Journal of Mathematical Biology

, Volume 22, Issue 1, pp 105–115

On evolutionarily stable sets

  • Bernhard Thomas

DOI: 10.1007/BF00276549

Cite this article as:
Thomas, B. J. Math. Biology (1985) 22: 105. doi:10.1007/BF00276549


As an extension of the concept of an evolutionarily stable strategy (ESS) evolutionarily stable sets are introduced, i.e. sets of equilibrium strategies (EQS) which have much of the properties of an ESS. They are primarily used with evolutionary game models that allow a continuum of EQSs, none of which can be an ESS, but also include common ESSs as a special case. For a large class even of nonlinear models it can be shown that the standard dynamics converge towards some equilibrium point in an ES set if started within a neighbourhood of the set. Important applications of ES sets include e.g. mixed-strategist models and evolutionary game models in sexual populations.

Key words

ESSevolutiongame dynamicspopulation geneticssexual populationsstrategies

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Bernhard Thomas
    • 1
  1. 1.Institut für Entwicklungsphysiologie der Universität zu Köln, AG KybernetikKöln 41Federal Republic of Germany