The empirical Bayes approach as a tool to identify non-random species associations |
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Authors: | Nicholas J Gotelli Werner Ulrich |
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Institution: | (1) Department of Biology, University of Vermont, Burlington, VT 05405, USA;(2) Department of Animal Ecology, Nicolaus Copernicus University in Toruń, Gagarina 9, 87-100 Torun, Poland |
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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. |
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