Aggregation and stability in meta-population models

W.W Murdoch, C.J. Briggs, R.M. Nisbet, William Gurney, A. Stewart-Oaten

Research output: Contribution to journalArticle

84 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages41-58
Number of pages18
JournalAmerican Naturalist
Volume140
Issue number1
Publication statusPublished - Jul 1992

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metapopulation
predator
Emigration and Immigration
predators
Population
Mortality
density dependence
immigration
rate

Keywords

  • migration
  • density fluctuations
  • death rate
  • aggregation
  • metapopulation model

Cite this

Murdoch, W. W., Briggs, C. J., Nisbet, R. M., Gurney, W., & Stewart-Oaten, A. (1992). Aggregation and stability in meta-population models. American Naturalist, 140(1), 41-58.
Murdoch, W.W ; Briggs, C.J. ; Nisbet, R.M. ; Gurney, William ; Stewart-Oaten, A. / Aggregation and stability in meta-population models. In: American Naturalist. 1992 ; Vol. 140, No. 1. pp. 41-58.
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Murdoch, WW, Briggs, CJ, Nisbet, RM, Gurney, W & Stewart-Oaten, A 1992, 'Aggregation and stability in meta-population models' American Naturalist, vol. 140, no. 1, pp. 41-58.

Aggregation and stability in meta-population models. / Murdoch, W.W; Briggs, C.J.; Nisbet, R.M.; Gurney, William; Stewart-Oaten, A.

In: American Naturalist, Vol. 140, No. 1, 07.1992, p. 41-58.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Aggregation and stability in meta-population models

AU - Murdoch, W.W

AU - Briggs, C.J.

AU - Nisbet, R.M.

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N2 - 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.

AB - 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.

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Murdoch WW, Briggs CJ, Nisbet RM, Gurney W, Stewart-Oaten A. Aggregation and stability in meta-population models. American Naturalist. 1992 Jul;140(1):41-58.