Using entropy maximization to predict the form of species abundance distributions across taxa

Background/Question/Methods

Understanding broad-scale patterns in ecological systems is critical to predicting and mitigating impacts of global change. To that end, ecologists have developed and tested myriad models of numerous patterns that characterize community structure, typically studying one pattern at a time with one dataset from one taxonomic group. The species abundance distribution (SAD) is one of the most commonly studied of these patterns. Decades of research have revealed that all communities are comprised of a few common and many rare species, but a mechanistic or statistical framework to account for this universal form and link it to other important macroecological patterns has been lacking. Consequently, John Harte and colleagues have recently applied the maximum entropy method of inference from information theory (MaxEnt) to develop such a framework. In this framework, the state variables of an ecological community, species richness (S₀), total abundance (N₀), and total metabolic requirements (E₀), are used to predict the least-biased form of the SAD. Here, we test the ability of MaxEnt to characterize SADs using five databases of continental or global extent representing three major taxa (Breeding Bird Survey, Christmas Bird Count, Forest Inventory Analysis, Alwyn Gentry’s Forest Transects, and a compilation of published mammal community data).

Results/Conclusions

We compared MaxEnt predictions with observed SADs for 15,663 sites distributed throughout six continents, including 47,774,772 individuals representing 8,368 species. S₀ ranged from 10 to 250 and N₀ from 11 to 10,280,057. Goodness of fit was assessed by coefficients of determination (R²) that measured agreement between observed and predicted values. MaxEnt predictions were remarkably similar to observed species abundances for all taxa and datasets (R²: BBS = 0.91; CBC = 0.90; Mammals = 0.83; FIA = 0.96; Gentry = 0.93), with P values of < 0.001 (based on comparisons to simulated SADs sampled from the discrete uniform distribution). The Fisher log-series is the form of the SAD that emerges from the MaxEnt framework, and we found that, for each dataset, >75% of the observed SADs were better characterized by the log-series than by the log-normal (Akaike weights > 0.6).  These results provide compelling evidence that the MaxEnt approach can be used to infer species abundances, estimate the number of rare species, and predict extinction in various scenarios of global change. Further testing of this MaxEnt framework is planned, to further assess its potential to unify macroecological patterns and thereby simplify the search for the mechanisms underlying broad-scale patterns in ecology.