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An individual-based model for the Lenski experiment, and the deceleration of the relative fitness
Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany..
Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany..
Goethe Univ Frankfurt, Math Inst, Box 111932, D-60054 Frankfurt, Germany..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 126, no 8, 2211-2252 p.Article in journal (Refereed) PublishedText
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 126, no 8, 2211-2252 p.
Keyword [en]
Experimental evolution, Lenski experiment, Relative fitness, Yule processes, Cannings dynamics, Branching process approximation
National Category
Probability Theory and Statistics
URN: urn:nbn:se:uu:diva-299699DOI: 10.1016/j.spa.2016.01.009ISI: 000378179200002OAI: oai:DiVA.org:uu-299699DiVA: diva2:950026
German Research Foundation (DFG), RTG 1845Swedish Research Council, 2013-4688
Available from: 2016-07-26 Created: 2016-07-26 Last updated: 2016-07-26Bibliographically approved

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Stochastic Processes and their Applications
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