### Introduction

- Top of page
- Summary
- Introduction
- Model assumptions
- Model derivation
- Evaluating model predictions
- Results
- Discussion
- Acknowledgements
- References
- Appendix

Here we take a different approach. We extend a metabolic theory of ecology (Brown *et al*. 2004) to develop a model that focuses on the role of individual organisms in the global C cycle. This model provides a simple mathematical formulation based on first principles of biology, chemistry and physics. It relates the global C cycle directly to the flux, storage and turnover of C in individual organisms. The model highlights the fundamental influence of two variables – body size and temperature – on C dynamics at all levels of biological organization, from cellular organelles to the biosphere.

The model developed here differs in three important ways from those commonly used in ecosystem ecology. First, it explicitly links the rates of photosynthesis and respiration to the effects of body size and temperature on plant, animal and microbial metabolism. Temperature has long been recognized as an important determinant of C dynamics, but body size has rarely been included in ecosystem models. Second, by quantifying these two primary controls on individual metabolic rate, the model explicitly links ecosystem C cycling to cellular-, individual- and community-level processes. Third, it provides a theoretical baseline for assessing quantitatively the effects of other variables such as water, nutrients and light. Therefore the model provides a simple mechanism-based formulation that complements more complicated empirical and simulation studies of C cycling.

### Evaluating model predictions

- Top of page
- Summary
- Introduction
- Model assumptions
- Model derivation
- Evaluating model predictions
- Results
- Discussion
- Acknowledgements
- References
- Appendix

Equations 1–22 yield a series of testable, quantitative predictions on the size and temperature dependence of flux, storage and turnover within and among the C pools depicted in Fig. 1 (Table 1). We evaluate many of these predictions using global compilations of data from major biomes that include forests, grasslands, tundra and oceans. The predictions in Table 1 are derived by explicitly accounting for day-length and length of growing season. For example, NPP is expressed on a per daylight hour basis during the growing season, (τ/γ)<*n*>_{τ} (g C m^{−2} daylight h^{−1}); C storage in soil is corrected for average day-length, (τ/γ)*S* (g C m^{−2} h daylight h^{−1}); and C turnover in soil is expressed on a per hour basis during the growing season, <*r*_{H}>_{τ}/*S* (h^{−1}). Where possible we evaluate long-term temperature predictions using these ‘seasonality-corrected’ values to control for latitudinal variation in day-length and length of growing season, which might otherwise confound the predicted temperature relationships.

### Results

- Top of page
- Summary
- Introduction
- Model assumptions
- Model derivation
- Evaluating model predictions
- Results
- Discussion
- Acknowledgements
- References
- Appendix

Data support the predicted size dependence of C storage and turnover in the autotroph pool (Table 1). First, a log–log plot of C storage in autotrophs *vs* average plant size yields a linear relationship with a slope of 0·24, which is statistically indistinguishable from the predicted value of 0·25 (95% CI: 0·23–0·26; Fig. 2a). Second, a log–log plot of C turnover *vs* average plant size yields a linear relationship with a slope of −0·22, which is just slightly shallower than the predicted value of −0·25 (95% CI: −0·21 to −0·24; Fig. 2b). Third, C flux is predicted to be independent of body size if resource use is at equilibrium with supply. The analysis of Enquist *et al*. (1998) supports this prediction by finding a slope close to the predicted value of 0 for plant communities spanning 12 orders of magnitude in average plant size.

The model makes additional predictions based on the temperature dependence of photosynthesis () and respiration () (Table 1). Carbon storage is predicted to be independent of temperature for the autotroph pool because respiration and growth are constrained by photosynthesis at the level of the organism (equations 11 and 17). Carbon storage in heterotrophs and soil organic matter is predicted to decline with increasing temperature. This is because the sizes of these pools are determined by the balance between production and consumption, and consumption by heterotrophs increases more rapidly with temperature than does production by plants. Extensive data support model predictions for the autotroph and soil C pools. First, a plot of the logarithm of C storage in autotrophs *vs* 1/*kT* for forest tree communities yields a slope statistically indistinguishable from the predicted value of 0 eV (95% CI: −0·18 to 0·17; Fig. 3a). Second, a plot of the logarithm of seasonality-corrected labile C storage *vs* 1/*kT* for forest litter yields a linear relationship with a slope statistically indistinguishable from the predicted value of *E*_{r} − *E*_{p} = 0·33 eV (0·38 eV, 95% CI: 0·21–0·56; Fig. 3b).

