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

Abstract

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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Adaptation, Clonal Interference, and Frequency-Dependent Interactions in a Long-Term Evolution Experiment withEscherichia coli

“…Over time, this experiment has become a model for exploring many other aspects of evolution, including the emergence of new functions (Blount et al 2008), the evolution of mutation rates (Sniegowski et al 1997), the maintenance of genetic diversity (Elena and Lenski 1997;Rozen and Lenski 2000;Le Gac et al 2012), and the structure of the fitness landscape (Khan et al 2011;Woods et al 2011;Wiser et al 2013). The ability to examine these and other issues has grown tremendously as data that were difficult or impossible to obtain when the LTEE began have yielded to new technologies, particularly genome sequencing Lenski 2009, 2013;Blount et al 2012;Wielgoss et al 2013).The LTEE has also inspired theoretical work, especially on the dynamics of adaptation in large asexual populations (Gerrish and Lenski 1998;Hegreness et al 2006;Desai and Fisher 2007;Schiffels et al 2011;Park and Krug 2013;Wiser et al 2013). The LTEE populations are subject to clonal interference, a phenomenon that limits the rate of adaptation by natural selection in large asexual populations.…”

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