PUB - Publikationen an der Universität Bielefeld

It is well known that rather general mutation-recombination models can besolved algorithmically (though not in closed form) by means of Haldanelinearization. The price to be paid is that one has to work with a multipletensor product of the state space one started from. Here, we present a relevant subclass of such models, in continuous time, withindependent mutation events at the sites, and crossover events between them. Itadmits a closed solution of the corresponding differential equation on thebasis of the original state space, and also closed expressions for the linkagedisequilibria, derived by means of M\"obius inversion. As an extra benefit, theapproach can be extended to a model with selection of additive type acrosssites. We also derive a necessary and sufficient criterion for the mean fitnessto be a Lyapunov function and determine the asymptotic behaviour of thesolutions.