Academic journal article Genetics

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

Academic journal article Genetics

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

Article excerpt

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 (noneplstatlc) 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.

(ProQuest: ... denotes formulae omitted.)

Copyright © 2013 by the Genetics Society of America

Manuscript received July 8, 2013; accepted for publication August 7, 2013

THE evolutionary advantage of sex remains one of the most intriguing puzzles in evolutionary biology (Kondrashov 1993; de Visser and Elena 2007; Otto 2009). Many hypoth- eses 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 hypoth- esis (Kondrashov 1988), the Fisher-Muller (FM) mechanism (Fisher 1930; Muller 1932; Crow and Kimura 1965), and Mulleris 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 Mulleris ratchet can explain the advantage of sex if epistasis is negligible.

Theoretical analyses of the effect of epistasis on the speed of Mulleris ratchet have concluded that it practically stops operating when epistasis is synergistic (Charlesworth et al. 1993; Kondrashov 1994; Jain 2008). Furthermore, recent experimental analyses of empirical fitness landscapes seem to indicate that a particularly strong form of epistasis termed sign epistasis (Weinreich et al. 2005) is quite common (Weinreich et al. 2006; de Visser et al. 2009; Franke et al. 2011; Szendro et al. 2013b). Sign epistasis generally implies that the fitness landscape is rugged. On a rugged fitness landscape, sex can be detrimental, even without taking into account the twofold cost of sex, in that sexual populations, unlike the corresponding asexual populations, cannot escape from local fitness peaks (Crow and Kimura 1965; Eshel and Feldman 1970; de Visser et al. …

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