Letters, (2009) 12: 369–384 doi: 10.1111/j.1461-0248.2009.01302.x IDEA AND PERSPECTIVE Towards an integration of ecological stoichiometry and the metabolic theory of ecology to better understand nutrient cycling

Abstract Andrew P. Allen1* and James Ecologists have long recognized that species are sustained by the flux, storage and F. Gillooly2 turnover of two biological currencies: energy, which fuels biological metabolism and 1Department of Biological materials (i.e. chemical elements), which are used to construct . Ecological Sciences, Macquarie University, theories often describe the dynamics of populations, communities and in Sydney, NSW 2109, Australia terms of either energy (e.g. population-dynamics theory) or materials (e.g. - 2 Department of Zoology, theory). These two classes of theory have been formulated using different University of Florida, 223 assumptions, and yield distinct, but often complementary predictions for the same or Bartram Hall, P.O. Box 118525, similar phenomena. For example, the energy-based equation of von Bertalanffy and the Gainesville, FL 32611, USA *Correspondence: E-mail: nutrient-based equation of Droop both describe growth. Yet, there is relatively little [email protected] theoretical understanding of how these two distinct classes of theory, and the currencies they use, are interrelated. Here, we begin to address this issue by integrating models and concepts from two rapidly developing theories, the metabolic theory of ecology and ecological stoichiometry theory. We show how combining these theories, using recently published theory and data along with new theoretical formulations, leads to novel predictions on the flux, storage and turnover of energy and materials that apply to , plants and unicells. The theory and results presented here highlight the potential for developing a more general ecological theory that explicitly relates the energetics and stoichiometry of individuals, communities and ecosystems to subcellular structures and processes. We conclude by discussing the basic and applied implications of such a theory, and the prospects and challenges for further development.

Keywords , growth rate hypothesis, metabolic rate, nutrient limitation, .

Ecology Letters (2009) 12: 369–384

address the challenges brought on by environmental change INTRODUCTION will depend in part on developing a more predictive body of Since the early days of ecology, mathematical theory has ecological theory that elucidates inter-relationships among contributed substantially to our understanding of the factors biological currencies. that control ecological communities (e.g. Verhulst 1838; Two biological currencies in particular have been the Lotka 1925; Volterra 1926). Theories now exist to describe a focus of much theoretical work in ecology: energy, which is variety of ecological phenomena including individual required to fuel the metabolic processes of survival, growth growth, population regulation, food-web structure and and reproduction in ; and materials (i.e. chemical dynamics. However, these theories are often elements), which are required to construct biomass (Lotka derived using different assumptions, pertain to different 1925; Lindeman 1942; Redfield 1958; Reiners 1986; Brown levels of biological organization and yield predictions in et al. 2004). Cellular and molecular biologists have long different currencies (e.g. numbers of individuals, species or recognized that energy and materials are fundamentally trophic levels in communities; fluxes of nutrients, energy or linked through the biochemical reactions of metabolism biomass in ecosystems). In the decades ahead, our ability to (Morowitz 1968). However, understanding and quantifying

2009 Blackwell Publishing Ltd/CNRS 370 A. P. Allen and J. F. Gillooly Idea and Perspective interrelationships between energy and materials – particu- basic principles that apply to both unicellular organisms and larly for elements other than (C) – has proven to be a multicellular animals and plants. We focus mainly on leaf- far greater challenge for ecological phenomena (Elser & and individual-level rates of energy and material flux as they Hamilton 2007). pertain to growth and nutrient dynamics. We conclude with At the individual level, growth is among the most a more general discussion of prospects and challenges for thoroughly investigated biological processes in terms of fully integrating MTE and EST. energy and nutrient requirements. A number of nutrient- based models have been developed that quantify how CONTRIBUTIONS AND LIMITATIONS OF MTE AND growth rates are affected by the availability of elements EST including (N) and (P) (e.g. Michaelis & Menten 1913; Monod 1950; Droop 1973). These nutrient- MTE and the energetic-invariance concept based growth models serve as the basis for resource- The MTE focuses on understanding the interplay between competition theories in ecology (e.g. Tilman et al. 1981). , ecology and based on variation in A number of energy-based models have also been devel- metabolic rate among organisms (Brown et al. 2004). An oped that quantify growth rates in terms of metabolic rate underlying premise of MTE is that individual metabolism is (Brody 1945; von Bertalanffy 1957), and ⁄ or primary fundamental to ecology because it is through metabolism determinants of metabolic rate, namely body size and that organisms interact with their environments. Over the temperature (Arrhenius 1889; Kleiber 1961). These models last 10 years, MTE has yielded two general classes of also serve as the basis for ecological theories in areas such as models. The first predicts how two variables – body size and food-web dynamics (e.g. Yodzis & Innes 1992; Brown et al. temperature – affect the metabolic rates of organisms, and 2004; Reuman et al. 2008). However, energy- and nutrient- how these differences in turn affect and are affected by based models of growth, and ecological theories based on differences in life history (West et al. 1997, 1999, 2002; these models, have largely been developed independently. Gillooly et al. 2001; Allen & Gillooly 2007). MTEÕs focus on Here, we aim to integrate common principles and size and temperature is based on a rich literature in assumptions that underlie these two classes of models to comparative physiology, which has demonstrated that these better understand how energy and nutrient availability variables are primary determinants of metabolic rate across combine to constrain individual-level processes, and thereby the diversity of life (Arrhenius 1889; Krogh 1916; Kleiber affect the flux, storage, and turnover of energy and 1961; Allen & Gillooly 2007). The second class of models elements in ecosystems. We do so by integrating key explores the consequences of metabolic rate at different concepts from two emerging theoretical frameworks: the levels of biological organization, from the structure and metabolic theory of ecology (MTE, Brown et al. 2004), function of cellular components (e.g. the respiratory which focuses on the importance of individual energetics to complex, West et al. 2002) and genomes (Gillooly et al. ecology, and ecological stoichiometry theory (EST, Sterner 2005b; Allen et al. 2006), to the structure and function of & Elser 2002), which focuses on the importance of element cells (Savage et al. 2007), populations (Savage et al. 2004; availability to ecology. MTE and EST have both placed OÕConnor et al. 2007), communities (Reuman et al. 2008) special emphasis on understanding the mechanistic basis of and ecosystems (Enquist et al. 2003; Allen et al. 2005; individual growth down to the level of cellular Lopez-Urrutia et al. 2006). (e.g. Elser et al. 1996; Gillooly et al. 2002; Sterner & Elser One contribution of MTE – the energetic-invariance 2002; West et al. 2002). Results of several recent studies concept – is particularly relevant when considering integra- suggest that integrating models and concepts of MTE and tion with EST. This concept was put forward as an EST may lead to a new, more general theory that assumption in the model of West et al. (1997) (hereafter encompasses plant and physiology, and WBE), which was proposed to account for Ôquarter-power and (e.g. Brown et al. 2004; Gillooly scalingÕ of metabolic rate with body size. Quarter-power et al. 2005a; Kerkhoff et al. 2005, 2006; Niklas et al. 2005; scaling has been documented for diverse taxa including Kerkhoff & Enquist 2006). mammals (Kleiber 1961), ectotherms (Peters 1983), plants Towards this end, we begin here by reviewing some key (Niklas 1994) and unicells (Hemmingsen 1950). In this aspects of MTE and EST that are important for linking ) relationship, the mass-specific metabolic rate, B ⁄ M(Wg 1), these theories. In doing so, we define MTE and EST decreases with increasing body size, M (in mass units of g), broadly to encompass the current work and the foundations according to a power function of the form upon which this work is based. Then, we show using 1=4 recently published theory and data, along with some new B=M ¼ BoM ; ð1Þ theoretical formulations, how key features of these two where Bo is a Ônormalization constantÕ independent of size ) theories may be combined mathematically based on four (W g 3 ⁄ 4). The model derives the quarter-power scaling

