Complex Interactions Between Dispersal and Dynamics: Lessons From Coupled Logistic Equations

A study of one of the simplest systems incorporating both dispersal and local dynamics, coupling two discrete time logistic equations, demonstrates several surprising features. Passive dispersal can cause chaotic dynamics to be replaced by simple periodic dynamics. Thus passive movement can be stabilizing, even in a deterministic model without underlying spatial variation in the dynamics. The boundary between initial conditions leading to qualitatively different dynamics can be a fractal, so it is essentially impossible to specify the asymptotic behavior in terms of the initial conditions. In accord with several recent studies of arthropods and earlier theoretical work, density dependence may only be detectable at a small enough spatial scale, so efforts to uncover density dependence must include investigations of movement.