-based thinning law of plant ecology scaled as MϪ3/4. There are, however, at least two orders in which the number of stems, N, is predicted to vary of magnitude variation in the population densities of with plant mass as N ϰ MϪ3/4, or with stem diameter, species of any given size (Fig. 6). Most of this variation D,asN ϰ DϪ2 (Enquist et al. 1998, Belgrano et al. can almost certainly be attributed to variation in re- 2002; see also Lonsdale 1990). The theory assumes source supply. The data come from a wide variety of that sessile plants grow until limited by competition environments that differ considerably in resource avail- for resources, and that individual resource requirements ability, and from mammal species that vary in diet from scale as M 3/4. The theory accurately predicts thinning herbivores to carnivores. So to test the theory properly, trajectories in even-aged stands, which follow a MϪ3/4 the densities of all coexisting species within a trophic or DϪ2 power law. A more complex model that incor- group and body size category should be summed, as porates growth and mortality predicts size±frequency is done for trees in forest communities. distributions of the trees in steady-state forests with The MϪ3/4 scaling of equilibrium population density stable age and size distributions (G. B. West, B. J. with body size raises interesting theoretical questions. Enquist, and J. H. Brown, unpublished data). This mod- Because the number of individuals per unit area, N, el predicts the same scaling of number of stems of a scales as MϪ3/4 and whole-organism metabolic rate given size as a function of plant mass or stem diameter scales as M 3/4, total energy use per unit area for a size (N ϰ MϪ3/4 ϰ DϪ2). Data from forests throughout the class is MϪ3/4 M 3/4 ϰ M0. Within a functional group world show size distributions that are very similar to sharing a common resource, the rate of energy ¯ux per the predicted scaling (Enquist and Niklas 2001). unit area of the combined populations of different-sized Eq. 9 predicts that carrying capacity or equilibrium organisms is predicted to be independent of size. This population density should also scale as MϪ3/4 in mobile energy equivalence argument can also be turned animals if one again assumes that the rate of resource around. Whenever total population density scales em- supply is held constant. One potentially confounding pirically as MϪ3/4;, the resulting invariance in energy July 2004 MACARTHUR AWARD LECTURE 1781

TABLE 1. Studies in which relevant components of competitive or predator±prey interactions have been studied at different temperatures so as to allow estimation of the activation energy, E.

Interspeci®c Study interaction Taxon Measure E (eV) Burnett (1951) parasitism wasp/saw¯y rate of parasitism 0.81 Spitze (1985) predation ¯y larvae/zooplankton attack rate 0.56 Eggleston (1990) predation crab/oyster attack rate 0.80 Luecke and O'Brien (1983) predation zooplankton feeding rate 0.81 Verity (1985) grazing zooplankton/phytoplankton grazing rate 0.57 Park (1954) competition beetle time to competitive 0.64 exclusion Note: Although the number of measurements is usually small, resulting in wide con®dence intervals, note that the values of E vary around the theoretically predicted range of 0.60±0.70 eV. SI conversion: 1 eV ϭ 23.06 kcal/mol ϭ 96.49 kJ/mol.

¯ux implies that resources are available to and are used ological rates, as in Eq. 7. Other things being equal, by each body size class at equal rates. Why should this there are more species of small organisms than large be so? The resource-based thinning theory for plants ones and more species in warm environments than cold reasonably assumes that sessile individuals of different ones. size compete for the same limiting resources (light, The fact that species diversity varies inversely with water, nutrients). So far, however, we have no com- body size suggests that metabolism plays a central role parable theory to explain why the rate of supply of (e.g., Hutchinson and MacArthur 1959, May 1978, usable energy should be approximately constant for 1986, 1988, Brown 1995). As recently as a decade ago, differently sized mammals or other mobile animals that the available evidence suggested that the highest di- utilize a broad spectrum of resources. versity occurred in small, but not the smallest, organ- isms (i.e., in small insects; see May 1978, 1986). Re- Interspeci®c interactions cent data, however, reveal enormous microbial diver- Perspectives Since the theoretical studies of Lotka (1925) and sity and suggest that species richness may continue to Volterra (1926) and the classical experiments of Gause increase with decreasing body size right on down to (1934), Park (1948), and Huffaker (1958), ecologists the smallest prokaryotes and perhaps even to viruses have tried to understand how pairs of competing spe- (e.g., Pace 1997). cies or of predators and prey coexist with stability in It has long been known that diversity of most tax- the same environment. The experimental studies found onomic and functional groups is highest in the tropics, that coexistence was dif®cult to obtain in simple lab- but this has usually been attributed to higher produc- oratory environments: one of the populations almost tivity (resource availability) or reduced seasonality, invariably went extinct. For example, in Park's (1954) rather than to the kinetic effect of higher temperatures classic experiments with ¯our beetles, by varying the (e.g., Brown and Lomolino 1998; but see Rohde 1992). temperature, he was able to reverse the outcome of We have recently shown, however, that species richness competition, changing which species survived and in many groups of plants and animals has the same which went extinct. Less appreciated is the fact that Boltzmann relationship to environmental temperature time to competitive exclusion across three temperatures that metabolic rate does (Eq. 3; see Allen et al. 2002). was inversely related to temperature with an activation This result holds true not only along latitudinal gra- energy of 0.64 eV (1 eV ϭ 96.49 kJ/mol), nearly iden- dients, but also along elevational gradients where var- tical to the average for individual metabolism. A num- iables such as photon ¯ux, seasonal changes in day ber of other interaction rates and times, including rates length, and biogeographic history are held relatively of parasitism and predator attack rates, show similar constant (Fig. 7). The implication is that much of the temperature relations (Table 1; see also Tilman et al. variation in species diversity is directly attributable to 1981, Dunson and Travis 1991). Metabolic theory pre- the kinetics of biochemical reactions and ecological dicts the pace of these interactions, because rates of interactions. consumption and population growth are determined by The temperature dependence of population growth rates of individual metabolism and have the same body and interspeci®c interactions brings into question ex- size and temperature dependence. planations for diversity that invoke long time lags (e.g., Hutchinson 1961, Bell 2001, Hubbell 2001). The high- Species diversity est diversity on earth is found in warm, productive The scaling of rates of ecological interactions has environments, such as tropical rain forests and coral important implications for coexistence and species di- reefs, where the kinetics of interactions might be ex- versity. The qualitative empirical patterns of biodiver- pected to lead to rapid exclusion. We hypothesize that sity would suggest that the processes that generate and diversity is largely a consequence of evolutionary pro- maintain species richness scale similarly to other bi- cesses that obey Eqs. 7 and 8: small or warm organisms 1782 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

FIG. 7. Temperature dependence (temperature measured in K) of amphibian species richness in two geographic gradients (Allen et al. 2002). (A) A latitudinal gradient in North America (data from Currie 1991). (B) An elevational gradient over 2600 m on Volcan Barva in Costa Rica (data from Duellman 1988). The slopes indicate nearly identical effects of temperature on diversity in the two gradients, with activation energies close to the predicted value of 0.60±0.70 eV (95% con®dence intervals, from left to right, 0.63±0.77 and 0.55±0.87).

having faster ecological dynamics than large or cold the relationship between metabolism and biodiversity ones should also have faster evolutionary dynamics, is needed, but a metabolic perspective has sharpened resulting in higher rates of speciation and a higher many of the questions and has suggested where to look standing stock of species. We have shown that Eq. 7 for some of the answers. predicts rates of molecular evolution for a variety of genes and genomes for ectotherms and endotherms (J. ECOSYSTEM PROCESSES F. Gillooly and A. P. Allen, unpublished data). Van Some of these questions can be addressed by probing Valen (1973) attributed the origin and maintenance of more deeply the effects of biological metabolism on biodiversity largely to the ``Red Queen'' phenomenon, the fates of energy and materials in ecosystems. Bio- rates of species interaction and coevolution. We agree, logically regulated whole-ecosystem stores and ¯uxes and conjecture that the Red Queen runs according to of elements and compounds, such as phosphorus, ni- Perspectives Eq. 7: faster in warmer environments and smaller or- trogen, and carbon, are simply the sums of the stores ganisms. and ¯uxes of the constituent organisms. Metabolic the- Although this conjecture is consistent with many ory therefore makes explicit predictions about the con- facts about biodiversity, it raises additional questions. tribution of biota to biogeochemical cycles. Speci®- First, how can the kinetic effects of high temperature cally, Eq. 7 provides the basis for predicting how size, be distinguished from the resource supply effects of temperature, and stoichiometry determine magnitudes high productivity, which also increases with increasing of stores and rates of ¯ux within and between com- temperature? Second, how do faster rates of interspe- partments such as primary producers, herbivores, pred- ci®c interaction and evolution result in higher standing ators, and detritivores. stocks of species? This conjecture also raises the ques- tion of why ectotherms, whose body temperatures and Standing stock of biomass metabolic rates vary with environmental temperature, It is straightforward to derive an expression for and endotherms, which have relatively high and con- standing stock biomass. Eq. 9 gives the effects of body stant body temperatures, show qualitatively similar mass and temperature on equilibrium population den- geographic patterns of diversity. One hypothesis would sity (number of individuals per unit area). Multiplying again invoke the Red Queen and suggest that species this expression by the body size per individual, M, diversity of endotherms is due largely to interactions gives the corresponding equation for standing stock or with ectotherms: food resources, competitors, preda- stored biomass, W, per unit area: tors, parasites, and diseases. Alternatively, biodiversity W ϰ [R]Me1/4 E/kT. (10) gradients may be driven largely by ecosystem produc- tivity for endotherms, and by temperature effects on The rate of supply of limiting resource, [R], has direct biochemical kinetics for ectotherms. Consistent with linear effects on both carrying capacity and biomass. this latter hypothesis, average population densities of Total biomass increases nonlinearly with increasing ectotherms, but not endothermic mammals, decline ex- body size and decreasing temperature. Large and/or ponentially with temperature toward the warm tropics cold organisms retain more resources in their bodies (Allen et al. 2002). Clearly, much additional work on because they ¯ux them more slowly through their met- July 2004 MACARTHUR AWARD LECTURE 1783 abolic pathways, and vice versa for small and/or hot organisms. Energy ¯ux and biomass production At steady state, the rate of resource uptake by con- sumers or ``predators'' is some constant fraction of the rate of production of producers or ``prey.'' As individ- uals, both producers and consumers ¯ux energy with the whole-organism and mass-speci®c scalings given in Eqs. 4 and 7. However, the rate of energy ¯ux for populations should show a different mass dependence, but not temperature dependence, because of the scaling of population density and biomass. Rate of ¯ux per unit area, Ftot, can be derived by multiplying Eq. 4, for the whole-organism metabolic rate per individual, by MϪ3/4, the number of individuals per unit area (from Eq. 9). The result is

0 ϪE/kT Ftot ϰ [R]Me . (11) FIG. 8. Relationship of carbon turnover rate (measured as The rate of biological energy ¯ux or productivity per [day]Ϫ1) to average plant size for plant biomass (measured in unit area of an ecosystem is therefore predicted to be grams) in aquatic and terrestrial ecosystems (analysis by A. independent of body size but to increase with increas- P. Allen, J. F. Gillooly, and J. H. Brown, unpublished man- ing temperature. Enquist et al. (1998; also Niklas and uscript; carbon turnover data from Cebrian [1999] and for plant size data from Belgrano et al. [2002]). Data have not Enquist 2001) show that across diverse ecosystems, been temperature corrected, because environmental temper- rates of primary production, measured as rates of atures were not reported. The slope of the relationship (solid Perspectives whole-plant xylem ¯ux, are independent of plant size line) gives an allometric exponent close to the predicted value as predicted by Eq. 11. The data of Enquist et al. (1998: of Ϫ¼ (dashed line; 95% CI, Ϫ0.21 to Ϫ0.24). Fig. 4) show about two orders of magnitude variation in rates of productivity, which is small in comparison to the nearly 12 orders of magnitude variation in plant globe is well described by a Boltzmann relationship mass. Most of the variation in productivity is probably with an activation energy of ϳ0.33 eV (A. P. Allen, J. due to both temperature and stoichiometry. The data F. Gillooly, and J. H. Brown, unpublished manuscript). set includes ecosystems from around the world with This value is approximately half the magnitude of the substantially different temperatures and energy, water, activation energy for respiration or secondary produc- and nutrient availability. The size invariance explicit tion (ഠ0.63 eV). This has important consequences for in Eq. 11 means that ecosystems with similar temper- carbon cycles and organic matter storage (e.g., Schles- ature regimes and rates of resource supply, such as inger 1991). adjacent forests and grasslands, should have nearly equal rates of primary production. Clearly, however, Biomass turnover and energy ¯ux the forests contain much more stored biomass, as pre- In the ecological literature, especially in applied dis- dicted by Eq. 10. ciplines such as ®sheries, production is often expressed

One complication is that plant metabolic rate is the as the production/biomass ratio, Ptot/W, of total popu- rate of photosynthesis: the rate of conversion of solar lation production, Ptot, to standing stock biomass, W. energy into organic compounds. Photosynthesis con- Given that Ptot ϭ PN, and that W ϭ NM, this quantity sists of multiple biochemical reactions, some of which must scale as are temperature dependent and have a range of acti- P /W ϰ MeϪ1/4 ϪE/kT (12) vation energies (0.35±0.65 eV; Bernacchi et al. 2001), tot and some of which are dependent only on light (Far- the same as mass-speci®c metabolic rate (Eq. 7). Em- quhar et al. 1980). Terrestrial plants maximize photo- pirical studies have shown this predicted size depen- synthesis in different environments by differentially dence for populations of different species (Peters partitioning proteins among enzymatic reactions based 1983). For a steady-state population, production re- on their respective temperature and light dependencies ¯ects the replacement of individuals lost due to mor- (Farquhar et al. 1980, Field and Mooney 1986). Less tality, so production must scale with body size and well understood, however, is how photosynthesis at the temperature the same as mortality rate, Z, consistent level of individual plants is manifested in global pat- with Eqs. 7 and 12 and the empirically observed scaling terns of plant production. We ®nd that the activation (Savage et al., in press a; Fig. 4). Furthermore, because energy for terrestrial net primary production (gross rates of biomass production and consumption must be plant production minus plant respiration) across the equal at steady state, Eqs. 7 and 12 also predict rates 1784 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

FIG. 9. Temperature dependence (temperature in K) of short-term root decay rate (measured as [day]Ϫ1) as characterized by the rate constant, k (analysis by A. P. Allen, J. F. Gillooly, and J. H. Brown, unpublished manuscript; data from Silver and Miya [2001]). (A) The observed activation energy, as indicated by the slope, is within the range of values (0.60±0.70 eV) predicted on the basis of metabolic rate (95% CI, 0.43±0.76). (B) Plotting the residuals about the regression line in (A) as a function of C:N shows that much of the variation is due to stoichiometry (P Ͻ 0.05).

of biomass turnover. Fig. 8 (from A. P. Allen, J. F. ®res, or human perturbations, such as abandonment of Gillooly, and J. H. Brown, unpublished manuscript; agricultural ®elds. Metabolic theory also provides a data from Cebrian 1999) shows that carbon turnover framework for more explicitly incorporating stoichi- rates in a broad assortment of terrestrial and aquatic ometry and understanding the effects of limited water ecosystems scale with average plant size as MϪ0.22. Not and nutrients on variation in productivity and other only is this very close to the predicted MϪ1/4, but also processes across biomes and geographic gradients. Re- size varies over ϳ20 orders of magnitude and accounts gression models that incorporate these variables are for 84% of the variation in these data. Thus retention able to account for much of the observed variation (e.g., times for carbon and nutrients must show the reciprocal Lieth 1973), but it should be possible to replace these relation, as in Eq. 8. Temperature and nutrient supply with mechanistic analytical models based on ®rst prin- undoubtedly explain much of the remaining variation. ciples. Empirical studies also support the predicted tem- Perspectives perature dependence. Total ecosystem respiration from Trophic dynamics a broad assortment of terrestrial ecosystems around the Another major focus of ecosystem science has been world, measured by eddy covariance towers as night- the structure and dynamics of food webs, which depict

time CO2 ¯ux, varies with temperature as predicted the ¯ows of energy and materials through ecosystems based on individual metabolism. The average activa- due to trophic interactions. Metabolism has usually tion energy from 19 sites was 0.62 eV, within the pre- been incorporated into food web theory only to the dicted range of 0.60±0.70 eV (Enquist et al. 2003). extent of showing that the ¯uxes of energy and ma- Similarly, Fig. 9 shows that temperature alone accounts terials obey the laws of thermodynamics and conser- for 53% of the variation in short-term rates of decom- vation of energy, mass, and stoichiometry (but see Kerr position from sites around the world (A. P. Allen, J. F. and Dickie 2001). It should be possible to do much Gillooly, and J. H. Brown, unpublished manuscript; more, in particular to use metabolic theory to under- data from Silver and Miya 2001). The activation energy stand the abundance, biomass, energy use, and ele- is 0.60 eV, not signi®cantly different from the range mental chemical composition of species populations or 0.60±0.70 eV predicted on the basis of aerobic metab- entire functional groups in terms of the effects of body olism. Furthermore, 58% of the residual variation can size, temperature, and stoichiometry on metabolic rate. be explained by stoichiometry (in this case, the C:N We illustrate the possibilities with two examples. ratio of the litter; see Fig. 9). Ecologists have long depicted trophic organization This metabolic framework also could be applied to as pyramids of energy, biomass, or abundance. Each address more precisely and quantitatively the questions layer of a pyramid corresponds to a successively higher raised by Odum (1969) in his classic paper on ``The trophic level, starting with primary producers and go- Strategy of Ecosystem Development.'' For example, it ing up through herbivores, primary carnivores, and so should be possible predict the dynamics of succession: on. Metabolic theory makes quantitative predictions for how productivity, biomass, and material turnover rates how body size, temperature, and stoichiometry affect change with increasing plant size during transition from the pools and ¯uxes of biomass and energy. At steady herbaceous-dominated to tree-dominated ecosystems state, the Second Law of Thermodynamics demands following either natural disturbances, such as forest that there be less available energy at higher trophic July 2004 MACARTHUR AWARD LECTURE 1785

FIG. 10. A simple graphical model to explain the invariance of biomass as a function of body size of pelagic organisms in ocean and lake ecosystems (from Brown and Gillooly 2003), where M is body mass, E is activation energy of metabolism, B is mass-speci®c rate of metabolism, and N is number of individuals. If the ratio of predator size to prey size is 10 000, and 10% of energy is transferred between successive trophic levels, Eq. 13 predicts allometric scaling of total abundance, energy use, and biomass (A) within trophic levels (dashed lines: MϪ3/4, M0, M1/4, respectively) and (B) across trophic levels (continuous lines: MϪ1, MϪ1/4, M0, respectively) from phytoplankton (P) to zooplankton (Z) to planktivorous ®sh (F).

levels because, ®rst, energy is lost within a trophic level stants for metabolic rate and because some of the en- due to respiration and heat production, and second, ergy goes directly to decomposers rather than to tra- energy is lost between trophic levels due to inef®cien- ditional ``consumers'' at higher trophic levels. Perspectives cies in transferring the biomass produced at one trophic A second and related example concerns the rela- level, designated 0, to the next higher trophic level, tionship between body size, biomass, and abundance designated 1. The loss of energy between two adjacent in pelagic ecosystems. Since the 1970s, ecologists have trophic levels can be characterized by a Lindeman ef- noted the empirical pattern that in both freshwater and ®ciency, ␣, the ratio of total metabolic energy ¯uxes marine ecosystems, total standing biomass, W, is in- 0 at trophic level 1 to those at level 0. So, from Eq. 4 it variant with respect to body size (i.e., W ϰ M ) across follows that ␣ϭi N MM3/4eϪE/kT/i N 3/4eϪE/kT, where i all pelagic organisms from unicellular plankton to the 1 1 100 0 0 largest animals. Consequently, abundance varies with and i are the normalization constants for ®eld meta- 1 body size as N ϰ MϪ1 (e.g., Sheldon and Parsons 1967, bolic rate, and N , N , M , and M are the population 0 1 0 1 Sheldon et al. 1972, 1977, Peters 1983, Cyr 2000; see densities and body masses at trophic levels 0 and 1, also Kerr and Dickie 2001, Cohen et al. 2003). A simple respectively. Assuming that the system is in steady model can explain this pattern (Fig. 10; see also Brown state and that temperatures and normalization constants and Gillooly 2003). There are powerful body size con- do not differ between trophic levels, this simpli®es to straints on the ¯ow of energy in pelagic ecosystems. 3/4 3/4 ␣ϭN1MM10/N0 , and ␣ must always be Ͻ1. Given Primary producers are minute unicellular algae and these same assumptions, we can also derive comparable prokaryotes, whereas successive trophic levels consist 3/4 relations for abundance, N1/N0 ϭ␣(M0/M1) Ͻ of organisms of increasing size, zooplankton, plank- Ϫ3/4 Ϫ1/4 (M1/M0) ; and for biomass, W1/W0 ϭ␣,(M0/M1) tivorous ®sh, and so on. If the size of the unicellular 1/4 Ͻ (M1/M0) . Thus, it is impossible to observe inverted algae at trophic level 0 is equal to M0 and ␤ is the pyramids of energy ¯ux, but possible to observe in- average ratio of predator body size to prey body size, verted pyramids of abundance if the higher trophic lev- then the dependence of trophic level on mass can el is composed of organisms of suf®ciently smaller be described by the equation ␶ϭlog␤(M/M0) ϭ size; e.g., phytophagus insects feeding on trees. It is log(M/M0)/log(␤), where ␶ϭ0 is the trophic level for also possible to observe inverted pyramids of biomass algae of size M0. If we further assume that the total if the higher trophic level is composed of organisms rate of metabolism at trophic level 0 is equal to 3/4 ϪE/kT of suf®ciently larger size, e.g., whales feeding on i0N0M 0 e , and that ␶ and the Lindeman ef®ciency plankton. Note that the more explicit version incor- ␣ are constants across trophic levels, then the total rate porating normalization constants and temperature de- of metabolism for organisms of size M is 3/4 ϪE/kT ␶ pendence can be used to give a more exact prediction, Itotϭ (iNM 0 0 0 e )␣ as when, for example, a trophic level is composed pri- M log(␣)/log(␤) marily of endotherms with elevated body temperatures. 3/4 ϪE/kT ϭ (iNM00 0 e ). Usually, however, the simpler inequalities will be con- ΂΃M0 servative, because the organisms at higher trophic lev- Following Eq. 4, the total number of organisms of a els tend to have somewhat higher normalization con- given size is the following: 1786 JAMES H. BROWN ET AL. Ecology, Vol. 85, No. 7