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 371 relationship by invoking three simplifying assumptions: (i) invariance, is more general than eqn 3 in that it applies even biological distribution networks that deliver energy and if the other two assumptions of the WBE model are materials to cells are fractal-like in their geometries; (ii) the violated. For example, respiration rates of woody-plant energy required to distribute resources through these seedlings and saplings do not exhibit quarter-power scaling networks is minimized; and (iii) of particular relevance here, (Reich et al. 2006), as is expected given that the space-filling the terminal metabolic units (MUs) of these networks are assumption of WBE is violated (Enquist et al. 2007). energetically invariant, meaning that the energy flux per MU Nevertheless, these data are consistent with the energetic- is independent of body size. At the most fundamental level, invariance concept (eqn 2) because respiration rates are MUs can be defined as the protein complexes responsible proportional to total leaf mass (Reich et al. 2006; Enquist for the transformation of energy and materials in metabolic et al. 2007). organelles (West et al. 2002). Examples include respiratory A second contribution of MTE has been to extend this complexes in the cristae of animal mitochondria and concept of energetic invariance to encompass the kinetic photosystems in the thylakoid membranes of plant effects of temperature on MU- and individual-level energy chloroplasts. fluxes. In the case of mitochondria, the exponential effect of The energetic-invariance concept [assumption (iii) of temperature on energy flux, mmito (W), can be characterized WBE], when combined with eqn (1), implies that the energy by approximately the same Boltzmann–Arrhenius relation- Er=kT flux per MU, mMU, is size-invariant, and therefore that the ship, e , for animals, plants and unicells (Gillooly et al. mass-specific metabolic rate increases proportionally with 2001; Allen et al. 2005): )1 the density per unit mass of MUs, qMU (g ):

mito Er=kT mmito ¼ mo e ð4Þ B=M / qMUmMU ð2Þ ) ) Here k is BoltzmannÕs constant (=8.62 · 10 5 eV K 1), T is If assumptions (i) and (ii) are also upheld, WBE further absolute temperature in degrees Kelvin, and Er is the predicts that the density of MUs should exhibit quarter- average activation energy (»0.65 eV, which corresponds to a power scaling 15-fold increase in respiration rates from 0–30 C). Equa- tions 3–4), in turn, can be combined to characterize the combined effects of body size and temperature on the q ¼ qMUM 1=4; ð3Þ MU o respiration rate of an (Gillooly et al. 2001; Allen et al. 2005): MU where qo is a normalization constant independent of size )3 ⁄ 4 (g ). Thus, WBE predicts that declines in the mass- 1=4 E =kT B=M ¼ q m ¼ b M e r ; ð5Þ specific metabolic rate with increasing body size are directly mito mito o related to declines in the densities of MUs, which comprise ÔmetabolicÕ biomass. Note also that combining eqns 2 and 3 where MU demonstrates that Bo ¼ q mMU in eqn 1, meaning that the o mito mito normalization constant is in part determined by the flux per bo ¼ qo mo ð6Þ MU. )1 Two aspects of eqns 2 and 3 are noteworthy. First, they and qmito is the density of mitochondria per unit mass (g ). apply not only at the molecular level, but also at higher Together eqns 4–6 demonstrate how individual metabolic levels of biological organization. Specifically, the definition rate can be expressed in terms of subcellular-level processes of MU can be expanded to encompass cellular organelles based on the densities and energy fluxes of MUs (in this case responsible for energy and material transformation (e.g. mitochondria). mitochondria, chloroplasts, ), and the multicellu- lar structures responsible for energy and material exchange Limitations of MTE models between an organism and its environment (e.g. capillaries and alveoli in animals, fine roots and leaves in plants). For There are many strengths and limitations of MTE and EST, example, over a broad body-size range, densities of but we will consider only those that are most pertinent to chlorophyll, chloroplasts and leaves are all proportional to developing a more integrative theory. In this context, there rates of , and show approximately quarter- are two limitations of MTE worth mentioning. First, the power scaling with plant mass (Niklas & Enquist 2001), proposed mechanistic bases of MTE models require further suggesting that the energetic-invariance concept applies at theoretical investigation and experimental tests, especially at all of these levels. Second, eqn 2, which embodies energetic the subcellular level (see, for example, Clarke 2004). In

2009 Blackwell Publishing Ltd/CNRS 372 A. P. Allen and J. F. Gillooly Idea and Perspective particular, the WBE model, which itself builds upon a long Specifically, the elemental compositions of subcellular history of work (e.g. Thompson 1942), requires further constituents (e.g. ribosomes), and of structure (e.g. skeleton, evaluation before it can be viewed as the explanation for the fat, ), are often highly conserved across taxa (Williams ubiquity of quarter-power scaling in biology (Allen & & Frausto da Silva 1996; Sterner & Elser 2002), reflecting Gillooly 2007). Nevertheless, it has proven useful for the common biochemical heritage of life (Morowitz 1968; understanding biological scaling in general, and for under- Williams & Frausto da Silva 1996). This concept is useful for standing how MTE and EST can be integrated in particular. understanding the nutritional requirements of organisms for Second, MTE models generally do not account for the survival, growth and reproduction, and for understanding demonstrably important effects of factors other than size how these processes, in turn, affect the flux, storage and and temperature on metabolic rate, such as resource turnover of elements in ecosystems. For example, by limitation (Monod 1950), which may induce changes in invoking the concept of stoichiometric invariance, the the metabolic normalization constant, bo (Brown et al. 2004), Ôgrowth rate hypothesisÕ of Elser et al. (1996) predicts that or even the scaling exponent in some circumstances (e.g. variation in whole-body P concentrations is partially Finkel 2001). Consequently, the variance left unexplained by attributable to increases in the densities of P-rich ribosomal )1 MTE models can be substantial, as has been noted in some RNA, qribo (g ), required to sustain higher growth rates. critiques (e.g. Tilman et al. 2004). Still, the approach of MTE Given that the mass fraction of RNA in P, f RNA,isc. 0.09 g ) P has proven useful for generating first-order predictions for Pg 1 RNA for all organisms, and that ribosomes comprise RNA many ecological and evolutionary processes. most of the RNA (fribo 0:85), the contribution of relatively P-rich RNA to whole-body P concentration, P (g ) Pg 1), can be expressed as EST and the stoichiometric-invariance concept

