Hybrid approach to modeling spatial dynamics of systems with generalist predators

We consider hybrid spatial modeling approaches for ecological systems with a generalist predator utilizing a prey and either a second prey or an allochthonous resource. While spatial dispersion of populations is often modeled via stepping-stone (discrete spatial patches) or continuum (one connected spatial domain) formulations, we shall be interested in hybrid approaches which we use to reduce the dimension of certain components of the spatial domain, obtaining either a continuum model of varying spatial dimensions, or a mixed stepping-stone-continuum model. This approach results in models consisting of partial differential equations for some of the species which are coupled via reactive boundary conditions to lower dimensional partial differential equations or ordinary differential equations for the other species. In order to demonstrate the use of this approach, we consider two case studies. In the first case study, we consider a one-predator two-prey interaction between beavers, wolves and white-tailed deer in Voyageurs National Park. In the second case study, we consider predator-prey-allochthonous resource interactions between bears, berries and salmon on Kodiak Island. For each case study, we compare the results from the hybrid modeling approach with corresponding stepping-stone and continuum model results, highlighting benefits and limitations of the method. In some cases, we find that the hybrid modeling approach allows for solutions which are easier to simulate (akin to stepping-stone models) while maintaining seemingly more realistic spatial dynamics (akin to full continuum models).