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).