The comparative analysis of species occurrence patterns on archipelagos.

We present a technique based on recent developments in contingency table analysis to analyze species occurrence patterns on archipelagos. This technique, through a "logistic" transformation, fits a sigmoidal-shaped surface on the species presence-absence matrix using only three parameters. This technique does not follow from any a priori or theoretical motivation, but is simply a descriptive statistical procedure. It accounts for roughly half the variation of the empirical contingency matrices for 14 different island systems. The taxa studied included plants, birds, herps and mammals. The matrix technique for a set of species in an archipelago provides three biologically relevant summary statistics. The first statistic indicates the overall colonizing success of the species in the archipelago. The second statistic describes the orderedness of the matrix (species occurrences). The third indicates the distribution of colonizing success between species. The technique is useful in computing the range of these statistics across taxa and over archipelagos.