A Nonparametric Lower Bound for the Number of Species Shared by Multiple Communities.
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.
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H.-Y. Pan is Assistant Professor, Department of Applied Mathematics, National Chia-Yi University, Chia-Yi, Taiwan 60004 ( hypan@mail.ncyu.edu.tw ). Anne Chao is Tsing Hua Distinguished Chair Professor, Institute of Statistics, National Tsing Hua University, Hsin-Chu, Taiwan 30043 ( chao@stat.nthu.edu.tw ). Wilhelm Fossiner is University Professor, Universität Salzburg, FB Organismische Biologie, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria ( wilhelm.FOISSNER@sbg.ac.at ).
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