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

Department of Molecular Biology and Microbiology, Tufts University, 136 Harrison Avenue, Boston, MA 02111, USA.
Theoretical Population Biology (Impact Factor: 1.7). 03/2008; 73(1):24-46. DOI: 10.1016/j.tpb.2007.10.004
Source: PubMed


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.

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    • "Nevertheless, since our mutations were modeled by changes in the evolution coefficient, they can also be considered to be an implicit mimic of recombination processes. Rouzine et al. (2008) showed that the evolution coefficient rises logarithmically with the number of lesions until it becomes extremely large. This can be explained by the fact that a beneficial mutation may not go on to be fixed, because of interference with another mutation with a greater beneficial effect that arises either "
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    • "However, in finite populations and in the absence of beneficial mutations and recombination, deleterious mutations will eventually fix by genetic drift, leading to a fitness decline known as Muller's ratchet [15] [16]. Determining the rate of the ratchet as a function of population size, mutation rate and selection strength is a long-standing problem that continues to attract considerable interest [17] [18] [19] [10] [20] [21] [22] [23] [24]. Recombination can prevent Muller's ratchet and also mitigates the slowdown in the rate of evolution from clonal interference, which is why Muller's ratchet and clonal interference are often argued as reasons for an evolutionary advantage of sex [25] [26] [27]. "
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    • "Thus, the relevant deleterious fitness effects are usually much smaller than the size of a typical driver, which emphasizes the importance of the two-effect DFE that we used throughout our analysis. Previous work has often focused on a simpler " single-effect " DFE, where the fitness effects of beneficial and deleterious mutations are identical (s b = s d ) (Goyal et al., 2012; Rouzine et al., 2008, 2003; Woodcock and Higgs, 1996). Our present results suggest that these models may underestimate the importance of deleterious mutations, since they implicitly neglect mutations with the largest potential influence. "
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