The Speed of Evolution in Large Asexual Populations

Park, Su‐Chan; Simon, Damien; Krug, Joachim

doi:10.1007/s10955-009-9915-x

Cited by 99 publications

(181 citation statements)

References 66 publications

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“…In sufficiently large populations, it is often possible to separate the population-wide dynamics from the fate of any particular mutant (29). In this way, the distribution of fitnesses in the population can be highly predictable even though its exact genealogy is not.…”

Section: Discussionmentioning

confidence: 99%

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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.

226

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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Section: Discussionmentioning

confidence: 99%

“…29 for a review), although these typically operate under the simplifying assumption that all mutations have the same effect. The primary finding of these studies is that the population forms a traveling fitness wave that moves toward higher fitness with a constant average rate v and shape f ðxÞ.…”

mentioning

confidence: 99%

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.

226

446

View full text Add to dashboard Cite

show abstract

“…geographic locations, genetic configurations etc.). While the literature contains several models which allow for randomness in either the fitness [19,24] or stability [18,21,27], most relevant is [6] which considers a model in which both these characteristics vary. Indeed, the model considered in [6] is essentially identical to the BAM, except it is defined in a domain without any geometry: when an individual's state changes, the fitness and stability are re-sampled according to their respective distributions.…”

Section: 34mentioning

confidence: 99%

Localisation in the Bouchaud–Anderson model

Muirhead

Pymar

2016

Stochastic Processes and their Applications

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Abstract. It is well-known that both random branching and trapping mechanisms can induce localisation phenomena in random walks; the prototypical examples being the parabolic Anderson and Bouchaud trap models respectively. Our aim is to investigate how these localisation phenomena interact in a hybrid model combining the dynamics of the parabolic Anderson and Bouchaud trap models. Under certain natural assumptions, we show that the localisation effects due to random branching and trapping mechanisms tend to (i) mutually reinforce, and (ii) induce a local correlation in the random fields (the 'fit and stable' hypothesis of population dynamics). Minor revision to published version. This is an updated version of [23] containing the following minor revisions:• A typo in the statement of Proposition 3.14 has been corrected;• The coupling used in Section 5 has been slightly modified to fix a gap in its original statement; we thank Renato Soares dos Santos for pointing this out to us; • A slight correction has been made to the proof of Proposition 4.11; and • The bibliography has been updated.

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“…Evolutionary models of populations with random mutational advances have been studied in the context of fixed-size Wright-Fisher processes for both finite and infinite populations (Gerrish and Lenski 1998;Park and Krug 2007;Park et al 2010); Gerrish and Lenski (1998) studied the speed of evolution in a Wright-Fisher model with random mutational advances in the context of finite but large 1 populations while Park et al (2010) obtained accurate asymptotic approximations for the evolutionary dynamics of the population, following ideas presented in Park and Krug (2007). The latter work and references therein constitute a substantial exploration of the effects of random mutational advances in fixed-size populations.…”

mentioning

confidence: 99%

Intratumor Heterogeneity in Evolutionary Models of Tumor Progression

et al. 2011

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With rare exceptions, human tumors arise from single cells that have accumulated the necessary number and types of heritable alterations. Each such cell leads to dysregulated growth and eventually the formation of a tumor. Despite their monoclonal origin, at the time of diagnosis most tumors show a striking amount of intratumor heterogeneity in all measurable phenotypes; such heterogeneity has implications for diagnosis, treatment efficacy, and the identification of drug targets. An understanding of the extent and evolution of intratumor heterogeneity is therefore of direct clinical importance. In this article, we investigate the evolutionary dynamics of heterogeneity arising during exponential expansion of a tumor cell population, in which heritable alterations confer random fitness changes to cells. We obtain analytical estimates for the extent of heterogeneity and quantify the effects of system parameters on this tumor trait. Our work contributes to a mathematical understanding of intratumor heterogeneity and is also applicable to organisms like bacteria, agricultural pests, and other microbes.H UMAN cancers frequently display substantial intratumor heterogeneity in genotype, gene expression, cellular morphology, metabolic activity, motility, and behaviors such as proliferation rate, antigen expression, drug response, and metastatic potential (Fidler and Hart

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The Speed of Evolution in Large Asexual Populations

Cited by 99 publications

References 66 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

Localisation in the Bouchaud–Anderson model

Intratumor Heterogeneity in Evolutionary Models of Tumor Progression

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