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

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 , 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. provides a basis for using ®rst principles of , , and biology to link the biology of individual to the ecology of , , and . Metabolic rate, the rate at which organisms take up, transform, and expend and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and . Metabolic theory predicts how metabolic rate, by setting the rates of uptake from the environment and resource allocation to survival, growth, and , controls ecological processes at all levels of from individuals to the . Examples include: (1) history attributes, including devel- opment rate, mortality rate, age at maturity, life span, and growth rate; (2) population interactions, including , rates of and , and patterns of diversity; and (3) processes, including rates of 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 . Key words: ; biogeochemical cycles; body size; development; ecological interactions; ecological theory; metabolism; ; 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 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 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 , 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 at the molecular, cellular, and whole- reactions that form the basis of the TCA (tricarboxylic 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 , but the is a uniquely , 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 . to : 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 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 , 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 , the metabolic rate is biology, chemistry, and physics and, on the other hand, equal to the rate of respiration because can explain many emergent features of biological struc- obtain energy by oxidizing 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 , 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, 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 quanti®ed, related to each other, and explained in terms uptake in or the rate of consumption in July 2004 MACARTHUR AWARD LECTURE 1773 aerobic and (Withers 1992). free-living organism in , 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 - 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 (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 resources, or in It has been known for more than a century that bio- resource demand, such as the costs of reproduction or rates, metabolic rates, and nearly all of maintaining 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 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 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 and abolic rate, development , population growth rate, maintain relatively high and constant tem- or rate of molecular , 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 (Gillooly et al. 2001). I ϭ IM3/4 (2) 0 Nearly all other biological rates and , 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 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 , 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 . Under controlled lab- Ca, and K. N is found primarily in ; P in nucleic oratory conditions, 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 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 or water ( 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 , 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 of and lakes, which is regulated Perspectives environment, used for biological and func- in part by 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. 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 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. , 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), (n ϭ 64), (n ϭ 105), (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 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 , 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 (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 - 1/4 E/kT tB ϰ Me (8) , 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 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 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- , 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 - carbon, , 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 : chloroplasts, mi- to death, including competition, predation, , tochondria, and , which are, respectively, the and disease. As we will show, the rates of these inter- sites of photosynthesis, respiration, and 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 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 (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 DYNAMICS 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 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. 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 . So, for example, capacity, because the same supply of energy supports some of the residual variation is related to : 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 . inverse Boltzmann relationship between equilibrium 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 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 species that vary in diet from scale as M 3/4. The theory accurately predicts thinning herbivores to . 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 communities. distributions of the trees in steady-state 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 /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) zooplankton/ 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 varies inversely with water, ). 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 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 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 is found in warm, productive The scaling of rates of ecological interactions has environments, such as tropical forests and 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 species richness in two geographic gradients (Allen et al. 2002). (A) A latitudinal gradient in (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 ones should also have faster evolutionary dynamics, is needed, but a metabolic perspective has sharpened resulting in higher rates of 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 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'' , the fates of energy and materials in ecosystems. Bio- rates of species interaction and . 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 , 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 . 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 - 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 , measured as rates of atures were not reported. The slope of the relationship (solid Perspectives whole-plant ¯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 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 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 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 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 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 -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 and 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 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 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., 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 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 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 . 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 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 over Brown, J. H., and J. F. Gillooly. 2003. Ecological food webs: high-quality data facilitate theoretical uni®cation. Proceed- time or . 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. . 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 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 have altered Carbone, C., and J. L. Gittleman. 2002. A common rule for size distributions of organisms, environmental tem- the scaling of 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 . 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 . 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 - 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 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. LITERATURE CITED Duellman, W. E. 1988. 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