On the Bayesian Estimation of the Number of Species in a Community

This note is concerned with the estimation of the number of species in a sampled community. Specifically, let Nm be the observed number of species in a random sample of m individuals from a community containing an unknown number N of species. Methods of estimating N from Nm were reviewed by Bunge and Fitzpatrick (1993). This paper focuses on Bayesian estimation, which is outlined in the next section. Under the Bayesian approach, N is treated as a random variable and attention focuses on finding the posterior distribution of N given Nm. As discussed below, a key difficulty in implementing the Bayesian approach is specifying the conditional prior distribution of the vector of relative abundances given that N = n. The standard approach has been to assume that this vector has a particular form-the symmetric Dirichlet distribution. Although this distribution is mathematically convenient, its use is problematic in two respects. First, it has no theoretical or empirical justification as a model for the abundance distribution. Second, it requires the prior specification of a parameter that essentially controls the evenness of the abundance distribution. There has been considerable interest in abundance