Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment.

In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka-Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal increases the fitness of species in a spatially heterogeneous environment. The results are obtained through an eigenvalue analysis of the semi-trivial steady state solutions for the linearized operator derived from the model with nonuniform random diffusion on IGPrey and IGPredator, respectively. Finally, a simulation and its biological interpretations are presented based on our results.