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Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

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Aggregation and stability in meta-population models

Murdoch, W.W and Briggs, C.J. and Nisbet, R.M. and Gurney, William and Stewart-Oaten, A. (1992) Aggregation and stability in meta-population models. American Naturalist, 140 (1). pp. 41-58. ISSN 0003-0147

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We analyze a metapopulation model of the interactions between Lotka-Volterra-type prey and predators that occur in two environmentally distinguishable patches and are linked by migration. Environmental differences between the patches tend to stabilize the otherwise neutrally stable model by causing the per capita immigration rate on a patch to be temporally density-dependent, partly as a consequence of out-of-phase fluctuations in density. However, the environmental differences can also lead to indirect effects on the temporal dependence of per capita prey death rate on prey density in each patch and on temporal dependence of per capita predator birthrate on predator density in each patch. Spatially density-dependent movement by the prey can be either uniformly destabilizing or initially stabilizing and then destabilizing as the degree of density dependence increases, depending on the overall rate of prey movement. Aggregation by the predator to the patch with more prey modifies one or more of the three processes listed above. Typically, weak aggregation is stabilizing, and strong aggregation is destabilizing. Aggregation can also render unstable an initially stable model. We conclude that metapopulation and single-population models are not good analogues of each other and that predator aggregation affects the two types of models via different mechanisms.