IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics

We examine spatially explicit models described by reaction-diffusion partial differential equations for the study of predator–preypopulation dynamics. The numerical methods we propose are based on the coupling of a finite difference/element spatial discreti-zation and a suitable partitioned Runge–Kutta scheme for the approximation in time. The RK scheme here implemented uses animplicit scheme for the stiff diffusive term and a partitioned RK symplectic scheme for the reaction term (IMSP scheme). We revisitsome results provided in literature for the classical Lotka–Volterra system and the Rosenzweig–MacArthur model. We then extendthe approach to metapopulation dynamics in order to numerically investigate the effect of migration through a corridor connectingtwo habitat patches. Moreover, we analyze the synchronization properties of subpopulation dynamics, when the migration occursthrough corridors of variable size.