A stepwise Bayesian estimator for the total number of distinct species in finite populations: Sampling by elements

A stepwise Bayesian estimator for the total number of distinct species in the region of investigation is constructed when sampling by elements is used to collect the sample of species. The species in the region are supposed to be divided into two groups: the first containing those species the researcher believes are present in the region and the second group containing the species in the region which are completely unknown to the researcher. The abundance values of the second group are supposed to follow a Dirichlet distribution. Under this model, the obtained stepwise Bayesian estimator is an extension of that proposed by Lewins & Joanes (1984). When the negative binomial distribution is chosen as a prior distribution for the true value T of species in the region, the stepwise estimator takes a simple form. It is then shown that the estimator proposed by Hill (1979) is a particular case and that the stepwise Bayesian estimator can also be similar to the estimator proposed by Mingoti (1999) for quadrat sampling. Some results of a simulation study are presented as well as one application using abundance data and another in the estimation of population size when capture and recapture methods are used.