Interspecific Segregation and Phase Transition in a Lattice Ecosystem with Intraspecific Competition

Many empirical studies of ecological community indicate the coexistence of competing species is extremely common in nature. However, many mathematical studies show that coexistence of competitive species is not so easy. In the present article, we focus on the segregation of habitat (microhabitat). If habitats of species are spatially separated, they can coexist easily: under the habitat segregation, net competition does not work between species. We study a lattice ecosystem composed of two competitive species. The dynamics of this system is found to be asymptotically stable. In this system both species can coexist, because intraspecific competition is stronger than interspecific competition. It is found that this system exhibits a phase transition: if the mortality rate of both species increases, they go extinct. Our main result shows a selforganized isolation of microhabitat; that is, at the phase transition point, the living regions of both species are naturally and completely separated from each other. In this critical state, each species independently forms clusters, and the shape of each cluster greatly varies with time proceed. Such a phase transition occurs, even though (i) there is no special condition in space, and (ii) the intraspecific competition is stronger than interspecific competition. We conclude that such segregation comes from an inherent nature of species. Despite no attraction acts between individuals, each species forms clusters. This conclusion suggests that all biospecies may have some mechanism that naturally causes the isolation of habitats.