Multidimensional epistasis and the disadvantage of sex

Abstract

Sex is thought to facilitate accumulation of initially rare beneficial mutations by allowing simultaneous allele replacements at many loci. However, this advantage of sex depends on a restrictive assumption that the fitness of a genotype is determined by fitness potential, a single intermediate variable to which all loci contribute additively, so that new alleles can accumulate in any order. Individual-based simulations of sexual and asexual populations reveal that under generic selection, sex often retards adaptive evolution. When new alleles are beneficial only if they accumulate in a prescribed order, a sexual population may evolve two or more times slower than an asexual population because only asexual reproduction allows some overlap of successive allele replacements. Many other fitness surfaces lead to an even greater disadvantage of sex. Thus, either sex exists in spite of its impact on the rate of adaptive allele replacements, or natural fitness surfaces have rather specific properties, at least at the scale of intrapopulation genetic variability.

Figure 1

Accumulation of new beneficial mutations by sexual (a) and asexual (b) populations in the case of extreme multidimensional epistasis. The number of loci L is 20, the population size N is 10⁶, the per locus mutation rate μ is 3 × 10⁻⁵, the advantage of an allele 1 a is 0.1, and the disadvantage of an allele 1 preceded by 0 d is 0.01. The average frequency of allele 1 at all of the loci (bold line, increasing), the variance in the number of alleles 1 per genotype (bold line, fluctuating), and the frequencies of allele 1 at individual loci (thin lines) are shown.

Figure 2

(a) An example of a generic, continuous, narrow fitness ridge connecting the points (0,0) and (18,18) where a point (p,q) corresponds to any genotype that has p alleles 1 at the first L₁ loci and q alleles 1 at the rest L₂ loci (L₁ = L₂ = 18). (b) A continuous fitness ridge used in our simulations. (c) A discontinuous fitness ridge such that, to evolve from the phenotype (10,10) to the phenotype (11,11), a population must acquire two alleles 1 that are individually deleterious.

Figure 3

Accumulation of new beneficial mutations by sexual (a, c) and asexual (b, d) populations in the case of a continuous, narrow fitness ridge, as shown in Fig. 2b. The population size N is 10⁶, the per locus mutation rate μ is 3 × 10⁻⁵, the advantage of an allele 1 a is 0.1, and the rate of fitness decline caused by deviation of a genotype from fitness ridge δ is 0.3. The means (thick lines) and variances (thin lines) of the numbers of allele 1 at the loci from the first group (solid lines) and from the second group (broken lines) are shown in a and c. The frequencies of allele 1 at individual loci from the first group (solid lines) and from the second group (broken lines) are shown in b and d.