Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-20T01:38:26.721Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear ESS models and polymorphism

Published online by Cambridge University Press:  14 July 2016

W. G. S. Hines  and
John Haigh
W. G. S. Hines*
Affiliation:
University of Guelph
John Haigh
Affiliation:
University of Guelph
*
∗Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

ANIMAL CONFLICT MODELSFREQUENCY-DEPENDENT PAYOFF FUNCTIONSNON-LINEAR PAYOFF FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 747 - 756
Copyright
Copyright © Applied Probability Trust 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

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

Research supported by NSERC Operating Grant A6187.

References

Abakuks, A. (1980) Conditions for evolutionarily stable strategies. J. Appl. Prob. 17, 559–562.Google Scholar
Grafen, A. (1979) The hawk-dove game played between relatives. Anim. Behav. 27, 905–907.Google Scholar
Haigh, J. (1975) Game theory and evolution. Adv. Appl. Prob. 7, 8–11.Google Scholar
Hines, W. G. S. (1980) Strategy stability in complex populations. J. Appl. Prob. 17, 600–610.Google Scholar
Hines, W. G. S. (1982) Mutations, perturbations and evolutionarily stable strategies. J. Appl. Prob. 19, 204–209.Google Scholar
Hines, W. G. S. and Maynard Smith, J. (1979) Games between relatives. J. Theoret. Biol. 79, 19–30.Google Scholar
Maynard Smith, J. (1982) Evolution and the Theory of Games. Cambridge University Press, Cambridge.Google Scholar