Journal of Mathematical Biology

, Volume 23, Issue 1, pp 41–53

The selection mutation equation

  • Josef Hofbauer

DOI: 10.1007/BF00276557

Cite this article as:
Hofbauer, J. J. Math. Biology (1985) 23: 41. doi:10.1007/BF00276557


Fisher's Fundamental Theorem of Natural Selection is extended to the selection mutation model with mutation rates ɛijii.e. depending only on the target gene, by constructing a simple Lyapunov function. For other mutation rates stable limit cycles are possible.

Key words

Fundamental theorem Maximum principle Shahshahani gradients Limit cycles 

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Josef Hofbauer
    • 1
  1. 1.Institut für MathematikUniversität WienWienAustria
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA

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