The empirical Bayes approach as a tool to identify non-random species associations

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Abstract
A statistical challenge in community ecology is to identify segregated and aggregated pairs of species from a binary presence–absence matrix, which often contains hundreds or thousands of such potential pairs. A similar challenge is found in genomics and proteomics, where the expression of thousands of genes in microarrays must be statistically analyzed. Here we adapt the empirical Bayes method to identify statistically significant species pairs in a binary presence–absence matrix. We evaluated the performance of a simple confidence interval, a sequential Bonferroni test, and two tests based on the mean and the confidence interval of an empirical Bayes method. Observed patterns were compared to patterns generated from null model randomizations that preserved matrix row and column totals. We evaluated these four methods with random matrices and also with random matrices that had been seeded with an additional segregated or aggregated species pair. The Bayes methods and Bonferroni corrections reduced the frequency of false-positive tests (type I error) in random matrices, but did not always correctly identify the non-random pair in a seeded matrix (type II error). All of the methods were vulnerable to identifying spurious secondary associations in the seeded matrices. When applied to a set of 272 published presence–absence matrices, even the most conservative tests indicated a fourfold increase in the frequency of perfectly segregated “checkerboard” species pairs compared to the null expectation, and a greater predominance of segregated versus aggregated species pairs. The tests did not reveal a large number of significant species pairs in the Vanuatu bird matrix, but in the much smaller Galapagos bird matrix they correctly identified a concentration of segregated species pairs in the genus Geospiza. The Bayesian methods provide for increased selectivity in identifying non-random species pairs, but the analyses will be most powerful if investigators can use a priori biological criteria to identify potential sets of interacting species.