Abstract
A game theoretical model for the evolution of strategies in animal conflicts is considered, using methods from dynamical systems and population genetics. It is shown that the Hardy-Weinbergequilibrium is readily approached. The differential equation for the gene frequencies is more complicated than that which has been studied previously in the corresponding asexual case.
Similar content being viewed by others
References
Hofbauer, J., Schuster, P., Sigmund, K.: A Note on evolutionary stable strategies and game dynamics. J. Theor. Biol. 81, 609–612 (1979)
Hofbauer, J.: On the occurrence of limit cycles in the Volterra-Lotka differential equation. J. Nonlinear Anal. 5, (1981) (to appear)
Marsden, J., McCracken, M.: The Hopf bifurcation and its applications. In: Applied mathematical sciences, vol. 19. Berlin, Heidelberg, New York: Springer 1976
Maynard-Smith, J.: The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47, 209–221 (1974)
Schuster, P., Sigmund, K., Hofbauer, J., Wolff, R.: Selfregulation of behaviour in animal societies. Biol. Cybern. 40, 1–8 (1981)
Schuster, P., Sigmund, K., Wolff, R.: Mass action kinetics of selfreplication in flow reactors. J. Math. Analysis & Applications 78, 88–112 (1980)
Taylor, P., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)
Zeeman, E.C.: Population dynamics from game theory. In: global theory of dynamical system, Nitecki (ed.). In: Lecture Notes, Vol. 819. Berlin, Heidelberg, new York: Springer 1980
Zeeman, E.C.: Dynamics of the evolution of animal conflicts. J. Theor. Biol. 89, 249–270 (1981)
Author information
Authors and Affiliations
Additional information
This work has been supported financially by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, Projekt No. 3502
Rights and permissions
About this article
Cite this article
Hofbauer, J., Schuster, P. & Sigmund, K. Game dynamics in mendelian populations. Biol. Cybern. 43, 51–57 (1982). https://doi.org/10.1007/BF00337287
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00337287