tromeur2016impact
Impact of dispersal on the stability of metapopulations
Eric Tromeur, Lars Rudolf and Thilo Gross
Journal of Theoretical Biology 392, 1-11, 2016
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 $$\omega$$.