Ecological stoichiometry theory focuses on understanding RNA RNA RNA P ¼ f q Mribo=f þ PO ¼ f ½RNAþPO ð7Þ how differences in the balance of biologically important P ribo ribo P elements both affect and are affected by organisms and the environments in which they live (Sterner & Elser 2002). The Here Mribo is the mass of a , ½RNAqriboMribo= RNA RNA foundations of this work are based on first principles of fribo is the total RNA concentration, fP ½RNA is the physics, chemistry and biology, including LavoisierÕs law of concentration of RNA-associated P, and PO is the concen- conservation of mass and ProustÕs law of constant tration of other P ÔpoolsÕ such as skeleton (see Table 1 for proportions. Since the early days of ecology, EST has parameter definitions and estimates). So, eqn 7, which is applied these principles to better understand the structure our mathematical formulation of Elser et al.Õs (1996) growth and function of ecological systems at multiple levels. For rate hypothesis, uses stoichiometric invariance and the law example, at the individual level, Lotka (1925) noted that the of conservation of mass to relate the elemental composition stoichiometry of biomass differs substantially from that of of the organism to that of subcellular constituents, in this the lithosphere due to the biological processing of materials. case ribosomes. At the community level, Lindeman (1942) recognized that A second contribution of EST has been the development biota obey the laws of thermodynamics and mass-balance of theory for understanding the effects of nutrient limitation when energy and biomass are transferred between trophic on species. For example, this theory has helped ecologists to levels. And at the ecosystem level, Redfield (1958) observed understand why biological activity is often constrained by a that the C : N : P stoichiometry of the worldÕs oceans is single limiting resource at a given point in time. This maintained within relatively narrow bounds because phyto- observation, which is referred to as LiebigÕs (1840) law, is in plankton biomass tends to obey the law of constant fact a consequence of stoichiometric invariance: if biomass proportions. Anticipating the approach advocated here, has a fixed elemental composition, then whichever necessary Reiners (1986) recognized that predicting ecosystem dynam- element is most depleted in the environment tends to ics from individual- and community-level processes would constrain the amount of biomass produced. For unicells, the require explicitly linking element fluxes to energetics. Today, effects of resource availability on biota are often quantified EST continues to successfully apply these principles to aid by the equations of Michaelis & Menten (1913), in understanding many aspects of the structure and function of ecological systems. V ¼ VmaxR=ðÞK þ R ð8Þ One particularly relevant contribution of EST, which we shall refer to as the stoichiometric-invariance concept, is the observation that the constituents of ÔmetabolicÕ and Ôstruc- or Droop (1973) turalÕ biomass fractions comprising organisms are often relatively fixed with respect to elemental composition. l ¼ l1ðÞ1 Qmin=Q ð9Þ

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 373

Table 1 Kinetic and stoichiometric para- meters used in models, along with estimates Parameter Estimate Source and sources Ribosome parameters ribo 11 Ribosome flux (mo )1· 10 bonds Gillooly et al. (2005a) ) ) ribosome 1 s 1 Ribosome kinetics (Es) 0.65 eV Gillooly et al. (2005a) RNA )1 Fraction of RNA in ribosomes (fribo ) 0.85 g rRNA g RNA Sterner & Elser (2002) RNA )1 RNA fraction in P (fP ) 0.09 g P g RNA Sterner & Elser (2002) )18 Ribosome mass (Mribo) 4.2 · 10 g rRNA Gillooly et al. (2005a) )22 Amino-acid mass (Maa) 1.8 · 10 g Gillooly et al. (2005a) Animal parameters 8 )3 ⁄ 4 Endotherm flux (bo) 3.9 · 10 Wg Gillooly et al. (2005a) s 7 )3 ⁄ 4 Ectotherm flux (bo) 9.9 · 10 Wg Gillooly et al. (2005a) 7 )3 ⁄ 4 Unicell flux (bo) 2.8 · 10 Wg Gillooly et al. (2005a) Respiratory kinetics (Er) 0.65 eV Gillooly et al. (2001) )20 Energy content of ATP (EATP)5· 10 J Gillooly et al. (2005a) Fraction of metabolic energy allocated 0.2 Gillooly et al. (2005a) to protein synthesis (a) )1 Energy to produce biomass (EM) 1140 J g Gillooly et al. (2008) Ontogenetic growth parameter (x) 3.13 Gillooly et al. (2002) P assimilation efficiency (AP) 0.5–0.9 Frost et al. (2006) Gross growth efficiency (GGEC) 0.09–0.77 Frost et al. (2006) ) Energy per unit C flux (e)2· 104 Jg 1 C Nelson & Cox (2004) Plant parameters N N scaling (bo ) 0.02 Niklas et al. (2005) P )1 ⁄ 3 P scaling (bo ) 0.002 g Niklas et al. (2005) leafN )1 Fraction of leaf N in protein (fprotein ) 0.55 g protein g N Niklas et al. (2005) Protein retention efficiency (re) 0.6 Niklas et al. (2005) depending on whether resource limitation is considered in Frost et al. 2006). For example, Frost et al. (2006) demon- terms of external or internal nutrient concentrations. In strated that if the concentrations of P and C in these expressions, V is the rate of resource uptake per cell biomass are fixed (represented by P and C in the expression ) ) (lmol nutrient cell 1 day 1) at a given environmental below), and food is readily available, the threshold C : P )1 resource concentration, R (lmol nutrient L ), K is the ratio of food, TERC:P, is partly determined by the half-saturation constant, Vmax is the rate of resource uptake consumerÕs respiration rate, B, and its rate of C consump- )1 when resources are not limiting, l is the specific growth rate tion, IC (g C s ): ) of a population (day 1) at a given cell-nutrient quota, Q )1 (lmol nutrient cell ), l¥ is the growth rate at infinite quota AP C AP C and Q is the minimum quota required for growth. TERC:P ¼ ¼ ð10Þ min AC B=eIC P GGEC P Equations 8 and 9 serve as the basis for the influential R* theory of resource competition in ecology (Tilman et al. In this expression, the gross growth efficiency, ) 1981). GGEC ” AC B ⁄ eIC, is the fraction of ingested C Another important consequence of stoichiometric invari- allocated to growth, AC is the C assimilation efficiency, ance is that element ratios can be as important as absolute AP is the P assimilation efficiency and e is a conversion resource availability in constraining biological activity. In factor used to express C consumption in units of energy flux ) particular, stoichiometric invariance, when combined with (J g 1 C, Table 1). conservation of mass for element fluxes between trophic levels, following Lindeman (1942), yields the prediction that Limitations of EST models there exists a threshold element ratio (TER) for food (prey) at which the nutrient limiting consumer growth shifts from Two limitations of EST models are pertinent to our one element to the other (Sterner & Hessen 1994). TER is a discussion. First, EST models do not predict the partitioning useful concept for linking MTE with EST because it of biomass between ÔmetabolicÕ and ÔstructuralÕ fractions, encompasses the elemental composition of biomass, and the and therefore do not yield a priori predictions on the energetics of growth and respiration (Schindler & Eby 1997; elemental composition of an entire organism. For example,

