Numerical methods for spatially explicit models describing population and metapopulation dynamics

The interest about the effects of habitat fragmentation on wolf – wild boar pair populating the Italian "Alta Murgia" Natura 2000 site, aimed the study of spatially implicit/explicit models for predator-prey population and metapopulation dynamics. Numerical methods based on partitioned Runge-Kutta schemes which use an implicit scheme for the stiff diffusive term and a partitioned symplectic scheme for the reaction function are described. We are motivated by the classical results about Lotka-Volterra model described by ordinary differential equations to which the spatially explicit model reduces for diffusion coefficients tending to zero: for their accurate solution, Poisson schemes provided by composition of symplectic Euler steps are used for the long run preservation of the dynamics invariant.