Mutation, selection, and recombination in a model of phenotype evolution

Pages: 221 - 236, Volume 6, Issue 1, January 2000

doi:10.3934/dcds.2000.6.221       Abstract        Full Text (290.3K)       Related Articles

P. Magal - Faculte des Sciences et Techniques, 25, rue Philippe Lebon, B.P. 540, 76058 Le Havre, France (email)
G. F. Webb - Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States (email)

Abstract: A model of phenotype evolution incorporating mutation, selection, and recombination is investigated. The model consists of a partial differential equation for population density with respect to a continuous variable representing phenotype diversity. Mutation is modeled by diffusion, selection is modeled by differential phenotype fitness, and genetic recombination is modeled by an averaging process. It is proved that if the recombination process is suffciently weak, then there is a unique globally asymptotically stable attractor.

Keywords:  Semigroups, asymptotic behavior, evolution, mutation, recombination.
Mathematics Subject Classification:  35K55, 47H20, 58F11, 92D15.

Received: October 1999;      Published: December 1999.