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Mutations, perturbations and evolutionarily stable strategies

  • W. G. S. Hines (a1)

Abstract

The changes in diversity of competitive strategies in a Maynard Smith population model with mixed strategies are related to the changes in population mean strategy. The effects of slight mutations in strategy frequencies, and of slight perturbations of the contest payoff rules are then investigated, and found to increase and decrease diversity respectively (to a third-order approximation). A relation among mutational effects, payoff perturbation effects and stable population diversity is suggested.

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

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Research supported by a National Science and Engineering Research Council Grant A6187.

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References

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Abakuks, A. (1980) Conditions for evolutionarily stable strategies. J. Appl. Prob. 17, 559562.
Haigh, J. (1975) Game theory and evolution (abstract). Adv. Appl. Prob. 7, 811.
Hines, W. G. S. (1978) Mutations and stable strategies. J. Theoret. Biol. 72, 413428.
Hines, W. G. S. (1980a) Three characterizations of population strategy stability. J. Appl. Prob. 17, 333340.
Hines, W. G. S. (1980b) Strategy stability in complex populations. J. Appl. Prob. 17, 600610.
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209221.
Zeeman, E. C. (1979) Population dynamics from game theory. In Proc. Internat. Conf. Global Theory of Dynamical Systems.

Keywords

Mutations, perturbations and evolutionarily stable strategies

  • W. G. S. Hines (a1)

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