A Generalized Species-Area Relationship for Estimating Species Diversity: The Poisson Distribution Case

The species diversity is related to several factors, such as the mutation, interaction, competition and the amount of available resources for survival, amongst others. Besides, species diversity is related to the size of the habitat area (species-area relationship). A major problem in ecology is to identify the best function that models this relationship. The main idea of the paper is to propose a generalized species-area relationship that has as particular cases relations proposed earlier, including ones that consider the effects of minimum area and upper asymptote. The proposed model is suitable for areas of different scales (small, intermediate and large) and considers a Poisson (discrete) probability distribution for the species diversity. The advantage of our formulation is to lead to a unique function for species-area relationship, which takes into account both effects of minimum area and asymptotic behavior of the growth curve for large areas, providing a unique algorithm for fitting different dataset, and choosing the best model in the light of the data. The applicability of our approach was tested via a simulation study conducted in order to determine if the AIC and BIC selection criteria are suitable to decide for the best model to be considered for describing the species-area relationship. We also consider applications to a set of artificial data and a set of real data from of the diversity of fish in 70 lakes of different sites. In both cases our proposed extension overcome its particular cases.