2009 Blackwell Publishing Ltd/CNRS 374 A. P. Allen and J. F. Gillooly Idea and Perspective while the growth rate hypothesis identifies an important link Principle (I) because together they imply that adding an between whole-body P concentration and the concentration additional MU to a unit of biomass induces a predictable of ribosomal RNA (eqn 7), a substantial fraction of P is change in both the energy flux and elemental composition found in constituents other than ribosomes, particularly for of that biomass. multicellular organisms (Gillooly et al. 2005a; also see Two recently published models, the Gillooly et al. (2005a) Fig. 3). Second, many variables in nutrient limitation models model of RNA concentration in animals, and the Niklas – including Vmax, K, l¥, AP, AC and GGEC in eqns 8–10 – et al. (2005) model of leaf growth in plants (see Table 1 for a are not predicted by EST and must therefore be empirically list of model parameters) point to the importance of estimated. This limits the predictive power of EST models Principle (I). On the surface, these models appear quite across taxa and environments. different. But upon closer examination, one can see that both models assume energetic and stoichiometric invariance to derive unique predictions. Each model assumes that the PRINCIPLES FOR INTEGRATING MTE AND EST masses and elemental compositions of ribosomes and The models of MTE and EST both utilize assumptions that amino-acids are fixed (stoichiometric invariance), and that are grounded in energetic principles and energy balance (e.g. ribosomes have a fixed capacity to synthesize proteins Boltzmann–Arrhenius temperature kinetics), and principles (energetic invariance). In addition, the model of Gillooly of nutrient availability and mass balance (e.g. LeibigÕs law). et al. (2005a) incorporates the well-established exponential Indeed, some of the patterns and relationships described by effect of temperature on the rate of protein synthesis per these two bodies of theory could be described equivalently ribosome: in fluxes of energy or elements. Nevertheless, MTE and ribo Es=kT EST could both benefit from explicitly quantifying inter- mribo ¼ mo e ð11Þ relationships between currencies. And, as we will demon- ribo strate in this section, some limitations of these two theories In this expression, mo is a normalization constant )1 can be addressed using four key principles that bridge MTE independent of temperature (peptide bonds s ) and and EST. To be sure, none of these principles is new, but Es » Er » 0.65 eV. considered together in light of MTE and EST models, they The model of Gillooly et al. (2005a) builds on Elser et al.Õs may provide a roadmap for linking the biological currencies (1996) growth rate hypothesis (defined above) to yield of energy and materials in an integrative theoretical predictions on whole-organism RNA concentration based framework. Specifically, these four principles integrate on the size- and temperature-dependence of metabolic rate MTE and EST models by linking individual-level energetics (eqn 5), and the observation that protein synthesis and stoichiometry to higher-order processes based on two consumes a relatively constant fraction of metabolic energy complementary forms of invariance – energetic and in adult animals (a » 0.2). The model predicts both the stoichiometric – at the level of cellular organelles. To slope and intercept of the log–log relationship between the s demonstrate the utility and generality of these principles, we standardized RNA concentration, log½ RNA bo=bo , and discuss recent models and analyses that apply these body size, log[M], irrespective of temperature: principles to both animals and plants (unicellular and multicellular). 1 aM bs s = ribo o log½ RNA bo bo ¼ log½þM log ribo RNA 4 4mo EATPfribo Principle I: Fluxes of energy and materials are linked based ð12Þ on the kinetics and elemental compositions of subcellular structures and processes This expression establishes the quantitative relationships of Principle (I) is important for linking the structure and metabolic rate to the rates of ATP production and protein function of subcellular components to the structure and synthesis, and to the concentrations of RNA and RNA- function of organisms, particularly with respect to growth. associated P. It therefore links energy and materials at the While this principle has long been recognized as a truism by cellular level to yield predictions at the level of the organism. biochemists and cell biologists (Morowitz 1968), it is less Empirical data showing the relationship between RNA and often considered by ecologists working at higher levels of body mass for diverse taxa support model predictions biological organization. In part, this is because it has not (Fig. 1). been clear until recently how higher-level processes such as Using a similar approach, Niklas et al. (2005) extended the growth are related to the structure and function of model of Dobberfuhl (1999) to predict how the rate of organelles, either qualitatively or quantitatively. The ener- accumulation of leaves in the canopy of a plant, getic and stoichiometric forms of invariance, in fact, yield lleaf ¼ ðÞ1=Mleaf ðÞdMleaf =dt , varies with the total mass of

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 375

0.5 y = 0.23x – 0.54 y = 0.33x – 0.38 r ² = 0.78, n = 86 r² = 0.78, n =131 2 ) –1 mass)

–1 0.0 ) (day

1 leaf (µ 10 –0.5 /bo) (mg RNA g s o 0 Birds & mammals ([RNA] b Marine & freshwater fish –1.0 10 Marine & freshwater Canopy growth, log Log –1 Other invertebrates Unicells –1.5 –10 –5 0 5 –3 –2 –1 0 1 2 Body mass, log10 (M) (g) Canopy mass, log10 (Mleaf) (g) Figure 1 Whole-body RNA content corrected for taxon-specific Figure 2 Relationship of mass-specific rate of leaf accumulation to metabolic normalization constants, bo, plotted as a function of dry body mass for unicellular eukaryotes, multicellular ectotherms and total leaf-canopy size for 131 species (data from Niklas et al. 2005). et al. The model (eqn 13) was fitted to the data by finding the value of endotherms (data compiled in Gillooly 2005a). The normal- leafP ization constant, bs , used to control for differences among taxa in fRNA that minimized the sum of the squared deviations. o Independent estimates for the other parameters of eqn 13 are bo (eqn 6) is arbitrary (see Table 1). The OLS-fitted solid line is close to the predicted dashed line of y = )0.25x + 0.69 mg listed in Table 1. ) RNA g 1 dry mass (eqn 12), which was calculated based on the parameter estimates in Table 1. fraction of P in RNA, after accounting for the temperature dependence of ribosome kinetics (eqn 11, Table 1), if we assume a growth temperature of 25 C. This estimate is leaves, Mleaf. In the absence of direct measures of RNA concentration, Niklas et al. (2005) parameterized their model plausible given the range of estimates reported for ecto- by combining previous estimates of leaf-level parameters thermic animals (see, for example, Gillooly et al. 2005a). with allometric expressions characterizing the size-depen- The studies of Gillooly et al. (2005a) and Niklas et al. N (2005) both demonstrate how relationships between energy dencies of total canopy N (Nleaf ¼ bo Mleaf ) and P P 4=3 flux and elemental composition at higher levels of organi- (Pleaf ¼ boMleaf ) (Table 1). Using these parameters, Niklas et al. (2005) proposed a model similar in form to the zation (leaf, individual) can be predicted based on subcel- following (see Appendix S1 in Supporting Information): lular structures and processes by combining the energetic- and stoichiometric-invariance concepts of MTE and EST "#respectively. These two models yield predictions on distinct RNA leafP P 1 f f b mriboMaare phenomena for diverse organisms based on common l M ribo RNA o log½¼leaf log½þleaf log RNA leafN N 3 fP Mribofprotein bo principles and parameters. For example, the animal model of Gillooly et al. (2005a) and the plant model of Niklas et al. ð13Þ (2005) both assume essentially the same protein-synthesis rate at the level of the ribosome. Equation 13 yields predictions for the slope and intercept of the log–log linear relationship between the rate of leaf Principle II: Biomass is comprised of ÔmetabolicÕ and growth and canopy size. However, as Niklas et al. (2005) ÔstructuralÕ pools, which can exhibit distinct allometries pointed out, it was necessary to estimate the fraction of leaf leafP and elemental compositions P in RNA, fRNA , from their data due to an absence of independent measurements. Given this caveat, Niklas et al. Principle (I) must be combined with Principle (II) to predict (2005) concluded that data for 131 plant species (depicted in element dynamics at the level of the organism, and at the Fig. 2) were broadly supportive of their model. Here, the level of the ecosystem, as we discuss below. This is because, fitted intercept in Fig. 2 yields an estimate of 9% for the by itself, Principle (I) is only useful for relating fluxes (e.g.

