Effects of symmetric and asymmetric dispersal on the dynamics of heterogeneous metapopulations: two-patch systems revisited

Abstract

Although the effects of dispersal on the dynamics of two-patch metapopulations are well studied, potential interactions between local dynamics and asymmetric dispersal remain unexplored. We examined the dynamics of two Ricker models coupled by symmetric or asymmetric constant-fraction dispersal at different rates. Unlike previous studies, we extensively sampled the r1-r2 space and found that stability of the coupled system was markedly affected by interactions between dispersal (in terms of strength and asymmetry) and local dynamics. When both subpopulations were intrinsically chaotic, increased symmetry in the exchange of individuals had a greater stabilizing impact on the dynamics of the system. When one subpopulation showed considerably more unstable dynamics than the other, higher asymmetry in the exchange of individuals had a stabilizing or destabilizing effect on the dynamics depending on whether the net dispersal bias was from the relatively stable to the relatively unstable subpopulation, or vice versa. The sensitivity of chaotic dynamics to stabilization due to dispersal varied with r-value in the chaotic subpopulation. Under unidirectional or bidirectional symmetric dispersal, when one subpopulation was intrinsically chaotic and the other had stable dynamics, the stabilization of chaotic subpopulations with r~3.3-4.0 occurred at the lowest dispersal rates, followed by chaotic subpopulations with r~2.7-2.95 and, finally, chaotic subpopulations with r~2.95-3.3. The mechanism for this pattern is not known but might be related to the range and number of different attainable population sizes possible in different r-value zones.

Keywords: Chaos; Periodicity; Ricker model; Stability; Stabilization.