Authors: M. Lemire 1 , S. Lessard, and Yi Tao
View More View Less
  • 1 Please ask the editor of the journal.
Restricted access

A local stability analysis is made in two-sex two-locus frequency-dependent selection models in order to precise the definition for an ESS that has to be used for such models. Uninvadability of fixation states and stability of polymor- phic equilibria are studied. It is shown that Cressman's conditions for a two-population ESS, which are less restric- tive than Taylor's conditions, are sufficient for local stability of fixation states but not for local stability of polymor- phic equilibria when selection is strong.

  • Cressman, R. and Dash, A. T. (1991): Strong stability and evolutionarily stable strategies with two types of players. J. Math. Biol. 30: 89-99.

    'Strong stability and evolutionarily stable strategies with two types of players ' () 30 J. Math. Biol. : 89 -99.

    • Search Google Scholar
  • Lessard, S. and Karlin, S. (1982): A criterion for stability-instability at fixation states involving an eigenvalue one with applications in population genetics. Theor. Popul. Biol. 22: 108-126.

    'A criterion for stability-instability at fixation states involving an eigenvalue one with applications in population genetics ' () 22 Theor. Popul. Biol : 108 -126.

    • Search Google Scholar
  • Maynard Smith, J. (1974): The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47: 209-221.

    'The theory of games and the evolution of animal conflicts ' () 47 J. Theor. Biol. : 209 -221.

    • Search Google Scholar
  • Maynard Smith, J. and Price, G. R. (1973): The logic of animal conflict. Nature 246: 15-18.

    'The logic of animal conflict ' () 246 Nature : 15 -18.

  • Morris, M., Matessi, C. and Karlin, S. (1987): Models of intergenerational kin altruism. Amer. Nat. 130: 544-569.

    'Models of intergenerational kin altruism ' () 130 Amer. Nat. : 544 -569.

  • Nagylaki, T. (1976): The evolution of one- and two-locus systems. Genetics 83: 583-600.

    'The evolution of one- and two-locus systems ' () 83 Genetics : 583 -600.

  • Tao, Y., Lessard, S. and Lemire, M. (2000): Evolutionarily stable strategy in a sex- and frequency-dependent selection model. J. Theor. Biol. 204: 191-200.

    'Evolutionarily stable strategy in a sex- and frequency-dependent selection model ' () 204 J. Theor. Biol. : 191 -200.

    • Search Google Scholar
  • Taylor, P. D. (1979): Evolutionarily stable strategies with two types of players. J. Appl. Prob. 16: 76-83.

    'Evolutionarily stable strategies with two types of players ' () 16 J. Appl. Prob. : 76 -83.

    • Search Google Scholar
  • Vickers, G. T. and Cannings, C. (1987): On the definition of an evolutionarily stable strategy. J. Theor. Biol. 129: 349-353.

    'On the definition of an evolutionarily stable strategy ' () 129 J. Theor. Biol. : 349 -353.

    • Search Google Scholar
  • Tao, Y. (1998): Frequency-dependent selection: A two-phenotype, two-allele, single-locus, two-species diploid model. J. Theor. Biol. 191: 289-294.

    'Frequency-dependent selection: A two-phenotype, two-allele, single-locus, two-species diploid model ' () 191 J. Theor. Biol. : 289 -294.

    • Search Google Scholar
  • Nagylaki, T. (1977): Selection in One- and Two-locus Systems. Springer-Verlag, Berlin.

    Selection in One- and Two-locus Systems , ().

  • Cressman, R. (1992): The Stability Concept of Evolutionary Game Theory (A Dynamic Approach). Lecture Notes in Biomathematics, Vol. 94, Springer-Verlag, Berlin, Heidelberg, New York.

    The Stability Concept of Evolutionary Game Theory (A Dynamic Approach) , ().

    • Search Google Scholar
  • Cressman, R. (1996): Frequency-dependent stability for two-species interactions. Theor. Popul. Biol. 49: 189-210.

    'Frequency-dependent stability for two-species interactions ' () 49 Theor. Popul. Biol. : 189 -210.

    • Search Google Scholar

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Sep 2020 2 0 0
Oct 2020 0 0 0
Nov 2020 3 3 1
Dec 2020 4 0 0
Jan 2021 0 0 0
Feb 2021 0 0 0
Mar 2021 0 0 0