Modelling and simulating Lenski's long-term evolution experiment

TL;DR

This paper refines a model of Lenski's long-term evolution experiment by integrating a Cannings model with diminishing returns epistasis, providing new insights into fitness growth dynamics and the effects of epistasis.

Contribution

It advances the existing model both conceptually and mathematically, clarifying the role of epistasis and the daily growth dynamics in the experiment.

Findings

Identification of a runtime effect with shortening daily growth periods

Clarification of epistasis contribution to fitness increase

Development of approximations supported by simulations

Abstract

We revisit the model by Wiser, Ribeck, and Lenski (Science \textbf{342} (2013), 1364--1367), which describes how the mean fitness increases over time due to beneficial mutations in Lenski's long-term evolution experiment. We develop the model further both conceptually and mathematically. Conceptually, we describe the experiment with the help of a Cannings model with mutation and selection, where the latter includes diminishing returns epistasis. The analysis sheds light on the growth dynamics within every single day and reveals a runtime effect, that is, the shortening of the daily growth period with increasing fitness; and it allows to clarify the contribution of epistasis to the mean fitness curve. Mathematically, we explain rigorous results in terms of a law of large numbers (in the limit of infinite population size and for a certain asymptotic parameter regime), and present approximations based on heuristics and supported by simulations for finite populations.