Inferential permutation tests for maximum entropy models in ecology

Maximum entropy (maxent) models assign probabilities to states that (1) agree with measured macroscopic constraints on attributes of the states and (2) are otherwise maximally uninformative and are thus as close as possible to a specified prior distribution. Such models have recently become popular in ecology, but classical inferential statistical tests require assumptions of independence during the allocation of entities to states that are rarely fulfilled in ecology. This paper describes a new permutation test for such maxent models that is appropriate for very general prior distributions and for cases in which many states have zero abundance and that can be used to test for conditional relevance of subsets of constraints. Simulations show that the test gives correct probability estimates under the null hypothesis. Power under the alternative hypothesis depends primarily on the number and strength of the constraints and on the number of states in the model; the number of empty states has only a small effect on power. The test is illustrated using two empirical data sets to test the community assembly model of B. Shipley, D. Vile, and E. Garnier and the species abundance distribution models of S. Pueyo, F. He, and T. Zillio.