Null model analysis of species co-occurrence patterns

The analysis of presence-absence matrices with "null model" randomization t ests has been a major source of controversy in community ecology for over t wo 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 column s are treated as fixed sums, equiprobable, or proportional. The three model s that maintain fixed row sums are invulnerable to Type I errors (false pos itives). 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 signif icant patterns in noisy data sets. L. Stone and A. Robert's checkerboard sc ore has good power for detecting species pairs that do nut co-occur togethe r frequently, whereas D. Schluter's V ratio reveals nonrandom patterns in t he row and column totals of the matrix. Degenerate matrices (matrices with empty rows or columns) do not. greatly alter the outcome of null model anal yses. The choice of an appropriate null model and index may depend on wheth er the data represent classic "island lists" of species in an archipelago o r standardized "sample lists" of species collected with equal sampling effo rt. Systematic examination of a set of related null models can pinpoint how violation of the assumptions of the model contributes to nonrandom pattern s.