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January  2000, 6(1): 221-236. doi: 10.3934/dcds.2000.6.221

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

P. Magal 1, and  G. F. Webb 2,

1. 

Faculte des Sciences et Techniques, 25, rue Philippe Lebon, B.P. 540, 76058 Le Havre, France
2. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States

Received  October 1999 Published  December 1999

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: recombination., evolution, mutation, Semigroups, asymptotic behavior.
Mathematics Subject Classification: 35K55, 47H20, 58F11, 92D1.
Citation: P. Magal, G. F. Webb. Mutation, selection, and recombination in a model of phenotype evolution. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 221-236. doi: 10.3934/dcds.2000.6.221
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