Self-organized habitat segregation in an ambush-predator system: Nonlinear migration of prey between two patches with finite capacities

Many species live in spatially separated patches. In real ecosystems, the capacity of patch is finite. If a patch is already occupied by the individuals of some species, then the migration into the patch is impossible. For the migration, empty cells are necessary in the destination patch (“nonlinear migration”). In the present article, we deal with two-patch system composed of prey and ambush predator. Preys can migrate between both patches, but predators stay in a single patch. Agent-based model (ABM) is applied in respective patches. Each patch contains a finite number of cells; “capacity” of a patch is defined by the total cell number in the patch. Each cell is either empty or occupied with prey or predator. Reaction-migration equations are presented for non-spatial system of ABM. Both non-spatial and spatial models indicate that the population dynamics are largely affected by the finiteness of respective patches. In particular, we find a self-organized habitat segregation, depending on parameter values. The prey density becomes nearly zero in the predator patch, although many preys live in non-predator patch. Although the migration occurs between both patches, the prey almost disappears in one patch. Such a segregation may be caused by the finite capacity of patches.