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Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns

  • R. Cressman (a1) and W. G. S. Hines (a1)

Abstract

The assumption of arbitrary and biologically implausible inheritance patterns in sexual diploid populations can yield population models in which convergence of a population's mean strategy to an evolutionarily stable strategy will not occur, even though this strategy is attainable with the correct choice of gametic frequencies. The present paper investigates the effect of imposing a simplifying and biologically reasonable restriction on the assumed inheritance patterns; namely, that dominance or underdominance occurs.

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

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This research was partially supported by NSERC operating grants A5247 (R.C.) and A6187 (W.G.S.H.)

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References

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[1] Akin, E. (1980) Domination or equilibrium. Math. Biosci. 50, 239250.
[2] Akin, E. and Hofbauer, J. (1982) Recurrence of the unfit. Math. Biosci. 61, 5162.
[3] Bishop, D. T. and Cannings, C. (1976) Models of animal conflict. Adv. Appl. Prob. 8, 616621.
[4] Hines, W. G. S. (1980) Three characterizations of population strategy stability. J. Appl. Prob. 17, 333340.
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[7] Hines, W. G. S. and Bishop, D. T. (1984) The local stability of an evolutionarily stable strategy in a diploid population. J. Appl. Prob. 21 (2).
[8] Hines, W. G. S. and Bishop, D. T. Reported by W. G. S. Hines at the Animal Conflicts Workshop, Queen's University, Kingston, Ontario. 1982.
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[11] Treisman, M. (1981) Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid species with simple Mendelian inheritance. J. Theoret. Biol. 93, 97124.

Keywords

Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns

  • R. Cressman (a1) and W. G. S. Hines (a1)

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