| Abstract: | A minimal model for predator-prey interaction in a composite environment is
presented and analysed. We first consider free migrations between two patches for both
interacting populations, and then the particular cases where only one-directional migration
is allowed and where only one of the two populations can migrate. Our findings
indicate that in all cases the ecosystem can never disappear entirely, under the model
assumptions. The predator-free equilibrium and the coexistence of all populations are
found to be the only feasible stable equilibria. When there are only one-directional migrations,
the abandoned patch cannot be repopulated. Other equilibria then arise, with
only prey in the second patch, coexistence in the second patch, or prey in both patches
but predators only in the second one. For the case of sedentary prey, with predator
migration, the prey cannot thrive alone in either of the two environments. However,
predators can survive in a prey-free patch due to their ability to migrate into the other
patch, provided prey is present there. If only the prey can migrate, the predators may
be eliminated from one patch or from both. In the first case, the patch where there are
no predators acts as a refuge for the survival of the prey. |
