Beneficial Fitness Effects Are Not Exponential for Two Viruses

Rokyta, Darin R.; Beisel, Craig J.; Joyce, Paul; Ferris, Martin T.; Burch, Christina L.; Wichman, Holly A.

doi:10.1007/s00239-008-9153-x

Cited by 104 publications

(146 citation statements)

References 30 publications

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“…Many experimental studies are roughly consistent with this exponential prediction (4-6), although here, too, we find significant exceptions (6)(7)(8)(9)(10). In the present work, we maintain a relatively agnostic view toward the precise form of ρðsÞ, although we devote special attention to the exponential case because of its popularity in the literature.…”

supporting

confidence: 76%

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

Good

Rouzine

Balick

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

223

446

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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.E volutionary adaptation is driven by the accumulation of beneficial mutations, and yet many aspects of this process are still poorly understood. In asexual populations, this subject can be distilled into two main lines of inquiry: (i) what are the possible mutations available to the population? and (ii) which of these mutations are actually incorporated into the population, and what are the dynamics by which they fix?The first question is essentially an empirical matter. At any given instant in time, the set of accessible beneficial mutations is likely to depend on the history of the population as well as its environment and any epistatic interactions between mutations. Nonetheless, if history and epistatic effects do not significantly affect the statistics of the available mutations, we can define a constant distribution of fitness effects ρðsÞ that gives the relative probability of obtaining a mutation that increases the fitness of an individual by s.Gillespie (1) and Orr (2) have argued that there are general theoretical reasons to expect that ρðsÞ should follow an exponential distribution, although more recent theoretical work has challenged the ubiquity of this claim (3). Many experimental studies are roughly consistent with this exponential prediction (4-6), although here, too, we find significant exceptions (6-10). In the present work, we maintain a relatively agnostic view toward the precise form of ρðsÞ, although we devote special attention to the exponential case because of i...

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supporting

confidence: 76%

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

Good

Rouzine

Balick

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

223

446

View full text Add to dashboard Cite

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“…Kassen and Bataillon 18 found support for an exponential distribution assessing antibiotic-resistance mutations in Pseudomonas. Rokyta et al 36 found support not for the Gumbel domain but rather for a distribution with a righttruncated tail (that is, suggesting that there is an upper bound on potential fitness effects), using two viral populations. MacLean and Buckling 37 , again using Pseudomonas, argued that an exponential distribution well explained the data when the population was near optimum, but not when the population was far from optimum, owing to a long tail of strongly beneficial mutations.…”

Section: Nature Communications | Doi: 101038/ncomms6281mentioning

confidence: 99%

On the unfounded enthusiasm for soft selective sweeps

2014

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Underlying any understanding of the mode, tempo and relative importance of the adaptive process in the evolution of natural populations is the notion of whether adaptation is mutation limited. Two very different population genetic models have recently been proposed in which the rate of adaptation is not strongly limited by the rate at which newly arising beneficial mutations enter the population. However, empirical and experimental evidence to date challenges the recent enthusiasm for invoking these models to explain observed patterns of variation in humans and Drosophila.I dentifying the action of positive selection from genomic patterns of variation has remained as a central focus in population genetics. This owes both to the importance of specific applications in fields ranging from ecology to medicine, but also to the desire to address more general evolutionary questions concerning the mode and tempo of adaptation. In this vein, the notion of a soft selective sweep has grown in popularity in the recent literature, and with this increasing usage the definition of the term itself has grown increasingly vague. A soft sweep does not reference a particular population genetic model per se, but rather a set of very different models that may result in similar genomic patterns of variation. Further, it is a term commonly used in juxtaposition with the notion of a hard selective sweep, the classic model in which a single novel beneficial mutation arises in a population and rises in frequency quickly to fixation. Patterns expected under the hard sweep model have been well described in the literature (see reviews of refs 1,2; Box 1), and consist of a reduction in variation surrounding the beneficial mutation owing to the fixation of the single haplotype carrying the beneficial, with resulting well-described skews in the frequency spectrum 3-5 and in patterns of linkage disequilibrium [6][7][8] . Indeed, a part of the recent popularity of soft sweeps comes from the seeming rarity of these expected hard sweep patterns in many natural populations (for example, see refs 9-11).In terms of patterns of variation, the primary difference between soft and hard selective sweeps lies in the expected number of different haplotypes carrying the beneficial mutation or mutations, and thus in the expected number of haplotypes that hitchhike to appreciable frequency during the selective sweep, and which remain in the population at the time of fixation. This key difference results in different expectations in both the site frequency spectrum and in linkage disequilibrium, and thus in the many test statistics based on these patterns (see Box 1). Owing to this ambiguous definition, a number of models have been associated with producing a soft sweep pattern-including selection acting on previously segregating mutations, and multiple beneficials arising via mutation in quick succession (see review ref. 11 and Box 1).

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“…The isolation and initial characterization of the nine beneficial mutations for our wild-type ID11 at 37°were described previously (Rokyta et al 2005(Rokyta et al , 2008. We sequenced the entire genome of each isolate by means of Sanger sequencing to confirm the presence of the mutation(s) of interest and the absence of additional mutations.…”

Section: Constructing the Mutants And Fitness Assaysmentioning

confidence: 99%

“…The model explained these patterns by positing that most single mutations were near or in excess of the optimum and adding the second mutation therefore resulted in a movement away from the optimum. In the present work, we attempted to shift the wild-type genotype, ID11, and its nine previously described beneficial mutations (Rokyta et al 2005(Rokyta et al , 2008(Rokyta et al , 2011 closer to and farther from the optimal phenotype by changing the temperature at which fitness was measured, to quantify the changes in fitness effects and patterns of epistatic interactions between mutations. Previous work has shown that close relatives of ID11 in the G4-like group of microvirid coliphages (Rokyta et al 2006b) tend to have fitnesses inversely correlated with temperature (Knies et al 2009).…”

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confidence: 99%

Environment Determines Epistatic Patterns for a ssDNA Virus

2014

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Despite the accumulation of substantial quantities of information about epistatic interactions among both deleterious and beneficial mutations in a wide array of experimental systems, neither consistent patterns nor causal explanations for these interactions have yet emerged. Furthermore, the effects of mutations depend on the environment in which they are characterized, implying that the environment may also influence epistatic interactions. Recent work with beneficial mutations for the single-stranded DNA bacteriophage ID11 demonstrated that interactions between pairs of mutations could be understood by means of a simple model that assumes that mutations have additive phenotypic effects and that epistasis arises through a nonlinear phenotype-fitness map with a single intermediate optimum.To determine whether such a model could also explain changes in epistatic patterns associated with changes in environment, we measured epistatic interactions for these same mutations under conditions for which we expected to find the wild-type ID11 at different distances from its phenotypic optimum by assaying fitnesses at three different temperatures: 33°, 37°, and 41°. Epistasis was present and negative under all conditions, but became more pronounced as temperature increased. We found that the additive-phenotypes model explained these patterns as changes in the parameters of the phenotype-fitness map, but that a model that additionally allows the phenotypes to vary across temperatures performed significantly better. Our results show that ostensibly complex patterns of fitness effects and epistasis across environments can be explained by assuming a simple structure for the genotype-phenotype relationship.

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Beneficial Fitness Effects Are Not Exponential for Two Viruses

Cited by 104 publications

References 30 publications

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

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

On the unfounded enthusiasm for soft selective sweeps

Environment Determines Epistatic Patterns for a ssDNA Virus

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