Journal of Mathematical Biology

, Volume 34, Issue 5–6, pp 556–578 | Cite as

Evolutionary dynamics of predator-prey systems: an ecological perspective

  • Paul Marrow
  • Ulf Dieckmann
  • Richard Law
Article

Abstract

Evolution takes place in an ecological 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 context of 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 dynamics; 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 different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species.

Key words

Dynamical systems Evolution Game theory Asymptotic stability Population dynamics 

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Paul Marrow
    • 1
  • Ulf Dieckmann
    • 2
  • Richard Law
    • 3
  1. 1.Theoretical Biology Section, Institute of Evolutionary and Ecological SciencesUniversity of LeidenLeidenThe Netherlands
  2. 2.Theoretical Biology Section, Institute of Evolutionary and Ecological SciencesUniversity of LeidenLeidenThe Netherlands
  3. 3.Department of BiologyUniversity of YorkYorkUK

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