The influence of dispersal on a predator-prey system with two habitats

TL;DR

This study investigates how dispersal between two habitats affects the stability and bifurcation patterns of a simple predator-prey system, revealing complex effects including potential destabilization and stabilization depending on dispersal characteristics.

Contribution

It provides a comprehensive analysis of dispersal effects on a minimal two-species, two-habitat model using generalized modeling, highlighting the role of nonrandom dispersal in stability and bifurcations.

Findings

Dispersal often destabilizes equilibria.

Nonrandom dispersal can positively correlate with stability.

Multiple bifurcation types, including pattern-forming, are observed.

Abstract

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with migration rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.