IM[log(␣)/log(␤)]Ϫ3/4 Second, metabolic theory suggests that energy and N tot N . (13) ϭϭ0 materials (or energy and stoichiometry) are not fun- IM΂΃0 damentally different ecological currencies that operate Within a trophic level, where resource supply is rela- independently of each other to affect the structure and tively constant, Eq. 13 predicts that abundance should dynamics of ecological systems. They are inextricably Ϫ3/4 decrease with size as M , as has been observed em- linked. The ¯uxes, stores, and transformations of en- pirically (e.g., Belgrano et al. 2002, Li 2002). Between ergy and materials are stoichiometrically constrained trophic levels, the transfer of energy, characterized by by the biochemistry and physiology of metabolism. the Lindeman ef®ciency ␣, has been estimated empir- Energy is required to perform biological work, includ- ically to be ϳ10% (Lindeman 1942). The range of body ing acquiring and transforming material resources. Ma- sizes within a trophic level, and the difference in av- terials, both carbon compounds and elemental nutri- erage size between trophic levels, is about four orders ents, are required to synthesize the chemical com- of magnitude. Consequently, (log ␣)/(log ␤) ഠ Ϫ¼ pounds that are the basis of all biological structures in Eq. 11, and abundance declines with body size as and functions. At all levels, from individual organisms Ϫ1/4Ϫ3/4 Ϫ1 M ϭ M across all trophic levels and the entire to ecosystems, the processing of energy and materials spectrum of body sizes (Brown and Gillooly 2003). It is linked due to metabolic constraints. follows that energy ¯ux, F, declines with body mass Third, metabolic processes relate the structure and (log␣)/(log␤) Ϫ1/4 0 as M ϭ M , and that biomass scales as M function of individual organisms to the roles of organ- and therefore is invariant (Fig. 10). isms in ecosystems. On the one hand, many of these We do not yet have a mechanistic theory to explain linkages are not yet well understood. Both more and Ϫ1 4 why ␣ is often ϳ10 or why ␤ is often ϳ10 . The better data and new and better theories are needed. On fraction of metabolic energy allocated to biomass pro- the other hand, much progress can be made using ex- duction by the lower trophic level sets an upper limit isting data and theories. We have shown how the same on ␣, because production at the lower trophic level principles of allometry, kinetics, and stoichiometry can fuels metabolism at the next highest trophic level (Kerr be used to understand quantitatively the ¯uxes of both and Dickie 2001). This is only an upper limit, however, energy and materials in different kinds of organisms because it does not include energy losses incurred by and in different kinds of ecosystems. This is because the higher trophic level due to foraging and assimila- the biogeochemical processes in ecosystems are largely 4 tion. The fact that ␤ϳ10 in size-structured pelagic consequences of the collective metabolic processes of ecosystems is intriguing (see also Kerr and Dickie the constituent organisms. 2001, Cohen et al. 2003). The quarter-power allometry Fourth, we envision a metabolic theory that would implies that predator±prey body size ratios potentially eventually provide a conceptual basis for ecology sim- Perspectives can be explained in terms of metabolic constraints. ilar to that which genetic theory provides for evolution. Metabolism, like inheritance, is one of the great uni- CONCLUSIONS AND CAVEATS fying processes in biology, making connections be- We close with a few words about the strengths and tween all levels of organization, from molecules to eco- limitations of the theory that we have presented. First, systems. Metabolic theory would by no means be the we should be explicit about what we mean by a met- only ecological theory nor would it account for all abolic theory of ecology. We consider it to be a mech- important patterns and processes. It does, however, pro- anistic, quantitative, synthetic framework that (1) char- vide a conceptual framework for ecological energetics acterizes the effects of body size and temperature on and stoichiometry. It does account for much of the the metabolism of individual organisms, and (2) char- variation in ecological rates and times. It is based on acterizes the effects of metabolism of individual or- ®rst principles of energy, mass, and stoichiometric bal- ganisms on the pools and ¯ows of energy and matter ances, thermodynamics, biochemical energy transfor- in populations, communities, and ecosystems. Many mations, chemical reaction kinetics, and fractal-like bi- parts of this framework were established decades ago. ological designs. It uses the biological processing of Our work has built upon this foundation, primarily by energy and materials to make linkages between indi- developing mechanistic models that explain quarter- vidual organisms and the ecology of populations, com- power allometric scaling in biology, combining the ef- munities, and ecosystems. fects of body size and temperature on metabolic rate Fifth, metabolic theory is emphatically not a ``theory in a single expression, and showing how the metabo- of everything.'' As presently formulated, its domain is lism of individual organisms affects the structure and restricted to effects of allometry, kinetics, and stoi- dynamics of ecological systems. Other parts of the chiometry on the biological processing of energy and framework are still incomplete. Many other investi- materials. Within this domain, it appears to explain gators are contributing to the emerging theory. Nev- much of the variation in pools, rates, and times. As our ertheless, in its current state metabolic theory appears ®gures show, however, it cannot explain all of the var- to predict the magnitudes and to elucidate the mech- iation. The existence of residual variation calls atten- anisms of many empirical phenomena in ecology. tion to the importance of other variables and processes July 2004 MACARTHUR AWARD LECTURE 1787 not included in either the speci®c models or the general a common rule for marine phytoplankton and terrestrial theory. A strength of the theory, however, is that it plants. Ecology Letters 5:611±613. Bell, G. 2001. Ecology: neutral macroecology. Science 293: makes explicit quantitative predictions based on ®rst 2413±2418. principles. The residual variation can then be measured Bernacchi, C. J., E. L. Singsaas, C. Pimentel, A. R. Portis, as departures from these predictions, and the magnitude and S. P.Long. 2001. Improved temperature response func- and direction of these deviations may provide clues to tions for models of Rubisco-limited photosynthesis. Plant Cell and Environment 24:253±259. their causes. Additionally, much of ecology lies outside Blueweiss, L., H. Fox, V. Kudzma, D. Nakashima, R. Peters, the domain of metabolic theory. There are many phe- and S. Sams. 1978. Relationships between body size and nomena for which metabolic processes either do not some life history parameters. Oecologia 37:257±272. apply or play at most a small contributing role. Ex- Boltzmann, L. 1872. Weitere Studien uÈber das WaÈrmegleich- amples include species±area and species±time rela- gewicht unter GasmolekuÈlen. Sitzungsberichte der mathe- matisch-naturwissenschlaftlichen Classe der kaiserlichen tionships, distributions of abundances among coexist- Akademic der Wissenschaften Wien 66:275±370. ing species of similar size, temperature and resource Brown, J. H. 1995. Macroecology. University of Chicago requirements, and the Taylor power law relationship Press, Chicago, Illinois, USA. between mean and variance of population size over Brown, J. H., and J. F. Gillooly. 2003. Ecological food webs: high-quality data facilitate theoretical uni®cation. Proceed- time or space. ings of the National Academy of Sciences (USA) 100: Finally, in this paper we have been concerned only 1467±1468. with basic science, with developing a conceptual Brown, J. H., and M. V. Lomolino. 1998. Biogeography. framework for ecology based on ®rst principles of bi- Sinauer, Sunderland, Massachusetts, USA. ology, physics, and chemistry. This is not the place to Burnett, T. 1951. Effects of temperature and host density on the rate of increase of an insect parasite. American Natu- apply the theory to practical problems of environmental ralist 85:337±352. policy and management. It should be apparent, how- Cadenas, E., and L. Packer, editors. 1999. Understanding the ever, that there are many such applications, from wild- process of aging. Marcel Dekker, New York, New York, life, ®sheries, and forest management to global change USA. Calder, W. A., III. 1984. Size, function and life-history. Har- ecology. The theory helps one to understand some of vard University Press, Cambridge, Massachusetts, USA. Perspectives the changes that have occurred as humans have altered Carbone, C., and J. L. Gittleman. 2002. A common rule for size distributions of organisms, environmental tem- the scaling of carnivore density. Science 295:2273±2276. peratures, and chemical stoichiometry of ecosystems. Cebrian, J. 1999. Patterns in the fate of production in plant The theory offers a predictive framework for assessing communities. American Naturalist 154:449±468. Chapin, F. S., III., P. A. Matson, and H. A. Mooney. 2002. and responding to human-induced changes in the abun- Principles of ecosystem ecology. Springer-Verlag, New dance, distribution, and diversity of organisms, and the York, New York, USA. ¯uxes of energy and materials in ecological systems. Charnov, E. L. 1993. Life history invariants: some explo- rations of symmetry in evolutionary ecology. Oxford Uni- ACKNOWLEDGMENTS versity Press, Oxford, UK. Cohen, J. E., T. Jonsson, and S. R. Carpenter. 2003. Ecolog- This paper is dedicated to the memory of Robert MacArthur ical community description using the food web, species for his contribution to ecological theory and his encourage- abundance, and body size. Proceedings of the National ment of young ecologists, including J. H. Brown. We thank Academy of Sciences (USA) 100:1781±1786. the many people who have contributed data and ideas that Currie, D. J. 1991. Energy and large-scale patterns of animal- have in¯uenced our thinking. The list is long. In addition to and plant-species richness. American Naturalist 137:27± many others, it includes B. Enquist, E. Charnov, W.Woodruff, 49. H. Olff, and colleagues, students, and visitors at the Univer- Cyr, H. 2000. Individual energy use and the allometry of sity of New Mexico, the Santa Fe Institute, and Los Alamos population density. Pages 267±295 in J. H. Brown and G. National Laboratory. S. Dodson, S. Levin, R. Paine, D. Til- B. West, editors. Scaling in biology. Oxford University man, and several anonymous reviewers read the manuscript Press, New York, New York, USA. and made helpful comments. G. B. West and J. H. Brown Damuth, J. 1981. Population density and body size in mam- were supported by a Packard Interdisciplinary Science mals. Nature 290:699±700. Award, a NSF Biocomplexity grant (DEB-0083422), and the Damuth, J. 1987. Interspeci®c allometry of population-den- Thaw Charitable Trust. G. B. West was also supported by sity in mammals and other animals: the independence of NSF grant PHY-0202180. body-mass and population energy-use. Biological Journal of the Linnean Society 31:193±246. 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Brooks/ petitive arena. American Naturalist 163:209±229. Cole Thompson Learning, Paci®c Grove, California, USA. FORUM

The Metabolic Theory of Ecology1

Scaling in biology has a rich and important history. Typically body mass, or some other parameter relating to organism size, is related to anatomical, physiological, and ecological pa- rameters across species. Quite remarkably, diverse organisms, from tiny microbes to the earth's largest organisms are found to fall along a common slope, with a high degree of variance explained. The beauty of such scaling ``laws'' has been the generality in biotic organization that they suggest, and the challenge (for ecologists) has often been interpreting their mechanistic bases and eco- logical consequences. Scaling laws have thus far inspired scientists in at least three major areas. First, scaling laws may illuminate biology that is otherwise shrouded. For example, if scaling relationships can account for variation in a parameter of interest, the residual variation may be much more easily examined because the major in¯uence of some trait, say, body size, is removed. Second, some scientists have taken an interest in ``the exponent''Ðessentially the exponential scaling values that produce the allometric relationship. What are the precise values of these exponents? Are they all from a family of particular values (quarter powers) for many different biological rela- tionships? This area seeks to de®ne the generality of patterns in nature and to explore the empirical robustness of the relationships. Third, from a mechanistic perspective, if scaling laws are mech- anistic and truly general, then this suggests some underlying common biological process that forms the structure and function of species and ultimately generates biological diversity. The mechanistics of scaling from metabolism and the currently favored fractal network model of resource acquisition and allocation may allow scientists to understand the laws of how life diversi®ed and is constrained. Perhaps more importantly, such a mechanistic understanding should allow the successful prediction of evolutionary trends, responses of organisms to global change, and other basic and applied biological problems. The Ecological Society of America's MacArthur Award winner, James H. Brown, working together with colleagues for over a decade on scaling in biology, has arrived at an outline for a metabolic theory of ecologyÐa proposal for a unifying theory employing one of the most fun- damental aspects of biology, metabolism. This metabolic theory incorporates body size, tem- perature (metabolic kinetics described by the Boltzmann factor), and resource ratios of the es- sential elements of life (stoichiometry). Indeed, this bold and visionary proposal is likely to inspire ecologists and provoke much discussion. My goal in assembling this Forum was to work toward a balanced discussion of the power and logic of the metabolic theory of ecology. I have asked both junior and senior scientists to evaluate the ideas presented in the metabolic theory and to go beyond the listing of strong and weak points. As such, this collection of commentaries should be viewed neither as a celebration of the theory nor as a roast of Jim Brown. It should, however, serve as a springboard for future research and re®nements of the metabolic theory. Several themes and axes of admiration and agitation emerge from the forum. The focus on metabolism, and metabolic rate in particular, is an advance that most agree is the fundamental basis for the processes of acquisition of resources from the environment and, ultimately, survival and reproduction of organisms. The combination of size, temperature, and nutrients has compelling predictive power in explaining life-history traits, population parameters, and even broader-scale ecosystem processes. The key point here is that Brown et al. are making a direct link between factors that affect the functioning of individuals and the complex role that those individuals play in communities and ecosystems. Although what we have before us is a proposal for a uni®ed theory of ``biological processing of energy and materials'' in ecosystems, Brown et al. embrace the unexplained variation and acknowledge other areas of ecology that may not be subject to metabolic laws.

1 Reprints of this 51-page Forum (including the MacArthur Lecture) are available for $7.75 each, either as pdf ®les or as hard copy. Prepayment is required. Order reprints from the Ecological Society of America, Attention: Reprint Department, 1707 H Street, N.W., Suite 400, Washington, D.C. 20006.

1790 Forum GRAWAL A. A NURAG Special Features Editor ÐA 2004 by the Ecological Society of America ᭧ Key words: allometry; biological scaling; body size; Boltzmann factor; ecophysiology; functional ecology; laws in ecology; MacArthur Award paper; macroecology; nutrient stoichiometry. The commentaries presented in this Forum are unanimous in their admiration of Brown et al.'s broad theoretical proposal andwidely: its What clear really predictions. is Yet, theexplanatory points correct power? of exponent? discussion Does Are the aboundaddition the scale of and at temperature range laws which and resource scaling reallyis limitation is based enhance scaling applied the affect on up power its community of mechanism from structure, scaling and or relationships? the ecosystem And, phenomena? processes metabolicto possible? How the This rate Forum commentaries. does ends and Although with there the at Brown's body will response hand be mass from continued the debate ofover broadest over organisms the taxonomic the issue correct groups to exponent, of support the scale population quarterhave data and more powers. dynamics, the or There fact less is that, to generaltheory, depending offer. agreement Finally, and on nutrient all the stoichiometry agree scale is that ofratios the further interest, most research in metabolic recent and theory addition the re®nement may to willauthors ecological metabolic determine of the scaling. role this The for such Forumwill bene®ts nutrient evaluate have of these outlined a theses. some metabolic of theory the of future ecology challenges, are and clear. tomorrow's The questions Forum ᭧ Ecology, 1792 rpsdb rw ta.(04 hsise r likely categories. are following issue) the this into (2004, fall al. to et Brown by proposed h aAtu wr ae) e otoe1 .1790. (including p. Forum 1, this footnote of see paper), reprints Award For MacArthur Agrawal. the A. A. itor: oase hs rcia usin;unfortunately, here. questions; us help practical not will these MTE inde®- answer waiting ecology of of to re- theory luxury comprehensive design future the some for best have nitely not we do can We How serves? managed? what be and ecosystems and restored can sustains How services? What look ecosystem warming? ecosystems threatens global will under What ecology. in like far applied ques- critical best, in also at are tions there is, meantime, the ecology In in future. the everything the- nearly parsimonious of A ory behavior. disturbance organism of and in¯uence regimes, the variability, cy- and temporal stochastic clic species, reproductive and as individuals dis- of such spatial tribution webs, ecology, things food in stability, the succession, of about strategies, most care about we useful cannot that it anything but say traits, to ecosystem of hope subset limited very a T r ag n l hs goe set fecology of aspects in ignored those (listed all and large are MTE ati naed o ecology. at for Here agenda ecology. parsimo- an in a is everything of last nearly component of major theory a nious be tempera- will environmental MTE ture). effective determining dis- in its of role (including behavior in¯uence organism the and regimes, variability, turbance stochastic temporal species, cyclic and and individuals of distribution repro- tial spa- as webs, food such stability, succession, theory, strategies, comprehensive ductive essen- any be to to input thought tial probably had concepts ecologists the most of that many about nothing assumes that theory given the impressive, particularly ecosystem- is This in resource partitioning. and and density, traits, population turnover, history carbon level life other mor- and or- rates, tality, in developmental variability natural productivity, the ganism-level of explain fraction can impressive temperature an prin- and physical energy well-founded concerning simple, ciples few a how strates insi n hoyta ol ovnigyexplain convincingly would that theory any in dients 04b h clgclSceyo America of Society Ecological the by 2004 kpia dismissal Skeptical admiration Limited support Enthusiastic (MTE) ecology of theory metabolic the to Reactions 1 Ed- Corresponding 2003. October 14 received Manuscript -al [email protected] E-mail: 57,20,p.1792±1794 pp. 2004, 85(7), nryadRsucsGop nvriyo aiona 1 arw al ekly aiona970USA 94720 California Berkeley, Hall, Barrows 310 California, of University Group, Resources and Energy iie admiration Limited H AU FNL HOISI ECOLOGY IN THEORIES NULL OF VALUE THE ÐT xlisparsimoniously explains .ÐMTE Ðh nxlie aine in variances unexplained .ÐThe ÐT esaieydemon- persuasively .ÐMTE ol aet eingre- be to have would ) EAOI HOYO ECOLOGY OF THEORY METABOLIC J OHN H ARTE hnmn titreit cls hr elive. we where physical scales, emergent intermediate encompass at also phenomena any could whether theory is however, such cos- clear, and Less subatomic the scales. at of mological all occur mean that that to phenomena achieve understood physical of well is ``theory ``everything'' may if a they goal of and goal this. (TOE), the than everything'' accept bounded physicists tightly all more Nearly are advances radical are ecology and ex- parsimony to immiscible. ecology; everything ex- in nearly to anything consider purports plain to MTE needs that One things plain. limited the just even rspri st dniystain nwihanon- a which science drives in forward. what is Failure situations needed. is identify alternative to null fail- us their null permit because and latter ures the hypotheses accomplish to null help stated models (empir- Clearly options testing). those narrowing ical na- and how work) might for ture options (envisioning possibilities larging than rather MTE. embracing, as such can haveÐby approaches we we dismissing, think than I farther because tend go hesitantly, I ``no.'' although resounding agree, a to with question possible?'' rhetorical TOE our a ecol- ``Is answer most probably that, would of en- ogists Because to warming. temporally global and compass geologic edges the with continent deal of to spatially contingency a would up grant scale of NSF to an scale have of also spatial scale temporal the the at and meadow organisms distribution of the abundance describes beautifully and that contingen- theory with A deal Unlike cy. to environment. has their ecology however, and inter- physics, other in each organisms with of action abundance and of all distribution scales, the temporal across and understanding, spatial interesting predictive ecologically and accurate an here? from would how there so, get if and we TOE ecology, in ecological possible it an Is like? sug- would look al. what et generally, Brown More as gest? trick, the and do evolution conceivably plus genetics MTE for could TOE phenomena, physics-based a biological skep- of dispel possibility to the successes unlikely about are ticism the MTE Although physics-based TOE. the of ecological the an provide for indeed can basis evolution, and genetics ulation support rw ta.(04,mkn h aefor case the making (2004), al. et Brown new proposed to responses science, of ®elds some In rgesi cec oe rmteitrlyo en- of interplay the from comes science in Progress least, very the at provide, would TOE ecological An 1 ugs htME ncmiainwt pop- with combination in MTE, that suggest , clg,Vl 5 o 7 No. 85, Vol. Ecology, Enthusiastic July 2004 METABOLIC THEORY OF ECOLOGY 1793

