Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 847328, 6 pages
http://dx.doi.org/10.1155/2014/847328
Research Article

An Algebraic Derivation of Chao’s Estimator of the Number of Species in a Community Highlights the Condition Allowing Chao to Deliver Centered Estimates

1Société d’Histoire Naturelle du Creusot, 12 rue des Pyrénées, 71200 Le Creusot, France
2Biogéosciences, Université de Bourgogne, 21000 Dijon, France

Received 30 June 2014; Accepted 19 September 2014; Published 11 November 2014

Academic Editor: Arthur P. Schwab

Copyright © 2014 Jean Béguinot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Anne Chao proposed a very popular, nonparametric estimator of the species richness of a community, on the basis of a limited size sampling of this community. This expression was originally derived on a statistical basis as a lower-bound estimate of the number of missing species in the sample and provides accordingly a minimal threshold for the estimation of the total species richness of the community. Hereafter, we propose an alternative, algebraic derivation of Chao’s estimator, demonstrating thereby that Chao’s formulation may also provide centered estimates (and not only a lower bound threshold), provided that the sampled communities satisfy a specific type of SAD (species abundance distribution). This particular SAD corresponds to the case when the number of unrecorded species in the sample tends to decrease exponentially with increasing sampling size. It turns out that the shape of this “ideal” SAD often conforms approximately to the usually recorded types in nature, such as “log-normal” or “broken-stick.”. Accordingly, this may explain why Chao’s formulation is generally recognized as a particularly satisfying nonparametric estimator.