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Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective

Author

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

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.

Suggested Citation

  • P. Marrow & U. Dieckmann & R. Law, 1996. "Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective," Working Papers wp96002, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp96002
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    Cited by:

    1. Yasuhiro Shirata, 2012. "The evolution of fairness under an assortative matching rule in the ultimatum game," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 1-21, February.
    2. 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.
    3. Wu, Jiabin, 2017. "Political institutions and the evolution of character traits," Games and Economic Behavior, Elsevier, vol. 106(C), pages 260-276.
    4. 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.
    5. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 221-247, June.
    6. Parvinen, Kalle, 2013. "Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations," Theoretical Population Biology, Elsevier, vol. 85(C), pages 12-19.
    7. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    8. Meng, Xin-zhu & Zhao, Sheng-nan & Zhang, Wen-yan, 2015. "Adaptive dynamics analysis of a predator–prey model with selective disturbance," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 946-958.
    9. McAllister, A. & McCartney, M. & Glass, D.H., 2023. "Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    10. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    11. Cressman, Ross & Hofbauer, Josef & Riedel, Frank, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers 12/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).
    12. Cressman, Ross & Garay, József, 2009. "A predator–prey refuge system: Evolutionary stability in ecological systems," Theoretical Population Biology, Elsevier, vol. 76(4), pages 248-257.
    13. R. Law & U. Dieckmann, 1997. "Symbiosis Without Mutualism and the Merger of Lineages in Evolution," Working Papers ir97074, International Institute for Applied Systems Analysis.
    14. Jian Zu & Jinliang Wang & Gang Huang, 2016. "Evolutionary Diversification of Prey and Predator Species Facilitated by Asymmetric Interactions," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-28, September.
    15. Zu, Jian & Wang, Jinliang, 2013. "Adaptive evolution of attack ability promotes the evolutionary branching of predator species," Theoretical Population Biology, Elsevier, vol. 89(C), pages 12-23.
    16. 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.

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