An estimator of number of species from quadrat sampling

We consider the problem of estimating the number of distinct species Sin a study area from the recorded presence or absence of species in each of a sample of quadrats. A generalized jackknife estimator of S is derived, along with an estimate of its variance. It is compared with the jackknife estimator for S proposed by Heltshe and Forrester (1983, Biometrics 39,1-12) and the empirical Bayes estimator of Mingoti and Meeden (1992, Biometrics 48, 863-875). We show that the empirical Bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution. We compare the new estimators of S to the empirical Bayes estimator via simulation. We characterize circumstances under which each is superior.