Small mammals on Massachusetts islands: the use of probability functions in clarifying biogeographic relationships

Thirty-three insular small mammal communities along the coast of Massachusetts (USA) were surveyed to investigate the biogeographic relationships of the insular communities and to examine the distribution patterns of individual species. Nine species of terrestrial small mammals were observed in the total insular fauna, whereas thirteen occurred on the mainland. The species-area relation yielded a z value of 0.06, which is the lowest value yet reported for insular mammal communities.Multiple logistic regression was used to calculate probability functions for each species in order to identify variables potentially important in determining a species' occurrence on islands and to estimate probabilities of occurrence on islands. Statistically significant and ecologically interpretable functions were obtained for all but one species. Occurrence on islands was positively related to increasing island size in four species and to decreasing island isolation in four species. The extremely low z value, negative correlations of species number with isolation variables, and the inclusion of an isolation variable in the logistic functions of four species indicated that immigration was an important determinant of small mammal occurrence on these islands. There was a positive relationship between population density and number of islands occupied.Logistic regression has several advantages over linear discriminant function analysis, and we suggest that it may be useful in other ecological studies and in the preservation of endangered species.