Monatshefte für Mathematik

, Volume 110, Issue 3, pp 189–206

Dynamical aspects of evolutionary stability


  • Immanuel M. Bomze
    • Institut für Statistik und InformatikUniversität Wien

DOI: 10.1007/BF01301675

Cite this article as:
Bomze, I.M. Monatshefte für Mathematik (1990) 110: 189. doi:10.1007/BF01301675


Selection is often viewed as a process that maximizes the average fitness of a population. However, there are often constraints even on the phenotypic level which may prevent fitness optimization. Consequently, in evolutionary game theory, models of frequency dependent selection are investigated, which focus on equilibrium states that are characterized by stability (or uninvadability) rather than by optimality. The aim of this article is to relate these stability notions with asymptotic stability in the so-called “replicator dynamics”, by generalizing results, which are well-known for elementary situations, to a fairly general setting applicable, e.g. to complex populations. Moreover, a purely dynamical characterization of evolutionary stability and uninvadability is presented.

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© Springer-Verlag 1990