Consider the problem of estimating the total number of distinct species in some specified region under investigation. Suppose the region is divided into N disjoint subregions or quadrats of equal area. A sample of size n quadrats is chosen, n < N. Within each sampled quadrat the distinct species present are observed and an empirical Bayes estimator of the total number of species in the region is constructed. This estimator is based on a model that is an adaptation for presence and absence data of a model originally due to Fisher. The estimator and a corresponding interval estimator are compared to bootstrap and jackknife estimators.