A similarity measure based on species proportions

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species ( Jaccard's index) and the conditional probability of observing a shared species ( Smith et al., 1996). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator ( NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.