2009 Blackwell Publishing Ltd/CNRS 376 A. P. Allen and J. F. Gillooly Idea and Perspective

growth rate in the models above) to MU-associated 1.0 nutrients (e.g. ribosomal P), and not to total nutrient concentrations in biomass, which include metabolic and structural contributions. This need to distinguish between 0.5 metabolic biomass (comprised of MUs) and the remaining structural biomass has been central to the development of 0.0 MTE and EST. For example, in the WBE model of MTE, ) (% mass)

the size-dependence of metabolic rate is proximately related P (

to changes in the densities of MUs (eqn 3). Thus, MTE 10 –0.5 yields predictions on the partitioning of biomass between metabolic and structural fractions. Similarly, in the Droop –1.0 equation of EST, structure contributes to Qmin (eqn 9),

which is the minimum internal nutrient content necessary P content, log Whole-body P for growth. –1.5 We illustrate the importance of Principle (II) using two RNA P examples that pertain to the flux, storage and turnover of P and N. First, we consider the formulation of Gillooly et al. –2.0 (2005a) for the body-size dependence of whole-body P. As –6 –4 –2 0 2 RNA Body mass, log (M) (g) P associated with RNA, fP ½RNA, exhibits a predictable 10 size dependence (Fig. 1), whole-body P concentration, P,is predicted to decline with increasing adult size, M, following Figure 3 Relationships of whole-body P concentration and RNA concentration to adult size for 169 insect species from the Sonoran eqns 7 and 12: desert ( et al. 2004). The solid lines were predicted using RNA eqns 12 and 14 based on the parameter estimates listed in Table 1. f aMribobo = P ¼ f RNA½RNA=f RNA þP ¼ P M 1 4 þ P See Gillooly et al. (2005a) for further details on how these P ribo O mriboE f RNA O 4 o ATP ribo parameter estimates were obtained. ð14Þ

following eqn 2, where B is the total metabolic rate of the Equation 14 assumes that P content in pools other than leaf leaf canopy (W), qchlor is the number of chloroplasts per unit RNA, P , shows negligible change with size, and varies ) O mass of leaf (g 1) and m is the photosynthetic flux per little among species. The model (solid line in Fig. 3), which chlor chloroplast (W). Then, based on Principle (II), we express was independently parameterized based on the biochemi- the overall N concentration of a leaf, N ⁄ M , as the sum cal parameters in Table 1 and an overall estimate of leaf leaf ) of the N pools associated with chloroplasts, N q , and P = 0.006 g P g 1 for invertebrates (Elser et al. 2003), chlor chlor O other leaf constituents, N leaf (e.g. cell wall) does reasonably well at predicting nonlinear declines in O whole-body P concentration for insects collected from the leaf Nleaf =Mleaf ¼Nchlorqchlor þ N ; ð16Þ Sonoran desert. This nonlinear relationship arises because O the animal P in RNA systematically declines with increasing where Nchlor is the N content of a chloroplast (g N). To- size (dashed line in Fig. 3). gether, eqns 15 and 16 yield the following linear function: Second, we consider the well-established positive rela- m m tionship between leaf-level N and the leaf-level rate of chlor chlor leaf qchlormchlor ¼ ðÞNleaf =Mleaf NO ð17Þ photosynthesis (Field & Mooney 1986; Wright et al. 2004), Nchlor Nchlor which is a primary determinant of plant growth. Based Provided that the invariance assumptions are upheld for only on Principle (I), one might conclude that this leaf relationship indicates that all leaf-level N is contained in chloroplasts, and that NO is independent of chloroplast chloroplasts. However, using Principles (I) and (II), we can density, eqn 17 predicts a linear relationship between the q m formulate a hypothetical model for this relationship to photosynthetic rate, chlor chlor and leaf-level N concentra- ⁄ quantify the leaf-level N fractions in metabolic and tion, Nleaf Mleaf. A plot of leaf-level flux against leaf-level N structural constituents. Based on Principle (I), we first concentration for 107 plant species supports this prediction note that the rate of photosynthesis per unit leaf , by showing a linear function that accounts for 69% of the B ⁄ M , is equal to variation, consistent with Principle (I) (Fig. 4). And with leaf leaf respect to Principle (II), the fitted slope and intercept of this relationship yield an estimate for the average concentration Bleaf =Mleaf ¼ q mchlor ð15Þ leaf chlor of structural leaf N (NO ¼ 0:006).

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 377

500 also inextricably linked to flux, following Principles (I)–(II), it

) y = 7995x – 50 should be possible to derive novel predictions on how body –1 r ² = 0.69, n = 107 s size, temperature and elemental composition combine to –1 400 influence fluxes of energy and matter. Three examples, one for unicellular plants and two for

(nmol g animals, illustrate the importance of combining Principles leaf 300 M (I)–(III) to better understand nutrient cycling. First, we /

leaf consider the study of Litchman et al. (2007), which uses a B nutrient-uptake model for phytoplankton (Aksnes & Egge 200 1991) to derive predictions for the body-size-scaling of parameters in the Michaelis–Menten equation (Michaelis & Menten 1913; Briggs & Haldane 1925) and the equation of 100 Droop (1973). With regard to the Michaelis–Menten equation, Litchman et al. (2007) predict a 2 ⁄ 3-power scaling Photosynthetic rate, 0 exponent for maximum rate of N uptake, Vmax, in relation to cell volume, V : 0.00 0.01 0.02 0.03 0.04 0.05 0.06 cell