MTE also will surely fail if pushed too far. The un- there is no reason to restrict null theories to those that explained variances in the ®gures in Brown et al. (2004) are random. are undoubtedly just a preview of what will arise as A decade ago, a null metabolic theory of ecology the theory attempts to widen its domain of applicabil- could have been constructed around the body-mass-to- ity. A recently proposed ``neutral theory'' of ecology the-two-thirds-power scaling law, because that is a null (Hubbell 2001) is probably also ``wrong,'' and, indeed, expectation based on surface : volume ratios. All of the instances of its failure to accurately describe patterns equations that Brown et al. (2004) discuss could have in nature have been suggested (Condit et al. 2002, Clark been written then, with ⅔ replacing ¾, and an equally and McLachlan 2003). If ecology were physics, this comprehensive theory developed. Although such a the- might be considered suf®cient evidence to dismiss such ory was never constructed, falsi®cation of the two- theories entirely, but given the parsimony of both of thirds-power metabolic rule paved the way for what these theories, that would not promote progress in ecol- Brown et al. have accomplished. ogy. Just as it is the failures of null hypotheses and null Theories are of most interest when the ratio of the models that most enlarge our understanding, so it is number of predictions that they make to the number of the mismatches between collections of data and null assumptions and adjustable parameters in the theory is theories that make null theories useful. We should ex- large. The MT of Brown et al. (2004) and Hubbell's pect null theories to ``fail,'' just as we expect null hy- neutral theory are examples of theories based on very potheses and null models to fail under many circum- few assumptions and very few adjustable parameters, stances. However, by examining the instances in which yet they are potentially capable of predicting a wide a null theory fails to describe all of the data, and in range of phenomena. particular looking carefully at the patterns in the dis- Suppose that the interrelationships among many crepancies, we can establish more ®rmly the existence types of phenomena are reasonably well predicted by of mechanisms in nature that explicitly violate the sim- a theory, yet each phenomenon is, separately, better ple assumptions underlying the theory, and thereby predicted by some ad hoc explanation or cobbled-to- learn a great deal about how nature works. Whether gether model than by that theory. If those successful the outcome of this is an improvement of the null the- explanations or models each require a different set of ory or the development of a whole new theoretical Forum assumptions or parameters for each comparison, then construct may be less important than is the added in- it may be premature to reject the theory. In other words, sight into the mechanisms at work in ecology. the insight afforded by the theory into the intercon- Eventually, the patterns of success and failure of null nections among phenomena previously thought to be theories may suggest the outlines of an ecological the- disconnected ought to trump slightly better ®ts afforded ory of nearly everything. Such a theory, rising from by ad hoc explanations. the ashes of null theories, might even be considered As a natural extension of the idea of null hypotheses just another null theoryÐit won't really matter what and null models, I suggest that the notion of a ``null we call it. The important thing is that it be falsi®able, theory'' is of value in ecology. By a null theory, I mean and that it parsimoniously predict many more phenom- a set of relatively few and clearly stated assumptions ena than it has parameters to adjust. It would be ex- that can be used to make a comprehensive set of fal- citing if its base were broader than physics. si®able predictions about a wide variety of issues in MTE is certainly parsimonious and its predictions ecology. In contrast to null models, which address spe- match observations in nature to a remarkable degree ci®c ecological questions, null theories attempt to pro- over many orders of magnitude of variation in biolog- vide a single coherent set of answers to many questions. ical parameter space. At the same time, it appears so Without a null theory, those questions might have been far to be able to address only a modest fraction of considered independent of one another; a null theory questions of concern to ecologists. It is a ®ne example would unify them under one framework. Each of those of a null theory in that (1) it ties together multiple questions might be addressed with a null model, but phenomena within one set of extremely simple as- in typical applications of null models, a unique null sumptions, and (2) departures from its predictions can model is tailored to each question. Thus, there are many inform us about other factors besides metabolism and ways to create models of what nature might be like if temperature that are at work in ecology. In the search it were random. For example, random models for the for a TOE, or at least a more comprehensive null theory species±area relationship could involve random as- of ecologyÐone that would improve, and expand the signments of individuals, random assignments of spe- scope of, MTEÐBrown et al. should look forward to cies, or random shuf¯ing of census quadrats. If a com- MTE's failures with enthusiasm. mon set of assumptions about randomness were used to create an array of null models that together addressed LITERATURE CITED a comprehensive collection of questions, then the array Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and of models would ®t our notion of a null theory; indeed, G. B. West. 2004. Toward a metabolic theory of ecology. it might be called a random null theory. But surely Ecology 85:1771±1789. 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Theory et the Metabolic Brown by the outlined to (MTE) way work the This networks. paved biological fun- of of consequence attributes a 1999) damental as (1997, al. relationship et this West explains of that model the to metabolism of where etrfrAvne tde nEooyadBoiest n eatmnod Ecologõ de Departamento and Biodiversity and Ecology in Studies Advanced for Center n h ocnrto ftemtras( materials the of concentration the and blcequation abolic 04b h clgclSceyo America of Society Ecological the by 2004 h hoyi ae nwa ecl a call we what on based is theory The theory metabolic emerging the of success ultimate The growth, the controls and life sustains Metabolism 3 Ed- Corresponding 2003. October 20 received Manuscript odt . ta.20.Bt-dvriyi rpclfrs trees. forest tropical in forest diversity Beta- of 2002. Stability al. et 2003. R., Condit, McLachlan. S. J. and S., J. Clark, -al [email protected] E-mail: Science Nature biodiversity. EAOI CLG:LNIGIDVDAST ECOSYSTEMS TO INDIVIDUALS LINKING ECOLOGY: METABOLIC 1 P 57,20,p.1794±1796 pp. 2004, 85(7), T HEORETICAL stert fsm eaoi rcs,which process, metabolic some of rate the is 2 eateto ihre n idie ihgnSaeUiest,Es asn,Mcia 82 USA 48823 Michigan Lansing, East University, State Michigan Wildlife, and Fisheries of Department 295 :666±669. (GME): M F ETABOLIC P fbd as( mass body of I NTRODUCTION ϭ P ¾ U 423 ABLO F DRINNSO THE OF NDERPINNINGS oe a h etpredictor best the was power ( ,T R T, M, :635±638. .M A. T HEORY (1) ) M ARQUET ,tmeaue( temperature ), eCie lmd 4,Snig,Chile Santiago, 340, Alameda Chile, de EAOI HOYO ECOLOGY OF THEORY METABOLIC R eea met- general eddto needed ) , 1,3 F ABIO T ), .L A. l 20)adBone l 20) h ru htthe that argue who (2003), of al. effects et et Brown Gillooly and Following (2001) al. metabolism. maintain and fuel ABRA htteefcso ocnrto fmtrasi also is materials becomes of 1 concentration Eq. of multiplicative, effects the that ta bouetemperature absolute an at metabolism,'' eaoimadtemperature. a and of metabolism approximation between relationship an functional as complicated (2001) more much al. formulation et Boltzmann Gillooly by the We used consider metabolism. therefore comprise should that different of reactions number mechanistic large biochemical a very in the derive considering to fashion, dif®cult extremely approach metabolism be describing heuristic would in This factor de- Boltzmann reaction. the to using the used for of be rate can the factor scribe to Boltzmann energy the suf®cient Hence, the attain react. increases that Temperature molecules of 1970). proportion (Pauling must state change to they energy their suf®cient is, with another that one with energy,'' collide ``activation possess must ubl,S .20.Teuie eta hoyo biodiversity of theory neutral uni®ed The 2001. 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The concentration of resources (R, or stoichiometry) say that the interesting biology is in the scatter and that is the third component of the GME. However, its re- such a thing as an average ecological system does not lationship to metabolism lacks an analytical expres- exist, but just different realizations of the average sys- sion, which prevents the MTE from making explicit tem, it is important to recognize that unless we have a how it interacts with T and M in affecting individual mechanistic theory that provides us with an expected or population attributes. At ®rst glance, it is not entirely baseline, we are not able to identify any deviation worth clear how to include stoichiometric effects in the GME explaining in the ®rst place. In this sense, both ap- (the function f in Eq. 2). However, it is reasonable to proaches are interesting and complementary. expect that f should have a multiplicative effect on We have no doubt that the MTE can provide many metabolism, and because organisms often show a insights on fundamental ecological questions at local, ``functional response'' in reaction to changes in the regional, and global scales. In particular, at a local abundance of a limiting resource, f could be modeled scale: (1) it provides an explanation of why, in a local as a Michaelis-Menten function (Real 1978, Maurer community, population density should scale as MϪ3/4 1990). If the ingestion rate is proportional to the met- within trophic levels and as MϪ1 across them, a pattern abolic rate, then one would expect that metabolic pro- that has been empirically observed in aquatic ecosys- cesses, such as biomass production, would show a sim- tems (e.g., Marquet et al. 1990); and (2) it predicts that ilar sort of saturating response and that the Michaelis- population energy use should be independent of body Menten equation could be used. There is, in fact, ex- mass within trophic levels, but should decrease at high- perimental evidence that such responses do occur er trophic levels. Further, the amount of energy that (Giebelhausen and Lampert 2001). moves from one level to the next should be affected Interestingly, each term in the GME relates to pro- by the characteristic metabolic scaling of the species cesses whose primary mechanistic effects occur on dif- in each trophic level. However, there are other impor- ferent spatial and temporal scales. Temperature has its tant patterns within local communities, such as species primary effect at the molecular scale, by in¯uencing abundance and species size distributions, to which the the rate of molecular movements through the parts of MTE could be applied, and that, in principle, it should the metabolic machinery that depend on passive dif- be able to explain, since they affect and are affected fusion. Body size affects metabolism at a larger scale by energy ¯uxes. Forum via constraints derived from fractal-like distribution A close examination of the MTE shows that several networks. Finally, stoichiometric effects occur at the predictions can be made regarding the effects of re- scale of the whole organism in interaction with its en- source supply upon equilibrium abundance and how vironment. This feature of the GME bequeaths the MTE abundance should vary across resource and tempera- with a desirable property: cross-scale integration. ture gradients for metabolically different organisms. In We think that the MTE still requires re®nement and particular, Eq. 9 of Brown et al. (2004) states that the further articulation. However, there is suf®cient evi- equilibrium number of individuals or carrying capac- dence to suggest that the MTE may provide a funda- ity (K) in a local community should vary as K ϰ mental theoretical link between what we know about RMϪ3/4eE/kT. Further, because metabolic rate (P)isP ϰ physical systems and what we know about ecological M 3/4eϪE/kT (Brown et al. 2004: Eq. 4), we can express systems. carrying capacity as THE MTE AND THE STRUCTURE OF LOCAL R ECOLOGICAL SYSTEMS K ϰ . (3) P The MTE rests heavily on individual-level phenom- ena, which by aggregation allow one to make predictions Eq. 3 implies that, given a ®xed amount of resources upon whole-system patterns, processes, and rates. It is R, organisms with lower metabolic demands will striking how strong the ®t between predicted and ob- achieve higher equilibrium population numbers or car- served patterns usually is, considering that most data on rying capacities. For any given temperature, mass-cor- individuals and species populations come from different rected metabolism is higher in some groups than others places around the world, with different biogeographic (see Brown et al. 2004: Fig. 1a); thus, everything else histories, disturbance regimes, and productivities. It being equal, carrying capacities should follow the in- might seem striking that a theory that is, for the most verse pattern, decreasing from plants to endotherms. In part, free of ecological context (Marquet 2002) can be other words, there should be a negative relationship so powerful. However, this is to some extent expected, between the intercept of the mass-corrected relation- given that the theory focuses on ``bulk properties'' of ship between metabolic rate and temperature and the ecological systems that are less affected by local eco- total abundance of metabolically different organisms logical idiosyncrasies. The MTE is a theory about central in a given community. This relationship would be even tendencies in ecological phenomena that predicts how stronger if we were to consider trophic structure and the average individual, population, and ecosystem the fact that energy or resources become more limiting should behave and be structured. Although many would farther up in a food chain. Because organisms with Forum sssos(i.1 htteei nedangtv re- negative a indeed is there ( that lationship 1) (Fig. shows be ysis anal- should Our demands. group metabolic metabolic with correlated given spe- inversely community, any local in 1983, a diversity Wright in cies that (e.g., predicts energy 1991), diversity of Currie effect species the on explain the availability to to used similar with traditionally argument, groups one This for needs. expected metabolic higher be lower Thus, should persistence. the richness for above species required species different size of minimum populations sustain sup- more average, to on port will, likely they more numbers, population are higher demands metabolic lower exp(15.6 1796 rse steitreto h ascretdmtblcrate metabolic ( mass-corrected the temperature of vs. intercept the as pressed pce xrse steitreto h pce±racurve species±area the of intercept ( the as expressed species iecrepnst h et® xoeta equation exponential best-®t the solid The to available. were corresponds groups all line use on only data we which system, land for each reptiles, islands Within plants, mammals. include and and birds, Indies, snails, West and Cortes, of C etbepeitost dac u nesadn of understanding and our insights advance fruitful to provide can predictions MTE testable the that is ysis seems pattern this. be- the to groups yet robust species be position, all to trophic for their same of the cause not resource addition, is In rate islands. supply on species affect of signi®cant metabolism number especially besides the factors is other It pre- many MTE. and because the value of rela- heuristic power this the dictive That indicates islands. exists in tionship organisms of groups ferent h necp fteseisae relationship species±area the by of (represented intercept species the of number area-corrected the blcrt s temperature, vs. rate rate met- abolic mass-corrected the metabolic of intercept mass-corrected the by (represented and temperature- the F S ,adms-adtmeauecretdmtblcrt ex- rate metabolic temperature-corrected and mass- and ), h anpitta ewn omk ihti anal- this with make to want we that point main The IG .Rltosi ewe racretdnme of number area-corrected between Relationship 1. . Ϫ 0.75 F 1,12 C C ϭ M M ). .Dt r o h hne sad,Sea Islands, Channel the for are Data ). 67.07, P Ͻ C 0.001, M o eaoial dif- metabolically for ) r 2 EAOI HOYO ECOLOGY OF THEORY METABOLIC ϭ .4 between 0.84) C S and ) C S ϭ n ucin rte`eooe' a ept aethe save earth. to on help enterprise can abundance, ``econome,'' human composition, the or in species function, systems total and ecological their characterize of to terms to help but can dollars lives, genome of human save millions the sequencing and in years invested 13 The eco- of systems. analyses logical might complete and This understanding, comprehensive our scale. need in advance we local to but a task, daunting at a be predictions MTEs tests the rigorous for of allow will which the biodiversity, standardized on on of data need We data activity ecosystems. local metabolic better within and species and biomass, more density, of re- richness, will collection approach the this of quire testing and development fur- However, ther systems. ecological local of structure the rw,J . .F iloy .P le,V .Svg,and Savage, M. V. Allen, P. A. Gillooly, F. J. H., J. Brown, rw,J . .F iloy .B et n .M Savage. M. V. and West, B. G. Gillooly, F. J. H., J. Brown, 01(oht .A aqe)adaCNCTgaut fel- graduate CONICYT Labra. a A. and F. Marquet) to A. lowship P. 1501- to (both FONDAP-FONDECYT 0001 Fellowship, through Institute International Fe Santa Storch. an the David of support and the Gillooly, acknowledge James We Savage, Van Dunne, iffer iblasn . n .Lmet 01 eprtr re- Temperature 2001. Lampert. W. and B., Giebelhausen, ure .J 91 nryadlresaepten fanimal of patterns scale large and Energy 1991. J. D. Currie, el .A 98 h ieiso ucinlrsos.Amer- response. functional of kinetics The 1978. A. L. Real, New York, New Dover, chemistry. General 1970. L. Pauling, et .B,J .Bon n .J nus.19.Tefourth The 1999. Enquist. J. B. and Brown, H. J. B., G. West, general A 1997. Enquist. J. B. and Brown, H. J. B., Dover, G. West, thermodynamics. Statistical 1941. E. Schrodinger, rgt .H 93 pce±nryter n xeso of extension and theory Species±energy 1983. H. D. Wright, arr .A 1990. A. B. Maurer, iloy .F,J .Bon .B et .M aae and Savage, M. V. West, B. G. Brown, H. J. F., J. Gillooly, aqe,P . .A aart,adJ .Csil.1990. Castilla. C. J. and Navarrete, A. laws. S. power A., and P. prey, Marquet, predators, Of 2002. A. Hilgardia P. metabolism. Marquet, and size Body 1932. M. Kleiber, .B et 04 oadamtblcter fecology. of theory metabolic a Toward Ecology 2004. West. B. G. iia atrst nvra clgcllw.Pgs408± Pages em- laws. general ecological from universal 423 macroecology: to in patterns step pirical next The 2003. eapeit omnsaddsuso rvddb Jen- by provided discussion and comments appreciate We cinnrsof norms action 49. n ln pce ihes mrcnNaturalist American richness. species plant and Ox- Blackwell, UK. consequences. ford, and concepts croecology: raiain clgclModelling hierarchical Ecological and organization. competition, regulation, systems: cessing cnNaturalist ican USA. York, n fognss Science scal- organisms. allometric the of and ing geometry fractal life: of dimension biology. in laws scaling allometric of Science origin the for model USA. York, New York, New pce±rater.Oikos theory. species±area .L hro.20.Efcso ieadtmeaueon temperature and size of Science Effects rate. metabolic 2001. Charnov. L. E. Biology Freshwater centration. cln ouaindniyt oysz nrcyintertidal rocky in size Science body communities. to density population Scaling Science 315±332. in .M lcbr n .J atn dtr.Ma- editors. Gaston, J. K. and Blackburn M. T. 85 276 295 :1771±1789. :122±126. :2229±2230. 111 ahi magna Daphnia A L CKNOWLEDGMENTS Dipodomys :289±300. ITERATURE 250 293 :1125±1127. 284 41 :2248±2251. :496±506. :1677±1679. ouain seeg pro- energy as populations C 46 h feto odcon- food of effect the : ITED :281±289. clg,Vl 5 o 7 No. 85, Vol. Ecology, 50 :157±176. 137 :27± 6 : July 2004 METABOLIC THEORY OF ECOLOGY 1797

Ecology, 85(7), 2004, pp. 1797±1799 ᭧ 2004 by the Ecological Society of America

DOES METABOLIC THEORY APPLY TO COMMUNITY ECOLOGY? IT'S A MATTER OF SCALE

DAVID TILMAN,1 JANNEKE HILLERISLAMBERS,STAN HARPOLE,RAY DYBZINSKI,JOE FARGIONE, CHRIS CLARK, AND CLARENCE LEHMAN Department of Ecology, Evolution and Behavior, 1987 Upper Buford Circle, University of Minnesota, St. Paul, Minnesota 55108 USA

When the seven of us read and discussed Brown et Might growth rate (McMahon and Bonner 1983) be the al. (2004), there were moments of insight, of enthu- controlling variable, rather than metabolic rate? Or siastic consensus, and of strongly divergent opinion. might body size and metabolism be easily measured We agreed that the empirical relations and scaling the- surrogates of the actual traits that determine species ory of Brown et al. (2004) hold great appeal because interactions and abundances? After all, within the of their power to abstract and simplify some of the framework of community ecology, it is traits such as complexity of nature. The earth harbors several million competitive ability, dispersal, and predator defenses, species, each having unique aspects to its morphology, and not metabolism and body size, that directly deter- physiology, and life history. A fundamental goal of mine which species win or lose, which persist and spe- science is to simplify and explain such complexity. ciate, or which go extinct. Brown et al. (2004) do just this. They have documented Of the various predictions that Brown et al. (2004) robust patterns relating the body size and temperature derived, perhaps the most surprising to community of species to their basal metabolic rate; plotted on log± ecologists may be that within a trophic level, species log scales, these empirical functions are well ®t by of vastly different body sizes should get equal shares straight lines. Moreover, they have used these scaling of their limiting resources. Simply put, all of the her- Forum relations to make numerous predictions about other pat- bivorous arthropods within a 10-fold range of body terns and processes, thus greatly extending an approach sizes should consume roughly the same amount of food that already had been shown to have considerable pow- as all of the herbivorous mammals within a 10-fold er (e.g., Huxley 1932, McMahon and Bonner 1983, range of body sizes. This suggests that, on average, Peters 1983, May 1986). species should be getting approximately equal-sized One question that generated considerable debate ``slices'' of the limiting resources for which they com- among us was whether metabolic scaling theory rep- pete. Does this mean that there are limits to similarity resents a fundamental mechanism that has shaped life that lead to relatively even packing of competing spe- on earth, or whether it is a description of correlated cies along gradients? If so, what mechanisms could patterns of as yet poorly known causes. Brown et al. cause this, and how would community ecologists test (2004) hypothesize that scaling relations have a fun- this prediction in the ®eld? damental basis that comes from the universality of met- Another prediction made by Brown et al. (2004) is abolic activation energy and of the fractal branching that higher temperatures in the tropics may lead to fast- networks that determine resource distribution within er metabolism, shorter generation times, and thus faster individual organisms. This elegant hypothesis intrigued rates of speciation, accounting for the latitudinal bio- us. It brought to the forefront questions raised when diversity gradient. This is an interesting alternative to we spent a semester last year reading many of the pa- other hypotheses for latitudinal diversity gradients, pers upon which Brown et al. (2004) is based. Are such as the hypothesis that diversity is lower toward slopes really multiples of ¼, or is this just the best the poles because of higher rates of extinction from a small-whole-number ratio approximation? How might less stable climate and glaciation, or that there are few- mechanical constraints, which may scale differently er ways to survive and grow in progressively colder with body size (e.g., McMahon and Bonner 1983), con- habitats because life is a water-based (not an ice-based) tribute to these patterns? Larger organisms must, after process. The metabolic approach may also offer insight all, have a higher proportion of their mass in woody into r vs. K selection. Brown et al. (2004) suggest that stems or bones or other support tissues that have low species selected for fast population growth rates would metabolic costs but high costs for their construction. necessarily have higher metabolism, smaller body size, and higher temperature. K-selected species are not nec- Manuscript received 3 November 2003. Corresponding Editor: A. A. Agrawal. For reprints of this Forum (including essarily selected for slow population growth rates, but the MacArthur Award paper), see footnote 1, p. 1790. this may be a consequence of selection for predation 1 E-mail: [email protected] resistance or resource use ef®ciency, which often are Forum in fpplto n omnt clg,sc as such ecology, ques- community central and the population of of many tions addressing in useful prove bacteria from as ecosystems. such in species, sequoias, of to by range caused size ¯uxes large energy the and nutrient in- ecosystem understand- for of and ing may, parameterization better theory allow Metabolic interactions stance, ab- essential. impossible, the are is ecosystem an straction of in species treatments all among de- Because mechanistic 1A). (Fig. eco- tailed, globe an the within or megafauna) continent, to system, microbes sizes body from ex- of as when spectrum (such wide best a hold across relationships patterns amining scaling It that theory. clear scaling is metabolic of applicability of breadth nature. of complexity some the abstract of to and dimensionality reduce pow- to a al. way be erful can et relations Brown scaling in that demonstrate predictions (2004) the com- be, making underlying might the when mechanisms Whatever traits scales. ab- broad correlated to across size, of parisons body suite variable, a single a stract but of relevance, may ability mechanistic the relations direct from scaling their from of again not robustness come examples the These that size. suggest body larger by enhanced 1798 aineaon h ersinlnsi is ,3 ,ad6o rw ta.(04 sn h lp,nme fsml points, sample of number slope, the using (2004) al. et Brown of 6 and 5, 3, unexplained 2, the calculated Figs. we First, in size. lines of and power regression explanatory the the and around studied sizes variance organism of range the between relationship ags(rm0t h ierneue nBone l 20].Lnscnettemean the connect Lines [2004]). al. et Brown in used range size the to 0 (from ranges est.Nx ecalculated we Next density. ierne h etclai stenme fppr htsuidseisi htrange. that in species studied that papers of number the is axis vertical the range; size est)uigosre lpsaditret n siae aine ial,w sdsml ierrgesost calculate to regressions linear simple used we population Finally, and variance. rate, estimated growth and population generated mortality, next intercepts We ®sh and range. rate, the size slopes growth speci®ed biomass observed a predicted between using (i.e., sizes density) species body each of for distribution variables uniform response a from ``species'' 100 sampled randomly F ti escer oee,i eaoi cln will scaling metabolic if however, clear, less is It the about though, debate, considerable had We ierneo tde raim,bsdo aesi h journal the in papers on based organisms, studied of range Size IG R R eeecdseicognsso ye fognss(9 aesfo sus19 oue8,20) etbltdthe range tabulated size magnitude We of 2003). orders 84, the volume determined then 1±9, and issues classes, from size papers to them (190 log assigned the organisms paper, between (difference of each in types described or organisms organisms speci®c referenced 2 2 .()Peitv oe fbd ie eue h aai rw ta.(04 n iuain oepoethe explore to simulations and (2004) al. et Brown in data the used We size. body of power Predictive (A) 1. . ewe raimsz n h rcs fitrs.W eetdti 0 ie o aho 0 qal itiue size distributed equally 200 of each for times 200 this repeated We interest. of process the and size organism between frltosisbtensz n raimlboasgot ae s otlt,pplto rwhrt,adpopulation and rate, growth population mortality, ®sh rate, growth biomass organismal and size between relationships of 10 R siae asi rm ftelretadsals raim) h oiotlai sorganism is axis horizontal The organisms). smallest and largest the of grams in mass estimated 2 o iuae aast fseiscvrn arwrrne nbd ie od hs we this, do To size. body in ranges narrower covering species of sets data simulated for EAOI HOYO ECOLOGY OF THEORY METABOLIC raim fsmlrbd iecnhave can size body similar of organisms grass prairie forb. large a prairie or a looms oaks, with to elephants trees beech to comparing when bacteria small so seems comparing (Fig. that traits decreases when species sizes in body variation The size in 1A). range body the and as correlation processes diminishes the ecological of strength various the between that shows (2004) Brown by al. reported et relations the of similar-sized analysis often An species. among interactions local of mech- anisms community the exploring of by questions Much Elser these pursues 2003). and ecology Leibold Sterner and 2001, Chase diversity Hubbell 2002, of 1999, and Tilman patterns, (e.g., of abundance coexistence, relative of species controls and regulation population h aapeetdi rw ta.(04 hwthat show (2004) al. et Brown in presented data The ogl afo apeo aesrcnl published recently papers of ecology; sample in of a part of half central roughly Such a size. in are similar however, ability more comparisons, of predictive organisms limited of comparisons increasingly relations have Scaling 1A). thus (Fig. a sizes within body fall in vari- range species observed 10-fold when the responses predicted of in 2±20% ance only that explains show data size these body Moreover, traits. their in ferences Ecology Ecology eeaie l eetppr in papers recent all examined We . oue nol n pce ro several on or species one only on focused R 2 ausfrec ierne (B) range. size each for values clg,Vl 5 o 7 No. 85, Vol. Ecology, Ͼ 0fl dif- 20-fold Ecology that July 2004 METABOLIC THEORY OF ECOLOGY 1799 species that were within an order of magnitude in body at small scales. The vast diversity of alternative roles mass (Fig. 1B). that can be ®lled by organisms of equal body size prob- Much of our recent work has focused on how the ably accounts for the Ն20-fold variation observed identity and number of grassland plant species inter- around the mean scaling trend. Perhaps when compar- acting in a local neighborhood in¯uences processes isons are made across larger body size ranges, the con- such as primary productivity. The species that we study straints of body size and its correlates increasingly pre- are herbaceous perennials that differ by less than ¾ of dominate over the interspeci®c trade-offs in resource an order of magnitude in adult body size. In our bio- use, dispersal, and disease resistance that are the more diversity experiment (Tilman et al. 2001), the number proximate determinants of species interactions and of plant species explained 37% of the variance in total abundance. If, as seems likely, scaling relations do have biomass in 2002 (linear regression: N ϭ 168, P Ͻ their basis in metabolic activation energy, fractal 0.0001). Species number and functional group com- branching, and structural constraints, then these forces position explained 68% of this variance in total bio- must be acting at a deeper level, such as by de®ning mass (multiple regression: F28, 139 ϭ 10.4, P Ͻ 0.0001). body size and metabolic constraints that shaped the The scaling approach, which works so well across large form and functioning of life as single-celled organisms scales of body size, predicts at most 12% of the vari- evolved into multicellular plants and animals. ance in various ecological processes for the range of In summary, Brown et al. (2004) have provided a body sizes in our study (Fig. 1A). Thus, on our scale, new window through which we can ponder nature. The plant functional traits and plant diversity are much simplicity and potential generality of the view that they more important than body size. Conversely, our work provide is welcome; ecology as a discipline cannot af- on the local neighborhood effects of diversity gives ford to wallow in special cases. Metabolic theory pro- little, if any, insight into the potential relationship be- vides a unique and insightful macroscopic perspective, tween diversity and productivity on geographic scales one that appears to have great utility for comparisons where species come from different species pools and of organisms of vastly different sizes. The possible where other factors, such as climate, soil, and plant causes of these patterns, the applicability of the ap- traits, are correlated and change simultaneously. proach to studies of similar-sized organisms, and the

