Topological Phase Transition in Biological Ecosystems

Spatial pattern in an ecosystem composed of competing species (Lotka-Volterra model: LVM) is studied. Two-dimensional lattice systems of LVM attain the stationary state in which topological defects (vortices) are excited. It is found from the simulation that a nonequilibrium phase transition in the vortex excitation, which is essentially different from that of Kosterlitz-Thouless, takes place under the slight change of environmental parameters. By the phase transition, the average size of clumps of each species is drastically altered. The phase diagram is well explained by the stability theory for the moderately concentrated gas system of LVM.