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Bulletin of Mathematical Biology

, Volume 59, Issue 3, pp 497–515 | Cite as

Controlling spatial chaos in metapopulations with long-range dispersal

  • Michael Doebeli
  • Graeme D. Ruxton
Article

Abstract

We propose two methods to control spatial chaos in an ecological metapopulation model with long-range dispersal. The metapopulation model consists of local populations living in a patchily distributed habitat. The habitat patches are arranged in a one-dimensional array. In each generation, density-dependent reproduction occurs first in each patch. Then individuals disperse according to a Gaussian distribution. The model corresponds to a chain of coupled oscillators with long-range interactions. It exhibits chaos for a broad range of parameters. The proposed control methods are based on the method described by Güémez and Matías for single difference equations. The methods work by adjusting the local population sizes in a selected subset of all patches. In the first method (pulse control), the adjustments are made periodically at regular time intervals, and consist of always removing (or adding) a fixed proportion of the local populations. In the second method (wave control), the adjustments are made in every generation, but the proportion of the local population that is affected by the control changes sinusoidally. As long as dispersal distances are not too low, these perturbations can drive chaotic metapopulations to cyclic orbits whose period is a multiple of the control period. we discuss the influence of the 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.

Keywords

Local Population Pulse Control Fixed Proportion Metapopulation Model Spatiotemporal Chaos 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Michael Doebeli
    • 1
  • Graeme D. Ruxton
    • 2
  1. 1.Zoology InstituteUniversity of BaselBaselSwitzerland
  2. 2.Division of Environmental and Evolutionary BiologyUniversity of GlasgowGlasgowUK

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