An analogy and an insight into the power and limits potential synthesis of mechanistic and macro-ecolog- Forum of the scaling approach come from a consideration of ical approaches are challenges that are likely to be pur- another complex system with which we are familiar: sued for years to come. computers and related digital devices. Like an organ- LITERATURE CITED ism, a silicon circuit has a metabolism, measured by Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and how much electricity it consumes. The volume of in- G. B. West. 2004. Toward a metabolic theory of ecology. Ecology 85:1771±1789. formation that a digital device can process, the air¯ow Chase, J. M., and M. A. Leibold. 2003. Ecological niches: needed to cool it, its reliability and longevity, and other linking classical and contemporary approaches. University properties are all a function of its size and, thus, its of Chicago Press, Chicago, Illinois, USA. metabolism. Such macroscopic properties of digital de- Hubbell, S. P.2001. The uni®ed neutral theory of biodiversity and biogeography. Monographs in Population Biology, vices are essential for whole-system tasks like design- Princeton University Press, Princeton, New Jersey, USA. ing power supplies and writing warranties. The rela- Huxley, J. S. 1932. Problems in relative growth. Methuen, tionship of metabolic scaling to ecology is analogous; London, UK. it gives signi®cant insights into macroscopic ecological May, R. M. 1986. The search for patterns in the balance of nature: advances and retreats. Ecology 67:1115±1126. patterns and predicts other patterns and processes McMahon, T. A., and J. T. Bonner. 1983. On size and across large scales and whole systems. Many different life.Scienti®c American/W. H. Freeman, New York, New functions, however, can be performed by digital de- York, USA. vices with identical sizes and energy demands, just as Peters, R. H. 1983. The ecological implications of body size. many different ecological roles can be performed by Cambridge University Press, New York, New York, USA. Sterner, R. W., and J. J. Elser. 2002. Ecological stoichiometry. organisms of similar size and temperature. It is these Princeton University Press, Princeton, New Jersey, USA. ecological roles, not metabolisms per se, that determine Tilman, D. 1999. The ecological consequences of changes species coexistence and abundances and ecosystem in biodiversity: a search for general principles. Ecology 80: functioning. 1455±1474. Tilman, D., P. B. Reich, J. Knops, D. Wedin, T. Mielke, One of the mysteries of scaling theory is why it has and C. Lehman. 2001. Diversity and productivity in a such great explanatory power at large scales, but not long-term grassland experiment. Science 294:843±845. Forum i Kelvin), (in Ϫ ᭧ Ecology, 1800 rm fcro e qaemtrprya) h MTA The familiar year). per the (in meter that predicts Productivity square on per Primary carbon us Net of grams like places metrics which of grounds energy, on focus h aAtu wr ae) e otoe1 .1790. (including p. Forum 1, this footnote of see paper), reprints Award For MacArthur Agrawal. the A. A. itor: ie n hteprec h aeevrnet This environment. same similar of the of formulation experience resources, that same and the size, by limited ectotherms es u stenme fc-curn nrytrans- energy co-occurring of number formers. with the units as reproductive but mortal, of legs, arrival net the as not years for subject this come. on to work It guide 2000). to potential al. the et has Kaspari mass 1971, a (Odum uses approach Metabolic MTA), balance the (henceforth answer, Abundance Their of time? Theory move and we space as in vary abundance about equilibrium should at how communities entire question: in different a Ecology on of focus Theory Metabolic the introducing in (2004) ta.1996). groups Siemann al. (e.g., functional study et of and worthy taxa themselves shown higher have of habits, trophic abundance size, and body the But school. demographic est hs eore,adtewytersucsare resources the individuals: way among the up and divided resources, those to cess R prahhsbe eorpi (i.e., this demographic of been has basis approach conceptual tradi- pop- The species timeÐhave generations. local and over of area ulations dynamics given the on a focused in tionally taxon a of uals [ eeeaigfnto fevrnetltemperature environmental of function decelerating eV ok n ec oacs vial [ available metabolic access do to to hence cells and living work, this of support ability to The presented prediction. are data no although paribus, 04b h clgclSceyo America of Society Ecological the by 2004 SN H EAOI HOYO CLG OPEITGLOBAL PREDICT TO ECOLOGY OF THEORY METABOLIC THE USING stersuc upyrt.Bonadcolleagues and Brown rate. supply resource the is ] tde faudne( abundance of Studies et rate death 1 Ed- Corresponding 2003. October 14 received Manuscript rw n olausaku opcueabundance picture to us ask colleagues and Brown nteMTA, the In ϭ -al [email protected] E-mail: 64 Jml,and kJ/mol), 96.49 57,20,p.1800±1802 pp. 2004, 85(7), K steeulbilaudneo individual of abundance equilibrial the is K E ϩ hudices ierywt [ with linearly increase should K steatvto nry( energy activation the is K irto ae.Bonadcolleagues and Brown rate). migration eateto olg,Uiest fOlhm,Nra,Olhm 31-25USA 73019-0235 Oklahoma Norman, Oklahoma, of University Zoology, of Department a esrnet clgssfo the from ecologists to strange be may K aiswt eoreaalblt,ac- availability, resource with varies I ϳ NTRODUCTION [ R ] k N Me sBlzansfco.This factor. Boltzmann's is Ðh ubro individ- of number )Ðthe Ϫ 3/4 E/kT ATRSO ABUNDANCE OF PATTERNS (1) . EAOI HOYO ECOLOGY OF THEORY METABOLIC dN/dt R ,i negative a is ], ϳ ϭ .3e;1 eV; 0.63 R it rate birth M ,ceteris ], ICHAEL T K K by ®nd captured To group. energy trophic of or taxon amount our the far So described 2002). have al. et col- we (Allen a ectotherms for animal messily, of more lection and trees, for holds prediction h supinta h rprino [ of (an proportion group the that trophic with assumption come same the would abundance the taxon ideally on of abundance focus members alternative that all specify to to refers colleagues careful and are Brown (2004) respired, and excreted, vested, to- pulls cor- it priori Finally, a [ temperature). gether by and (e.g., mass data for our recting plot we way even the would change and other 1981), predicts (Damuth patterns 1997), long-standing non-intuitive Gaston of and shape (Blackburn the patterns addresses principles, ®rst attoe yidvdas eas vial energy available Because [ individuals. by partitioned ASPARI Suhod17) ukl,tretilbonfood habitats pred- their brown and across microbivores, terrestrial microbes, (detritus, standardize webs Luckily, to 1978). hard (Southwood are abundance relative and estimators count to hard are mo- because organisms however, bile scarce, are data Such ecology. of iisd efc sw eru ots h MTA? the test to up gear we opportu- as and face challenges we do what nities So isolation. in treated inso [ of dients R R t hl-raimmtbls aesae to scales use rate to metabolism capacity individual's Whole-organism the it. on based up divided be aooi clssann ra ag of and range spatial broad broad a at spanning tested scales be taxonomic to meant 1995), (Brown ru.Pat r loes ocut u hr r the are where for But count. sets to data easy trophic also are unambiguous Plants an group. occupy global Plants mined (Enquist sets. has MTE 2001) data Niklas in plant and sur- work Enquist not early 1998, al. thus the et is of It much sites). that across prising invariant is taxon that otlt rmpeaini sue ob negligible with be invariant to least 1992); assumed at (Power or is bottom-up predation MTA re- explicitly from the and thus mortality harvested sum, is is In It energy spired. 1998). available how al. on et focuses Enquist 1981, muth [ hudb eaiedclrtn ucinof function decelerating negative a be should teutsec iecro-ihmlclsaehar- are molecules carbon-rich time each attenuates ] from builds It do. should theory good what does It ]. h T oue nhweeg scpue and captured is energy how on focuses MTA The lblaudnedt essol eabscgoal basic a be should sets data abundance Global T h T sacerofpigo macroecology of offspring clear a is MTA The SIGTHE ESTING 1 R ], R T and ] and , consumer MTAÐQ T M ? he atr hthv fe been often have that factors three , bnac cosgoa gra- global across abundance ,T, M, UANTIFYING n [ and clg,Vl 5 o 7 No. 85, Vol. Ecology, K hseeg must energy this , R R ]. A avse by harvested ] BUNDANCE ,T, M, M M 3/4 (Da- ,so and July 2004 METABOLIC THEORY OF ECOLOGY 1801

TWO VARIATIONS ON A THEME OF METABOLISM AND ABUNDANCE The MTA characterizes environments by their mean [R] and T. Both, however, become more seasonal mov- ing from the equator toward the poles. The MTA may thus ignore a key reality of ectotherm life: metabolic costs and productivity vary seasonally. For example, in all but the most productive biomes (i.e., wet tropical rain forests), the same NPP can be squeezed into a few months or spread out over the year (contrast tundra with mediterranean shrubland). In a seasonally cold biome where NPP is concentrated in the summer FIG. 1. Studies of 49 ant communities arrayed along the months, ectotherms can eat when food is plentiful and productivity gradient ([R] is the resource supply rate) show respire less of that energy away when winter comes. that trophic groups accumulate at different rates with net In contrast, an ever-warm environment extracts year- aboveground productivity (Kaspari 2001). Note the log±log scale. long respiration costs. Somewhat counterintuitively then, environments with winters can provide a meta- bolic refuge and enhance K compared to aseasonal en- vironments with the same mean [R] and T (Kaspari et ators) address many of these limitations (Copley 2000): al. 2000). Seasonality matters. This may be another they occur everywhere from the poles to the tropics; reason for the observation of Allen et al. (2002) that 2 they can be quanti®ed in 1-m plots (Coleman and Cros- N's for ectotherms, but not endotherms, decline toward sley 1996); and the taxa (the microbivores in a patch the warm tropics. of litter may include ciliates, rhizopods, nematodes, Finally, holding [R] and T constant, K is predicted collembola, oribatids, millipedes, and ants) span a to decrease as MϪ3/4. But why should M vary from place range of M (Moore et al. 1988). I am con®dent that the to place? Intriguingly, two of the leading models for

MTA will foster the collection of new abundance data body size gradients have [R] and T as their independent Forum in the same way that quantitative biodiversity theory variables. Where predation risk is high, the optimal (Rosenzweig 1995, Hubbell 2001, Allen et al. 2002) is body size should decrease with NPP (Kozlowski 1992). promoting studies of species richness. Ectotherm size at maturity has long been shown to Ecological stoichiometry constitutes a second chal- decrease with T (Atkinson 1995). If community body lenge to the MTA. Individuals regularly confront ele- size gradients are real, this suggests that where M is a mental de®cits beyond carbon (Mertz 1987). For ex- function of T and [R], the MTA may be overparame- ample, primary consumers from the green and brown terized! food webs (herbivores and decomposer microbes, re- spectively) appear especially likely to face stoichio- PROSPECTS metric imbalances (Kaspari and Yanoviak 2001, Stern- The MTA challenges community ecologists to look er and Elser 2002, Davidson et al. 2003). How can an beyond our traditional focus on species toward the energy-based theory deal with environmental de®cits properties of higher taxa and functional groups. It chal- in elements like N, P, and Mb? lenges us to pursue fundamental natural historyÐsize, One solution is to quantify the energy costs of those abundance, trophic relationshipsÐfor all taxa at a glob- activities required to meet elemental de®cits. The her- al scale. As ecologists, we obviously have some dis- bivores that travel to ®nd limiting sodium-rich plants tance to go before we understand even the basic pat- (Belovsky 1978) or that compensate for defensive com- terns of abundance. The MTA provides one interesting pounds in their food (Berenbaum and Zangerl 1994) and quantitative road map for the journey ahead. are both doing so by catabolizing sugars. If so, the slope of the [R]±K curve should be an inverse function of ACKNOWLEDGMENTS the group's stoichiometric de®cit. For example, soil ant This material is based upon work supported by the National abundance increases as NPP3/4 (net primary production, Science Foundation under Grant No. 0212386. as yet uncorrected for M; personal observation) across LITERATURE CITED the New World (Kaspari et al. 2000). Different ant Allen, A. P., J. H. Brown, and J. F. Gillooly. 2002. Global trophic groups, however, accumulate differently (Fig. biodiversity, biochemical kinetics, and the energetic-equiv- 1; see Kaspari 2001). Herbivore abundance increases alence rule. Science 297:1545±1548. slowly with NPP, predators and fungivores more quick- Atkinson, D. 1995. Temperature and organism sizeÐa bio- ly. Omnivores have an intermediate slope. A working logical law for ectotherms? Advances in Ecological Re- search 25:1±58. hypothesis is that ant herbivores have low [R]±K slopes Belovsky, G. 1978. Diet optimization in a generalist herbi- because they must work harder than predators to meet vore: the moose. Theoretical Population Biology 14:103± their stoichiometric de®cits. 134. Forum ᭧ Ecology, 1802 hoycudln clg sawoei neetn and interesting metabolic is whole a a as that is ecology claim link approach could The the theory terms, reasonable. general and in familiar biology thus, of ecology; aspects have many and drive stoichiometry to recognized and been temperature, long size, Body think- ecological ing. unify to framework mechanistic of- a constraints, fers stoichiometric and include effects to al. temperature expanded et metabolism, general for their (West that model argue do allometric al. et they Brown Here, that 1999). of 1997, everything size body and the organisms between relationships ubiquitous explaining in the interest of resurgence recent a of forefront aAtu wr ae,sefont ,p 1790. p. the 1, including footnote Forum see this paper, of Award reprints For MacArthur Agrawal. A. A. itor: 04b h clgclSceyo America of Society Ecological the by 2004 ae rw n i olaus(04 r tthe at are (2004) colleagues his and Brown James 1 Ed- Corresponding 2003. October 20 received Manuscript ubl,S 01 h n®dnurlter fbiodiversity of theory neutral uni®ed The 2001. S. re- Hubbell, scaling Invariant 2001. Niklas. J. K. and J., B. Enquist, Allometric 1998. West. B. G. and Brown, H. J. J., B. Enquist, Chua. H. T. and Snelling, R. R. Cook, C. S. W., D. Davidson, den- population of allometry Interspeci®c 1981. J. Damuth, oly .20.Eooyge negon.Nature underground. goes Ecology 2000. J. of Fundamentals Copley, 1996. Crossley. A. D. and C., and D. Coleman, Savage, M. V. Allen, P. A. Gillooly, F. J. Chicago, H., of J. Brown, University Macroecology. 1995. H. J. Brown, assess- critical A 1997. Gaston. J. K. in- and M., of T. Costs Blackburn, 1994. Zangerl. R. A. and R., M. Berenbaum, -al [email protected] E-mail: n igorpy rneo nvriyPes Princeton, USA. Press, Jersey, New University Princeton biogeography. and Nature communities. 655±660. tree-dominated across lations Nature density. population and 395 energetics plant of scaling tropical Science lowland in canopies. ants rainforest of abundance the Explaining 2003. Journal Society Biological of Linnaean use. independence the energy the of population animals: and other mass and body mammals in sity 452±454. oleooy cdmcPes e ok e ok USA. York, New York, New Press, Academic ecology. soil ecology. of theory metabolic a Toward Ecology 2004. West. B. G. USA. Illinois, Animal Chicago, of Journal animals. in between size relationship Ecology body interspeci®c the and of abundance form the of ment Ecology detoxi®- webworms. and parsnip growth, in limitation, cation protein defense: ducible 57,20,p.1802±1804 pp. 2004, 85(7), :163±165. 85 66 :1771±1789. :233±249. NILSO FMCAITCUNDERSTANDING MECHANISTIC OF ILLUSION AN eateto olg,Uiest fTrno oot,Otro aaaMS3G5 M5S Canada Ontario, Toronto, Toronto, of University Zoology, of Department I NTRODUCTION 31 :193±246. 300 :969±972. H EAOI HOYO ECOLOGY OF THEORY METABOLIC E Â 75 LE Á :2311±2317. NE C YR 1 n S and 410 406 : : TEVE ta.(04.W ics w anpolm ihtheir with problems main two argument. discuss We (2004). al. Brown et by justi®ed poorly surprisingly but challenging, apr,M,L lno n .ODnel 00 he en- Three 2000. O'Donnell. S. and Alonso, L. M., Kaspari, oe,M .19.Tpdw n otmu ocsi food in forces bottom-up and Top-down 1992. edition. E. M. Third Power, ecology. of Fundamentals 1971. P. E. Odum, the and biology, trophic level, Taxonomic 2001. M. Kaspari, tre,R . n .J le.20.Eooia stoichiom- Ecological 2002. Elser. J. J. and W., R. edi- Sterner, Second methods. Ecological 1978. E. R. T. Southwood, species Insect 1996. Haarstad. J. and Tilman, D. E., Siemann, time. and space in diversity Species 1995. L. M. Rosenzweig, Arthropod 1988. Hunt. W. H. and Walter, E. D. C., J. nutrition. Moore, animal and human in elements to Trace resources 1987. Mertz. of allocation Optimal 1992. J. Kozlowski, litter tropical in use Bait 2001. Yanoviak. S. and M., Kaspari, aoietasotto,Dee n ui 20] Ban- [2001], Puzio and Dreyer op- transportation, as- me- tabolite internal history [1997]; and Weiner (life and processes proposed Kozlowski timization, been different have very also other sumptions, on Several 2001). based al. been models, has et approach (Dodds this criticized but strongly network, fractal a energy of of through metabolism distribution the optimal assumes on and focuses individuals 1999) by (1997, al. proposed allo- et model West generates network that The no relationships. mechanism(s) currently metric the is There on premature. agreement is ecology of theory A rceig fteRylSceyLno B London Society scale. Royal geographic the a of at Proceedings abundance ant predict variables ergy es opat aepiay Ecology primacy? have plants do webs: USA. Pennsylvania, Philadelphia, Saunders, 439. Bio- and Ecology Global abundance. geography local of regulation ty h ilg feeet rmmlclst h bio- the to Jersey, New molecules USA. Princeton, from Press, University elements Princeton of sphere. biology the etry: UK. London, Hall, and Chapman tion. Nature relationships. size body 380 and abundance diversity, UK. Cambridge, Press, University Cambridge Entomology of de- Review below-ground Annual in webs. mesobiota food and trital micro- of regulation USA. California, Diego, San Press, Academic at Evolution size and and Ecology age in Trends for maturity. implications reproduction: and growth lim- nutrient Biotropica in differences itation. for antsÐevidence canopy and LLOMETRIC h li famcaitcbsst h metabolic the to basis mechanistic a of claim The .W C. :704±706. D O W ALKER E 10 K :229±244. R O THE NOW ELATIONSHIPS 33 :207±211. M ECHANISM ?D clg,Vl 5 o 7 No. 85, Vol. Ecology, O W 73 E B :733±746. 7 267 EHIND N :15±19. EED :485±490. 33 T :419± O ? July 2004 METABOLIC THEORY OF ECOLOGY 1803 avar et al. [2002]; resource partitioning, Kooijman this is not a trivial matter of adjusting coef®cients), [2000]; chemiosmosis and life history evolution, De- they will be of little use to population and community metrius [2003]; the multiplicity of biochemical path- ecologists. Few population ecologists would be satis- ways, Hochachka et al. [2003]), but have not yet been ®ed with values of rmax or K (sensu Brown et al. (2004), compared critically. We should not be lured by the i.e., mean population density) that span several orders illusion of mechanistic understanding. of magnitude. This is not to say that a metabolic ap- Moreover, no single allometric exponent is generally proach cannot work. accepted. We disagree with the dogmatic use of a ¾ A metabolic framework, if modeled at the right scale, exponent by J. Brown and colleagues, to the point of can be powerful. More re®ned physiological models correcting body mass in their analyses by this exponent. do exist, and have been applied successfully in pop- A unique ¾ exponent for allometric relationships of ulation ecology (Kooijman 2000, Nisbet et al. 2000). metabolic rates is currently undefensible, both on the- These models assume that organisms have clear con- oretical and on empirical grounds. In contrast to West straints on how they can partition resources. The energy et al. (1999), most of the recent alternative models of and material available to them (i.e., assimilated from metabolic rate allometry suggest a range of possible their food) are divided among metabolism (for main- exponents. Allometric exponents are expected to vary tenance of tissues and basic functions), somatic pro- with the mass dependence of survivorship (Kozlowski duction, and reproduction, and the input of energy and and Weiner 1997), thermal regulation (Ն⅔ for endo- material must match any change in biomass plus out- therms, Յ1 for ectotherms; Kooijman [2000]), balance puts. The dynamic energy and material budget models between metabolic supply and demand (although ¾ is proposed by Kooijman (2000) and Nisbet and col- an optimal value; Banavar et al. [2002]), level of ac- leagues (2000) account for the effects of body size, tivity (basal vs. maximum metabolic rate; Hochachka temperature, and stoichiometry, and can be used to et al. [2003]), and variability in population size (⅔ for predict various aspects of population dynamics. These species with rapidly ¯uctuating population sizes, ¾ for models offer a powerful framework to test theoretical species with stable population sizes; Demetrius issues in population ecology, but are much more com- [2003]). Deviations from a ¾ exponent also have been plex than the models proposed by Brown et al. (2004)

