Estimating the Total Number of Distinct Species Using Presence and Absence Data

SUMMARY 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 1. The other is to place at random n quadrats of equal area and fixed shape in the region of investigation. In both cases the n quadrats in the sample are assumed to be disjoint and are totally observed. So in fact when quadrat sampling is used, a random sample of space is taken instead of a random sample of individuals. It has been observed that species are often present with some natural clumping, which creates dependence between quadrats and within quadrats. Heltshe and Forrester (1983) and Smith and van Belle (1984) introduced some estimators for S when quadrat sampling is used; see also Burnham and Overton (1979). The estimators they proposed are nonparametric and were developed by using jackknife and bootstrap arguments. For a particular example, Palmer (1990) compared several estimators and showed that the first-order jackknife estimator is preferred within this group. In this paper we introduce some empirical Bayes estimators for S when quadrat sampling is used by imposing a grid on the region. The probabilistic model used to derive these estimators is basically a version of the Efron and Thisted (1976) model adapted to the case of quadrat