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Theor Popul Biol. 2008 Feb;73(1):24-46. Epub 2007 Oct 22.

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

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  • 1Department of Molecular Biology and Microbiology, Tufts University, 136 Harrison Avenue, Boston, MA 02111, USA. igor.rouzine@tufts.edu

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.

PMID:
18023832
[PubMed - indexed for MEDLINE]
PMCID:
PMC2246079
Free PMC Article
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