found empirically. Recent analyses of very large data and require careful parameterization for individual spe- Forum sets for birds and mammals support a ⅔ exponent cies. There are no shortcuts, yet. (Dodds et al. 2001, White and Seymour 2003). Simi- The extension of these physiological models to more larly, the exponents for population density±body size natural conditions and to communities is less obvious. relationships vary among communities, and the overall Careful tests of the dynamic budget models have shown relationship has an exponent signi®cantly steeper than that even simple aspects of more natural systems (e.g., Ϫ¾ (Cyr et al. 1997a, b). The energy equivalence rule low food availability, low food quality) can alter the and the suggestion that trophic transfers explain the dynamics of a population in very signi®cant ways (e.g., steep slopes measured in pelagic systems were specif- Nelson et al. 2001). It is well recognized that popu- ically tested with an extensive data set, and discounted lation dynamics are context dependent, and will change by Cyr (2000). Despite more than a century of work depending on interactions with other species (compet- on this topic, the jury is still out on the magnitude of itors, predators) and with the environment (e.g., Chase the allometric exponents. et al. 2002). The dynamics of natural populations are This lack of mechanistic understanding does not de- unlikely to simply follow from constraints on the en- ter from the potential importance of a metabolic theory ergy budget of individual organisms, but must take into of ecology. The existence and the strength of allometric account a suite of external factors. Increasing the com- and of temperature relationships are well established. plexity of models beyond a few variables is generally The question raised by Brown et al. is really whether counterproductive, so a simple extension of these phys- these powerful relationships account for ecological in- iological models to natural populations or to commu- teractions at all other scales of interest, from population nities may not be possible. A different modeling frame- to community to ecosystem ecology. work may be required. Community ecology is replete with general patterns HOW DO WE CROSS SCALES WITH A METABOLIC (e.g., species±abundance curves, species±area curves, THEORY OF ECOLOGY? diversity±productivity relationships, density±body size A second, more serious problem arises in extending relationships, community size spectra, food web struc- this metabolic framework to scales of increasing com- ture, predator±prey size ratios). The mechanisms gen- plexity. The approach proposed by Brown et al. (2004) erating these relationships are still uncertain, but there is largely justi®ed by the existence of macroecological is no doubt that the availability of energy and material patterns. These general relationships are very useful in affects the biomass, productivity, and diversity of or- providing a broad context to interpret data, but are not ganisms in communities. However, measuring how meant to provide precise predictions under speci®c much resource is really available to organisms is a conditions. Unless these models are greatly re®ned (and dif®cult task, and there is no reason to believe that Forum aaa,J . .Dmt,A aia,adA iad.2002. Rinaldo. A. and Maritan, A. Damuth, J. R., mechanistic J. Banavar, a patterns. on of across than interpretation processes complexity and increasing variables of relate scales to depend to ability likely our more on con- is the ecology However, of by interesting. uni®cation proposed are ceptual (2004) mechanisms al. et The Brown settings communities. natural for con- more made and under be populations to eco- remains for in case vincingly and the but ecology ecology, population system theoretical promising shown in already results has at approach relationships This well-known scales. all these explore to of metabolic us implications challenge a al. the et proposing Brown ecology, By of biology. theory in tem- plays that role perature ubiquitous the and relationships lometric 2002). Vanni ecosystem (e.g., in effective- ecology approach the allometric/metabolic of an examples of good ness pos- many is are 2000) There Kooijman sible. (e.g., use models the detailed necessary, scales. more are temporal of predictions and precise spatial more large When with estimates dealing commonly and when measurements ecologists low-precision eco- use many to Ecosystem have with variables. associated errors unrealistically system not to predictions is compared with models large allometric associated general error from the Second, the are same. elements) interest chemical of other currencies and the nutrients, First, (energy, this. for There has reasons context. two and this are in ecology, successfully applied ecosystem been for indeed justi®ed easily most in tested be to manner. remains convincing but a promising, commu- is integrate task. ecology would this nity that for useless framework sources are metabolic other and A many 2000) too (Cyr those include variability as al., of et such col- Brown communities, by data different used from many environment. in same built lected the relationships in allometric or- live of Global communities actually on that tested ma- be ganisms and to energy need of transfer trans- Models terial it webs? is food ef®ciently among through how ferred divided and community energy a is in for species how ecologists example, ap- baf¯ed For Even have decades. rule). questions (as equivalence simple resources energy parently to the access equal by have suggested sizes all of species 1804 upydmn aac n eaoi cln.Proceed- scaling. metabolic and balance Supply±demand clgsshv ogrcgie h tegho al- of strength the recognized long have Ecologists is (2004) al. et Brown by proposed approach The L ITERATURE C ITED EAOI HOYO ECOLOGY OF THEORY METABOLIC rw,J . .F iloy .P le,V .Svg,and Savage, M. V. Allen, P. A. Gillooly, F. J. H., J. Brown, hs,J . .A bas .P rvr .Del .Chesson, P. Diehl, S. Grover, P. J. Abrams, A. P. M., J. Chase, y,H 00 h loer fpplto est n inter- and density population of allometry The 2000. H. Cyr, .B et 04 oadamtblcter fecology. of theory metabolic a Toward Ecology 2004. West. (USA) B. G. Sciences of Academy National 10506±10509. the of ings .D ot .A ihrs .M ibt n .J Case. Letters J. Ecology T. synthesis. and competition: and Nisbet, and review predation M. a between R. interaction Richards, The A. 2002. S. Holt, D. R. nulvraiiy ae 267±295 Pages variability. annual ryr . n .Pzo 01 loercsaigi animals in scaling Allometric 2001. Puzio. R. and O., Dreyer, ohck,P . .A ava,R .Ades n .K. R. and Andrews, D. R. Darveau, A. C. W., P. Hochachka, olwk,J,adJ enr 97 neseicallometries Interspeci®c 1997. Weiner. J. and J., Kozlowski, bud- mass and energy Dynamic 2000. M. L. A. S. Kooijman, esn .A,E caly n .J rn.20.Multiple 2001. Wrona. J. F. and McCauley, E. A., W. Nelson, ibt .M,E .Mle,K ia n .A .M Kooij- M. L. A. S. and Lika, K. Muller, B. E. M., R. Nisbet, an,M .20.Ntin yln yaiasi freshwater in animals by cycling Nutrient 2002. J. M. Vanni, et .B,J .Bon n .J nus.19.Tefourth The 1999. Enquist. J. B. and Brown, H. J. B., G. West, general A 1997. Enquist. J. B. and Brown, H. J. B., G. West, ht,C . n .S emu.20.Mmainbasal Mammalian 2003. Seymour. S. R. and R., C. White, y,H,J .Dwig n .H ees 1997 Peters. H. R. and Downing, A. J. H., Cyr, od,P . .H oha,adJ .Wiz 01 Re- 2001. Weitz. S. J. and Rothman, H. D. S., P. scal- Dodds, allometric and statistics Quantum 2003. L. Demetrius, y,H,R .Ptr,adJ .Dwig 1997 Downing. A. J. and Peters, H. R. H., Cyr, n lns ora fMteaia Biology Mathematical of Journal plants. and sr n hsooy atA Part Biochem- Physiology, resolving Comparative and metabolism. for istry on model effects a mass cascade: body Allometric 2003. Suarez. Biology oretical r ypout fbd ieotmzto.Aeia Nat- American optimization. size uralist body of by-products are Press, University Cambridge UK. systems. Cambridge, biological in gets fet ffo ult.Poednso h oa Society Royal the B of London Proceedings of experimental quality. system: food predator±prey of single effects a in dynamics ai nrybde oes ora fAia Ecology dy- Animal through of Journal ecosystems 69 models. to budget molecules energy namic From 2000. man. csses nulRve fEooyadSystematics and Ecology of 33 Review Annual ecosystems. ieso flf:fatlgoer n loercscaling allometric Science and organisms. geometry of fractal life: of dimension biology. in laws scaling allometric of Science origin the for model eaoi aei rprinlt oymass body to proportional is rate metabolic .Ws,eios cln nbooy xodUniversity Oxford biology. in UK. Oxford, Scaling Press, editors. West, B. 4049. fteNtoa cdm fSine (USA) Sciences of Academy National the of cadtretilsses Oikos systems. terrestrial and aquat- of ic comparison structure: size community and density xmnto fte`` the of examination A Physica organisms. of ing oysz eainhp nlclautccmuiis Oikos communities. 79 aquatic local in relationships size body :913±926. :341±370. :333±346. 85 149 :1771±1789. 276 :352±380. :122±126. 268 209 :1223±1230. ¾ :9±27. lw'o eaoim ora fThe- of Journal metabolism. of -law'' 284 :1677±1679. 134 322 :675±691. :477±490. 80 clg,Vl 5 o 7 No. 85, Vol. Ecology, in :139±149. 5 .H rw n G. and Brown H. J. :302±315. 2/3 b 43 Proceedings . Population . a :144±156. Density± . 100 99 :4046± : July 2004 METABOLIC THEORY OF ECOLOGY 1805

Ecology, 85(7), 2004, pp. 1805±1807 ᭧ 2004 by the Ecological Society of America

METABOLIC RATE OPENS A GRAND VISTA ON ECOLOGY

KATHRYN L. COTTINGHAM1 AND M. SCOT ZENS Department of Biological Sciences, Dartmouth College, Hanover, New Hampshire 03755 USA

INTRODUCTION linked by the chemical equations of metabolism'' (p. Wouldn't it be nice if ecologists could use a few 1774). This alternative viewpoint will de®nitely pro- simple parameters, such as the size of an organism and voke spirited discussions among ecosystem ecologists the temperature at which it operates, to predict indi- and may spark a careful reconsideration of the here- vidual mortality, population growth rate, species di- tofore independent research on energy and materials. versity, or ecosystem production? Boldly going where THE COMBINED EFFECTS OF MASS AND few ecologists tread, Jim Brown seeks a grand synthesis TEMPERATURE ON METABOLISM in ecology that transcends speci®c organisms and en- After making their argument for the primacy of met- vironments. For much of the past decade, he and his abolic rate, Brown et al. (2004) provide an equation colleagues have worked to develop unifying ecological for metabolic rate as a function of body size (as indexed principles from basic physical and chemical constraints by mass; West et al. [1997], Enquist et al. [1998]) and on organisms. temperature (as summarized by the Bolzmann factor; In this new paper, Brown et al. (2004) open a new Gillooly et al. [2001]). Their equation predicts indi- vista on ecology by (1) nominating metabolic rate as vidual metabolic rate (MR) from the average mass (M, the essential integrator of organismal biology, (2) pro- in grams) and the average operating temperature (T,in viding a bold new synthesis of the effects of mass and Kelvin): temperature on metabolic rate, and (3) proposing a Forum number of hypotheses about the in¯uences of mass and MR ϭ aM3/4 eϪE/(kT) (1) temperature on aggregate ecological phenomena rang- where a is a scaling constant, E is the activation energy, ing from whole organisms to community structure to and k is Boltzmann's constant. ecosystem processes. In this commentary, we address We believe that Eq. 1 has the potential to revolu- each of these contributions, emphasizing the second. tionize the ®eld of ecology. However, we consider it METABOLIC RATE AS THE INTEGRATOR AND to be a working hypothesis for two reasons. First, the ORGANIZER OF DISPARATE THEORY equation needs to be more explicitly rooted in quan- Brown et al. (2004) begin by de®ning metabolism titative derivations from axiomatic properties of phys- as the biological processing of energy and materials. ical and chemical systems. Second, the fundamental Although it is dif®cult to measure ®eld metabolic rates, hypotheses generated by this theory must face stronger much evidence suggests that basal metabolic rate is and more appropriate empirical tests. We will detail governed by resource uptake, chemical transformation, each of these concerns. and the distribution of transformed resources through- Concerns about the derivation out the body. Metabolic rate is therefore both a simple Eq. 1 is the cornerstone of Brown et al. (2004), but and valuable integrating concept and a key linkage be- a full derivation of the form of the equation has not tween physical and chemical processes and the indi- yet been provided. The partial derivation provided by vidual, community, and ecosystem. If we can measure Gillooly et al. (2001) suggests that the equation rests it, metabolic rate gives us a holistic measure of indi- on the following logical steps. vidual performance unconfounded by issues of allo- 1) Whole-organism metabolic rate (MR) is de®ned cation to growth and reproduction. as the sum of the rates of energy produced by individual A particularly novel component of this paper by biochemical reactions R : Brown and colleagues is their deliberate challenge to i the long-standing tradition of considering energy and MR R . (2) ϭ ͸ i materials as separate currencies for examining ecolog- i ical questions (e.g., Reiners 1986). Instead, Brown et We believe that this link between MR and its mecha- al. argue that energy and materials ``are inextricably nistic underpinnings requires explicit support from the biochemical literature, especially because the behavior Manuscript received 16 October 2003. Corresponding Ed- itor: A. A. Agrawal. For reprints of this Forum including the of a chain of reactions is usually better described by MacArthur Award paper, see footnote 1, p. 1790. the behavior of the limiting reaction than by the sum 1 E-mail: [email protected] of the reactions in the chain (e.g., Voet and Voet 1995). Forum E 1806 ob ofotdwt elwrdmaueet (Hil- measurements real-world with confronted be to ( reactants of concentration the components: three of ol ta.(01 atrdottems n temper- and mass the obtain: to out terms factored ature (2001) al. et looly otoa oteBlzanfco o ahrato,we reaction, each for obtain: factor Boltzmann pro- the therefore to is ap- portional and shown) an not 2001:2249; result empirical al. parent et (Gillooly dependence'' ature eprtr fet nmtblcrt mle by implied rate and metabolic mass 1. on Eq. of independence effects the ®rst temperature chemical support and physical to to principles links the provide yet not properties. h ytm( system the nGlol ta.(01 n rw ta.(04 in- (2004) al. et of Brown range and a (2001) dicating al. provided et data Gillooly by in supported component is the metabolism among of reactions differ energies activation That eprtr fet nmtblcrt se[5]). (see and rate mass the metabolic separate on to effects possible temperature dependen- it mass makes equal what is of cies assumption the et and Hochachka 2003) (e.g., al. dependencies do mass reactions different different have because carefully, more plained i hne ihteevrnet ewudlk osee to like of ex- would substitution We are the environment. resources the which with across that changed ef- predicted areas the who surface by 1998), fective constrained al. is et metabolism (West Enquist whole-organism al. 1997, et West al. of work et the on rests substitution This product as their mass that body such with empirical paper), scales the apparent in shown (an not dependence,'' that result, state mass of majority (2001:2249) body the al. ``contain the ¯uxes et and Gillooly concentrations 1, the Eq. in ature con- to claim. references this appreciate ®rm chain would a We in energy reactants reactions? kinetic of of ¯uxes can the but from 1, isolated to Eq. be really of necessary form logically simple the is allow assertion unsupported This h ue fratns( reactants of ¯uxes the tsm on nisdvlpet e hoyneeds theory new development, its in point some At product the on depends reaction individual Each 2) r dnia o l ecin ntesmain Gil- summation, the in reactions all for identical are hs ebleeta h vial ieauedoes literature available the that believe we Thus, )Asmn that Assuming 4) )Fnly yasmn htteatvto energies activation the that assuming by Finally, 5) temper- and mass of independence the justify To 3) ocrsaotteeprclanalyses empirical the about Concerns MR k i ): ϭ ϰ R ͸͸ ( M ii i M ϰ 3/4 R k R E i 3/4 ii R i ( )( `otistedmnn temper- dominant the ``contains i M ϰ sfrdfeetognssand organisms different for 's ϰ iiii e o ( for ϰ f Ϫ ( 3/4 i ,adtekntceeg of energy kinetic the and ), M E M cfk /( )( kT 3/4 3/4 [( e c ) Ϫ i .(6) ). M ) f . E k i o ahreaction: each for o ahrato ex- reaction each for ) i /( 3/4 . kT ) )( ). e EAOI HOYO ECOLOGY OF THEORY METABOLIC Ϫ E /( kT ) )] c (4) (3) (5) i ), h nlsspoie yBone l (2004). al. et on Brown based by theory, provided metabolic data analyses by from the predicted estimated values effects the it similarity temperature to short, the and In about (2004). mass conclusions ®t analyses al. of draw et best the to Brown for the premature of is least not 1 Fig. at is in data, line depicted observed a the that and through indicate (Draper tests 1981) of lack-of-®t Smith and Moreover, lack (Harvey the 1991). taxa and Pagel within 2003) independence McArdle 1995, phylogenetic Rohlf So- intro- and regression; complications II kal the (Model for errors-in-variables correct by to duced fail they stud- as comparative ies, for standards statistical current with a use organisms? to real values appropriate by of really distribution exhibited the it summarize to Is median or issue). mean trivial value a in- single not a or is choosing dimorphism which sexual for growth, with de- determinate were species species in per told (even values are rived single we the op- how and and about species, mass, little each rate, for metabolic temperature of et Ford value erating Brown single (sensu of a analyses use measurements the al. that Second, of chasm bridge. theory could inferential 2000) strong an as a but assumption ®eld, only the this in and see organisms FMR we to of inference rate'' proportionality permits metabolic assumed basal BMR the The of 1773). three, (p. typi- to the multiple, two constant which about ``fairly cally in some (2004) is phenomenon al. FMR biological et average Brown curious by the justi®ed by is metabolic basal This of (BMR). the- estimates metabolic rates laboratory the used of have tests measure most ory to so impossible, organisms, whole most not for in if (FMR) al. dif®cult, rates et are Brown metabolic organisms by ®eld used First, methods (2004). statistical about and concerns data some have the We 1997). Mangel and born )wudceryidct ytm edn ute in- further Fig. needing 2004: systems al. vestigation. indicate et clearly Brown would (e.g., 9) turnover biomass Fig. or 2004: pre- al. 3) et from monitor Brown (e.g., deviations to growth ontogenetic variables Strong dicted what interpretation. both their to and biomass us on- and guide of biomass, turnover predictions standing Consequent rate, growth mass. togenetic given organ- of a rate of metabolic isms increased the of on effects in- temperature the predicts operating the under 1 with Eq. expected change. example climate temperatures an environmental patterns Consider for creased look residuals. to the then (2004) and in temperature al. effects and confounding et the mass Brown disentangle of to of way 1 a Eq. provides example, natural of For complexity the systems. studying for ®lter valuable ef- a unique for temperature and groundwork and the lays mass metabolism of on al. fects et Brown by synthesis hr,teaaye nBone l ontcomply not do al. et Brown in analyses the Third, ept u ocrs esrnl eiv htthe that believe strongly we concerns, our Despite h xiigpopcsrie yE.1 Eq. by raised prospects exciting The clg,Vl 5 o 7 No. 85, Vol. Ecology, July 2004 METABOLIC THEORY OF ECOLOGY 1807

Alternatively, consider the genetically modi®ed or- in this commentary. Drew Allen, Jamie Gillooly, and Brian ganisms (GMOs) with modi®cations to growth rates Enquist ®elded our esoteric inquiries while Jim Brown was unreachable in the Australian Outback. (e.g., Atlantic salmon; Hew et al. [1995], Abrahams and Sutterlin [1999]) and abiotic tolerances (e.g., many LITERATURE CITED food crops; Sharma et al. [2002]) which are rapidly Abrahams, M. V., and A. Sutterlin. 1999. The foraging and being incorporated into our environment. A metabolic antipredator behaviour of growth-enhanced transgenic At- theory of ecology could provide a baseline prediction lantic salmon. Animal Behaviour 58:933±942. for how GMOs with altered growth rate or temperature Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and responses should be different from their parent popu- G. B. West. 2004. Toward a metabolic theory of ecology. lations. In fast-growing GMO salmon, for instance, Ecology 85:1771±1789. Draper, N. R., and H. Smith. 1981. Applied regression anal- metabolic rate should be elevated and the strengths of ysis. Second edition. John Wiley, New York, New York, interactions with both competitors and prey should be USA. predictable. Enquist, B. J., J. H. Brown, and G. B. West. 1998. Allometric scaling of plant energetics and population density. Nature EXTENSIONS OF THE METABOLIC THEORY BEYOND 395:163±165. INDIVIDUALS Ford, E. D. 2000. Scienti®c method for ecological research. The third major component of the Brown et al. Cambridge University Press, New York, New York, USA. (2004) paper extends the metabolic theory to popula- Gillooly, J. F., J. H. Brown, G. B. West, V. M. Savage, and E. L. Charnov. 2001. Effects of size and temperature on tion, community, and ecosystem metrics. Although metabolic rate. Science 293:2248±2251. space prevents us from making a full comment on this Harvey, P. H., and M. D. Pagel. 1991. The comparative meth- aspect of the paper, we would like to point out that in od in evolutionary biology. Oxford University Press, New deriving the equations for these metrics, Brown and York, New York, USA. colleagues generally assume that the combined dynam- Hew, C. L., G. L. Fletcher, and P.L. Davies. 1995. Transgenic salmon: tailoring the genome for food production. Journal ics of multiple organisms are at steady state. For ex- of Fish Biology 47:1±19. ample, the equation to predict population-level survival Hilborn, R., and M. Mangel. 1997. The ecological detective: and mortality rates from the average individual mass confronting models with data. Cambridge University Press, and operating temperature relies on a ``population bal- New York, New York, USA. ance'' in which organisms that die are replaced by new Hochachka, P. W., C. A. Darveau, R. D. Andrews, and R. K. Forum individuals (i.e., the net population growth rate is 0). Suarez. 2003. Allometric cascade: a model for resolving body mass effects on metabolism. Comparative Biochem- This assumption allows Brown et al. to bypass the com- istry and Physiology AÐMolecular and Integrative Phys- plexity of temporal dynamics within particular organ- iology 134:675±691. isms or ecosystems, which matches the static, cross- McArdle, B. H. 2003. Lines, models, and errors: regression system comparisons used in their paper. However, it is in the ®eld. Limnology and Oceanography 48:1363±1366. much less likely to apply when the focus is on the Reiners, W. A. 1986. Complementary models for ecosystems. dynamics of speci®c real-world populations. We be- American Naturalist 127:59±73. Sharma, H. C., J. H. Crouch, K. K. Sharma, N. Seetharama, lieve that the same physical and chemical principles and C. T. Hash. 2002. Applications of biotechnology for will almost certainly constrain individuals whether or crop improvement: prospects and constraints. Plant Science not they are at a population or community equilibrium, 163:381±395. and we urge ecologists to work toward relaxing the Sokal, R. R. and F. J. Rohlf. 1995. Biometry, Third edition. equilibrium assumption in further extensions of the W. H. Freeman, New York, New York, USA. Voet, D., and J. G. Voet. 1995. Biochemistry. Second edition. metabolic theory to higher level ecological processes. John Wiley, New York, New York, USA. ACKNOWLEDGMENTS West, G. B., J. H. Brown, and B. J. Enquist. 1997. A general We thank Mark McPeek, Eric Schaller, Roger Sloboda, and model for the origin of allometric scaling laws in biology. Megan Donahue for their advice on some of the issues raised Science 276:122±126. Forum ᭧ Ecology, 1808 aesol cl sbd asrie othe to raised mass body as scale metabolic should basal rate whole-organism that metabolic predicts its limit and can rate, rates organism transport an within and resources uptake of how mecha- shows or- This approach systems. within nistic et transport distributed Brown branching are by by materials ganisms cited how modeling of (2004) the al. is works approach of system an example An such the mechanisms. underlying how build these on of and based system, description a quantitative of Koehl a behavior the 1986, pro- determine particular Schoener cesses that assume by models Mechanistic (reviewed 1989). have debated approaches The two been these phenomenological. of limitations or and mechanistic strengths be can ology ap- their in general or correct their be not plicability. to or out whether turn ecology, theories and advancement physiology the are both to their of colleagues contribution with signi®cant his pot a and the making Brown stirring By ideas, ®elds. broad-reaching num- different a in of between research ber new and spawned within have stim- and debate have disciplines, 2004) intellectual al. lively et ulated Brown in their and (cited West, Brown, collaborators based by are papers ideas the these controversial, which are on broad, unifying models so the is powerful because vision and a their of be scope met- the can a Because ecology principle. that of propose theory they abolic biosphere, the the eco- from to organization, controls of individual levels rate all metabolic at processes that logical arguing pro- By link ecological to to cesses. organisms used individual be of function can the biology'' and physics, chemistry, h aAtu wr ae) e otoe1 .1790. p. 1, footnote (including see Forum paper), this Award of reprints MacArthur For the Agrawal. A. A. Editor: ytm en lte eae showing behave, the plotted how being of et systems expressions Brown regression quantitative in provide 1±5 the (2004) Figs. example, al. in data For the de- describing system. phenomenological equations a are of models scriptions other contrast, In 04b h clgclSceyo America of Society Ecological the by 2004 ahmtclmdl neooyadognsa bi- organismal and ecology in models Mathematical of principles ``®rst that propose (2004) al. et Brown M 1 Corresponding 2003. November 13 received Manuscript -al [email protected] E-mail: CAITCVS ECHANISTIC 57,20,p.1808±1810 pp. 2004, 85(7), eateto nertv ilg,Uiest fClfri,Bree,Clfri 42-10USA 94720-3140 California Berkeley, California, of University Biology, Integrative of Department A UCINA H RAIMLLVLEXPLAIN LEVEL ORGANISMAL THE AT FUNCTION CAN I .P NTRODUCTION HENOMENOLOGICAL .A .K R. A. M. CLGCLPATTERNS? ECOLOGICAL EAOI HOYO ECOLOGY OF THEORY METABOLIC that M processes OEHL ¾ ODELS power. 1 AND B cu tpriua ae,rte than rather rates, particular at occur sshv enue oepaneooia atrsin patterns ecological explain to anal- used such been from designs, have emerging different yses insights of functional guts the by understand and digestion to of used kinetics been the has processes. theory ecological reactor re- to Chemical organisms to of physics function and the chemistry late of principles basic using 1999). So- mero and biogeographic Tomanek ex- (e.g., to distributions to species relates of used patterns tolerance being thermal also how is plore proteins, func- heat-shock A the of 2002). on tion al. focusing et approach, Helmuth reductionist 1992, different Porter of change and climate some Grant global explore (e.g., of to consequences used ecological been the bio- has this reproductive approach recently, to physical More 1975) 1983). al. (Kingsolver et strategies (Porter interactions predator± to prey from used ranging been phenomena has inter- ecological approach explain and This distributions organisms. on of environ- actions constraints the reveal of aspects to physical ment of analyses with pled organismal- and those of functions. of physics consequences ecological aspects the of and de®ned function laws level explain basic use to to al. chemistry et attempts examples few Brown earlier a Schoener mention of of will by theory we perspective, metabolic in discussed (2004) the were put To ecology (1986). reductionist a in such phil- approach using The of 1989). underpinnings Koehl communities, osophical in populations, (reviewed ecosystems of de- and can properties organisms the individual of termine level the at operating processes how studying although of long, tradition a ignored, ecolog- of sometimes part many is in approach This observed processes. patterns ical the explain to help u nesadn fhwasse works. developing system for a how tools of powerful understanding be our can the mech- data, models about have anistic we predictions which to for making systems observations of of performance organizing and of patterns way reveal effective an vide pro- models phenomenological Although produced. are RYCE rw ta.(04 ru htmtblcter can theory metabolic that argue (2004) al. et Brown oaigeooypoie oeohreape of examples other some provides ecology Foraging cou- been have transport mass and heat of Theories S TUDYING U W D. NDERSTAND OLCOTT O RGANISM E COLOGICAL -L EVEL clg,Vl 5 o 7 No. 85, Vol. Ecology, F P NTO TO UNCTION ROCESSES how hs rates those July 2004 METABOLIC THEORY OF ECOLOGY 1809 foraging strategies (e.g., Penry and Jumars 1987). Sim- chondrial structure and function (Porter 2001) in ani- ilarly, basic rules of aerodynamics have been used to mals of different sizes. explain the mechanical and energetic constrains on for- Physiologists studying metabolic pathways have ob- aging by ¯ying animals, providing functional expla- jected to the idea that a single process, transport of nations of ecological patterns, such as the absence of materials through hierarchical, fractal-like networks, folivory among ¯ying animals (Dudley and Vermeij limits metabolic rate (e.g., Darveau et al. 2002). Al- 1992), or the different foraging strategies used by hum- though the alternative model proposed by Darveau et mingbirds living at low vs. high altitudes (Feinsinger al. (2003) is seriously ¯awed (e.g., Banavar et al. 2003), et al. 1979). we should not ignore the body of experimental work Basic principles of ¯uid and solid mechanics have showing that a variety of interrelated physiological and also been used to analyze the susceptibility of benthic biochemical processes all contribute to limiting the and intertidal marine organisms to physical disturbance rates of ATP synthesis and use in cells. These pro- (e.g., Denny 1999, Koehl 1999), an important process cesses, some of which are important in controlling the in structuring many communities. A scaling rule that overall metabolic rate of an animal when it is at rest emerged from the physics was hypothesized to explain while others play a larger control role when the animal the observation that organisms on wave-swept shores is active, scale differently with body size. are small, but subsequent research showed that this Another assumption of the metabolic theory of physical constraint is usually not what limits the size Brown et al. (2004) is that natural selection has acted of those organisms (Denny 1999). However, investi- to minimize energy expenditure within a biological gation of the hypothesis led to many discoveries about transport system. This assumption ¯ies in the face of the mechanical design of marine organisms, the spatial long-standing arguments that complex physiological or and temporal patterns of physical stresses in wave- morphological systems that perform a variety of dif- swept habitats, and the interplay of mechanical design ferent functions that affect ®tness, and that evolve in and life history strategy in variable environments (re- changing environments, are not likely to show opti- viewed in Denny 1999, Koehl 1999). mization of a single criterion (reviewed in Dudley and The metabolic theory of ecology of Brown et al. Gans 1991). Nonetheless, optimization models have

