An Evolving Genetic Architecture Interacts with Hill-Robertson Interference to Determine the Benefit of Sex

Abstract

Sex is ubiquitous in the natural world, but the nature of its benefits remains controversial. Previous studies have suggested that a major advantage of sex is its ability to eliminate interference between selection on linked mutations, a phenomenon known as Hill-Robertson interference. However, those studies may have missed both important advantages and important disadvantages of sexual reproduction because they did not allow the distributions of mutational effects and interactions (i.e., the genetic architecture) to evolve. Here we investigate how Hill-Robertson interference interacts with an evolving genetic architecture to affect the evolutionary origin and maintenance of sex by simulating evolution in populations of artificial gene networks. We observed a long-term advantage of sex-equilibrium mean fitness of sexual populations exceeded that of asexual populations-that did not depend on population size. We also observed a short-term advantage of sex-sexual modifier mutations readily invaded asexual populations-that increased with population size, as was observed in previous studies. We show that the long- and short-term advantages of sex were both determined by differences between sexual and asexual populations in the evolutionary dynamics of two properties of the genetic architecture: the deleterious mutation rate ([Formula: see text]) and recombination load ([Formula: see text]). These differences resulted from a combination of selection to minimize [Formula: see text] which is experienced only by sexuals, and Hill-Robertson interference experienced primarily by asexuals. In contrast to the previous studies, in which Hill-Robertson interference had only a direct impact on the fitness advantages of sex, the impact of Hill-Robertson interference in our simulations was mediated additionally by an indirect impact on the efficiency with which selection acted to reduce [Formula: see text].

Keywords: deleterious mutation rate; evolution of sex; gene network; population size; recombination load.

Figure 1

Sex has a long-term advantage. (A) Changes in mean fitness $\left(W\right),$ deleterious mutation rate $\left(U_{\mathrm{d}}\right),$ epistasis $\left(\epsilon \ast \right),$ and recombination load $\left(L_{\mathrm{R}}\right)$ over time in asexual (black) and sexual (red) populations of various sizes $\left(N\right).$ (B) Means at generation ${10}^4,$ after populations of all sizes achieved equilibrium in all properties. Values are means and 95% confidence intervals based on 50 replicate populations initiated from different randomly chosen founders.

Figure 2

Equilibrium mean fitness shows the effects of Muller’s ratchet, mutation load, and recombination load. The equilibrium mean fitness of large populations differed only slightly from the expectation at mutation–selection balance (Box 1). Values are means and 95% confidence intervals of the observed fitness in asexual (black) and sexual (red) populations after ${10}^4$ generations of evolution (replotted from Figure 1B). Solid lines show the expectation under the mutation load equation in Box 1 and dashed lines show 95% confidence intervals calculated from the observed $U_{\mathrm{d}}$ in each population. A and B show data from all populations (A) or from only the largest populations (B).

Figure 3

Hill–Robertson interference affected asexual populations of all sizes. (A) Hill–Robertson interference depressed variance at a neutral locus $\left(V\right)$ in asexual (black) compared to sexual (red) populations (top row). The LD that accumulated in asexual populations also decreased genetic variance in log fitness, V_G = $\mathrm{var}\left(\ln W\right),$ and increased mean log fitness, $\overline{\ln W}.$ Data in the middle and bottom rows compare these metrics in the real asexual populations (solid circles) and populations of chimeras with the same allele frequencies but no LD (open circles). (B) Means of each metric at generation ${10}^4.$ Effective population size $\left(N_{\mathrm{e}}\right)$ was estimated as $\widehat{V}$ (see Materials and Methods, Population metrics). Values are means and 95% confidence intervals based on 50 replicate populations initiated from different randomly chosen founders.

Figure 4

Sex has a short-term advantage in large populations. Asexual (black) or sexual (red) mutants were introduced into equilibrium sexual or asexual populations, respectively, at an initial frequency of $1/N.$ Frequencies of the modifier mutations were monitored until the modifiers were either fixed or lost. Values are the proportion of fixations $\left(u\right)$ divided by the neutral expectation ($u\ast =1/N$) and 95% confidence intervals based on $\ge 5N$ replicate invasion trials for each population size N. The data shown here are from the separate sex implementation of the reproductive mode (see Materials and Methods, Reproductive mode). Analogous data for recessive sex and dominant sex are shown in Figure S4.

Figure 5

Changes in the genetic architecture influence both the origin and maintenance of sex. We monitored the fixation and loss of asexual mutants introduced into equilibrium sexual populations (black lines, A), of sexual mutants introduced into equilibrium asexual populations (red lines, B), and of neutral mutants introduced into both sexual and asexual populations (solid gray lines, A and B, respectively). Lines show the evolution of mean fitness among invading mutants, averaged over at least 10 successful invasions. The equilibrium mean fitness of the populations being invaded is represented by a gray dashed line across each plot. Points and corresponding boxplots shown at the bottom of each plot indicate the time of fixation for individual neutral $\left(t_{\mathrm{fix},\mathrm{n}}\right),$ sexual $\left(t_{\mathrm{fix},\mathrm{s}}\right),$ or asexual $\left(t_{\mathrm{fix},\mathrm{a}}\right)$ mutations.

Figure 6

Evolution of the recombination rate under recurrent mutation at the recombination modifier locus. Solid and shaded lines show the change in mean and $95\text{\%}$ confidence interval, respectively, of the genome map length (i.e., mean crossover probability) over time. Data are from 50 replicates initiated with the equilibrium asexual populations of size $N={10}^3$ shown in Figure 1.

Figure 7

Hill–Robertson interference explains part of the difference in equilibrium $U_{\mathrm{d}}$ between sexual (red) and asexual (black) populations. Shown are equilibrium values of the genome-wide deleterious mutation rate $U_{\mathrm{d}}$ vs. census population size N (open circles, replotted from Figure 1) and vs. effective population size $N_{\mathrm{e}}$ (solid circles). Lines are best fit linear models obtained separately using N (dashed lines) or $N_{\mathrm{e}}$ (solid lines) as a dependent variable together with reproductive mode. The total difference in $U_{\mathrm{d}}$ exhibited by sexual and asexual populations of census size $N={10}^4$ (gray line a) is attributable to differences in both the strength and the efficiency of selection acting on genetic architecture. The difference in $U_{\mathrm{d}}$ exhibited by sexual and asexual populations of effective size $N_{\mathrm{e}}=510$ (gray line b) is the proportion of the total difference that remained after controlling for differences in the efficiency of selection that arise through Hill–Robertson interference.