Directed movement of predators and the emergence of density-dependence in predator-prey models

We consider a bitrophic spatially distributed community consisting of prey and actively moving predators. The model is based on the assumption that the spatial and temporal variations of the predators' velocity are determined by the prey gradient. Locally, the populations follow the simple Lotka-Volterra interaction. We also assume predator reproduction and mortality to be negligible in comparison with the time scale of migration. The model demonstrates heterogeneous oscillating distributions of both species, which occur because of the active movements of predators. One consequence of this heterogeneity is increased viability of the prey population, compared to the equivalent homogeneous model, and increased consumption. Further numerical analysis shows that, on the spatially aggregated scale, the average predator density adversely affects the individual consumption, leading to a nonlinear predator-dependent trophic function, completely different from the Lotka-Volterra rule assumed at the local scale.