The allocation of mass and energy among individuals and species within an assemblage has long been studied in ecology. Recently, a new unified theory, Maximum Entropy (MaxEnt), provides the first attempt to link patterns of energy consumption with patterns of diversity. Originated from informatics, MaxEnt has been used to derive a variety of macroecological patterns including species-abundance distribution (SAR) and species-area relationship (SAR), as well as individual-level and species-level metabolic rate distributions, with four state variables constraining the community – total abundance, total species richness, total metabolic rate, and area (Harte 2011).
While the SAD predicted by MaxEnt is supported by extensive tests with empirical data (White et al. in revision), tests on the predicted energy distributions have been scarce (but see Harte et al. 2008, Harte 2011). Furthermore, current construction of MaxEnt machinery allows substitution of the metabolic rate constraint with another variable, without affecting the predictions for SAD and SAR. Here we try to answer the following two questions: 1. Does MaxEnt accurately predict energy allocations of real communities? 2. If not, is there a surrogate of energy that leads to better predictions under the MaxEnt framework?
To answer these questions, we have compiled a large number of community-level data including trees, birds, and mammals. The individual-level and species-level energy distributions predicted by MaxEnt will be compared with the empirically observed patterns. Different measures correlated with energy consumption (e.g., body mass, diameter for trees) will be adopted to substitute metabolic rate, and goodness of fit of these measures will be examined.
Preliminary analysis has been conducted with data from two tropical forests, Barro Colorado Island (BCI) and Sherman plot. The predicted metabolic rate distribution among individuals shows a clear deviation from empirical data for both communities, with MaxEnt overpredicting the energy consumption of individuals with high metabolic rate. Moreover, while MaxEnt predicts relatively constant total within-species energy consumption across species (i.e., Damuth’s energetic equivalence rule), in both communities the measure is shown to increases with abundance. The relationship between intraspecific average metabolic rate and species abundance is polygonal, similar to the pattern observed by Brown and Maurer (1987) in bird communities. Substituting metabolic rate with body mass yields qualitatively similar results.
Based on the preliminary results, MaxEnt’s prediction for energy distributions is unlikely to work with the current constraint on metabolic rate, and other surrogates for energy consumption need to be explored.