A species accumulation curve is a plot of the number of species identified in a given region as a function of some measure of effort used to find them. In ecological studies, important goals are achieved when the relationship between these two variables is understood. In this article, we construct a model based on the premise that the form of the accumulation curve depends on the combined behavior of species' recording probabilities. These probabilities are assumed to be constant in time, and recordings of species are assumed to be independent. Maximum likelihood and profile likelihood methods are explored for the estimation of parameters, for the case in which recording probabilities may be described by a beta distribution. The expectation-maximization algorithm is described for dealing with incomplete collecting lists. Two examples that illustrate the techniques developed are considered, and comparisons are made with estimates based on other approaches. A brief discussion is made regarding robustness of the model.

Key Words
EM algorithm; Number of species; Profile likelihood.

Miguel Nakamura is Professor, Department of Probability and Statistics, Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato, Gto. 36000, Mexico. Felipe Peraza is instructor, Escuela de Ciencias Físico-Matemáticas, Universidad Autónoma de Sinaloa, Apartado Postal 1872, Ciudad Universitaria, Culiacán, Sin. 80030, Mexico.