NULL MATRICES AND THE ANALYSIS OF SPECIES COOCCURRENCES

Patterns in species occurrences on islands have been analyzed by sever al authors. At issue is the number of non-occurring pairs of species ( also known as checkerboards). Previous authors have suggested that if the number of checkerboards differs from what is expected by chance, t hen island communities might have been structured by competition. Inve stigators have pursued this problem by first generating random (or nul l) matrices and then testing a metric derived from the collection of n ull matrices against the metric calculated from the actual species co- occurrence matrix. The random matrices were constrained by requiring t he number of species on each island, and the number of islands on whic h each species occurred to be equal to their observed values. We show that results from previous studies are generally flawed. We present a fast, efficient algorithm to generate null matrices for any set of fix ed row and column sums, and propose a modification of a previously pro posed metric as a test statistic. We evaluated the efficacy of our con struction method for null creation and our metric using incidence matr ices from the avifauna of Vanuatu (formerly New Hebrides).