Abstract
The concept of metapopulation is widely used by modelers exploring the effects of spatial heterogeneity on population dynamics. Yet prima facie, it is a remarkably restrictive idealization implying that a population is distributed over a number of patches, each sufficiently well defined to permit local definition of vital rates, with migration between patches occurring over time scales comparable in magnitude to that of population change. For a small number of systems, this abstraction may be defensible, but metapopulation models commonly are poor approximations to real systems. For example, it is often unclear what constitutes a patch, with a suitable definition for considering vital rates being inappropriate for modeling migration. Therefore, metapopulation models are mainly useful for developing intuitive understanding on broader questions concerning the relationship between spatial heterogeneity and population density and stability. For this reason, it is not only important to derive mathematical results on particular models, it is also essential to understand intuitively the various stabilizing and destabilizing mechanisms, as this intuition is likely to be of more general applicability than the models from which it was obtained.
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References
Chewning, W.C. 1975. Migratory effects in predator-prey systems. Math. Biosci. 23: 253–262.
Crowley, P.H. 1981. Dispersal and the stability of predator-prey interactions. Am. Nat. 127: 696–715.
Diekmann, O., J.A.J. Metz, and M.W. Sabelis. 1988. Mathematical models of predator-prey-plant interactions in a patchy environment. Exp. Appl. Acarology 5: 319–342.
Godfray, H.C.J., and S.W. Pacala. 1992. Aggregation and the population dynamics of parasitoids and predators, Am. Nat., in press.
Gurney, W.S.C. and R.M. Nisbet. 1978. Single-species population fluctuations in patchy environments. Am. Nat. 112: 1075–1090.
Harrison, S. 1991. Local extinction in a metapopulation context: An empirical evaluation. Biol. J. Linnean Soc. 42: 73–88.
Hastings, A. 1991. A metapopulation model with local disasters of varying sizes. J. Math. Biol, (submitted).
Ives, A. In press. Continuous time models of host-parasitoid interactions. Am. Nat.
May, R.M. 1973. Stability in randomly fluctuating versus deterministic environments. Am. Nat. 107: 621–650.
Maynard Smith, J. 1974. Models in Ecology. Cambridge University Press, Cambridge, UK.
Murdoch, W.W., C.J. Briggs, R.M. Nisbet, W.S.C. Gurney, and A. Stewart-Oaten. In press. Aggregation and stability in metapopulation models. Am. Nat.
Murdoch, W.W. and A. Oaten. 1975. Predation and population stability, Adv. Ecol. Res. 9:1–131.
Murdoch, W.W. and A. Stewart-Oaten. 1989. Aggregation by parasitoids and predators: Effects on equilibrium and stability. Nat. 134: 288–310.
Nisbet, R.M., and Gurney, W.S.C. 1982. Modeling Fluctuating Populations. John Wiley and Sons, Chichester, UK.
Reeve, J.D. 1988. Environmental variability, migration and persistence in host-parasitoid systems. Am. Nat. 32: 810–836.
de Roos, A.M., E. McCauley, and W. Wilson. 1991. Mobility versus density limited predator-prey dynamics on different spatial scales. Proc. Roy. Soc. London 246: 117–122.
Taylor, A.D. 1988. Large-scale spatial structure and population dynamics in arthropod predator-prey systems. Ann. Zool. Fenn. 25: 63–74.
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© 1993 Springer-Verlag Berlin Heidelberg
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Nisbet, R.M., Briggs, C.J., Gurney, W.S.C., Murdoch, W.W., Stewart-Oaten, A. (1993). Two-Patch Metapopulation Dynamics. In: Levin, S.A., Powell, T.M., Steele, J.W. (eds) Patch Dynamics. Lecture Notes in Biomathematics, vol 96. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50155-5_10
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DOI: https://doi.org/10.1007/978-3-642-50155-5_10
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