Skip to main content
Log in

Game dynamics in mendelian populations

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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)

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • Schuster, P., Sigmund, K., Hofbauer, J., Wolff, R.: Selfregulation of behaviour in animal societies. Biol. Cybern. 40, 1–8 (1981)

    Google Scholar 

  • Schuster, P., Sigmund, K., Wolff, R.: Mass action kinetics of selfreplication in flow reactors. J. Math. Analysis & Applications 78, 88–112 (1980)

    Google Scholar 

  • Taylor, P., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)

    Google Scholar 

  • 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

    Google Scholar 

  • Zeeman, E.C.: Dynamics of the evolution of animal conflicts. J. Theor. Biol. 89, 249–270 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work has been supported financially by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, Projekt No. 3502

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00337287

Keywords

Navigation