Predator-Prey Interactions in Communities with prey dispersal and Allee effects
The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey-dispersal between patches, with the fragile prey populations, that is, populations subject to the Allee effect. The resulting four-dimensional model's mathematical analysis is carried out via sub-models that focus in lower dimensional settings. The outcomes depend on, and in fact they are quite sensitive to, the structure of the system, the range of parameter values, and initial conditions. We show that the system can support multi-stability and a diverse set of predator-prey life-history dynamics that includes rather complex dynamical system outcomes. It is argued that in general evolution should favor heterogeneous settings including Allee effects, prey-refuges, and patch-specific predators.