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Strategy stability in complex randomly mating diploid populations

Published online by Cambridge University Press:  14 July 2016

W. G. S. Hines
W. G. S. Hines*
Affiliation:
University of Guelph
*
∗Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.
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Abstract

A class of Lyapunov functions is used to demonstrate that strategy stability occurs in complex randomly mating diploid populations. Strategies close to the evolutionarily stable strategy tend to fare better than more remote strategies. If convergence in mean strategy to an evolutionarily stable strategy is not possible, evolution will continue until all strategies in use lie on a unique face of the convex hull of available strategies.

The results obtained are also relevant to the haploid parthenogenetic case.

Keywords

ANIMAL CONFLICT MODELSCOMPLEX POPULATIONSCONDITIONAL EVOLUTIONARILY STABLE STRATEGIESEVOLUTIONARILY STABLE STRATEGIESGAME DYNAMICSLYAPUNOV FUNCTIONSPOPULATION DYNAMICSPOPULATION STRATEGY STABILITYSEXUAL DIPLOIDY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 653 - 659
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported by NSERC Operating Grant A6187.

References

Akin, E. (1980) Domination or equilibrium. Math. Biosci. 50, 239–250.Google Scholar
Bishop, D. T. and Cannings, C. (1976) Models of animal conflict (abstract). Adv. Appl. Prob. 6, 616–621.Google Scholar
Bishop, D. T. and Cannings, C. (1978) A generalized war of attrition. J. Theoret. Biol. 70, 85–124.Google Scholar
Hines, W. G. S. (1980a) An evolutionarily stable strategy model for randomly mating diploid populations. J. Theoret. Biol. 87, 379–384.Google Scholar
Hines, W. G. S. (1980b) Strategy stability in complex populations. J. Appl. Prob. 17, 600–610.CrossRefGoogle Scholar
Hines, W. G. S. (1980C) Three characterizations of population strategy stability. J. Appl. Prob. 17, 333–340.Google Scholar
Hines, W. G. S. (1982) Mutations, perturbations and evolutionarily stable strategies. J. Appl. Prob. 19, 204–209.Google Scholar
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209–221.Google Scholar
Taylor, P. D. and Jonker, L. B. (1978) Evolutionarily stable stratégies and game dynamics. Math. Biosci. 40, 145–156.Google Scholar
Zeeman, E. C. (1980) Population dynamics from game theory. In Global Theory of Dynamical Systems, Proceedings, Northwestern 1979, Springer-Verlag, Berlin, 471–497.Google Scholar