Dispersal and Dynamics

Mixing and asynchrony of interactions can be expected to stabilize the dynamics of populations. One way such mixing occurs is by dispersal, and Hastings and Gyllenberg et al. have shown that symmetric dispersal between two local populations governed by logistic difference equations can simplify the dynamics. These results are extended here by using a more flexible difference equation and allowing asymmetric dispersal. Although there are some instances where dispersal is destabilizing, its stabilizing effect is enhanced by asymmetry. In addition, very high dispersal rates can induce a stable equilibrium of the metapopulation despite highly chaotic local dynamics. If this equilibrium loses stability, the route to intermittent chaos can be observed. Two new conditions under which dispersal can be stabilizing are discussed. One occurs when the timing of reproduction and dispersal differs in the two patches of the metapopulation. This enlarges the asynchrony of the interactions, and simple dynamics due to dispersal are more likely. The second works by slightly adjusting dispersal rates to control chaotic dynamics. The control can replace chaos by a stable equilibrium. The evolution of dispersal rates is discussed. Since obtaining general criteria for invasion into a population with chaotic dynamics is difficult, no clear conclusions are possible as to whether evolution leads to more stable metapopulations. However, a mutant that controls chaos can invade a resident having the same local dynamics but no control mechanism, so that evolution can lead from chaos to a stable equilibrium.