A model of weak selection in the infinite alleles framework (Q1084038)

\textit{W. J. Ewens}, Theor. Popul. Biol. 3, 87-112 (1972; Zbl 0245.92009) has proposed a model in the infinite allele framework for populations with neutrality of all alleles at a particular locus. This paper proposes a generalisation of Ewens' result for situations where there is a form of weak selection. The models considered here are continuous time, discrete state space Markov processes. Each class of alleles is assumed to evolve according to a birth and death process. Alleles in a given class are assumed to be selectively neutral, so they have the same birth and death rates. But alleles in different classes have different birth and death rates. The classes are then coupled by assuming that mutants arising from births in one class may belong to another class. Though the number of classes is assumed fixed the number of possible alleles within any class may be infinite.