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An individual-based model for the Lenski experiment, and the deceleration of the relative fitness

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  • González Casanova, Adrián
  • Kurt, Noemi
  • Wakolbinger, Anton
  • Yuan, Linglong

Abstract

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 Wiser et al. (2013), there attributed to effects of clonal interference and epistasis.

Suggested Citation

  • González Casanova, Adrián & Kurt, Noemi & Wakolbinger, Anton & Yuan, Linglong, 2016. "An individual-based model for the Lenski experiment, and the deceleration of the relative fitness," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2211-2252.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:8:p:2211-2252
    DOI: 10.1016/j.spa.2016.01.009
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    References listed on IDEAS

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    1. Parsons, Todd L. & Quince, Christopher & Plotkin, Joshua B., 2008. "Absorption and fixation times for neutral and quasi-neutral populations with density dependence," Theoretical Population Biology, Elsevier, vol. 74(4), pages 302-310.
    2. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.
    3. Schweinsberg, Jason, 2003. "Coalescent processes obtained from supercritical Galton-Watson processes," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 107-139, July.
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    Cited by:

    1. Hermann, Felix & Pfaffelhuber, Peter, 2020. "Markov branching processes with disasters: Extinction, survival and duality to p-jump processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2488-2518.
    2. González Casanova, Adrián & Miró Pina, Verónica & Pardo, Juan Carlos, 2020. "The Wright–Fisher model with efficiency," Theoretical Population Biology, Elsevier, vol. 132(C), pages 33-46.
    3. Baake, Ellen & González Casanova, Adrián & Probst, Sebastian & Wakolbinger, Anton, 2019. "Modelling and simulating Lenski’s long-term evolution experiment," Theoretical Population Biology, Elsevier, vol. 127(C), pages 58-74.

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