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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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    ABSTRACT: • Quantitative plant disease resistance is believed to be more durable than qualita-tive resistance, since it exerts less selective pressure on the pathogens. However, the process of progressive pathogen adaptation to quantitative resistance is poorly un-derstood, which makes it difficult to predict its durability or to derive principles for its sustainable deployment. Here, we study the dynamics of pathogen adaptation in response to quantitative plant resistance affecting pathogen reproduction rate and its carrying capacity. • We developed a stochastic model for the continuous evolution of a pathogen popu- lation within a quantitatively resistant host. We assumed that pathogen can adapt to a host by the progressive restoration of reproduction rate or of carrying capacity, or of both. • Our model suggests that a combination of QTLs affecting distinct pathogen traits was more durable if the evolution of repressed traits was antagonistic. Other- wise, quantitative resistance that depressed only pathogen reproduction was more durable. • In order to decelerate the progressive pathogen adaptation, QTLs that decrease the pathogen’s ability to extend must be combined with QTLs that decrease the spore production per lesion or the infection efficiency or that increase the latent period. Our theoretical framework can help breeders to develop principles for sustainable deployment of quantitative trait loci.
    New Phytologist 10/2014; 206(3). DOI:10.1111/nph.13295 · 7.67 Impact Factor
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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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    ABSTRACT: Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Mullerʼs ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using, again, an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation.
    Physical Biology 08/2014; 11(5):056003. DOI:10.1088/1478-3975/11/5/056003 · 2.54 Impact Factor
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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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    ABSTRACT: Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial "driver" mutations and linked deleterious "passengers" during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations, with a non-monotonic dependence on both the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix, and how many of these mutations must arise before the progress of adaptation is significantly reduced.
    Genetics 05/2014; 198(3). DOI:10.1534/genetics.114.170233 · 5.96 Impact Factor
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