A generalization of Kingman's model of selection and mutation and the Lenski experiment

TL;DR

This paper extends Kingman's model of selection and mutation to analyze the long-term evolution of E. coli in the Lenski experiment, allowing for more general fitness functions and demonstrating convergence to a unique distribution.

Contribution

It introduces a generalized model with weaker assumptions on fitness functions to study bacterial evolution, bridging theoretical models with experimental data.

Findings

Convergence to a unique limit type distribution is proven.

The model accommodates general macroscopic epistasis.

Applicable to long-term bacterial evolution studies.

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 analyse 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.