Implementation of the lattice model in the coexistence of species and its potential consequences on environment

Abstract

The population dynamics of a system of two competing species have been investigated in the mean-field and lattice approximation. The two species are denoted by A and B. Each site of the square lattice is either occupied by an individual or vacant. The two species complete for vacant sites to reproduce. There is a reproduction only to the nearest neighbours. We consider the invasion of a rare species into a population composed of a resident species based on a pair – approximation method in which the dynamics of both average densities and nearest neighbour correlations are considered. The results are then compared with those obtained by the mean-field approximation. Whenspecies B contain intraspecific interaction term, invasion of the rare species A into resident species B becomes easier in lattice structured populations. But the rare species B invading species A is difficult in lattice models in comparison to mean-field approximation. The overall coexistence of species is enhanced in lattice models. These results were verified by simulation on a square lattice although the range of the enhancement of the species coexistence is reduced. This calls for the attention that pair-approximation is an oversimplification of the real situation.