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We develop a dynamic model of island biogeography based on immigration and extinction probabilities of individual species rather than on the usual biogeographic parameters of the number of species immigrating or going extinct per unit time. In the real world, these probabilities vary enormously among species, and three field studies suggest lognormal distributions. Based on such distributions of individual probabilities, our model proceeds by calculating the conditional probability of species occurrence--the likelihood that a given species will occur on a given island--as a function of total species number on the island. The model succeeds in predicting two observed features of species communities; (i) staggered, sigmoidally-shaped incidence functions ("differing area requirements of different species") and (ii) concave immigration and extinction curves.

Immigration and extinction probabilities for individual species: relation to incidence functions and species colonization curves.