Continuous probabilistic approach to species dynamics in Hubbell's zero-sum local community

In this paper a continuous probabilistic approach formulated using Kolmogorov-Fokker-Planck forward and backward models is applied to Hubbell's zero-sum neutral theory for species dynamics in local community. Using this technique the probability density of species abundance, distribution of the first passage time to extinction or fixation and probability of extinction are defined. The resulting values for the distribution of the first passage time to extinction are verified by the simulation study of Hubbell's zero-sum neutral model for the local community. Based on the sensitivity analysis for the continuous probabilistic models, the realistic classification of local communities subject to their diversity and species dynamics is proposed with respect to the immigration probability, the species metacommunity relative abundance, and the size of local community.