Leaf N concentration, Nleaf/Mleaf 2=3 Vmax / Vcell ð18Þ Figure 4 Relationship of photosynthetic rate per unit leaf mass to leaf N concentration for measurements taken from species around the world (Reich et al. 1999). The model (eqn 17) was fitted to the This predicted exponent differs from the value of 3 ⁄ 4 data using reduced major-axis regression. predicted by WBE because Litchman et al. (2007) invoke the assumption of Aksnes & Egge (1991) that the rate of Both examples above demonstrate the need to distinguish nutrient uptake, and hence the cellular metabolic rate, is between metabolic and structural biomass when relating controlled by the surface area of the cell. As shown in Fig. 5, fluxes of energy and materials to the elemental composition there is a tight relationship between Vmax and cell volume of biomass. This issue is particularly relevant because the for phytoplankton. Moreover, the slope of this log–log sizes of the metabolic and structural biomass fractions may relationship is closer to 2 ⁄ 3than3⁄ 4(x ¼ 0:61, 95% CI: exhibit distinct allometric scaling relationships, leading to 0.45–0.77). These findings are consistent with the surface- more complicated relationships between overall nutrient concentration and size, as demonstrated by eqn 14 and the data depicted in Fig. 3. Moreover, the elemental composi- –3 ) y = 0.61x – 7.87 tions of these fractions may differ considerably, as –1 r² = 0.83, n = 16 leaf demonstrated by the low estimate of NO relative to leaf day –4 N for many of the taxa depicted in Fig. 4. –1

Principle III: At the level of the organism, fluxes of energy –5 and elements are governed by metabolic rate and its ) (µmol cell max V

determinants ( –6 10 Principle (III) is important for understanding how differ- ences among species with respect to body size, temperature and resource availability influence the flux, storage and –7 turnover of energy and elements in ecosystems. This N uptake, log principle, which is a central tenet of MTE, reflects the fact –8 that the uptake and transformation of energy and materials by an organism requires metabolic energy (Brown et al. 01234567 Cell volume, log (V ) (µm3) 2004). It has two important consequences. First, as body size 10 cell and temperature have predictable effects on energy flux Figure 5 Relationship of maximum uptake rate of nitrate to cell (eqn 1), these variables should also have predictable effects volume for a compilation of data for diatoms, coccolithophores, on material fluxes in nutrient-limitation models such as the dinoflagellates and green (Litchman et al. 2007). The 95% CI Michaelis–Menten equation (eqn 8) and the Droop equation for the OLS-fitted regression slope is significantly less than unity (eqn 9). Second, as the elemental composition of biomass is (0.45–0.77), as predicted by eqn 18.

2009 Blackwell Publishing Ltd/CNRS 378 A. P. Allen and J. F. Gillooly Idea and Perspective

to-volume-scaling arguments of Litchman et al. (2007), 5 × 105 although a 3 ⁄ 4-power slope is also consistent with their ) data. More generally, these findings are consistent with a –1 large body of literature demonstrating that body size is a (s 4 × 105 kT / r primary determinant of nutrient dynamics in unicellular and E e multicellular organisms (e.g. Wen et al. 1997; Vanni et al. G 3 × 105 2002; Hall et al. 2007). For the second example, we combine the RNA model of Gillooly et al. (2005a) (eqns 12 and 14) with the ontogenetic 2 × 105 growth model of West et al. (2001) to characterize how body size, temperature and whole-body P influence the temper- ature-corrected rate of individual growth, GeEr ⁄ kT, where 1 × 105

1 ⁄ G is the time from the juvenile stage to the size at T-corrected growth rate, adulthood, M: 0 × 105 b M 1=4 f RNAmriboE GeEr=kT ¼ o ¼ ribo o ATP ðÞðP P 19Þ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 RNA O % body mass in P 4xEM xEMaMribofP This expression includes all of the parameters in the RNA Figure 6 Relationship of temperature-corrected growth rate to model along with EM, which characterizes the energy to whole-body P concentration for eight species of zooplankton (data produce biomass (West et al. 2001; Gillooly et al. 2008; compiled in Gillooly et al. 2002). The model (solid line, eqn 19) was Moses et al. 2008), and x, which characterizes taxon-specific fitted to the data by finding the value of PO that minimized the attributes of the ontogenetic growth curve (Table 1, sum-of-squared deviations. Independent estimates for all of the Appendix S1). This equation demonstrates that growth other parameters in eqn 19 are listed in Table 1. (a flux) can be expressed in terms of size and temperature, or in terms of stoichiometry and temperature, without Holding other variables constant, eqn 20 predicts a reference to size, reflecting linkages between body size, negative relationship between TERC:P and G because temperature, metabolic rate, and the energy and density of maintaining a higher growth rate requires more P-rich P-rich ribosomes required for growth. The correspondence ribosomes which, in turn, requires eating foods richer in P. of model (eqn 19) to data is reasonable (Fig. 6), given that In addition to providing the first theoretical support for the the cluster of four points exhibiting the largest negative hypothesis of Frost et al. (2006), eqn 20 highlights that the deviations corresponds to only one of the eight species extent to which growth is P-limited is influenced not only by analysed. Moreover, the slope of the line, the nutrient-use efficiencies (GGEC, AP, AC), but also by RNA ribo RNA RNA ribo ðfribo mo EATPÞ=ðxEMaMribofP Þ, is independently cal- the kinetics and stoichiometry of ribosomes (fribo , mo , RNA culated based on the parameter estimates listed in Table 1 Mribo, fP ), following Principle (I), the amount of P stored rather than being fitted to the data. We note, however, that in biomass pools other than RNA, PO, following Principle the confidence interval of the one fitted parameter, PO,is (II), and the energetics of individual metabolism (B, IC, Er, substantial (x ¼ 0:0006, 95% CI: 0.00001–0.04), perhaps x, EM, a), following Principle (III). indicating significant variation in structural P among taxa. As a first step towards empirically evaluating this new For the third example, we extend the model above to model, we fit eqn 20 to the invertebrate data of Frost et al. predict the TER for food at which consumer growth shifts (2006) using nonlinear least-squares regression. The fitted from nutrient (P) to energy (C) limitation, TERC:P. Frost model yields an estimate for PO (=0.0068; 95% CI: 0.0020– et al. (2006) reported a significant negative relationship 0.030) similar to previous estimates (Elser et al. 2003), and between TERC:P and growth, and proposed that the growth an estimate for GGEC (=0.29; 95% CI: 0.09–0.65) within rate hypothesis of EST could account for this relationship. the range of values reported by Frost et al. (2006) (0.09– By integrating EST with MTE using eqns 10, 12, 14 and 19, 0.77) (see Fig. 7 legend for details on these calculations). we can explicitly quantify this hypothesis: Thus, predictions of the model appear broadly consistent

A C f RNAmriboE f RNAmriboE P ribo o ATP Er=kT ribo o ATP TERC:P ¼ RNA Ge þ RNA PO ð20Þ GGEC xEMaMribofP xEMaMribofP

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 379

energetics-based approach of MTE and the mass-balance 3.0 approach of EST.

