Journal of Mathematical Biology

, Volume 30, Issue 5, pp 457–471

Travelling waves and dominance of ESS's

  • V. C. L. Hutson
  • G. T. Vickers

DOI: 10.1007/BF00160531

Cite this article as:
Hutson, V.C.L. & Vickers, G.T. J. Math. Biol. (1992) 30: 457. doi:10.1007/BF00160531


We consider a simple two strategy game in which each pure strategy is an evolutionarily stable strategy (ESS). Under the usual dynamical equations, the large-time behaviour of the system will depend upon the initial conditions and the pay-off matrix. If spatial effects are included to give a reaction-diffusion system, we prove that travelling wavefronts can occur which in effect replace one ESS by another. The ‘strength’ or ‘dominance’ of each ESS which decides the ‘winner’ in a precisely defined sense is determined by its pay-off and by its diffusion rate. Good strategies have large pay-offs and small diffusion rates.

Key words

Reaction-diffusion Travelling wave ESS 

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • V. C. L. Hutson
    • 1
  • G. T. Vickers
    • 1
  1. 1.Department of Applied and Computational MathematicsUniversity of SheffieldSheffieldUK

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