Impact of dispersal on the stability of metapopulations

• We propose a metapopulation model that captures the spatial dynamics of a species.
• We explore the model without restricting the kinetics to specific functional forms.
• The results offer a broad perspective on the dynamical stability of metapopulations.
• Density-dependent dispersal and settlement are shown to influence stability.
• Network topology is shown to affect the impact of dispersal on stability.

Dispersal is a key ecological process that enables local populations to form spatially extended systems called metapopulations. In the present study, we investigate how dispersal affects the linear stability of a general single-species metapopulation model. We discuss both the influence of local within-patch dynamics and the effects of various dispersal behaviours on stability. We find that positive density-dependent dispersal and positive density-dependent settlement are destabilizing dispersal behaviours while negative density-dependent dispersal and negative density-dependent settlement are stabilizing. It is also shown that dispersal has a stabilizing impact on heterogeneous metapopulations that correlates positively with the number of patches and the connectance of metapopulation networks.