Rate of adaptation in sexuals and asexuals: A solvable model of the Fisher-Muller effect

TL;DR

This paper presents an exact analysis of the Fisher-Muller effect, showing that sexual populations adapt twice as fast as asexual ones under certain conditions, with implications for viral reassortment.

Contribution

It provides an exact solution for the adaptation speed in a two-locus model and extends the understanding of the Fisher-Muller effect in large populations.

Findings

Sexual populations adapt twice as fast as asexuals in the model.

Recombination suppresses mutation imbalance between loci.

The adaptation speed ratio approaches the number of loci in large populations.

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. 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 fitness effects. We solve the 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. 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.