Predator migration decisions, the ideal free distribution, and predator-prey dynamics

The aim of the present work is to analyze the influence of optimal predator emigration decisions that can lead to the ideal free distribution (IFD) on the stability of predator-prey systems. The assumption of optimal decisions is then relaxed to analyze the possible influence of different degrees of deviation from the IFD. The first migration rule we analyze is based on the marginal-value theorem and assumes perfect knowledge of capture rate in the patch of residence and in the environment as a whole. When migration rates are high, this rule leads the predator population to the IFD. The results suggest that under these conditions predator migration plays no major role in the stability of the system. This is so because the systems naturally merge into a single patch. This result is independent of the particular functional response used. The other two rules we analyze take into account lower migration rates, the limitations in making optimal decisions by predators, and the possible constraints in the assessment of intake rate in the different patches. The results suggest that the processes that hinder the convergence of the populations to the IFD might make a major contribution to the stability of the system.