CONTROLLING SPATIAL CHAOS IN METAPOPULATIONS WITH LONG-RANGE DISPERSAL

We propose two methods to control spatial chaos in an ecological metap opulation model with long-range dispersal. The metapopulation model co nsists of local populations living in a patchily distributed habitat. The habitat patches are arranged in a one-dimensional array. In each g eneration, density-dependent reproduction occurs first in each patch. Then individuals disperse according to a Gaussian distribution. The mo del corresponds to a chain of coupled oscillators with long-range inte ractions. It exhibits chaos for a broad range of parameters. The propo sed control methods are based on the method described by Guemez and Ma tias for single difference equations. The methods work by adjusting th e local population sizes in a selected subset of all patches. In the f irst method (pulse control), the adjustments are made periodically at regular time intervals, and consist of always removing (or adding) a f ixed proportion of the local populations. In the second method (wave c ontrol), the adjustments are made in every generation, but the proport ion of the local population that is affected by the control changes si nusoidally. As long as dispersal distances are not too low, these pert urbations can drive chaotic metapopulations to cyclic orbits whose per iod is a multiple of the control period. We discuss the influence of t he magnitude of the pulses and wave amplitudes, and of the number and the distribution of controlled patches on the effectiveness of control . When the controls start to break down, interesting dynamic phenomena such as intermittent chaos can be observed. (C) 1997 Society for Math ematical Biology.