Sign of selection on mutation rate modifiers depends on population size

Abstract

The influence of population size (N) on natural selection acting on alleles that affect fitness has been understood for almost a century. As N declines, genetic drift overwhelms selection and alleles with direct fitness effects are rendered neutral. Often, however, alleles experience so-called indirect selection, meaning they affect not the fitness of an individual but the fitness distribution of its offspring. Some of the best-studied examples of indirect selection include alleles that modify aspects of the genetic system such as recombination and mutation rates. Here, we use analytics, simulations, and experimental populations of Saccharomyces cerevisiae to examine the influence of N on indirect selection acting on alleles that increase the genomic mutation rate (mutators). Mutators experience indirect selection via genomic associations with beneficial and deleterious mutations they generate. We show that, as N declines, indirect selection driven by linked beneficial mutations is overpowered by drift before drift can neutralize the cost of the deleterious load. As a result, mutators transition from being favored by indirect selection in large populations to being disfavored as N declines. This surprising phenomenon of sign inversion in selective effect demonstrates that indirect selection on mutators exhibits a profound and qualitatively distinct dependence on N.

Keywords: experimental evolution; indirect selection; mutation rate; mutators; population size.

Fig. 1.

Population size (N) determines the sign of indirect selection on mutators. Sign inversion for mutators occurs when their normalized fixation probability ($N{P}_{\text{fix}}^{\text{mutator}}$) crosses the neutral expectation (horizontal dotted line). Mutators fare better than neutral alleles above $N_{crit}\approx U_{del}/(P_{\text{fix}}\left(N,s_{ben}\right)\cdot U_{ben})$ (vertical line), but worse below. Solid black line: analytic approximation (see text). Blue dots: stochastic simulations, 10⁶ replicates. In contrast, the normalized fixation probability of a directly beneficial mutation [$P_{\text{fix}}\left(N,s_{ben}\right)$; green dashed line] asymptotically approaches but never crosses the neutral threshold. Parameter values: U_del = 10⁻⁴, U_ben = 10⁻⁶, s_ben = 0.1, and s_del = −0.1. Mutators mutate 100 times faster than nonmutators.

Fig. 2.

Sign inversion in experimental yeast populations: Mutators are favored in large populations but disfavored in small populations. (Left) Mutator dynamics in populations propagated through bottlenecks of differing size: (A) large (∼8,000 cells), (B) medium (∼80 cells), and (C) small (∼20 cells). Blue curves: individual population frequencies; red dots: all population averages. (Right) Frequency histograms on the last day of propagation.

Fig. 3.

Mutators win large competitions by hitchhiking; nonmutators win small competitions by outlasting the mutators. (A) Mean fitness of simulated competition winners. In simulation, mutators (red dots) are favored at large N ($P_{\text{fix}}^{\text{mutator}}$ ∼ 99%) and disfavored at small N ($P_{\text{fix}}^{\text{mutator}}$ ∼ 20%). Large N mutator winners are always fitter than their ancestors. In contrast, some small N mutator winners are fitter than their ancestors, while some are not. Nonmutator winners (blue dots) of small N simulations are almost never fitter than their ancestors. $P_{\text{fix}}^{\text{mutator}}$ averaged over 10⁶ runs. Each point represents population fitness at the end of simulation (a random 100 replicates shown for clarity; 99/100 nonmutator winners have a relative fitness of 1). Parameter values: U_del = 10⁻³, U_ben = 10⁻⁵, s_ben = 0.1, s_del = −0.1. Mutators mutate 20 times faster than nonmutators. (B) Mean fitness of experimental competition winners. Mean fitness of large populations in which mutators had won (red dots) is always considerably higher than their ancestors, consistent with hitchhiking. In contrast, only some small populations in which mutators had won show evidence of hitchhiking. Mean fitness of small populations in which nonmutators had won (blue dots) is very close to their ancestors, ruling out hitchhiking. Each point represents an average of five replicate fitness assays. See Fig. S4 for 95% CI.