A Generalization of Kingman's Model of Selection and Mutation

Linglong Yuan

Published 2015-06-07Version 1

This paper generalizes Kingman's model of selection and mutation which studies the limit distribution of type values (or fitness values) in an asexual population of discrete generations and infinite size undergoing selection and mutation. A small set of assumptions for selection effects are proposed and for the mutation, as in Kingman's model, we assume that the type value of a mutant is independent of that of parent's. General macroscopic epistasis (or individual interactions) are designable through selection effect functions. Convergence to the unique limit type distribution is obtained for the general model. This setting covers the specific case studied in Kingman's model and also partially generalizes the framework of B\"urger's. The generalized model is then applied to Lenski experiment which investigates in the laboratory the long-term evolution of 12 initially identical populations of Escherichia coli in identical environments.