Interspecific Segregation and Phase Transition in a Lattice Ecosystem with Intraspecific Competition
Keywords
habitat segregation, lattice model, competition, lotka-volterra model
Start Date
1-7-2004 12:00 AM
Abstract
Many empirical studies of ecological community indicate the coexistence of competing species isextremely common in nature. However, many mathematical studies show that coexistence of competitivespecies is not so easy. In the present article, we focus on the segregation of habitat (microhabitat). If habitatsof species are spatially separated, they can coexist easily: under the habitat segregation, net competition doesnot work between species. We study a lattice ecosystem composed of two competitive species. The dynamicsof this system is found to be asymptotically stable. In this system both species can coexist, becauseintraspecific competition is stronger than interspecific competition. It is found that this system exhibits aphase transition: if the mortality rate of both species increases, they go extinct. Our main result shows a selforganizedisolation of microhabitat; that is, at the phase transition point, the living regions of both species arenaturally and completely separated from each other. In this critical state, each species independently formsclusters, and the shape of each cluster greatly varies with time proceed. Such a phase transition occurs, eventhough (i) there is no special condition in space, and (ii) the intraspecific competition is stronger thaninterspecific 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 allbiospecies may have some mechanism that naturally causes the isolation of habitats.
Interspecific Segregation and Phase Transition in a Lattice Ecosystem with Intraspecific Competition
Many empirical studies of ecological community indicate the coexistence of competing species isextremely common in nature. However, many mathematical studies show that coexistence of competitivespecies is not so easy. In the present article, we focus on the segregation of habitat (microhabitat). If habitatsof species are spatially separated, they can coexist easily: under the habitat segregation, net competition doesnot work between species. We study a lattice ecosystem composed of two competitive species. The dynamicsof this system is found to be asymptotically stable. In this system both species can coexist, becauseintraspecific competition is stronger than interspecific competition. It is found that this system exhibits aphase transition: if the mortality rate of both species increases, they go extinct. Our main result shows a selforganizedisolation of microhabitat; that is, at the phase transition point, the living regions of both species arenaturally and completely separated from each other. In this critical state, each species independently formsclusters, and the shape of each cluster greatly varies with time proceed. Such a phase transition occurs, eventhough (i) there is no special condition in space, and (ii) the intraspecific competition is stronger thaninterspecific 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 allbiospecies may have some mechanism that naturally causes the isolation of habitats.
