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It is often of interest to biologists to evaluate whether two populations are alike with respect to a similarity index; assessing the numbers of shared species is one way to do this. In this study, we propose two Turing-type estimators for the probability of discovering new shared species and two jackknife-type estimators for the number of shared species in two populations. We use computer simulation and empirical data analysis to evaluate the proposed approach. The jackknife-type estimators provide stable and reliable estimates, for both the probability of discovering new shared species and the number of shared species. We also compare the jackknife-type estimates with that of using sample coverage to estimate the number of shared species. The estimate of using sample coverage has better performance in the case of even populations, while the jackknife-type estimates have smaller bias in the case of unbalanced populations. When combined with a stopping rule based on the probability of observing new shared species, confidence intervals based on the proposed jackknife-type estimators can provide better coverage probability for the true number of shared species. The jackknife-type estimates can provide coverage probability close to 0.95 in all examples.

Comparing Nonparametric Estimators for the Number of Shared Species in Two Populations