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arXiv · 1803.09995

Modelling and simulating Lenski's long-term evolution experiment

Ellen Baake·Adrián González Casanova·Sebastian Probst·Anton Wakolbinger
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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.

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Ellen Baake, Adrián González Casanova, Sebastian Probst, Anton Wakolbinger. 2018-03-27. Modelling and simulating Lenski's long-term evolution experiment. https://arxiv.org/abs/1803.09995

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