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The traveling-wave approach to asexual evolution: Muller's ratchet and speed of adaptation

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  • Rouzine, Igor M.
  • Brunet, Éric
  • Wilke, Claus O.

Abstract

We use traveling-wave theory to derive expressions for the rate of accumulation of deleterious mutations under Muller's ratchet and the speed of adaptation under positive selection in asexual populations. Traveling-wave theory is a semi-deterministic description of an evolving population, where the bulk of the population is modeled using deterministic equations, but the class of the highest-fitness genotypes, whose evolution over time determines loss or gain of fitness in the population, is given proper stochastic treatment. We derive improved methods to model the highest-fitness class (the stochastic edge) for both Muller's ratchet and adaptive evolution, and calculate analytic correction terms that compensate for inaccuracies which arise when treating discrete fitness classes as a continuum. We show that traveling-wave theory makes excellent predictions for the rate of mutation accumulation in the case of Muller's ratchet, and makes good predictions for the speed of adaptation in a very broad parameter range. We predict the adaptation rate to grow logarithmically in the population size until the population size is extremely large.

Suggested Citation

  • Rouzine, Igor M. & Brunet, Éric & Wilke, Claus O., 2008. "The traveling-wave approach to asexual evolution: Muller's ratchet and speed of adaptation," Theoretical Population Biology, Elsevier, vol. 73(1), pages 24-46.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:1:p:24-46
    DOI: 10.1016/j.tpb.2007.10.004
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    Cited by:

    1. Jain, Kavita & John, Sona, 2016. "Deterministic evolution of an asexual population under the action of beneficial and deleterious mutations on additive fitness landscapes," Theoretical Population Biology, Elsevier, vol. 112(C), pages 117-125.
    2. Rouzine, Igor M. & Coffin, John M., 2010. "Multi-site adaptation in the presence of infrequent recombination," Theoretical Population Biology, Elsevier, vol. 77(3), pages 189-204.
    3. Good, Benjamin H. & Desai, Michael M., 2013. "Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution," Theoretical Population Biology, Elsevier, vol. 85(C), pages 86-102.
    4. Jakob J Metzger & Stephan Eule, 2013. "Distribution of the Fittest Individuals and the Rate of Muller's Ratchet in a Model with Overlapping Generations," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-10, November.

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