(2004) is much more ambitious than any of the ex- proven to be powerful tools in guiding empirical re- Forum amples just cited. Earlier applications of organismal search (reviewed in, e.g., Koehl 1989), and the models functional biology to address ecological problems have of Brown and colleagues are clearly serving as a cat- focused on speci®c processes, such as foraging or dis- alyst for interesting new discussions and experiments turbance. In contrast, Brown et al. (2004) point out the in physiology. applicability of the metabolic theory to a wide range IFTHEMODEL IS PHENOMENOLOGICAL,WILL IT of ecological issues, from life history to population STILL BE USEFUL TO ECOLOGISTS? interactions and ecosystem processes. Therefore, as or- ganismal biologists and ecologists debate and test the Even if the mechanisms responsible for the size de- assumptions and predictions of the metabolic theory, pendence of metabolic rate that have been hypothesized its impact no doubt will be far greater than that of the by Brown et al. (2004) turn out to be inconsistent with earlier, more narrowly focused links between basic future experimental evidence, the allometric equations chemistry and physics with ecology. produced by their model may still prove to be useful descriptions of how the rates of various ecologically THE MODEL HAS STIMULATED NEW SYNTHESIS important processes vary with body size and temper- AND RESEARCH IN ORGANISMAL BIOLOGY ature. However, several cautionary notes should be mentioned about their central theme that metabolic rate An earlier attempt to provide a mechanistic expla- varies with body mass raised to the ¾ power. Whether nation for the scaling of metabolic rate with body size, an exponent of ¾ can be statistically distinguished from the elastic similarity model of McMahon (1973), was one of ⅔, given the scatter in the data, has been ex- controversial and spawned a ¯urry of research activity amined by a number of investigators (e.g., Dodds et and new discoveries about the biomechanics of skeletal al. 2001). Furthermore, although the universal model design in animals and plants, and of locomotion. The describing the metabolic rate data spanning 20 orders controversies swirling around the models proposed by of magnitude in body mass (from tiny microbes to large Brown and collaborators seem to be having a similar mammals) has an exponent of ¾, the exponents for effect on the ®eld of physiology. For example, debate speci®c clades of organisms within the composite data about one of the underlying assumptions of the model, set can be higher or lower (e.g., RiisgaÊrd 1998, Dawson that the terminal branches of a biological transport net- 2001, Dodds et al. 2001). Perhaps more worrying is work (such as capillaries, or mitochondria) are invari- the observation, for a variety of invertebrates, that the ant in size, has led to re-examination of experimental metabolic rates of young, rapidly growing individuals data about the morphology and performance of car- scale with body mass raised to higher exponents than diovascular systems (Dawson 2001) and about mito- do those of slowly growing older stages and adults Forum en,M 99 r hr ehncllmt osz nwave- in size to limits mechanical there Are 1999. M. Denny, asn .H 01 iiiuei h adoaclrsystem cardiovascular the in Similitude 2001. H. T. Dawson, ava,C . .K urz .D nrw,adP W. P. and Andrews, D. R. Suarez, K. R. A., C. and Darveau, Savage, M. V. Allen, P. A. Gillooly, F. J. H., J. Brown, aaa,J . .Dmt,A aia,adA iad.2003. Rinaldo. A. and Maritan, A. Damuth, J. R., J. Banavar, organis- ecologists. between and communication biologists for serv- mal catalyst is pro- and a research, as ecological new ing much to so metabolism inspiring is of attention cesses, focusing importance is the it on because organisms signi®cant work how make ecosystems of will and understanding theory our this to right, (2004) contributions al. be et to Brown out of turn theory the metabolic of the all of not aspects or Whether me- processes. im- determine ecological the might portant which organisms in individual of ways of tabolism various way about useful predictions mak- a for ing tool powerful is a or- providing 4) thereby of size, range ganism Eq. vast a 2004: spanning observations al. summarizing et production (Brown or metabolic rate tem- whole-organism and size on of effect perature de- explanation. combined have the metabolic predict they to that a veloped expression have simple the not patterns Nonetheless, ecological do some probably list that they ecolog- and and size metabolic processes, body affect ical than can other that factors temperature metabolic and to their by clues explained provides not theory data the of variation re- about species. predictions particular make of stages to sponses life organisms different of types across that and comparisons models on using based against are Rom- cautions sensitivity, also (2003) temperature bough in differences species (Riisga 1810 wp raim?Junlo xeietlBiology Experimental of 3463±3467. Journal organisms? swept 407. fmmas ora fEprmna Biology Experimental of Journal mammals. of 170. il fbd asefcso eaoim Nature prin- metabolism. on unifying effects a mass body as of cascade ciple Allometric 2002. Hochachka. ecology. of theory metabolic a Toward Ecology 2004. West. B. G. loerccsae.Nature cascades. Allometric rw ta.(04 r h rtt on u that out point to ®rst the are (2004) al. et Brown r 98.Bcueo noeei hne and changes ontogenetic of Because 1998). Êrd 85 :1771±1789. L ITERATURE 421 :713±714. C ITED EAOI HOYO ECOLOGY OF THEORY METABOLIC 204 417 :395± :166± 202 : od,P . .H oha,adJ .Wiz 01 Re- 2001. Weitz. S. J. and Rothman, H. D. S., P. Dodds, xmnto fte``` the of examination otr .P,J .Mthl,W .Bcmn n .R Tracy. R. C. and Beckman, A. W. Mitchell, W. J. P., W. Porter, oxygen cellular mammalian of Allometry 2001. K. R. Porter, oh,M .R 99 clgclboehnc:lf history, life biomechanics: Ecological 1999. R. A. M. Koehl, er,D . n .A uas 97 oeigaia guts animal Modeling 1987. Jumars. A. P. Science and biology. L., in D. shape Penry, and Size 1973. A. T. McMahon, oh,M .R 99 rmidvdast ouain.Pages populations. to individuals From 1989. R. A. M. Koehl, uly . n .Gn.19.Aciiu fsymmorphosis of critique A 1991. Gans. C. and R., Dudley, uly . n .J emi.19.D h oe require- power the Do 1992. Vermeij. J. G. and R., Dudley, enigr . .K owl,J ebrh n .B Chaplin. B. S. and Terborgh, J. Colwell, K. R. P., Feinsinger, igovr .G 93 clgclsgicneo ih ac- ¯ight of signi®cance Ecological 1983. G. J. Kingsolver, O'Donnell, M. Halpin, M. P. Harley, G. D. C. B., Helmuth, mac- global Modeling 1992. Porter. P. W. and W., B. Grant, Riisga obuh .20.Mdligdvlpetltm n tem- and time developmental Modelling 2003. P. Rombough, oae,L,adG .Smr.19.Eouinr and Evolutionary 1999. Somero. N. G. and community L., to Tomanek, approaches Mechanistic 1986. W. T. Schoener, 95 niomna osrit nsm predator±prey 347±364 some Pages on interactions. constraints Environmental 1975. 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D. clg,Vl 5 o 7 No. 85, Vol. Ecology, Tegula 202 129 ¾ 64 rmdifferent from ) :3469±3476. oe scaling power :546±551. :69±96. 26 1 :81±106. :71±73. 202 58 : : July 2004 METABOLIC THEORY OF ECOLOGY 1811

Ecology, 85(7), 2004, pp. 1811±1813 ᭧ 2004 by the Ecological Society of America

ENERGY PARTITIONING BETWEEN DIFFERENT-SIZED ORGANISMS AND ECOSYSTEM STABILITY

BAI-LIAN LI,1,3 VICTOR G. GORSHKOV,2 AND ANASTASSIA M. MAKARIEVA2 1Department of Botany and Plant Sciences, University of California, Riverside, California 92521 USA 2Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300, Gatchina, St. Petersburg, Russia

INTRODUCTION A variable of critical importance in both ecology and organismal biology is body size. A successful biolog- The metabolic approach to ecology presented by ical theory is expected to be able to predict the de- Brown et al. (2004) stems from the seminal work of pendence of individual metabolic power on body size West et al. (1997). They hypothesized that material on the basis of some fundamental assumptions per- transport within living beings is organized such as to taining to organismal morphology and biochemistry. minimize the scaling of total hydrodynamic resistance For example, the assumptions that underlie Eq. 1 can through vascular networks. Based on this assumption, be classi®ed as being of this kind. the organismal metabolic power P was theoretically Similarly, an ecological theory will be able to suc- predicted to scale with body mass M as P ϰ M 3/4.By cessfully predict the scaling of population energy use, additionally assuming that organismal metabolic pro- R, with body size only if it identi®es and takes into cesses accelerate with temperature in the same manner account some fundamental principles of an ecological as individual biochemical reactions, a temperature cor- community's organization. As long as the basic prin- rection factor was added to this scaling: ciples of the metabolic approach are restricted to the P ϰ Me3/4 ϪE/kT. (1) organismal level, none of them is relevant to the eco- Forum system-level question of whether larger organisms At the organismal level, these results were criticized should claim larger, smaller, or equal shares of an eco- on both theoretical and empirical grounds (e.g., Dodds system's productivity than smaller organisms. The met- et al. 2001, Chen and Li 2003, Makarieva et al. 2003, abolic approach stretches to the ecosystem scale by 2004a). In particular, Makarieva et al. (2004a) showed making a simplifying assumption that if R is indepen- how the application of the metabolic approach to the dent of body size, then the scaling of population density ontogenetic growth problem (West et al. 2001) resulted N with body size will be determined by the scaling of in violation of the energy conservation law. In this short individual metabolic power. commentary, however, we will focus on the potential However, it is unclear whether there is a dependence of the metabolic approach to explain patterns in pop- of R on body size. If there is such a dependence, what ulation and ecosystem dynamics. are the fundamental causes and consequences? Al- LINKING INDIVIDUAL AND ECOSYSTEM ENERGETICS: though the metabolic approach refrains from answering THE LOGIC this question, a growing body of evidence suggests that the scaling of R with body size varies predictably with The relationship linking individual to population en- the degree of ecosystem stability, thus providing clues ergetics is: to this central problem of modern ecology (McCann NP ϭ R (2) 2000). where N (number of individuals per square meter) is ENERGETIC DOMINANCE OF SMALLER ORGANISMS the population density of individuals of a given body IN STABLE ECOSYSTEMS size, P is the rate of individual energy use (Watts per There is some evidence showing that the smaller individual), and R (Watts per square meter) is the area- organisms claim larger shares of an ecosystem's pro- speci®c rate at which the population consumes energy ductivity in relatively stable ecosystems. For example, resources from the environment. Eq. 2 is obvious and Sprules and Munawar (1986) studied the scaling of essentially identical to Eq. 9 of Brown et al. (2004), if phytoplankton population density N ϰ M␤ in 67 sites the latter is related to unit area and Eq. 1 is taken into forming a stability gradient: from self-sustainable, account. oligotrophic ecosystems of open ocean and large lakes to highly unstable, ``¯ushing'' eutrophic ecosystems Manuscript received 20 October 2003. Corresponding Ed- itor: A. A. Agrawal. For reprints of this Forum (including of shallow lakes and coastal zones that receive major the MacArthur Award paper), see footnote 1, p. 1790. discharges of nutrients and contaminants. They found 3 E-mail: [email protected] that the scaling exponent consistently increases from Forum ␤ 1812 ϳ sosre httecoe mr tbe ecosystems stable) (more closed the it that ecosystems, observed open is vs. closed in separately exponents otd3 auso cln exponent scaling of values 39 ported ecosystems. real re¯ecting than of more procedure properties assortment being data margins, of broad function scaling a within the set, vary data can cumulative exponent ecosystems the unstable in and represented stable are which Depending to degree sup- questionable. the as is on [2004] approach) al. their et of Brown portive by (interpreted result this aaaepoe noepo L 02 i.2) one 2b), Fig. 2002: (Li plot one in obtains pooled phytoplankton all are and data ignored are ecosystems studied yDmt 19)vr from vary (1993) listed Damuth exponents scaling by like 39 The processes 1990). (Lal degradation erosion soil environmental Prins and and terms Koppel de in 1998) Van both (e.g., unstable ¯uctuations biomass more of be open to de®ned, appear Thus ecosystems grasslands). woods) (savannahs, (forests, closed open into and habitat classi®ed he to which according types, grouped species mammalian 557 enof mean raim nsal csses nusal ecosys- between unstable difference In the ecosystems. tems, smallest stable the of in dominance organisms energetic with faced are we lp of approximate slope an producing only, magnitude of order one asbtentesals n h ags lse is classes ( magnitude largest of the orders and three smallest about the cell between in difference mass the phytoplankton classes; size the three into grouped community (2002) Li samples), water ecosystems. stable heterotrophs less larger in of role to growing decreases the respiration indicating 9%, bacterial eutrophic of highly share the In waters, 91±98% respiration. for ecosystem's accounting total use, of energy the control stable organisms) fully most smallest the (the bacteria in ecosystems, that aquatic showed the and con®rmed pattern (2001) al. emerging et becomes Biddanda equitable. organisms more different-sized larger par- energy among than the ¯ux titioning ecosystems unstable energy in ecosystem's whereas ones, the stable pro- of larger in a portion that consume indicate organisms smaller results ecosystems These ones. unstable losteetmto ftesaigexponent scaling the of estimation the allows es h mletclsotubrtelretoe by magnitude, ones of largest orders the four ecosys- outnumber about stable cells In smallest (Li respectively). the mixing 3a, tems, water and 2a of Figs. intensity 2002: and the eutrophy by of the estimated of degree being degrees latter increasing the stability, with ecosystem's the grows and smallest cells that the largest was of the (2002) densities population Li between by ratio characterized pattern The ഠ unn otretileoytm,Dmt 19)re- (1993) Damuth ecosystems, terrestrial to Turning hntedfeecsi h ereo tblt of stability of degree the in differences the When log na xesv uvyo htpako 63 sea- (6339 phytoplankton of survey extensive an In Ϫ 10 ( .6i tbeeoytm to ecosystems stable in 1.16 ␤ϭϪ N ␤ϳϪ Ϫ small .1 oee,i n nlzstescaling the analyzes one if However, 0.71. / N .8 h clgclmaiguns of meaningfulness ecological The 0.78. large 1/3. )/log 10 ( M small N / Ϫ M small N . to 1.4 large small M and small ) EAOI HOYO ECOLOGY OF THEORY METABOLIC / N ϳϪ ␤ ␤ large / ϩ M N o oa of total a for ഠ .2 iha with 0.42, large large /.Again, 4/3. ϳ Ϫ 10 ϳ sabout is .6in 0.76 ␤ 4 10 This . as Ϫ 3 ). ␤ r,o vrg,caatrzdb in®atymore signi®cantly exponent a scaling by negative characterized average, on are, M Ϯ tblt stnil n al o eiu scrutiny serious a 2004 for al. calls et and (Makarieva tangible is stability cecosystems. ic aua iespotssesmkstepolmo eco- of problem the makes systems life-support natural organized. into are insights ecosystems important terrestrial yield emphasized how will currently size) the plant photosyn- than apparent of (rather size units and nature thesizing the studying that deciduous Webelieve 1975). and (Whittaker stages grasses early-successional photosyn- of than trees smaller (needles) much units have thesizing that dom- conifers are by forests boreal inated in stages having late-successional sta- plants example, ble For by units. photosynthesizing claimed smallest be the also terrestrial should stable in ecosystems energy solar (Li of ecosystems ¯ux major aquatic the stable 2002), in units) ¯ux energy photosynthesizing is dominate smallest the prediction which (unicellular in Our way phytoplankton the decomposition. to similar of that, therefore ¯ux sta- the to able same are bilize the heterotrophs to in small and numerous productivity, numbers as primary allows large manner of of This ¯ux law the the weakly. of stabilize use very make same only to the plants correlated of are units animal plant photosynthesizing In an within needles. different organs and body, correlated leaves rigidly size: to small contrast relatively the by exerted of Instead, is units plants 2003). terrestrial al. in conver- power et energy photosynthetic in (Makarieva participate tis- processes not inactive sion do metabolically of that amount (wood) large sues a to due is en- community's organisms a ¯ux. ergy of large portions where considerable ecosystems consume be to than expected stable therefore are more discuss) will terrestrial we for as is not plants, (but use organisms energy smaller where by stabilized dominated Ecosystems be minimized. money will loss your return and dividing investments; like several is among This processes. nutrient- cycling and or biomass community's reduc- underexploitation a and of ¯uctuations both resources ing available of the of risk overexploitation the organism, large lowering one does thus in than ¯ux manner energy balanced same more a the consume sev- organisms numbers, small large ac- of eral In law 2000). statistical the al. with et cordance (Gorshkov research way theoretical the opening for and stability ecosystem energy to the patterns of use relevance direct the justifying arguments csses ( ecosystems, P RPCIE FOR ERSPECTIVES hs nlsssgetta h oeta fthe of potential the that suggest analyses These 1 h nraigatrpgncpesr moe on imposed pressure anthropogenic increasing The trees) (e.g., plants many of size apparent large The cln sa nomtv niao fecosystem of indicator informative an as scaling SD ; P Ͻ A .1,cnitn ihterslsfraquat- for results the with consistent 0.01), Ϫ LLOMETRIC 0.88 T Ϯ HEORETICAL .1vs. 0.31 b .Teeaestraightforward are There ). Ð S RÐM ␤ hnaeoe ls stable) (less open are than Ϫ clg,Vl 5 o 7 No. 85, Vol. Ecology, CALING 0.50 R SAC FTHE OF ESEARCH Ϯ .0 mean 0.40, R Ð July 2004 METABOLIC THEORY OF ECOLOGY 1813 system stability a major challenge for ecological re- Li, W. K. W. 2002. Macroecological patterns of phytoplank- search (McCann 2000). This challenge is unlikely to ton in the northwestern North Atlantic Ocean. Nature 419: 154±157. be met by the ecological theory if it con®nes itself to Makarieva, A. M., V. G. Gorshkov, and B.-L. Li. 2003. A theoretically unjusti®ed, axiomatic assumptions, like note on metabolic rate dependence on body size in plants the assumption of R ϰ M0 within the metabolic ap- and animals. Journal of Theoretical Biology 221:301±307. proach of Brown et al. (2004), which, as we have ar- Makarieva, A. M., V. G. Gorshkov, and B.-L. Li. 2004a. gued, is empirically unsupported. Ontogenetic growth: models and theory. Ecological Mod- elling, in press. LITERATURE CITED Makarieva, A. M., V. G. Gorshkov, and B.-L. Li. 2004b. Body Biddanda, B., M. Ogdahl, and J. Cotner. 2001. Dominance size, energy consumption and allometric scaling: a new of bacterial metabolism in oligotrophic relative to eutrophic dimension in the diversity-stability debate. Ecological waters. Limnology and Oceanography 46:730±739. Complexity, in press. Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and McCann, K. S. 2000. The diversity±stability debate. Nature G. B. West. 2004. Toward a metabolic theory of ecology. 405:228±233. Ecology 85:1771±1789. Sprules, W. G., and M. Munawar. 1986. Plankton size spectra Chen, X., and B.-L. Li. 2003. Testing the allometric scaling in relation to ecosystem productivity, size, and perturba- relationships with seedlings of two tree species. Acta Oec- tion. Canadian Journal of Fisheries and Aquatic Science ologica 24:125±129. 43:1789±1794. Damuth, J. 1993. Cope's rule, the island rule and the scaling Van de Koppel, J., and H. H. T. Prins. 1998. The importance of mammalian population density. Nature 365:748±750. of herbivore interactions for the dynamics of African sa- Dodds, P. S., D. H. Rothman, and J. S. Weitz. 2001. Re- examination of the ``3/4-law'' of metabolism. Journal of vanna woodlands: an hypothesis. Journal of Tropical Ecol- Theoretical Biology 209:9±27. ogy 14:565±576. Gorshkov, V. G., V. V. Gorshkov, and A. M. Makarieva. 2000. West, G. B., J. H. Brown, and B. J. Enquist. 2001. A general Biotic regulation of the environment: key issue of global model for ontogenetic growth. Nature 413:628±631. change. Springer-Verlag, London, UK. West, G. B., B. J. Enquist, and J. H. Brown. 1997. A general Lal, R. 1990. Soil erosion and land degradation: the global model for the origin of allometric scaling laws in biology. risks. Pages 129±172 in R. Lal and B. A. Stewart, editors. Science 276:122±126. Advances in soil science. Volume 11. Soil degradation. Whittaker, R. H. 1975. Communities and ecosystems. Mac- Springer-Verlag, New York, New York. Millan, New York, New York, USA. Forum

Ecology, 85(7), 2004, pp. 1813±1816 ᭧ 2004 by the Ecological Society of America

A ONE-RESOURCE ``STOICHIOMETRY''?

