Master Equation and Relative Species Abundance Distribution for Lotka-Volterra Models of Interacting Ecological Communities

The understanding of the factors controlling the dynamics of interacting species is a fundamental problem in ecology. The nature of the interactions among different species is usually not completely understood, but it is assumed that the species interaction plays an important role in the ecosystems properties. However recent studies point out as a neutral hypothesis of non-interacting species with an external source from the surrounding environment allows to explain the relative species abundance (RSA) distribution when the community has reached a stationary situation. In this paper we use a Lotka-Volterra model to derive the (RSA) distribution in the case of different communities which interact each other. We derive a Master equation to study the join RSA distribution of the communities near the stationary state and their correlation. These results suggest a possible explanation of the deviation from the neutral models of empirical RSA distributions.