An individual-based model for the Lenski experiment, and the deceleration of the relative fitness. (English) Zbl 1358.92068
Summary: The Lenski experiment investigates the long-term evolution of bacterial populations. In this paper we present an individual-based probabilistic model that captures essential features of the experimental design, and whose mechanism does not include epistasis in the continuous-time (intraday) part of the model, but leads to an epistatic effect in the discrete-time (interday) part. We prove that under some assumptions excluding clonal interference, the rescaled relative fitness process converges in the large population limit to a power law function, similar to the one obtained by M. J. Wiser et al. [“Long-term dynamics of adaptation in asexual populations”, Science 342, No. 6164, 1364–1367 (2013; doi:10.1126/science.1243357)], there attributed to effects of clonal interference and epistasis.
Keywords:
experimental evolution; Lenski experiment; relative fitness; Yule processes; Cannings dynamics; branching process approximationReferences:
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