ROBERT W. S TERNER1 Ecology, Evolution and Behavior, University of Minnesota, St. Paul, Minnesota 55108 USA

The approach of Brown et al. (2004) might succeed course, is less certain than is the existence of good or fail on two levels. On one level, it can be used as statistical correlations. a purely statistical, predictive tool. Examples given by Brown et al. view the ``big three'' variables to be Brown and colleagues leave no doubt that temperature temperature, body size, and stoichiometry. Tempera- and body size ``explain'' (in the statistical sense) a great ture turns out to be approachable using decades-old deal. We do need good predictive models for many formulations of Arrhenius, Boltzmann, and others. It reasons, one of them for incorporating more ecology is a shock that these models, which have been shown and thus improving models of global change. The sec- to work for ``simple'' biological functions such as ox- ond, more dif®cult, level has to do with the reasons ygen consumption or even bacterial growth (Johnson why those statistical predictor variables work the way et al. 1974), also do a splendid job with the more com- they do, and why they are good predictors in the ®rst plex variables of standing stock and even diversity place. The processes that Brown et al. proposeÐfractal (which are not even rates). The critical and surprising scaling of distribution networks and thermodynamic result here is that so much ecological temperature de- kinetics of ``metabolism''Ðmay truly be the mecha- pendence is described by the Arrhenius-Boltzmann nistic basis for the observed patterns, but that, of equation, with near-constant activation energy. What that success itself means is a fascinating question, per- Manuscript received 3 November 2003. Corresponding haps related to just what is ``metabolism.'' In spite of Editor: A. A. Agrawal. For reprints of this Forum (including the MacArthur Award paper), see footnote 1, p. 1790. their complexity, do one or a small number of core 1 E-mail: [email protected] metabolic pathways regulate organism growth, so that Forum aiswith varies it although Therefore, some resource(s). of scarcity or involves material(s) usually al.) de- et as Brown Rate metabolism, by ®ned considered. But therefore (and be explain. growth must to of limitation sense left mechanistic is the much here not sense, in statistical might least why the At 1±8), needed? Figs. be 2004: thirdÐstoichiometryÐeven al. the et Brown (e.g., iables theory. distribution fractal has the literature by this reenergized laws thoroughly; been power very of family explored a been and have study, has of also history relationships long size a had Body lev- observation? higher these of at els signals the dominate kinetics those 1814 hste h adnleuto fmacroecology, Is of 9). equation Fig. cardinal 2004: the al. then et this Brown also (see stoichiometry including nutrient model organism comprehensive a like? with in- generate and linear They look content, term, possibility. ecology single one a suggest and corporate (2004) 1997) al. Fell et Brown (see con- metabolic theory of combination more trol a into stated does models Or, what generally, size models? body macroecology and broad-scale, temperature with tations in factors limiting of nature. multiplicity the about under- standings current Bolzmann- with the collides interpretation or temperature dependence, nearly temperature have con- steps identical biochemical limiting key multiple many face Either know staints. organisms ecologists that nature, fact in the that, very with one is metabolism of control of it temperature±kinetic to step but a materials, relate reconcile of to might hard kinds networks many of distribution movement the of include frac- scaling The explicity two). tal (level must processes we and steps do, rate-limiting they have to they structure one), why the and (level work systems tools these statistical how understand good be can resources and ely`epan'(nbt ess ttsia n mech- much? and so statistical anistic) senses, both (in ``explain'' really oeaaennierwt rdciiy vrbroad Over productivity. with nonlinear phe- are ecological nomena many abundance, resource productivity hence, of expectation and, ranges the broad reaction, Over complicated. a more limit is may reagent function more one when linear However, than simple amount. reagent's a limiting be the of indeed will equal, remains yield one else product but all and is reagent lim- there limiting a potentially if of Stoichiometrically, amount resource. the with iting varies interest of parameter and where usmdit h ro em n utepoehow explore just and term, error the into subsumed otejb fw orc for correct we If job. the do be ie h ucs fmdl ihjs hs w var- two these just with models of success the Given hti h etwyt noprt aeillimi- material incorporate to way best the is What ecnaki igelna emin term linear single a if ask can We htmdl ihu xlctmnino material of mention explicit without models that X R tnsfrsm clgclprmtro interest, of parameter ecological some for stands tnsfr`rsuc'?Mgtsc nequation an such Might ``resource''? for stands M , E , R k enwaesml sighwsome how asking simply are now we , and , X ϭ eR Me T Ϫ 3/4 r si rw ta.(2004), al. et Brown in as are Ϫ E / kT M ϩ and error EAOI HOYO ECOLOGY OF THEORY METABOLIC T rltte be them let or , R seog to enough is might X a owt eso nte.As,d ema resources mean and we do time, Also, another. you of one that less means with any resource do one can at of lot rates a having controlling are sometimes in sites plays resources role nesting these of some or one some than hiding In more Often, elements. or limiting. nutrient itself, of space handful energy contexts, a chemical and and water light to from range They perature. with dealing when Boltzmann-equivalent form substances. functional a limiting single is a there with whether term to considerable as cast doubt these and productivity effects, of examples to resource other nonlinear respect many are with There 1995). shape (Rosenzweig hump or some decrease, increase, have may Diversity on dependent structure. are trophic enrichment trophic nutrient to odd-link responses suggests and that 1992) DeAngelis 1981, even- al. et with (Oksanen models Work and (Sterner 2002). function linear, nu- Elser not limiting saturating, the a via with trient increases often biomass ranges, within ucinaesrnl otoldb h dniyo the of identity the by and controlled structure strongly ecosystem are and function follow Community effects these. trophic-level from other cells; very by smaller dominance and much structure different very of sys- tems produces of limitation species Fe or inedible P whereas large, cyanobacteria, by limitation soil N dominated to strong become under compared often systems light lakes, obtaining In for resources. re- strategies need different other plants the of for that think work only need not One of sources. might world one'' a ``resource in winning scarce for strategies with coef®cients, stoi- even ®xed ap- because uniform ``might'' a say highly I have However, some do chiometry. things At living etc. level, P, phospholipid proximate N, acids, proteins, C, need nucleic on things based membranes, living are all all and the they etc., alike different: that more are in are they ®ne, systems than broad living be different suf®ciently might of a assumption chemistries an At such another. scale, simple one all are of they every- proportions because substances, you all tells about substance thing one coef®cients. knowing stoichiometric ratios), trient ®xed nu- constant et (i.e., under coef®cients Brown stoichiometric is of ®xed With statement true link- the is the which of al. in nature context the is The point age. critical resources that The agree linked! I are and Elser these about linkages? not inextricable is it what if about, clari®cation: stoichiometry a ecological chemical is First, the metabolism.'' by of linked equations inextricably (Reiners are energy implied of materials currencies and the have 2002), Elser authors and Sterner 1986, some ecological distinct as being from currencies, ``Far assert: they when to re- limitation of real measures. pool these some what of provides universality determining involved of is act forms sources of simple plethora the a in and exist substances these contexts, eore r oehtrgnu o hni tem- is than lot heterogenous more a are Resources rw ta.(04 ietpalo hscomplexity this of all sidestep (2004) al. et Brown or xenlto external h raim ial,i many in Finally, organism? the clg,Vl 5 o 7 No. 85, Vol. Ecology, July 2004 METABOLIC THEORY OF ECOLOGY 1815 limiting resources. The saturating functions of biomass Biology has evolved fascinating responses to the op- and productivity alluded to in the previous paragraph timization problems that the shifting availability of are probably caused by shifts in the identity of limiting these resources creates. substances when one of them becomes very abundant. Again, so that this message is not lost: I'm a fan of Lessons can be learned from dynamic consumer±re- the Brown et al. (2004) approach. Macroecology has source models. A larger number of potentially limiting produced a set of amazing, inspiring, and, I believe, substances opens up opportunities for coexistence (Til- also extremely useful microbes-to-monsters plots. But man 1982), a theoretical prediction recently elegantly much of the important work ahead of us in ecology is shown empirically by Interlandi and Kilham (2001). at ®ner spatial and temporal scale. I also believe it to When the number of resources increases from one to be the case that the utility of macroecology models will only three, entirely new, complex dynamics are pos- be proportional to the scale of interest. Tools are most sible (Huisman and Weissing 2001). For another ex- useful when applied to the right job. ample, several of my co-workers and I have done work at a variety of time and space scales on light gradients ACKNOWLEDGMENTS where the ®xed stoichiometry of a simple, single-spe- Among my colleagues who read and commented on this cies population of herbivores creates positive relation- commentary, I want especially to thank Adam Kay, Bob Me- gard, and Dave Tilman, and, as usual, Jim Elser, for their ships between primary and secondary productivity in insightful reading. one range of the experiment, but negative relationships in the other range (Urabe and Sterner 1996, Sterner et LITERATURE CITED al. 1998, Urabe et al. 2002). At low light levels, both Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and primary and secondary production are energy limited, G. B. West. 2004. Toward a metabolic theory of ecology. whereas at high light levels, herbivores switch to ma- Ecology 85:1771±1789. terial (phosphorus, we believe) limitation. These kinds Dauner, M., T. Storni, and U. Sauer. 2001. Bacillus subtilis metabolism and energetics in carbon-limited and excess- of shiftsÐdriven by element linkage, not in spite of carbon chemostat culture. Journal of Bacteriology 183: element linkage, as a casual reading of Brown et al. 7308±7317. might implyÐare a signal that the identity of resources DeAngelis, D. L. 1992. Dynamics of nutrient cycling and food webs. Chapman and Hall, New York, New York, USA.

does matter a great deal; it will not generally work to Forum Elser, J. J., K. Acharya, M. Kyle, J. Cotner, W. Makino, T. boil them all down to a single, univariate measure. I Markow, T. Watts, S. Hobbie, W. Fagan, J. Schade, J. Hood, hypothesize that for most ``X,'' it does matter whether and R. W. Sterner. 2003. Growth rate: stoichiometry cou- the limiting resource is light, or nitrogen, or iron, or plings in diverse biota. Ecology Letters 6:936±943. some combination of all of these. Fell, D. 1997. Understanding the control of metabolism. Port- Furthermore, for many important ecological ques- land Press, London, UK. Hairston, N. G., Jr., and N. G. Hairston, Sr. 1993. Cause± tions, assumptions of ®xed stoichiometry simply break effect relationships in energy ¯ow, trophic structure, and down. Plants have different composition than animals, interspeci®c interactions. American Naturalist 142:379± for example, and even within species, differing growth 411. rates are associated with different chemical contents Huisman, J., and F. J. Weissing. 2001. Fundamental unpre- dictability in multispecies competition. American Natural- (Elser et al. 2003). Organisms do link the rates of up- ist 157:488±494. take and use of separate resources, but in an adaptive, Interlandi, S., and S. S. Kilham. 2001. Limiting resources ¯exible way that responds to shifting stoichiometric and the regulation of diversity in phytoplankton commu- ratios. Note, for example, the very different ¯uxes of nities. Ecology 82:1270±1282. C, N, and P in metabolic networks under different lim- Johnson, F. H., H. Eyring, and B. J. Stover. 1974. The theory of rate processes in biology and medicine. John Wiley, New iting factors in the study of Dauner et al. (2001). To York, New York, USA. what extent does the set of all possible resources con- Morowitz, H. J. 1992. Beginnings of cellular life: metabolism tain redundant information, so that the set can be col- recapitulates biogenesis. Yale University Press, New Ha- lapsed to a univariate measure? The claim by Brown ven, Connecticut, USA. et al. (2004) that one can overlook the multiplicity of Oksanen, L., S. D. Fretwell, J. Arruda, and P. NiemalaÈ. 1981. Exploitation ecosystems in gradients of primary produc- limiting resources because they are all linked together, tivity. American Naturalist 118:240±261. and are all linked to a single universal currency of Reiners, W. A. 1986. Complementary models for ecosystems. energy is an echo of a previous era in ecology, where American Naturalist 127:59±73. bioenergetics was the hoped-for organizing concept Rosenzweig, M. L. 1995. Species diversity in space and time. Cambridge University Press, Cambridge, UK. (Slobodkin 1972, Morowitz 1992, Hairston and Hair- Slobodkin, L. R. 1972. On the inconstancy of ecological ston 1993). It was not, and we are beyond that. ef®ciency and the form of ecological theories. Pages 293± Incorporation of materials into broad-scale macro- 305 in E. S. Deevey, editor. Growth by intussesception: ecology models need not be distastefully complex, or ecological essays in honor of G. Evelyn Hutchinson. Trans- so idiosyncratic as to resist all generality. I think that actions of the Connecticut Academy of Sciences, New Ha- ven, Connecticut, USA. there is quite a bit more work to do and that ultimately, Sterner, R. W., J. Clasen, W. Lampert, and T. Weisse. 1998. even at broad scale, we will almost always need a mul- Carbon : phosphorus stoichiometry and food chain pro- tivariate, not a univariate, perspective on resources. duction. Ecology Letters 1:146±150. Forum Science ᭧ Ecology, 1816 xeln o favrieet otyi h ae of pages the an in mostly done advertisement, have of questions. job proponents excellent evolutionary canonical interesting the pose Fortunately, is- to global and address ap- to sues useful needed give numbers to mea- of proximations scales allows those that throughout and physi- surements dynamics, intracellular community from to scaling ology expla- of the patterns unites of that nation theory a of potential interpretive of impression their wisdom. revise remain the my will will editors friends literature that that the and hope friends, I giving deserves. than it that rather review a points, cite my sup- shall to port construed I deliberately particular, papers In of at- selection piece. small any scholarly making a than at state- rather tempt public thoughts a tentative this of make ment and path offers, easy the commentary take that shall sense I Accordingly, misinformed expertise. a my from of manuscripts me send in controversial editors information the journal that privileged of from sides and both friend- part, on personal players from with comes ships information because my In- commenting of player. about active most uncomfortable an the am on than I spectator rather deed, a ®eld, am of the I some of that in sidelines confess controversial me and Let details. . accomplish- . its scope, . in promise, and exciting ments, and powerful is ogy'' h aAtu wr ae) e otoe1 .1790. p. 1, footnote (including see Forum paper), this Award of reprints MacArthur For the Agrawal. A. A. Editor: ev eues,aogwt tdnsadcolleagues that and abroad. points students and home with important at along some uneasy, still me read are have leave I there same what But the of most reached there. endorse also cheerfully have I who venues. critics their of those 04b h clgclSceyo America of Society Ecological the by 2004 ti adt a nuhaotteectmn and excitement the about enough say to hard is It ecol- of theory metabolic ``a called has Brown What 1 Corresponding 2003. November 13 received Manuscript imn .18.Rsuc optto n community and competition Resource 1982. D. Tilman, stoichiom- Ecological 2002. Elser. J. J. and W., R. Sterner, -al [email protected] E-mail: eateto clg n vltoayBooy rneo nvriy rneo,NwJre 84-03USA 08544-1003 Jersey New Princeton, University, Princeton Biology, Evolutionary and Ecology of Department tutr.PictnUiest rs,Pictn e Jer- New USA. Princeton, sey, Press, University Princeton structure. bio- the to Jersey, New molecules USA. Princeton, from Press, University elements Princeton of sphere. biology the etry: 57,20,p.1816±1818 pp. 2004, 85(7), OMNAYO RW TA.S`TWR METABOLIC A ``TOWARD AL.'S ET BROWN ON COMMENTARY and Nature n hyhv epne to responded have they and . . . , HOYO ECOLOGY'' OF THEORY EAOI HOYO ECOLOGY OF THEORY METABOLIC H ENRY .H S. h rmr cln atris factor scaling primary the cln uewt power and with . rule . . scaling theories ap- a the the of favor balances distribution different could of organisms of plicability of modalities shapes but different different thinking, that and re- analogical me these hazy strikes into of it go distribution opti- I for exactly Here network sources. and fractal explicitly a theory mizes the but surfaces, oecrflyadmr ocflyb od tal. et factors modulo scaling Dodds which are in by contexts of forcefully variety The more (2001). and carefully more etlgoer fognssi rca Ws tal. et (West fractal the is In organisms 1997). of geometry mental tween. oyms,hsabs-tvleo .1 exactly . . . 0.71, of value best-®t between a midway nor- has of plot against mass, log±log rate body a metabolic (2004), temperature-corrected al. et malized Brown of 1B Fig. rb,J,adR .Senr 96 euaino herbivore of Regulation 1996. Sterner. W. R. and J., Urabe, and Andersen, T. Yoshida, T. Makino, W. Kyle, M. J., Urabe, ntv et rmisacsi hc the which de- in separate instances to from literature tests this ®nitive review would to it worthwhile but therein), be references and 2004 al. et (Brown rca supinta isa h er ftedevel- the of heart the at the lies that that suggests fractal, strongly assumption not This fractal tree-like. but even tree-like not fractal, and variously are shapes net- and resource-distributing works sizes explicit of whose range organisms a over of well so works rule ing ino h hoeia ruetfrexactly for argument theoretical naõ The the choice. of ``either±or'' sion an be need there er the at assumption an as outset. entered size with metabolism nlagmn o exactly orig- for The argument of analysis. distribution the inal complicate the can but resources volumes, by these by acquired used are and resources surfaces spherical; and Euclidean organisms is of geometry organizing fundamental the that ORN h rtpiti h miia usino whether of question empirical the is point ®rst The rwhb h aac flgtadntins rceig of (USA) Proceedings Sciences nutrients. of and Academy light National of the balance the by growth bal- pro- nutrient : herbivore light Ecology increases of ance. effects light stoichiometric Reduced to due duction 2002. Elser. J. J. h hr on steprdxta the that paradox the is point third The hr sas h eitertclqeto fwheth- of question semi-theoretical the also is There 1 ¼ ¾ ahrta modulo than rather 83 hoy eore r loaqie by acquired also are resources theory, ⅔ :619±627. and ¾ ¾ hssm on smade is point same This . ¾ ⅔ , sue httefunda- the that assumes or ⅔ rsmtigi be- in something or , ¾ clg,Vl 5 o 7 No. 85, Vol. Ecology, hnfrexample, for when , ⅓ 93 sencouraging is ¼ :8465±8469. ¾ pwrscal- -power ⅔ cln of scaling assumes v ver- Ève July 2004 METABOLIC THEORY OF ECOLOGY 1817 opment of the original version of the theory needs to over again in a wide range of contexts, from physiology be replaced by a more general network. Such an ap- to evolution and from cell to ecosystem. proach should explore explicitly how the cost and ef- Indeed this is what makes the whole enterprise of ®ciency of that network change with departures from ``A Metabolic Theory of Ecology'' so exciting and the optimized fractal structure. Starts in this direction worthwhile. Brown et al. (2004) have derived an ex- have been made by the authors of the original theory traordinary range of interpretation and prediction from in its biological context (West et al. 1999, 2001), and ``®rst principles.'' The original framing of the ®rst prin- by others (Banavar et al. 1999, 2002, Dodds et al. 2001, ciples (West et al. 1997) engendered criticisms and sub- Gutierrez 2002), some of whom derive scaling rules sequent modi®cations that made them less con®ning that vary between ¾ power and ⅔ power. Particular (West et al. 1999, 2001), and such improvements con- exponents can also arise from mechanisms of compet- tinue. The extensions of the original theory to the pop- itive space-®lling at the community level (e.g., Kinzig ulation and community levels have an internal bio- et al. 1999), and it would be worthwhile to look for physical consistency, and strong empirical support that them anywhere where resources ¯ow through an array still allows enough variation to demand biological ex- of tiny consumers that remove a fraction of what they planation. Furthermore, the theory may help in the encounter (e.g., small leaves scattered through a big search for that explanation. tree [Horn 1971]; to pick an example only because I Robert MacArthur would have been very pleased know the author). It is too early to make a generaliza- with Brown et al. (2004). He was always interested in tion from this variety of ideas, but perhaps the network patterns at any scale from organism to community to of distribution need only be ef®cient and hierarchical, biogeography, and from ecology to evolution. He had not just near-fractal, for exponents to be modulo ¼ a particular interest in how body size affected those (West et al. 1999), or very near it (others cited pre- patterns. He was a theoretician and a naturalist, with viously). Other modi®cations may come from biolog- a conceptual brilliance when he combined the two. ical variations in the dimensionality of the surface over Here is how he might have viewed the controversy over which resources are acquired, and details of the metric details: of the volume over which they are distributed and used, Ecological patterns, about which we construct the-

