Dispersal and stability in metapopulations

Abstract

What are the stability consequences of density-independent dispersal between locally distinct populations? Can such dispersal stabilize population dynamics or is it more likely to be a destabilizing influence? If so, what are the conditions required for dispersalinduced instability? We address these questions firstly by briefly reviewing the current literature, where it has been established that equilibrium stability in single-species models is not affected by dispersal. We then present a general model for two-species interaction, and establish, using analytic techniques, that density-independent movement between populations is never stabilizing; it may, however, destabilize. We conclude that in discrete time models, dispersal may be destabilizing if the following three criteria are satisfied: (1) there is more than one variable (species or age class) in the system, (2) the movement fractions of the two variables (species or age classes) are very different, and (3) the interaction between the variables (species or age classes) is semi-antagonistic (e.g. a predator-prey system).