On the Bayesian estimation of species richness and related quantities: the homogeneous case.

Jérôme Dupuis (1)

1 LSP - Laboratoire de Statistique et Probabilités

We consider the problem of estimating the number of species of a biological community located in a region R divided in J quadrats. Recently, two 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 assumes that a list of species liable to be present in this community is available. The other, developed by Dorazio and Royle (2005, J.A.S.A.) ignores the unsampled part of R (and thus also J), and models the occurence of species in the sampled quadrats by independent Bernoulli outcomes. We show that this independence assumption is not correct, and we propose a new approach which models the occurence of species in the J quadrats and does not require the above list. We develop our approach within a simple model which assumes that the species population is homogeneous. We prove that this model is identifiable and a specific missing data structure is exhibited. We show that the approach of Dorazio and Royle is valid only asymptotically (with respect to J), and generates an error for finite J. A simulation study shows that this can be important when species are spatially rare or hard to detect.

Mots clés: Species richness; Bayesian estimate; Biodiversity; Identifiability; Jeffreys prior; Missing data; Quadrat sampling; Species richness.

Domaines: Théorie [stat.TH]; Statistiques [math.ST]; Méthodologie [stat.ME]

Jérôme Dupuis. On the Bayesian estimation of species richness and related quantities: the homogeneous case.. 2008. ⟨hal-00281829v2⟩