AN EXTREME-VALUE FUNCTION MODEL OF THE SPECIES INCIDENCE AND SPECIES-AREA RELATIONS

The power function model S = CA(z) of the species-area relation has a number of shortcomings: it is unbounded, is unable to deal with islands with zero species, and is inappropriate to the known sampling distribution of S. Using only the ''null'' assumption that species are randomly allocated to areas, I propose an extreme-value function (EVF) model of the species-area relation derived from Coleman's theory of random placement. This model accords with empirical and theoretical results that have called into question the accuracy of the power function model at large areas, and resolves two dilemmas in the power function model: the lack of any bound to species number, and heteroscedasticity in the sampling distribution of species number. The model is also able to deal with islands with zero species, without modification. The EVF is comparable to the power function model over most practical ranges of island sizes, but has properties that make it superior to the power function model. The EVF model also provides a logical synthesis of single-species incidence and multiple-species models, and as a model of single-species incidence has parameters with biological meaning.