Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations - PubMed (original) (raw)

Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations

Benjamin H Good et al. Proc Natl Acad Sci U S A. 2012.

Abstract

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.

Fig. 1.

A schematic illustration of the process of adaptation. The Gaussian fitness profile f(x) (i.e., the distribution of backgrounds) moves at a constant rate v. The fixation probability w(x) increases rapidly with x until it reaches a thin boundary layer near x = x c, after which it transitions to the standard Haldane result.

Fig. 2.

Fig. 2.

The rate of adaptation, v, as a function of the population size N (Left) and the beneficial mutation rate U b (Right) for the exponential (β = 1) and β = 10 distributions. Other parameters are N = 107, U b = 10-5, and σ = 0.01. Symbols denote the results of forward-time Wright–Fisher simulations, and the solid lines are obtained by solving Eqs. 13 and 14 for β = 1 and Eqs. 18 and 19 for β = 10. For comparison, the predictions from clonal interference theory are plotted as dashed lines.

Fig. 3.

Fig. 3.

The distribution of fitness effects of fixed mutations, ρ f(s), for the exponential (β = 1) (Top) and β = 10 (Bottom) distributions as measured in forward-time simulations. Other parameters are N = 107, U b = 10-5, and σ = 0.01. Our theoretical predictions are shown as solid red lines. For comparison, we also plot the predictions from clonal interference theory (blue dashed lines) as well as the distribution of mutational effects that would fix in the absence of interference (red dashed lines). All distributions are normalized by the total number of mutations that occur during the simulation.

Fig. 4.

Fig. 4.

The mean fitness effect of a fixed mutation as a function of the population size N (Left) and beneficial mutation rate U b (Right) for the exponential (β = 1) and β = 10 distributions. Symbols denote the results of forward-time simulations for the parameters given in Fig. 2. Our theoretical predictions are shown as solid lines, and the predictions from clonal interference theory (dashed lines) are shown for comparison.

Comment in

References

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