Evolutionary Advantage of Small Populations on Complex Fitness Landscapes

Jain, Kavita; Krug, Joachim; Park, Su‐Chan

doi:10.1111/j.1558-5646.2011.01280.x

Cited by 61 publications

(63 citation statements)

References 51 publications

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“…Clonal interference introduces a bias favoring mutations of large effect (32, 33), thus bringing the dynamics closer to the "greedy" limit, in which the mutation of largest effect is fixed deterministically in each step (34,35). Although this in itself tends to reduce the heterogeneity of evolutionary trajectories (12, 35-37) and thus increases predictability, it is counteracted by the increasing availability of genotypes carrying multiple mutations.…”

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confidence: 99%

Predictability of evolution depends nonmonotonically on population size

Szendro

Franke

Visser

et al. 2012

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

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To gauge the relative importance of contingency and determinism in evolution is a fundamental problem that continues to motivate much theoretical and empirical research. In recent evolution experiments with microbes, this question has been explored by monitoring the repeatability of adaptive changes in replicate populations. Here, we present the results of an extensive computational study of evolutionary predictability based on an experimentally measured eight-locus fitness landscape for the filamentous fungus Aspergillus niger. To quantify predictability, we define entropy measures on observed mutational trajectories and endpoints. In contrast to the common expectation of increasingly deterministic evolution in large populations, we find that these entropies display an initial decrease and a subsequent increase with population size N, governed, respectively, by the scales Nμ and Nμ 2 , corresponding to the supply rates of single and double mutations, where μ denotes the mutation rate. The amplitude of this pattern is determined by μ. We show that these observations are generic by comparing our findings for the experimental fitness landscape to simulations on simple model landscapes.clonal interference | epistasis | experimental evolution E volutionary adaptations arise from an intricate interplay of deterministic selective forces and random reproductive or mutational events, and the relative roles of these two types of influences on the outcome of evolution has been subject to longstanding controversy with significant philosophical implications (1, 2). Although the vision of "replaying the tape of life" on Earth or on some extrasolar planet remains confined to the realm of imagination (3, 4), evolution experiments with microbial populations have begun to address predictability of adaptation on a microevolutionary scale (5-9). In particular, strong signatures of parallel evolution have been observed in the context of the evolution of antibiotic resistance in pathogens, a finding that is of direct relevance to strategies of drug design and deployment (10-14). As lack of knowledge of crucial parameters (e.g., the frequency of beneficial mutations) in such experiments prevents forward predictions, predictability is used in a weaker, a posteriori sense implying repeatability of evolutionary trajectories in replicate populations. For this reason, the two terms will often be used interchangeably in the following (15).The repeatability of adaptive trajectories is expected to depend on the genetic constraints imposed by epistatic interactions as well as on parameters such as population size N, mutation rate μ, and the typical scale s of selection coefficients (16-18). To be specific, consider a population evolving in the regime of strong selection and weak mutation (SSWM), where mutations are so rare that normally not more than one mutant is present simultaneously and the population can be represented as a single entity that performs an adaptive walk in the space of genotypes (19)(20)(21). Such walks are constrained to ...

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mentioning

confidence: 99%

Predictability of evolution depends nonmonotonically on population size

Szendro

Franke

Visser

et al. 2012

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

Self Cite

129

178

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“…In the absence of standing genetic variation, small populations are expected to explore more trajectories than larger populations because of the low supply of beneficial mutations, and variation in what particular mutation arises across populations [18][19][20]. Trajectories and outcomes in small populations are therefore predicted to be less repeatable than in large populations because of the higher contribution of chance.…”

Section: Introductionmentioning

confidence: 99%

“…Clonal interference [5][6][7] will tend to lead to the fixation of the mutations with largest beneficial effect [21,22] and to a reduction in the number of different trajectories taken by independent lineages [18]. As such, adaptation in large populations is predicted to be more repeatable because of the greater efficiency of selection and lower contribution of chance [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Repeatability of adaptation in experimental populations of different sizes

