A generalized species-area relationship: The Poisson distribution case

Abstract

Species richness is related to various factors, such as mutation, interaction, competition and the amount of available resources for survival, among others. Additionally, species richness 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 aim of the paper is to propose a generalized fitting formula for the species-area relationship. The advantage of our model is that it leads to a unique formulation for species-area relationships, which takes into account both the effects of the minimal area and asymptotic behavior of the growth curve for large areas. This approach provides a unique algorithm for fitting different datasets, and choosing the best model in light of the data. The applicability of our approach was tested via a simulation study conducted to determine if two usual selection criteria are suitable to choose the best formulation to be considered to describe species-area relationships. Real datasets involving a species richness of fish in $70$ lakes was analysed using the proposed methodology.