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Non-linear ESS models and polymorphism

  • W. G. S. Hines (a1) and John Haigh (a1)

Abstract

Extensions of ESS theory to situations well outside the classical formulation often assume, as a convenience, that the population being modelled is, in some sense, monomorphic. While this assumption is in keeping with the original approach used in developing the theory, it is rendered less plausible by the observation that the original models do not preclude the possibility of polymorphism, a potentially serious omission. We consider a generalisation of the classical bilinear fitness function, and examine the circumstances that will tend to favour monomorphism.

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

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Present address: School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK.

Research supported by NSERC Operating Grant A6187.

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References

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Abakuks, A. (1980) Conditions for evolutionarily stable strategies. J. Appl. Prob. 17, 559562.
Grafen, A. (1979) The hawk-dove game played between relatives. Anim. Behav. 27, 905907.
Haigh, J. (1975) Game theory and evolution. Adv. Appl. Prob. 7, 811.
Hines, W. G. S. (1980) Strategy stability in complex populations. J. Appl. Prob. 17, 600610.
Hines, W. G. S. (1982) Mutations, perturbations and evolutionarily stable strategies. J. Appl. Prob. 19, 204209.
Hines, W. G. S. and Maynard Smith, J. (1979) Games between relatives. J. Theoret. Biol. 79, 1930.
Maynard Smith, J. (1982) Evolution and the Theory of Games. Cambridge University Press, Cambridge.

Keywords

Non-linear ESS models and polymorphism

  • W. G. S. Hines (a1) and John Haigh (a1)

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