On the Bayesian estimation of species richness and related quantities from quadrat sampling

We consider the problem of estimating the number of species of a biological community located in a region R divided into J quadrats. Recently, two parametric approaches have been developed which both take into account in a same modeling framework the detectability and the occurence of species in the quadrats. One developed by Dorazio and Royle (2005, J.A.S.A. 100, 389-398) ignores the unsampled part of R (thus also J) and models the occurence of species only in the sampled quadrats. We show that this approach can be used only if J is large, which limits its use in practice, since the value of J can strongly vary from one study to another. The other developed by Dupuis and Joachim (2006, Biometrics 62, 706-712) does not have this limitation but it applies only in the presence of prior information. In this paper, we propose a new approach which extends these two approaches since it can be used in non informative setups, and applies without limitation on J . We develop our approach within a simple model, which assumes that the species population is homogeneous. This constitutes the suitable framework for examining the effect that ignoring J has on the Bayesian estimate of species richness. In particular, a simulation study is undertaken which shows that the approach of Dorazio and Royle generates an error which can be important for small or moderate values of J , when species are spatially rare or hard to detect.