) C:P Principle IV: The storage, flux and turnover of energy and TER ( materials in biological communities and ecosystems can 10 2.5 be estimated by summing across individuals in that community Principle (IV) is important when considering the total flux, 2.0 storage and turnover of nutrients among communities of organisms. While conceptually straightforward, Principle (IV) yields novel predictions when combined with the other three principles above. For example, the total biomass per unit area, M , for a community comprised of J individuals in Threshold element ratio, log 1.5 T an area of size A is readily obtained by summing the biomass contributions of individuals comprising that 3.5 4.0 4.5 5.0 5.5 6.0 community: E kT –1 Temperature-corrected growth rate, log10 (Ge r/ ) (day ) XJ 1 MT ¼ A Mi ð21Þ Figure 7 Relationship of threshold C-to-P ratio (mass basis) to i ¼ 1 temperature-corrected growth rate for invertebrate data compiled by Frost et al. (2006). Equation 20 was fitted to the data (solid line) Equation 21 is generic in form, and is therefore applicable by estimating two parameters using nonlinear least-squares not only to total biomass, but also to storage of elements regression, assuming a growth temperature of 25 C. Excluding such as N and P in biota. However, due to the size two points deemed to be outliers based on their leverage in the dependence of element ratios (following Principle II), model fit (represented by triangles), this procedure yields an storage is influenced not only by total biomass, but also estimate of 0.0068 for P in pools other than RNA, PO. The second by the size distribution of individuals. For example, parameter, which corresponds to the product APC ⁄ GGEC, yields Kerkhoff & Enquist (2006) presented theory and data an estimate of 0.29 for the gross growth efficiency, GGE , given C indicating that the total quantities of N and P stored in typical values of C (=0.48) and A (=0.8) reported by Frost et al. P phytomass, N and P , increase nonlinearly with M ,when (2006), and estimates in Table 1 for other parameters. Results are T T T similar if the two outliers are included in the analysis, although 95% comparing ecosystems ranging from arctic tundra to tropi- cal forest (i.e. N / P / M 3=4), because smaller-bodied CIs for PO and GGEC are substantially wider. T T T plants contain higher concentrations of MUs and associated nutrients (as illustrated above for animals in eqn 14 and with the data of Frost et al. (2006). While these estimates Fig. 3). Principle (IV), when combined with Principle (III), can capture the overall relationship of growth rate to TERC:P (Fig. 7), it is important to recognize that there exist also be used to derive predictions on ecosystem flux by substantial differences among taxa with respect to other linking individual metabolic rate to population- and com- munity-level processes. For example, if population abun- variables predicted by eqn 20 to affect TERC:P, including dance per unit area, J=A, is at equilibrium with the supply the energy required to produce biomass, EM (see Moses et al. 2008), and the C:P stoichiometry of biomass (see Frost rate of a limiting resource in the environment, L, and if the et al. 2006). For example, the datum exhibiting the greatest flux by individual i, Fi, is proportional to metabolic rate (i.e. deviation from the fitted line (depicted by a triangular point Fi / Bi ), following Principle (III), then total flux per unit )1 )1 in Fig. 7) had a total P concentration lower than our overall area for a population, FT (flux g ha ), is equal to: estimate for the nonmetabolic P fraction, PO. Thus, more XJ XJ 1 1 detailed analyses are needed to assess how multiple variables FT ¼ A Fi / A Bi influence TERC:P, and thereby contribute to deviations iDE¼ 1 i ¼ 1 ð22Þ about the fitted line in Fig. 7. Equation 20 provides a 1=4 ¼ b M M eEr=kT / L; framework to perform such analyses. o T i Overall, the reasonable fits of models to empirical data in DE Figs 6 and 7 suggests that, by using Principles (I)–(III), it is 1=4 where Mi is a quarter-power average for body size possible to predict fluxes of energy and matter using PJ 1 3=4 models, assumptions, and principles that encompass the [¼ ðÞAMT Mi ] (Enquist et al. 2003; Allen et al. 2005). i¼1

2009 Blackwell Publishing Ltd/CNRS 380 A. P. Allen and J. F. Gillooly Idea and Perspective

Equation 22 provides a general expression for the total flux ships used to derive population- and ecosystem-level of a given element in a community comprised of different- predictions in these studies are ultimately related to the sized individuals, and at different body temperatures. fluxes, densities and stoichiometries of MUs comprising Importantly, however, while total ecosystem flux is, by biomass, following eqns 1–7 and Principle (I). These definition, equal to the sum of the individual fluxes, as examples highlight the potential to explicitly link element specified in eqn 22, predicting FT will be challenging for flux, storage and turnover in ecosystems to the energetics communities comprised of species that compete for and stoichiometry of cellular organelles. multiple limiting resources rather than a single resource, L. By combining Principles (III) and (IV), Habeck & DISCUSSION Meehan (2008) recently presented evidence that total N flux is about the same for populations of herbivorous The models discussed above suggest that the four principles mammals that range in size from a mouse to a moose. They highlighted in this paper, when combined with models and obtained this result by combining DamuthÕs (1981) rule, concepts of MTE and EST, offer a useful framework for which describes the size-dependence of population abun- linking the flux, storage and turnover of energy and 3=4 dance for mammals (J=A / Mi ), with the observation materials at different levels of biological organization. On that N excretion rate is proportional to metabolic rate (i.e. the one hand, by combining the energetic-invariance 3=4 Fi / Bi / Mi ). Irrespective of DamuthÕs rule, Habeck & concept of MTE with energy balance, it is possible, for MeehanÕs (2008) data indicate that N excretion per unit example, to relate energy and material fluxes from leaves biomass declines with increasing body size in the same way (eqn 15), individuals (eqns 2, 3, 5, 6) and ecosystems (eqn 1=4 as mass-specific metabolic rate (i.e. FT=MT / Mi , 22) to densities of metabolically active organelles including following eqn 22), consistent with the data depicted in chloroplasts, mitochondria and ribosomes. On the other Fig. 8. hand, by combining the stoichiometric-invariance concept The studies of Kerkhoff & Enquist (2006) and Habeck & of EST with mass balance, it is possible to relate organelle Meehan (2008) highlight the potential of combining densities to the storage of essential elements like N and P in energetic and stoichiometric principles to derive predictions biomass (eqns 7, 14, 16). Together these complementary on the storage and flux of elements in entire ecosystems. forms of invariance link the dynamics of energy and matter While not explicitly discussed, the individual-level relation- in individuals and ecosystems (eqns 12, 13, 17, 19, 22) to the kinetic and stoichiometric properties of organelles (eqns 4, 11; Table 1). These linkages are characterized using sum- mation rules (e.g. eqns 21, 22) because energy and materials )

–1 y = –0.27x – 2.38 are fluxed, stored and turned over at all levels of biological r² = 0.64, n = 26 organization. day –2.5 –1 Integration of these two theories may help address some of the limitations of MTE and EST. For example, with

) (g N g regard to EST models, mass-balance is insufficient to T M / –3.0 predict parameters of nutrient-limitation models such as T F

( those of Michaelis–Menten and Droop (eqns 8, 9).