2015

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The degree to which evolutionary trajectories and outcomes are repeatable across independent populations depends on the relative contribution of selection, chance and history. Population size has been shown theoretically and empirically to affect the amount of variation that arises among independent populations adapting to the same environment. Here, we measure the contribution of selection, chance and history in different-sized experimental populations of the unicellular alga Chlamydomonas reinhardtii adapting to a high salt environment to determine which component of evolution is affected by population size. We find that adaptation to salt is repeatable at the fitness level in medium (N e ¼ 5 Â 10 4 ) and large (N e ¼ 4 Â 10 5 ) populations because of the large contribution of selection. Adaptation is not repeatable in small (N e ¼ 5 Â 10 3 ) populations because of large constraints from history. The threshold between stochastic and deterministic evolution in this case is therefore between effective population sizes of 10 3 and 10 4 . Our results indicate that diversity across populations is more likely to be maintained if they are small. Experimental outcomes in large populations are likely to be robust and can inform our predictions about outcomes in similar situations.

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“…The essence of the FM mechanism is the competition between independently arising beneficial mutations, termed clonal interference, which slows down the adaptation of large asexual populations (Gerrish and Lenski 1998;Miralles et al 1999;Wilke 2004;Kim and Orr 2005;Park and Krug 2007;Fogle et al 2008;Sniegowski and Gerrish 2010;Schiffels et al 2011). The concept of clonal interference has played an important role in interpreting the behavior observed in laboratory selection experiments (Lenski et al 1991;Lenski and Travisano 1994;Barrick et al 2009) and has also been invoked in explaining the population-size dependence of evolutionary predictability in rugged fitness landscapes (Jain et al 2011;Szendro et al 2013a). Although in its original formulation clonal interference theory neglects the occurrence of secondary beneficial mutations within a growing clone (Gerrish and Lenski 1998;Gerrish 2001), in general the coexistence of multiple beneficial mutations cannot be neglected in large populations (Park and Krug 2007).…”

mentioning

confidence: 99%

“…The concept of clonal interference has played an important role in interpreting the behavior observed in laboratory selection experiments (Lenski et al 1991;Lenski and Travisano 1994;Barrick et al 2009) and has also been invoked in explaining the population-size dependence of evolutionary predictability in rugged fitness landscapes (Jain et al 2011;Szendro et al 2013a). Although in its original formulation clonal interference theory neglects the occurrence of secondary beneficial mutations within a growing clone (Gerrish and Lenski 1998;Gerrish 2001), in general the coexistence of multiple beneficial mutations cannot be neglected in large populations (Park and Krug 2007).…”

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confidence: 99%

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

Park

Krug

2013

Genetics

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The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. In classic work, Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher-Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects. We solve the deterministic, infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. This result is argued to hold for any nonzero value of the rate of recombination. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number L of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to L in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with L genomic segments.T HE evolutionary advantage of sex remains one of the most intriguing puzzles in evolutionary biology (Kondrashov 1993;de Visser and Elena 2007;Otto 2009). Many hypotheses explaining why sexual reproduction is widespread in nature despite apparent disadvantages such as the twofold cost of sex have been suggested (Maynard Smith 1978). Well-known examples are the deterministic mutation hypothesis (Kondrashov 1988), the Fisher-Muller (FM) mechanism (Fisher 1930;Muller 1932;Crow and Kimura 1965), and Muller's ratchet (Muller 1964;Felsenstein 1974), to name only a few. These three hypotheses are applicable when the fitness landscape in question has certain specific features. Specifically, the deterministic mutation hypothesis requires deleterious mutations to be synergistically epistatic, while the Fisher-Muller mechanism as well as Muller's ratchet can explain the advantage of sex if epistasis is negligible.Theoretical analyses of the effect of epistasis on the speed of Muller's ratchet have concluded that it practically stops operating when epis...

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Evolutionary Advantage of Small Populations on Complex Fitness Landscapes

Abstract: Recent experimental and theoretical studies have shown that small asexual populations evolving on complex fitness landscapes may achieve a higher fitness than large ones due to the increased heterogeneity of adaptive trajectories. Here, we introduce a

Cited by 61 publications

References 51 publications

Predictability of evolution depends nonmonotonically on population size

Predictability of evolution depends nonmonotonically on population size

Repeatability of adaptation in experimental populations of different sizes

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

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