The distance decay of similarity in tropical rainforests. A spatial point processes analytical formulation

In this paper we are concerned with the analytical description of the change in floristic composition (species turnover) with the distance between two plots of a tropical rainforest due to the clustering of the individuals of the different species. We describe the plant arrangement by a superposition of spatial point processes and in this framework we introduce an analytical function which represents the average spatial density of the Sørensen similarity between two infinitesimal plots at distance r. We see that the decay in similarity with the distance is essentially described by the pair correlation function of the superposed process and that it is governed by the most abundant species. We test our analytical model with empirical data obtained for the Barro Colorado Island and Pasoh rainforests. To this end we adopt the statistical estimator for the pair correlation function in Shimatani (2001) and we design a novel one for the Sørensen similarity. Furthermore, we test our analytical formula by modeling the forest study area with Neyman-Scott point processes. We conclude comparing the advantages of our approach with other ones existing in literature.