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Patterns in species occurrences on islands have been analyzed by several 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, then island communities might have been structured by competition. Investigators have pursued this problem by first generating random (or null) matrices and then testing a metric derived from the collection of null matrices against the metric calculated from the actual species co-occurrence matrix. The random matrices were constrained by requiring the number of species on each island, and the number of islands on which 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 fixed row and column sums, and propose a modification of a previously proposed metric as a test statistic. We evaluated the efficacy of our construction method for null creation and our metric using incidence matrices from the avifauna of Vanuatu (formerly New Hebrides).

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Several studies have argued that principal factor in determining the fate of bird introductions is introduction effort. In large part, these studies have emerged from analyses of historical records from a single place-New Zealand. Here we raise two concerns about these conclusions. First, we argue that although many bird species were introduced repeatedly to New Zealand, in many cases the introductions apparently occurred only after the species were already successfully naturalized. The inclusion of such seemingly superfluous introductions may exaggerate the importance of propagule pressure. And second, we question the reliability of the records themselves. In many cases these records are equivocal, as inconsistencies appear in separate studies of the same records. Our analysis indicates that species were successful not because they were introduced frequently and in high numbers, but rather it is likely that they were introduced frequently and in high numbers because the initial releases were successful.