. . . but I expect these to be small enough to contribute Forum ories, are only interesting if they are repeated. They more to explaining residuals than to changing the av- may be repeated in space or in time, and they may erage scaling of attributes to body size. be repeated from species to species. A pattern which The initial assumption of size-independent metabolic has all of these kinds of repetition is of special in- units (West et al. 1997) has received little published terest because of its generality, and yet these very criticism, perhaps because most biologists can cite so general events are only seen by ecologists with rath- many examples from their own specialties. According- er blurred vision. The very sharp-sighted always ®nd ly, Brown et al.'s (2004) extension of the consequences discrepancies and are able to say that there is no of this assumption to organism, population, and eco- generality, only a spectrum of special cases. This system is novel, interesting, and powerful, independent diversity of outlook has proved useful in every sci- of any arguable details. ence, but it is nowhere more marked than in ecology. Some would quibble about the possible role of mul- ÐMacArthur 1968:159. tiple normalization factors in ®tting varied organisms to a common line on a graph, but it doesn't bother me. LITERATURE CITED As Brown et al. (2004) point out, the normalization factors are appropriate subjects for interpretation in Banavar, J. R., J. Damuth, A. Maritan, and A. Rinaldo. 2002. Supply±demand balance and metabolic scaling. Proceed- terms of speci®c biological attributes. Indeed, one of ings of the National Academy of Sciences (USA) 99: the great strengths of this metabolic theory is that a 10506±10509. demonstrated allometry allows the all-pervasive effect Banavar, J. R., A. Maritan, and A. Rinaldo. 1999. Size and of body size to be accounted for, so that residuals from form in ef®cient transportation networks. Nature 399:130± 132. the allometry may call for detailed biological interpre- Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and tation. Alternatively, the residuals may provide data G. B. West. 2004. Toward a metabolic theory of ecology. from organisms of different sizes to test theoretical Ecology 85:1771±1789. predictions about such biological details. Brown et al. Dodds, P. S., D. H. Rothman, and J. S. Weitz. 2001. Re- (2004) also point out that even after normalization the examination of the ``¾-law'' of metabolism. Journal of The- oretical Biology 209:9±27. residuals from some of their regressions span a 20-fold Gutierrez, W. R. 2002. Volume integration of fractal distri- range (and I read some of their ®gures as providing a bution networks. Physical Review E 66:041906. 50-fold range between extremes). That offers plenty of Horn, H. S. 1971. The adaptive geometry of trees. Princeton opportunity for structural idiosyncracies and biologi- University Press, Princeton, New Jersey, USA. Kinzig, A. P., S. A. Levin, J. Dushoff, and S. Pacala. 1999. cally interesting details to ``®ne-tune'' an average re- Limiting similarity, species packing, and system stability lationship that spans as much as 20 orders of magnitude for hierarchical competition±colonization models. Ameri- in size. Brown et al. (2004) make this point over and can Naturalist 153:371±383. Forum ¾ ᭧ Ecology, 1818 od ta.(01 n ht n emu (2003) Seymour and mammals and of rates White metabolic basal and on data (2001) analyzed al. et Dodds Schmidt-Nielsen 1984, Calder 1983, 1984). Bonner of Peters and basis (McMahon the 1983, on scaling expected geometric powers Euclidean third the powers than quarter have were rather exponents to allometric most appeared conclud- that unanimously 1980s, ed books These the issue. the in resolved allometry on books rmsvrlcommentaries. several from our least defend at simply or than controversial paper. rather the issues, of unresolved some still clarify to progress, facilitate To try (2004). al. we et ``toward'' Brown the of progressÐhence title the in MTE in work The a much commentaries. very the is by raised and general issues some speci®c address will we and Here community years. rendered take ecological the probably wider be of the will evaluation by (MTE) full time over ecology A word. of aware last theory well the metabolic not are We is this Feature. that Special this in mentaries h aAtu wr ae) e otoe1 .1790. p. 1, footnote (including see Forum paper), this Award of reprints MacArthur For the Agrawal. A. A. Editor: et .B,J .Bon n .J nus.19.Ageneral A 1997. Enquist. J. B. and Brown, H. J. B., G. West, httesoeo i o±o ltwsams exactly almost was plot log±log his of found slope and and masses, the body mammals that of range of wide a rates spanning (1932) metabolic birds Kleiber basal since ever the bi- years, measured 70 intrigued about have for questions ologists em- These ultimately questions. are times pirical and rate rates metabolic biological other whole-organism and for exponents metric xesv tde,cliaigi eea synthetic several in culminating studies, Extensive . 04b h clgclSceyo America of Society Ecological the by 2004 oe o h rgno loercsaiglw nbiology. in laws scaling allometric of Science origin the for model USA. York, New Syracuse, Press, University Syracuse lution. h su a epndrcnl,i atclrwhen particular in recently, reopened was issue The ebgnwt oegnrlpit htemerged that exponent points the Is general some with begin We com- the to respond to opportunity the welcome We aucitrcie eebr20.Corresponding 2003. December 1 received Manuscript aAtu,R .16.Teter ftence ae 159± Pages niche. the of theory The 1968. H. R. MacArthur, 176 in 57,20,p.1818±1821 pp. 2004, 85(7), .C eotn dtr ouainbooyadevo- and biology Population editor. Lewontin, C. R. 3 hoeia iiin SB8,LsAao ainlLbrtr,LsAao,NwMxc 74 USA 87545 Mexico New Alamos, Los Laboratory, National Alamos Los B285, MS Division, Theoretical 276 :122±126. J AMES eateto ilg,Uiest fNwMxc,Abqeqe e eio811USA 87131 Mexico New Albuquerque, Mexico, New of University Biology, of Department `OADAMTBLCTER FECOLOGY'' OF THEORY METABOLIC A ``TOWARD 1 ⅔ 2 .B H. at eIsiue 39Hd akRa,SnaF,NwMxc 70 USA 87501 Mexico New Fe, Santa Road, Park Hyde 1399 Institute, Fe Santa or EPNET OU OMNAYON COMMENTARY FORUM TO RESPONSE ¾ ROWN ? Tevle fteallo- the of values ÐThe , 1,2 J AMES EAOI HOYO ECOLOGY OF THEORY METABOLIC .G F. AND ILLOOLY G EOFFREY , et .B,J .Bon n .J nus.20.A 2001. Enquist. J. B. and Brown, H. J. B., G. West, fourth The 1999. Enquist. J. B. and Brown, H. J. B., G. West, 1 A id n bandepnnscoe to closer exponents obtained and birds eea oe o noeei rwh Nature growth. 631. ontogenetic for model general scaling allometric Science and organisms. geometry of fractal life: of dimension aid u hwddsic ek n envle at values mean and exactly peaks almost distinct showed but exponents varied, The environ- levels. population aquatic and molecular whole-organism and to and cellular many from terrestrial ranged but variables The both birds, ments. from and The mammals taxa times. just other and not rates included biological metabolic data other whole-organism many and maximal rates, and per- including ®eld, (2004) sets, data al. basal, additional et many metabolic Savage of basal analyses birds. formed and on mammals only of data rates analyzed and compiled procedures statistical used. which are and included, are taxa and eaoi rates, metabolic n ayohrbooia ae eg,hatrtsand rates and heart rates), (e.g., rates growth biological population other many and hc ltdt o ae fwoeogns biomass whole-organism ( of growth (2004), population al. rates maximal et production, for Brown in data 8 plot and ex- 5, which For 2, Figs. data. to published refer ample, of exponents new analyses on based and quarter-power is compilations which research, of recent our from pervasiveness comes the evidence have for additional general Important in exponents. allometries third-power biological the reopening that for justi®cation argument little is there that cluded periods). gestation and times circulation blood (e.g., .W B. ytmcro unvrars ierneo body of range wide a across turnover carbon system aa eaoi ae.Teetmtdepnn varies exponent estimated avian from The and rates. mammalian on metabolic data basal existing of analyses on points: key We two studies. the these on only commented summarize have (2004) al. et age NDREW )Ddse l 20)adWieadSyor(2003) Seymour and White and (2001) al. et Dodds 2) ae nti vdne aaee l 20)con- (2004) al. et Savage evidence, this on Based )I spolmtct li entv au based value de®nitive a claim to problematic is It 1) ϳ EST .5t .5 eedn nwihmeasurements which on depending 0.85, to 0.65 .A P. 2,3 LLEN ¾ Ϫ o hl-raimbslad®eld and basal whole-organism for ¼ , 1 284 V o asseicmtblcrates metabolic mass-speci®c for AN :1677±1679. .S M. ¼ AVAGE clg,Vl 5 o 7 No. 85, Vol. Ecology, o ilgcltimes biological for , 2,3 ⅔ r max than 413 ,adeco- and ), :628± ¾ Sav- . July 2004 METABOLIC THEORY OF ECOLOGY 1819 sizes, taxa, and environments. The exponents, 0.76, about everything from satellite orbits to biomechanical Ϫ0.23, and Ϫ0.22, respectively, are very close to the properties of bones. We freely admit that there is abun- predicted values of ¾, Ϫ¼, and Ϫ¼, and the 95% con- dant room for additional research on mechanisms: from ®dence intervals do not include the Euclidean alter- (1) how the kinetics of the multiple biochemical re- natives of ⅔, Ϫ⅓, and Ϫ⅓. actions of metabolism determine the observed activa- What is the mechanistic basis for quarter-power ex- tion energies at whole-organism and ecological levels ponents?ÐThe data on biological allometries are well of organization; to (2) how the kinetics of species in- described by power laws, implying that they are the teraction, evolution, coevolution, speciation, and ex- result of self-similar or fractal-like processes. West et tinction cause the observed temperature dependence in al. (1997, 1999a, b) developed general mechanistic biogeographic gradients of species diversity. We hope models based on geometric and biophysical principles other research groups will investigate some of the that explain the quarter-power exponents. These mod- mechanisms and we welcome all contributions to pro- els address the general problem of distributing meta- ducing a more complete and mechanistic conceptual bolic resources within an organism and, more specif- framework for MTE. ically, describe the structure and function of mammal The second response is that mechanisms are de- and plant vascular systems. The models of West et al. scribed in much more detail in our other publications. hypothesize that the quarter-power scaling exponents Most equations in Brown et al. (2004) are the result of re¯ect the optimization of these transport networks due mathematical models described in separate publica- to natural selection. Although the organisms them- tions. These models make explicit mechanistic con- selves are three-dimensional, an additional length var- nections between the metabolic processes of individual iable is required to describe the branching networks, organisms and their ecological and evolutionary con- resulting in scaling exponents with 4, rather than the sequences. Euclidean 3, in the denominator. The structures and The third response is that empirical support for these dynamics of resource distribution networks are hy- models and, in particular, for the predicted scalings pothesized to be dominated by self-similar fractal-like with size and temperature, suggests that metabolic rate branching, although it is likely that some networks may is indeed the most fundamental biological rate, and that

be ``virtual'' (e.g., within cells of prokaryotes) rather its manifestations ramify to affect all levels of biolog- Forum than ``hard wired'' (e.g., vascular systems of verte- ical organization, from molecules to ecosystems. Data brates and higher plants). sources and statistical procedures are not described in These models of West et al. have been criticized by Brown et al. (2004), but are documented in the original several authors. Cyr and Walter (2004) cite most of the papers. It is important to recognize that the ®gures in published critiques. West and collaborators are trying Brown et al. (2004) are not just descriptive statistical to respond to the most serious criticisms, but this takes regression equations. Two points should be empha- considerable effort and introduces inevitable time lags sized: (1) theoretically predicted values for allometric (see Brown et al. 1997, Enquist et al. 1999, West et al. exponents and activation energies, based on metabolic 2002; 2003a, b, in press, Allen et al. 2003, Brown et processes within individual organisms, are incorporat- al. 2003, Gillooly et al. 2003). Several other responses ed directly into the analyses and into the plots of the are still in press or unpublished. We will not address data; and (2) support for model predictions comes not the criticisms here, except to state that we have yet to only from the high proportions of variation explained see compelling theoretical or empirical evidence that by the regression equations (high values of r2), but would cause us to retract or substantially change the more importantly from the fact that 95% con®dence models of West et al. Like the content and implications intervals for the slopes almost always include the pre- of the broader MTE, the rigor and realism of the models dicted allometric exponents and activation energies. for quarter-power scaling will be decided not by the What about all the variation?ÐThe authors of the participants in the immediate debates, but by the broad- commentaries represent a wide spectrum of biologists er scienti®c community in the fullness of time. and ecologists, from those who seek unifying princi- What is a mechanism, and a mechanistic theory?Ð ples, to those who emphasize diversity and complexity. Several commentaries question the extent to which Both approaches are validÐindeed both are required MTE, as we have presented it, is truly mechanistic. We to keep the science focused, balanced, realistic, and have three responses. progressing. We are at one end of the spectrum, un- The ®rst is that there is considerable variation in what abashedly seeking unifying theory. For those who are scientists consider to constitute a mechanism; one per- more concerned about the variation, we have three son's mechanism is another's empirical phenomenol- comments. ogy. This is a long-standing problem. For example, First, the in¯uence of metabolism on ecology is most physicists still don't completely understand the mech- apparent when comparisons can be made across wide anistic basis of gravity, even though the force of gravity ranges of body size and temperature, where the perva- can be characterized by analytical equations and used sive in¯uences of allometry and kinetics are strong. as a ®rst principle to make useful, accurate predictions When body mass differs by only two- or threefold, or Forum plcbe o xml,ormdlcnexplain can model directly our be example, to For theory applicable. metabolic for body temperature in and variation size suf®cient and have evaluated. population ecologists by be community studied to the systems factors of many other Nevertheless, design allowing the effect, thereby by In ``controlled'' study, temperature. are and variables little size is these body there because both forest, in a in variation in warblers or in value ®eld herbs old little of an diversity of species are and coexistence kinetics explaining For and theory. metabolic allometry of example, domain these the of outside Many are importance. factors greater or factors equal other two, assume or can degree a only by varies temperature 1820 oeaut hs possibilities. one these helps evaluate baseline to predicted theoretically a mod- the Having of se- el. operations or expose assumptions the that in ¯aws discrepancies rious (4) predict- and to deviations; how leads able assumptions showing model by rule'' theory; speci®c or the violating ``prove model the that in exceptions (2) included (3) data; not the factors in categories: of biases effects other four or into errors loosely measurement (1) grouped be can pre- from dictions Deviations variation. to residual pro- which the principles, departureÐfrom understand of ®rst point on baselineÐa based a soundly vides theory a that is yteBlzanfco iha ciaineeg of energy eV activation (1 an eV with 0.6±0.7 factor described Boltzmann as the increase by will processes and community-, ecosystem-level population-, individual-, predicts of it point: rates starting that good a provides theory vari- met- however, abolic variation, other of sources and these resources, Despite ables. material composition, limiting species of initial effects dynamics, transient time by lags, complicated be undoubtedly will responses tual att rdc h clgclcneune farise 2 a by of temperature consequences environmental average ecological in the we predict that to suppose Or want in¯uence importance. the major pro- Then, assumes ecosystem and forest. cesses interactions species a on to size plant ®eld of un- succes- old to an secondary from want in sion we involved that processes variation the Suppose by derstand processes. obscured other be to may even due operating in¯uences still their are biology and when processes to allometry These fundamental ecology. the are and rate that metabolic evidence of is kinetics plots forests'' ``oceans to and var- monster'' that the to ``microbe of fact log-scaled most in very for iation account The temperature and pervasive. size sys- and body ecological powerful and are organisms tems individual on kinetics lakes. temperate zoo- in of dynamics plankton community and population to variation inter- directly relevant seasonal results and these and make intra- temperature mass environmental of in body et magnitudes in Brown The variation in 3). speci®c rates Fig. egg-hatching 2004: also al. see [2002]; (Gillooly zooplankton al. of et rates growth in variation the of h hr on,as aei eea commentaries, several in made also point, third The h eodcmeti htefcso loer and allometry of effects that is comment second The ϭ 64 kJ/mol). 96.49 EAOI HOYO ECOLOGY OF THEORY METABOLIC Њ .Teac- The C. ϳ 90% eodta rvoseai clg,weebio- where ecology, in era previous are ``we . that . . Sterner that with How- beyond 2002). disagree Elser strongly and we Sterner ever, 2000, al. et contribution Elser major (e.g., a ecolog- represents on and concentrated stoichiometry, ical has others of and program Elser, research Sterner, major inter- A or- the ecosystems. both and of in ganisms materials many al. and address energy et to between Brown relationships begun in have indicated we As (2004), on kinetics. concentrated has and work allometry any earlier of Our ingredient MTE. organismal essential complete an to and be central must ¯uxes are and metabolism resources the material of vari- of compositions ecological pools chemical these The on temperature, ables. and with size for together body resources, hypotheses material levels. testable limiting as of ecosystem effects taken the be to can population models These the at productivity qaino macroecology, of equation applications. and weaknesses, strengths, as be- different have approaches consequently trade-offs and MTE generality, different and speci®city and tween make DEB They the taste, model view the complementary. of which We matter for purpose used. a the of part is matter in a part is in and necessary or model a desirable in delib- complexity is much our How functionsÐthan MTE. simple and erately variables detailÐ material more more and incorporate many indeed energy do they of And principles balance. metabolic ®rst of growth terms and describe in processes indeed individuals do of reproduction models and DEB 2000). al. Nisbet 2000, et Kooijman (e.g., Kooijman, collaborators and of Nisbet, approach (DEB) budget energy here. dynamic two only address we but attention, warrant that a htrsuc iiaini u oasnl reagent single to a respect with to linear due is is not and did limitation We resource models. our other that in say and included not environment, are that af®nity, factors group functional to due or be phylogenetic stoichiometry, may of We in¯uences variation ``error.'' unex- deterministic residual as the that regarded that noted be explicitly suggest should not variation did We plained the MTE. outside of are purview relationships, species±area species±abundance and macroecological including never ma- We of ecological phenomena, many equation that man. cardinal stated ``one explicitly straw We the croecology.'' is a this is that claimed This resource). material h niiulogns ee.W i nld linear a at include times did and We term, rates level. for organism 4±8) individual Eqs. the (our abundance reason models resource our this for from term for stoichiometry a and omitted ecological energetics, deliberately on we to do'' relationship to its work and more quite is bit ``there that a Sterner with agree do We content.'' otejb'(where job'' the do ...'' Speci®cs eod tre 20)ak hte `n cardinal ``one whether asks (2004) Sterner Second, the of virtues the extol (2004) Walker and Cyr First, R norEs ±1fraudne ims,and biomass, abundance, for 9±11 Eqs. our in , iha`...snl iertr in term linear single . . ``. a with Ðotcmetre as pc® issues speci®c raise commentaries .ÐMost R ste`aon' fsm limiting some of ``amount'' the is X R n `raimnutrient ``organism and ϭ clg,Vl 5 o 7 No. 85, Vol. Ecology, M 3/4 e Ϫ R E/kT seog to enough is R ϩ error July 2004 METABOLIC THEORY OF ECOLOGY 1821 energetics was the hoped for organizing concept.'' Just Gillooly, J. F., E. L. Charnov, J. H. Brown, V. M. Savage, change the (our italics) to a. Energetics, updated, based and G. B. West. 2002. Allometry: how reliable is the bi- ological time clock? Reply. Nature 424:270±270. more ®rmly on ®rst principles, and interrelated to stoi- Kleiber, M. 1932. Body size and metabolism. Hilgardia 6: chiometry, is a powerful organizing concept for ecol- 315±332. ogy. Kooijman, S. A. L. M. 2000. Dynamic energy and mass bud- We end by emphasizing that MTE is not intended to gets in biological systems. Cambridge University Press, Cambridge, UK. be the theory of everything that is interesting and im- McMahon, T. A., and J. T. Bonner. 1983. On size and life. portant in ecology. Nor is it intended to account for all Freeman Press, New York, New York, USA. of the variation among living things and ecological Nisbet, R. M., E. B. Muller, K. Lika, and S. A. L. M. Kooij- systems. Within its domain, however, MTE offers man. 2000. From molecules to ecosystems through dy- namic energy budget models. Journal of Animal Ecology mechanistic explanations for linking many ecological 69:913±926. patterns and processes to biological, physical, and Peters, R. H. 1983. The ecological implications of body size. chemical constraints on individual organisms. MTE Cambridge University Press, Cambridge, UK. suggests that underlying the diversity of living things Savage, V. M., J. F. Gillooly, W. H. Woodruff, G. B. West, A. P. Allen, B. J. Enquist, and J. H. Brown. 2004. The and the complexity of ecological systems are funda- predominance of quarter-power scaling in biology. Func- mental unities, some of which re¯ect how ®rst prin- tional Ecology, in press. ciples of biology, physics, and chemistry govern the Schmidt-Nielsen, K. 1984. Scaling: why is animal size so ¯uxes and pools of energy and materials within organ- important? Cambridge University Press, Cambridge, UK. Sterner, R. W. 2004. A one-resource ``stoichiometry''? Ecol- isms and between organisms and their environments. ogy 85:1813±1816. Sterner, R. W., and J. J. Elser. 2002. Ecological stoichiometry. LITERATURE CITED Princeton University Press, Princeton, New Jersey, USA. Allen, A. P., J. H. Brown, and J. F. Gillooly. 2003. Response West, G. B., J. H. Brown, and B. J. Enquist. 1997. A general to Comment on ``Global biodiversity, biochemical kinetics, model for the origin of allometric scaling laws in biology. and the energetic-equivalence rule.'' Science 299:346. Science 276:122±126. Brown, J. H., A. P. Allen, and J. F. Gillooly. 2003. Heat and West, G. B., J. H. Brown, and B. J. Enquist. 1999a. A general biodiversityÐResponse. Science 299:512±513. model for the structure and allometry of plant vascular Brown, J. H., B. J. Enquist, and G. B. West. 1997. Allometric systems. Nature 400:664±667. scaling laws in biologyÐResponse. Science 278:372±373. West, G. B., J. H. Brown, and B. J. Enquist. 1999b. The Forum Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284:1677±1679. G. B. West. 2004. Toward a metabolic theory of ecology. West, G. B., J. H. Brown, and B. J. Enquist. In press. Growth Ecology 85:1771±1789. models based on ®rst principles or phenomenology? Func- Calder, W. A. III. 1984. Size, function and life history. Har- tional Ecology. vard University Press, Cambridge, Massachusetts, USA. West, G. B., B. J. Enquist, and J. H. Brown. 2002. Onto- Cyr, H., and S. C. Walker. 2004. An illusion of mechanistic genetic growth: modelling universality and scalingÐreply. understanding. Ecology 85:1803±1805. Nature 420:626±627. Dodds, P. S., D. H. Rothman, and J. S. Weitz. 2001. Re- West, G. B., V. M. Savage, J. F. Gillooly, B. J. Enquist, W. examination of the ``¾-law'' of metabolism. Journal of The- H. Woodruff, and J. H. Brown. 2003a. Why does metabolic oretical Biology 209:9±27. rate scale with body size? Nature 421:713±713. Elser, J. J., R. W. Sterner, E. Gorokhova, W. F. Fagan, T. A. West, G. B., V. M. Savage, J. F. Gillooly, B. J. Enquist, W. Markow, J. B. Cotner, J. F. Harrison, S. E. Hobbie, G. M. H. Woodruff, and J. H. Brown. 2003b. Red herrings and Odell, and L. J. Weider. 2000. Biological stoichiometry rotten ®sh. arXiv. ͗http://arXiv.org/abs/physics/0211058͘. from genes to ecosystems. Ecology Letters 3:540±550. White, C. R., and R. S. Seymour. 2003. Mammalian basal Enquist, B. J., J. H. Brown, and G. B. West. 1999. Plant metabolic rate is proportional to body mass(⅔). Proceed- energetics and population densityÐReply. Nature 15:573± ings of the National Academy of Sciences (USA) 100: 573. 4046±4049.