title: A generalization of Kingman's model of selection and mutation and the Lenski experiment.
abstract: Kingman's model of selection and mutation studies the limit type value distribution in an asexual population of discrete generations and infinite size undergoing selection and mutation. This paper generalizes the model to analyze the long-term evolution of Escherichia. coli in Lenski experiment. Weak assumptions for fitness functions are proposed and the mutation mechanism is the same as in Kingman's model. General macroscopic epistasis are designable through fitness functions. Convergence to the unique limit type distribution is obtained.
authors.affiliation: Institut für Mathematik, Johannes-Gutenberg-Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany. Electronic address: http://linglongyuan.weebly.com.
authors.forename: Linglong
authors.initials: L
authors.lastname: Yuan
mesh_terms: D005075:Biological Evolution; D004926:Escherichia coli / Q000502:physiology*; D008954:Models, Biological; D009154:Mutation / Q000502:physiology*; D012641:Selection, Genetic / Q000502:physiology*
keywords: Escherichia coli; Fitness function; House of cards; Lenski experiment; Selection-mutation balance; Type distribution