Simulations of the heterogeneity of environments by finite element methods

The dependence of total population and population distribution on the spatial distribution of the intrinsic growth factor is studied. The existence of solutions of a nonlinear single species and the corresponding predator-prey model is established. The solutions are then approximated by the Galerkin finite element method. Simulations are performed to show, for instance, how (under the Dirichlet boundary condition) a more favorable distribution of growth factor for the prey in a predator-free situation may well be less favourable than another distribution under the pressure of the predator.