Null model analysis of species co-occurrence patterns

The analysis of presence-absence matrices with "null model" randomization tests has been a major source of controversy in community ecology for over two decades. In this paper, I systematically compare the performance of nine null model algorithms and four co-occurrence indices with respect to Type I and Type II errors. The nine algorithms differ in whether rows and columns are treated as fixed sums, equiprobable, or proportional. The three models that maintain fixed row sums are invulnerable to Type I errors (false positives). One of these three is a modified version of the original algorithm of E. F. Conner and D. Simberloff. Of the four co-occurrence indices, the number of checkerboard combinations and the number of species combinations may be prone to Type II errors (false negatives), and may not reveal significant patterns in noisy data sets. L. Stone and A. Robert's checkerboard score has good power for detecting species pairs that do nut co-occur together frequently, whereas D. Schluter's V ratio reveals nonrandom patterns in the row and column totals of the matrix. Degenerate matrices (matrices with empty rows or columns) do not. greatly alter the outcome of null model analyses. The choice of an appropriate null model and index may depend on whether the data represent classic "island lists" of species in an archipelago or standardized "sample lists" of species collected with equal sampling effort. Systematic examination of a set of related null models can pinpoint how violation of the assumptions of the model contributes to nonrandom patterns.