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On testing predictions of species relative abundance from maximum entropy optimisation


S. H. Roxburgh, CSIRO Sustainable Ecosystems, PO Box 284, Canberra 2601, Australia. E-mail:


A randomisation test is described for assessing relative abundance predictions from the maximum entropy approach to biodiversity. The null model underlying the test randomly allocates observed abundances to species, but retains key aspects of the structure of the observed communities; site richness, species composition, and trait covariance. Three test statistics are used to explore different characteristics of the predictions. Two are based on pairwise comparisons between observed and predicted species abundances (RMSE, RMSESqrt). The third statistic is novel and is based on community-level abundance patterns, using an index calculated from the observed and predicted community entropies (EDiff). Validation of the test to quantify type I and type II error rates showed no evidence of bias or circularity, confirming the dependencies quantified by Roxburgh and Mokany (2007) and Shipley (2007) have been fully accounted for within the null model. Application of the test to the vineyard data of Shipley et al. (2006) and to an Australian grassland dataset indicated significant departures from the null model, suggesting the integration of species trait information within the maximum entropy framework can successfully predict species abundance patterns. The paper concludes with some general comments on the use of maximum entropy in ecology, including a discussion of the mathematics underlying the Maxent optimisation algorithm and its implementation, the role of absent species in generating biased predictions, and some comments on determining the most appropriate level of data aggregation for Maxent analysis.