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A number of species richness estimators have been developed under the model that individuals (or sampling units) are sampled with replacement. However, if sampling is done without replacement so that no sampled unit can be repeatedly observed, then the traditional estimators for sampling with replacement tend to overestimate richness for relatively high-sampling fractions (ratio of sample size to the total number of sampling units) and do not converge to the true species richness when the sampling fraction approaches one. Based on abundance data or replicated incidence data, we propose a nonparametric lower bound for species richness in a single community and also a lower bound for the number of species shared by multiple communities. Our proposed lower bounds are derived under very general sampling models. They are universally valid for all types of species abundance distributions and species detection probabilities. For abundance data, individuals' detectabilities are allowed to be heterogeneous among species. For replicated incidence data, the selected sampling units (e.g., quadrats) need not be fully censused and species can be spatially aggregated. All bounds converge correctly to the true parameters when the sampling fraction approaches one. Real data sets are used for illustration. We also test the proposed bounds by using subsamples generated from large real surveys or censuses, and their performance is compared with that of some previous estimators. [ABSTRACT FROM AUTHOR]

A traditional approach for assessing similarity among N ( N > 2) communities is to use multiple pairwise comparisons. However, pairwise similarity indices do not completely characterize multiple-community similarity because the information shared by at least three communities is ignored. We propose a new and intuitive two-stage probabilistic approach, which leads to a general framework to simultaneously compare multiple communities based on abundance data. The approach is specifically used to extend the commonly used Morisita index and NESS (normalized expected species shared) index to the case of N communities. For comparing N communities, a profile of N− 1 indices is proposed to characterize similarity of species composition across communities. Based on sample abundance data, nearly unbiased estimators of the proposed indices and their variances are obtained. These generalized NESS and Morisita indices are applied to comparison of three size classes of plant data (seedling, saplings, and trees) within old-growth and secondary rain forest plots in Costa Rica. [ABSTRACT FROM AUTHOR]