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 behaviors on stability. We find that positive density-dependent dispersal and positive density-dependent settlement are destabilizing dispersal behaviors 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.
Figure 1: Influence of dispersal on stability for homogeneous patches. Analytical results (a) show that dispersal is stabilizing for low values of both \(\omega\), the elasticity of immigration with respect to the growth rate in the donor patch, and \(\zeta\), the elasticity of immigration with respect to the growth rate in the recipient patch. Numerical results (b), based on the analysis of \(10^4\) metapopulations show that the proportion of stable webs (PSW) decreases linearly as a function of parameters \(\zeta\) and \(\omega\).