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Evolutionarily stable strategies in differential and difference equation models

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Summary

A definition for an evolutionarily stable strategy (ESS) is given which is applicable to a general differential equation population model and two difference equation ‘analogs’. With the introduction of a fitnessgenerating function, it is possible to develop necessary conditions for the determination of an ESS for each of these systems. In most situations, an ESS for one system will also be an ESS for the other. Necessary conditions for an ESS are obtained. Under certain restrictions, they are shown to be valid, even under an unstable equilibrium in population density. the results are illustrated with an example which has the same ESS solution whether a continuous or discrete model is used. The behavior of the ESS for the discrete model is then examined under unstable equilibrium conditions in population density.

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, 85721, Tucson, Arizona, USA

    T. L. Vincent

  2. Department of Mathematics, University of Western Australia, 6009, Nedlands, WA, Australia

    M. E. Fisher

Authors
  1. T. L. Vincent
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  2. M. E. Fisher
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Vincent, T.L., Fisher, M.E. Evolutionarily stable strategies in differential and difference equation models. Evol Ecol 2, 321–337 (1988). https://doi.org/10.1007/BF02207564

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