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On the local stability of an evolutionarily stable strategy in a diploid population

Published online by Cambridge University Press:  14 July 2016

W. G. S. Hines  and
D. T. Bishop
W. G. S. Hines*
Affiliation:
University of Guelph
D. T. Bishop*
Affiliation:
University of Utah
*
∗ Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1.
∗∗ Postal address: Department of Human Genetics, School of Medicine, 50 North Medical Drive, Salt Lake City, UT 84132, U.S.A.
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Abstract

The evolutionarily stable strategy for a given payoff matrix contest, although originally determined in terms of a haploid population, has been shown elsewhere to correspond to an equilibrium of the mean strategy of a diploid population. In this note, the equilibrium is shown to be locally stable for diploid populations. This local stability is demonstrated primarily by relating the behaviour of the perturbed diploid population to one, or in some cases two, associated haploid populations.

Keywords

ANIMAL CONFLICT MODELSASSOCIATED STRATEGIESGAME DYNAMICSPOPULATION DYNAMICSPOPULATION STRATEGY STABILITYSEXUAL DIPLOIDY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 215 - 224
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by NSERC Operating Grant A6187.

References

Auslander, D. J., Guckenheimer, J. M. and Oster, G. (1978) Random evolutionary stable strategies. Theoret. Popn Biol. 13, 276–293.CrossRefGoogle Scholar
Cressman, R. and Hines, W. G. S. (1984) Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns. J. Appl. Prob. 21, 1–9.CrossRefGoogle Scholar
Haigh, J. (1975) Game theory and evolution (abstract). Adv. Appl. Prob. 7, 8–11.CrossRefGoogle Scholar
Hines, W. G. S. (1980a) An evolutionarily stable strategy model for randomly mating diploid populations. J. Theoret. Biol. 87, 379–384.CrossRefGoogle ScholarPubMed
Hines, W. G. S. (1980b) Strategy stability in complex populations. J. Appl. Prob. 17, 600–610.CrossRefGoogle Scholar
Hines, W. G. S. (1982) Strategy stability in complex randomly mating diploid populations. J. Appl. Prob. 19, 653–659.CrossRefGoogle Scholar
Hines, W. G. S. and Bishop, D. T. (1983a) Evolutionarily stable strategies in diploid populations with general inheritance patterns. J. Appl. Prob. 20, 689–695.CrossRefGoogle Scholar
Hines, W. G. S. and Bishop, D. T. (1983b) Can and will a sexual diploid population attain an evolutionarily stable strategy? CrossRefGoogle Scholar
Lloyd, D. G. (1977) Genetic and phenotypic models of natural selection. J. Theoret. Biol. 69, 543–560.CrossRefGoogle ScholarPubMed
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209–221.CrossRefGoogle Scholar
Maynard Smith, J. (1981) Will a sexual population evolve to an ESS? Amer. Nat. 117, 1015–1018.CrossRefGoogle Scholar
Treisman, M. (1981) Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid populations with simple mendelian inheritance. J. Theoret. Biol. 93, 97–124.CrossRefGoogle ScholarPubMed