Integrating elements and energy through the metabolic dependencies of gross growth efficiency and the threshold elemental ratio

Metabolic theory proposes that individual growth is governed through the mass- and temperature-dependence of metabolism, and ecological stoichiometry posits that growth is maximized at consumer-specific optima of resource elemental composition. A given consumer's optimum, the threshold elemental ratio (TER), is proportional to the ratio of its maximum elemental gross growth efficiencies (GGEs). GGE is defined by the ratio of metabolism-dependent processes such that GGEs should be independent of body mass and temperature. Understanding the metabolic-dependencies of GGEs and TERs may open the path towards a theoretical framework integrating the flow of energy and chemical elements through ecosystems. However, the mass and temperature scaling of GGEs and TERs have not been broadly evaluated. Here, we use data from 95 published studies to evaluate these metabolic-dependencies for C, N and P from unicells to vertebrates. We show that maximum GGEs commonly decline as power functions of asymptotic body mass and exponential functions of temperature. The rates of change in maximum GGEs with mass and temperature are relatively slow, however, suggesting that metabolism may not causally influence maximum GGEs. We additionally derived the theoretical expectation that the TER for C:P should not vary with body mass and this was supported empirically. A strong linear relationship between carbon and nitrogen GGEs further suggests that variation in the TER for C:N should be due to variation in consumer C:N. In general we show that GGEs may scale with metabolic rate, but it is unclear if there is a causal link between metabolism and GGEs. Further integrating stoichiometry and metabolism will provide better understanding of the processes governing the flow of energy and elements from organisms to ecosystems.