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Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective

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  • P. Marrow
  • U. Dieckmann
  • R. Law
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    Abstract

    Evolution takes place in an evolutionary setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals- the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the predator-prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator-prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather than different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species.

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    Bibliographic Info

    Paper provided by International Institute for Applied Systems Analysis in its series Working Papers with number wp96002.

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    Date of creation: Mar 1996
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    Handle: RePEc:wop:iasawp:wp96002

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    Cited by:
    1. Ross Cressman & Josef Hofbauer & Frank Riedel, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers bgse12_2005, University of Bonn, Germany.
    2. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    3. E. Kisdi & S.A.H. Geritz, 1998. "Adaptive Dynamics in Allele Space: Evolution of Genetic Polymorphism by Small Mutations in a Heterogeneous Environment," Working Papers ir98038, International Institute for Applied Systems Analysis.
    4. S.A.H. Geritz & E. Kisdi & G. Meszena & J.A.J. Metz, 1996. "Evolutionary Singular Strategies and the Adaptive Growth and Branching of the Evolutionary Tree," Working Papers wp96114, International Institute for Applied Systems Analysis.
    5. R. Law & U. Dieckmann, 1997. "Symbiosis Without Mutualism and the Merger of Lineages in Evolution," Working Papers ir97074, International Institute for Applied Systems Analysis.
    6. E. Kisdi & F.J.A. Jacobs & S.A.H. Geritz, 2000. "Red Queen Evolution by Cycles of Evolutionary Branching and Extinction," Working Papers ir00030, International Institute for Applied Systems Analysis.
    7. Åke Brännström & Jacob Johansson & Niels von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, Open Access Journal, vol. 4(3), pages 304-328, June.
    8. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer, vol. 38(2), pages 221-247, June.

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