10 However, as demonstrated by the study of Litchman et al. (2007), it is possible to predict the size-dependence of –3.5 nutrient uptake by incorporating energetics. And, with regard to MTE models, even after accounting for body size and temperature, the elemental composition of biomass has independent effects on biological rates, as demonstrated by –4.0 eqn 19 and Gillooly et al. (2002, 2005a). More generally, the Population N Flux, log models and results presented here indicate that individual 1234 5 energetics and biomass stoichiometry are inextricably linked Individual body mass, log10 (Mi) (g) with each other, and with nutrient availability in the environment. For example, our expression for the TER Figure 8 Size-dependence of average N flux per unit biomass for herbivorous mammal populations ranging in size from a mouse to (eqn 20) predicts that the extent to which growth is nutrient- a moose (species-level logarithmic averages of data compiled in limited is partly determined by biomass stoichiometry and Habeck & Meehan 2008). The fitted OLS regression slope is individual energetics. Thus, models that integrate MTE and statistically indistinguishable (P > 0.05) from the predicted value of EST to predict the combined effects of all three classes of )0.25 (following eqn 22). variables – biomass stoichiometry, energetics, resource

2009 Blackwell Publishing Ltd/CNRS Idea and Perspective Towards an integration of ecological stoichiometry and the metabolic theory of ecology 381 availability in the environment – should have greater how species adapt to nutrient limitation and changing predictive power. environmental conditions. For example, it is well established We do not mean to imply that this proposed theory that the normalization constant of plants respiration, bo synthesis can account for all ecological phenomena. Rather, (eqn 5), declines with long-term temperature increases. The we argue that efforts along these lines offer the potential to biochemical basis of this phenomenon is still poorly provide a firmer foundation for understanding how ener- understood despite its importance to C balance in ecosys- getic and stoichiometric constraints, including those tems (Atkin et al. 2005). A straightforward extension of the imposed by attributes of organelles, combine to influence theory presented here yields a novel hypothesis amenable to mito mito individual-level fluxes and stores of energy and matter. Such empirical testing. Given that bo ¼ qo mo (eqn 6), and constraints can then be integrated into models aimed at that plant respiration is ultimately constrained by photosyn- predicting higher-order ecological phenomena, including thesis, energetic invariance yields the prediction that competitive interactions among species, food-web structure respiratory acclimation occurs because plants grown at and ecosystem dynamics. higher temperatures maintain lower mitochondrial densities, mito Many important theoretical and empirical challenges qo , owing to the stronger temperature dependence of remain to achieve full integration of MTE and EST. Here respiration by mitochondria vs. photosynthesis by chlorop- we highlight four more specific challenges. First, at the lasts (Allen et al. 2005). The study of Armstrong et al. (2006) subcellular level, further work is needed to evaluate the provides qualitative support for this prediction, but far more energetic- and stoichiometric-invariance concepts or research is needed in this area. assumptions. Efforts along these lines are currently under- Third, further work is needed to understand what factors way. For example, with regard to stoichiometric invariance, control the sizes of structural-element pools, which can vary Elser et al. (2006a) demonstrated that the N contents of considerably among taxa, as demonstrated by the examples amino-acid residues are higher for proteomes of animals above. Knowing the sizes of these pools is important for than of plants, which are more likely to experience N predicting some phenomena, such as the relationship of limitation. And with regard to energetic invariance, growth rate to whole-body P concentration (eqn 19). Tcherkez et al. (2006) showed that Rubisco kinetics vary Furthermore, when resources are abundant, some organisms among plant taxa in different CO2 environments, and consume, assimilate and store elements in excess of argued that this pattern reflects evolutionary optimization of metabolic and structural requirements (Sterner and Elser protein structure to maximize photosynthesis. These exam- 2002; Klausmeier et al. 2004). Explicitly modelling the ples illustrate that evolutionary mechanisms may influence contribution of this Ôluxury consumptionÕ to biomass nutrient cycling through their effects on the structure, stoichiometry, and how it varies with energetics and function and stoichiometric composition of biological resource availability, seems critical for understanding why, . Such mechanisms would lead to deviations for example, eqn 19 predicts that individual growth rate from the energetic- and stoichiometric-invariance assump- increases linearly with internal P content, whereas the tions used to construct the models discussed here, and may Droop equation (eqn 9) models the rate of population thereby induce variation about the predicted relationships in increase as a saturating function of nutrient concentration. Figures 1–8. Evaluation of these two assumptions is A fourth challenge entails extending models to encom- therefore important for refining models, and more generally pass the effects of non-steady-state dynamics on energetics for assessing the extent to which evolutionary processes and stoichiometry. For example, at the individual level, Elser mediate linkages between energetics and stoichiometry. et al. (2006b) reported declines in P content over ontogeny Second, at the levels of tissue and individual, more for five species of Drosophila. These declines may be related experiments are needed that assess relationships between to decreased energy allocation to growth vs. maintenance as flux, stoichiometry and densities of subcellular constituents, organisms approach adulthood. This hypothesis is qualita- and how these variables are affected by ecological condi- tively consistent with the MTE model of ontogenetic tions. With the exception of efforts to evaluate the growth growth (West et al. 2001), but has yet to be quantitatively rate hypothesis, surprisingly few studies have simultaneously formulated and tested. Similarly, at the level of populations, measured these variables for the same individuals or tissues. MTE and EST models both indicate that resource allocation Such research could benefit many areas of basic and applied to the production of offspring should vary depending on ecology. For example, it may deepen our understanding of whether populations are growing exponentially or are near the biochemical basis of trait differences among species (e.g. (Klausmeier et al. 2004; Kuang et al. 2004; leaf-level N and photosynthesis, Fig. 4), which contribute to Savage et al. 2004). Yet, here again we lack a comprehensive fitness differences among species in particular environments understanding of non-steady-state dynamics. Such models and species turnover across environmental gradients may be important for understanding how populations are (McGill et al. 2006). It may also aid in understanding of affected by energy and nutrient limitation, and more

2009 Blackwell Publishing Ltd/CNRS 382 A. P. Allen and J. F. Gillooly Idea and Perspective generally for understanding how species respond to and ecological consequences. PhD Thesis. Arizona State Uni- environmental change. versity Tempe, AZ, p. 224. While these challenges point to the importance of future Droop, M.R. (1973). Some thoughts on nutrient limitation in algae. J. Phycol., 9, 264–272. work at the intersection of MTE and EST, the examples Elser, J.J. & Hamilton, A. (2007). Stoichiometry and the new presented here show how the energetics approach of MTE biology: the future is now. PLoS Biol., 5, e181. can be combined with the mass-balance approach of EST to Elser, J.J., Dobberfuhl, D.R., MacKay, N.A. & Schampel, J.H. yield novel, first-order predictions on the flux, storage and (1996). Organism size, life history, and N:P stoichiometry. Bio- turnover of elements across species and environments. science, 46, 674–684. From the perspective of basic science, integration of these Elser, J.J., Acharya, K., Kyle, M., Cotner, J., Makino, W., Markow, theories could help link different levels of biological T.A. et al. (2003). Growth rate–stoichiometry couplings in Ecol. Lett. organization, different biological currencies and different diverse biota. , 6, 936–943. Elser, J.J., Fagan, W.F., Subramanian, S. & Kumar, S. (2006a). scientific disciplines. From an applied perspective, such Signatures of ecological resource availability in the animal and integration could help address environmental issues. After plant proteomes. Mol. Biol. Evol., 23, 1946–1951. all, current and future challenges of environmental change Elser, J.J., Watts, T., Bitler, B. & Markow, T.A. (2006b). Ontoge- often involve simultaneous changes in the size structure, netic coupling of growth rate with RNA and P contents in five temperature and resource availability of ecological commu- species of Drosophila. Funct. 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