Dynamics of population communities with prey migrations and Allee effects: a bifurcation approach.

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, i.e. populations subject to the Allee effect. The resulting 3D and 4D non-linear systems depending on some parameters, which reflect 'measures' of factors under consideration, support rich dynamics and in particular a diverse number of predator-prey life history outcomes. The model's mathematical analysis is carried out via submodels that focus in lower-dimensional settings. The outcomes depend on and, in fact, are quite sensitive to the structure of the system, the range of parameter values and initial conditions. We show that the system can support multistability and a diverse set of predator-prey life-history dynamics that include rather complex dynamical system outcomes. It is argued that, in general, evolution should favour heterogeneous settings including Allee effects, prey refuges and patch-specific predators.