An Exactly Solved Model for Mutation, Recombination and Selection

[摘要] It is well known that rather general mutation-recombination models can besolved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with amultiple tensor product of the state space one started from.Here, we present a relevant subclass of such models, in continuous time,with independent mutation events at the sites, and crossover eventsbetween them. It admits a closed solution of the correspondingdifferential equation on the basis of the original state space, andalso closed expressions for the linkage disequilibria, derived by meansof M"obius inversion. As an extra benefit, the approach can be extendedto a model with selection of additive type across sites. We also derivea necessary and sufficient criterion for the mean fitness to be a Lyapunovfunction and determine the asymptotic behaviour of the solutions.

[学科分类] 数学（综合）