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Strategy stability in complex randomly mating diploid populations

  • W. G. S. Hines (a1)

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.

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Corresponding author

Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.

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Research supported by NSERC Operating Grant A6187.

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References

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Akin, E. (1980) Domination or equilibrium. Math. Biosci. 50, 239250.
Bishop, D. T. and Cannings, C. (1976) Models of animal conflict (abstract). Adv. Appl. Prob. 6, 616621.
Bishop, D. T. and Cannings, C. (1978) A generalized war of attrition. J. Theoret. Biol. 70, 85124.
Hines, W. G. S. (1980a) An evolutionarily stable strategy model for randomly mating diploid populations. J. Theoret. Biol. 87, 379384.
Hines, W. G. S. (1980b) Strategy stability in complex populations. J. Appl. Prob. 17, 600610.
Hines, W. G. S. (1980C) Three characterizations of population strategy stability. J. Appl. Prob. 17, 333340.
Hines, W. G. S. (1982) Mutations, perturbations and evolutionarily stable strategies. J. Appl. Prob. 19, 204209.
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209221.
Taylor, P. D. and Jonker, L. B. (1978) Evolutionarily stable stratégies and game dynamics. Math. Biosci. 40, 145156.
Zeeman, E. C. (1980) Population dynamics from game theory. In Global Theory of Dynamical Systems, Proceedings, Northwestern 1979, Springer-Verlag, Berlin, 471497.

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Strategy stability in complex randomly mating diploid populations

  • W. G. S. Hines (a1)

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