For both autotroph and heterotroph pools, C turnover varies with temperature in the same way as individual metabolic rate, because the fractions of metabolic energy allocated to growth (ɛ and δ in Fig. 1) are independent of temperature. For the soil C pool, turnover is controlled by heterotroph respiration. Carbon turnover is therefore predicted to show a weaker temperature dependence for the autotroph pool than for heterotrophs and soil C (Table 1). A plot of the logarithm of seasonality-corrected fine root turnover *vs* 1/*kT* yields a slope close to the predicted value of −*E*_{p} =−0·32 eV for the autotroph pool (−0·36 eV; 95% CI: −0·22 to −0·51; Fig. 3c). However, a plot of the logarithm of labile C turnover in soil *vs* 1/*kT* yields a slope somewhat steeper than the predicted value of −*E*_{r} =−0·65 eV (−0·79 eV, 95% CI: −0·66 to −0·93; Fig. 3d). This is perhaps because climatic data were not available to apply seasonality correction to the estimated temperatures and rates of C turnover.

Our model predicts a much stronger temperature dependence for short-term respiratory fluxes, and for rates of organic matter decomposition (characterized by κ in equation 19), than for long-term respiratory fluxes. Consequently, respiratory fluxes at a given temperature are predicted to decline with long-term temperature increases (characterized by in equation 22). Two compilations of data support the predicted temperature dependence of short-term flux, with slopes close to −*E*_{r} = −0·65 eV: (i) laboratory data on heterotroph respiration rates from diverse soils (−0·67, 95% CI: −0·62 to −0·71; Fig. 4a), and (ii) field data on seasonal variation in CO_{2} flux from soil heterotrophs and roots of forest, grassland and tundra autotrophs (−0·65, 95% CI: −0·60 to −0·70; Fig. 4b). A third compilation of data on root decomposition rates supports the predicted temperature dependence for κ, with a slope consistent with −*E*_{r} = −0·65 eV (−0·75, 95% CI: −0·44 to −1·06; Fig. 4c).

Three additional global data sets support the predicted temperature dependence of long-term flux, with slopes statistically indistinguishable from −*E*_{p} = −0·32 eV: (i) seasonality-corrected NPP (−0·35 eV, 95% CI: −0·20 to −0·50; Fig. 5a); (ii) seasonality-corrected litter fall (−0·30 eV, 95% CI: −0·24 to −0·35; Fig. 5b); and (iii) seasonality-corrected soil respiration (−0·41 eV, 95% CI: −0·28 to −0·54; Fig. 5c). Together, these results suggest that long-term ecosystem respiration rates are controlled primarily by the availability of organic C which, in turn, is controlled by the rate of photosynthesis.

The predicted relationship between short- and long-term flux is supported by a recent analysis of data collected from 19 eddy covariance towers in North America and Europe (Enquist *et al*. 2003). At individual sites, daily and seasonal variation in CO_{2} flux increased exponentially with temperature with an average activation energy close to *E*_{r} (*x̄* = 0·62 eV), but across sites, respiration rates at a given temperature (characterized by ) declined with increasing average growing season temperature, as predicted here by equation 22.

### Discussion

- Top of page
- Summary
- Introduction
- Model assumptions
- Model derivation
- Evaluating model predictions
- Results
- Discussion
- Acknowledgements
- References
- Appendix

The model presented here provides a means of characterizing the role of individual organisms in the global C cycle. Biota play key roles in the biogeochemical cycling of elements, but quantifying them explicitly is challenging (Jones & Lawton 1995). Our model quantifies these roles using three simplifying assumptions: (i) metabolic rate controls energy and material transformation rates by an organism; (ii) metabolic rate controls energy and material fluxes between an organism and its environment; and (iii) ecosystem storage and flux attributable to biota are equal to the sums of the storage and flux contributions of individual organisms. Assumptions (ii) and (iii) follow directly from (i) as a consequence of mass and energy balance, and link the cycling of elements in ecosystems to individual physiology.

The combined effects of body size and temperature on metabolic rate impose important constraints on C dynamics. Variation in C storage and turnover across biomes is driven largely by plant size (Fig. 2). Our model thus explains why oceanic phytoplankton contribute ≈50% of NPP globally despite comprising only 0·2% of the Earth's plant biomass (Field *et al*. 1998). Incorporating body size in C-cycling models could reveal other causes of variation in C dynamics across biomes. It could also predict the effects of land use on C dynamics, because land conversion often entails altering the size distribution of organisms, for example converting a forest to a field for agriculture.

