In biological and ecological statistical inference, it is practically useful to provide a lower bound for species richness in a community. Chao (1984, 1989) derived a nonparametric lower bound for species richness in a single community. However, there have been no lower bounds proposed in the literature for the number of species shared by multiple communities. Based on sample species abundance or replicated incidence records from each of the N communities, we derive in this article a nonparametric approach to constructing a lower bound for the number of species shared by N (N ≥ 2) communities. The approach is valid for all types of species abundance distributions (for abundance data) or species detection probabilities (for replicated incidence data). Variance estimators for the proposed lower bounds are obtained by using typical asymptotic theory. Simulation results are reported to examine the performance of the lower bounds. Replicated incidence data of ciliate species collected in three areas from Namibia, southwest Africa, are used for illustration. We also briefly discuss the application of the proposed method to estimate the size of a shared population (i.e., the number of individuals in the intersection of multiple populations) based on capture-recapture data from each population.

中文翻译：

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多个社区共享的物种数量的非参数下限。

在生物和生态统计推断中，为群落中的物种丰富度提供下限是非常有用的。Chao (1984, 1989) 推导出单个群落中物种丰富度的非参数下限。然而，文献中没有提出多个群落共享的物种数量的下限。基于样本物种丰度或来自每个 N 社区的重复发生率记录，我们在本文中推导出一种非参数方法来构建 N (N ≥ 2) 社区共享的物种数量的下限。该方法适用于所有类型的物种丰度分布（对于丰度数据）或物种检测概率（对于重复发生率数据）。建议下界的方差估计量是通过使用典型的渐近理论获得的。报告模拟结果以检查下限的性能。在非洲西南部纳米比亚的三个地区收集的纤毛虫物种的重复发生率数据用于说明。我们还简要讨论了所提出的方法在基于每个种群的捕获-重新捕获数据估计共享种群大小（即，多个种群的交集中的个体数量）方面的应用。