The temperature dependence of many rate processes typically considered separately in ecosystem models falls into one of three categories: those controlled by photosynthesis; by respiration; or by a balance between photosynthesis and respiration. Long-term rates controlled by photosynthesis (e.g. NPP, litter fall, fine-root turnover, annual CO_{2} flux from soils) all increase approximately fourfold from 0 to 30 °C (Figs 3c and 5), even after accounting for day-length and length of the growing season, and are predicted from the temperature dependence of Rubisco carboxylation (Appendix 1). These results challenge the idea that mean annual temperature and NPP are correlated, largely because temperature is an index of growing season length and incident solar radiation (Lieth 1973). Labile C turnover (Fig. 3d), organic matter decomposition, and short-term respiratory fluxes of CO_{2} from autotrophs, heterotrophs and soils (Fig. 4) all increase approximately 16-fold from 0 to 30 °C, and are predicted from the activation energy of the respiratory complex (*E*_{r} = 0·65 eV). Finally, three different phenomena – acclimation of plant respiration; geographic gradients in labile C storage; and differences between the short- and long-term temperature dependence of ecosystem CO_{2} flux – are predicted from the different temperature dependencies of photosynthesis and respiration, reflecting constraints of photosynthate production on oxidative metabolism (equations 14, 17, 18 and 19).

More generally, our model predicts many aspects of the global C cycle based on the primary effects of body size and temperature on photosynthesis and respiration. We attribute the model's explanatory power to the explicit dependence of ecosystem-level C flux and storage on individual-level fluxes. We are aware, however, that there is considerable residual variation about the relationships depicted in Figs 2–5. This variability points to the importance of other variables that affect C cycling, including water, light and nutrient availability (Lieth 1973; Vitousek 1984; Field *et al*. 1998; Schimel *et al*. 2001; Chapin *et al*. 2002). Deviations from model predictions reflect these other variables. Consider the following two examples. First, residual variation about the function describing the temperature dependence of root decomposition (Fig. 4c) is strongly correlated with the root C : N ratio (*r*^{2} = 0·65, *P* < 0·01). This residual variation reflects the influence of resource quality and nutrient availability on the normalization parameter for organic matter decomposition (κ_{o} in equation 19) which, in turn, reflects the sizes, abundances and metabolic rates of heterotrophic decomposers in soils (equation 21); and second, a global compilation of data on C storage in mineral soils (Zinke *et al*. 1984) yields a relationship between seasonality-corrected soil C and temperature that is much weaker than predicted by our model under the assumption that all organic matter is labile C accessible to heterotrophs (predicted slope: *E*_{r} − *E*_{p} = 0·33 eV; observed slope: 0·11 eV, 95% CI: 0·08–0·14 eV, *r*^{2} = 0·01, *n* = 4023). This supports evidence that much of the organic matter stored in mineral soils is inaccessible to heterotrophs, and therefore is not susceptible to the effects of global warming (Thornley & Cannell 2001). The model could be extended to incorporate the buildup of refractory C in soil.

Our model is relevant for understanding and predicting the effects of human activities on the C cycle at local to global scales. For example, it predicts ecosystem responses to global warming. While it does not predict the total size of the global fluxes and pools, it does predict that global warming should increase rates of photosynthesis and respiration. It also predicts that increases in temperature will cause a net loss of labile C from soils. The magnitude of this loss is controlled by the difference between the temperature dependence of respiration and Rubisco carboxylation (*E*_{r} − *E*_{p}). A sustained 1 °C increase in average growing season temperature should therefore result in approximately fourfold greater losses of labile C from boreal forest soils (<*T*>_{τ}= 0 °C) than from tropical forest soils (<*T*>_{τ} = 25 °C) (equation 21). We caution, however, that these predictions ignore possible short-term transient dynamics, and they assume that other variables, including atmospheric CO_{2} concentration and water and nutrient availability, are held constant.

In summary, the model presented here makes multiple predictions (Table 1), many of which are supported by previous studies (e.g. Kirschbaum 2000) or by compilations of data from the literature (Figs 2–5). However, unlike previous work, this simple, mechanistic model yields predictions by quantifying the combined effects of two key variables, body size and temperature, on biologically controlled components of the global C cycle. It does so by linking the pools and fluxes of C in ecosystems directly to the metabolic rates of individual organisms that proximally and ultimately control C dynamics.