Evolution of GC-biased gene conversion by natural selection

Abstract

GC-biased gene conversion is a recombination-associated evolutionary process that biases the segregation ratio of AT:GC polymorphisms in the gametes of heterozygotes, in favor of GC alleles. This process is the major determinant of the variation in base composition across the human genome and can be the cause of a substantial burden of deleterious GC alleles. While the importance of GC-biased gene conversion in molecular evolution is increasingly recognized, the reasons for its existence and its variation in intensity between species remain largely unknown. Using simulations and semi-analytical approximations, we investigated the evolution of GC-biased gene conversion as a quantitative trait evolving by mutation, drift, and natural selection. We show that in a finite population in which most mutations are deleterious, GC-biased gene conversion is under weak stabilizing selection around a positive value that mainly depends on the intensity of the mutational bias and on the selective constraints exerted on the genome. Importantly, the levels of GC-biased gene conversion that evolve by natural selection do not minimize the load in the population and even increase it substantially in regions of high recombination rate. Therefore, even if they reduce the fitness of the population, the levels of GC-biased gene conversion currently observed in humans may, in fact, have been (weakly) positively selected.

Keywords: gBGC; genetic load; modifier; mutation bias; natural selection; recombination.

Fig. 1.

Evolution of the strength of gBGC (mean of b over the population) over the generations, for the co-dominant a) and recessive b) cases. The blue horizontal line represents the mean over the entire run; the red horizontal line represents the equilibrium value $b^{*}$ predicted by the analytical approximation; the shaded area represents $b^{*}\pm 2{\sigma }_{eq}$, where ${\sigma }_{eq}=\sqrt{v_{eq}}$ is the analytically predicted standard deviation of the fluctuations at equilibrium.

Fig. 2.

Selective response $g(b)$, as a function of b (blue curve), under the co-dominant a) and recessive b) settings. Dark blue dotted vertical line: numerically estimated value of $b^{*}$, for which $g(b)=0$; orange line: numerically estimated tangent at $b^{*}$; light blue dotted vertical lines: twice the predicted standard deviation on each side of $b^{*}$.

Fig. 3.

Mean equilibrium $b^{*}$ and standard deviation, as a function of mutation bias λ a), mean selective effect $h\overline{s}$ b), number of selected positions in the genome L c), and mutation rate u d), under the co-dominant (blue) and recessive (orange) cases. The results are obtained via simulations (dots and associated vertical bars) and predicted from the analytical approximation (curve and associated shaded area), under a mutation rate of $w={10}^{-4}$ ($Nw=0.1$). The shaded areas and vertical bars correspond to one standard deviation on each side of the mean.

Fig. 4.

Mean segregation frequency of W alleles a) and b), S alleles c) and d), and induced selection e) and f), as a function of s, under the co-dominant (a, c, and e) and recessive (b, d, and f) settings, for different values of b. Plain lines correspond to the equilibrium value of b, dashed lines correspond to a slightly increased b, and dotted lines correspond to a slightly decreased b. The blue lines correspond to W alleles and the red lines correspond to S alleles.

Fig. 5.

Scaling of $b^{*}$ a) and $B^{*}=4N{b}^{*}$ b) as a function of N, under the co-dominant ($h=0.5$) and recessive ($h=0.1$) settings (plain curves), or assuming a mixture of co-dominant and recessive mutations (dashed curves).

Fig. 6.

Mean segregation frequency of W alleles a and b), S alleles c) and d), and induced selection e) and f), as a function of s, under the co-dominant (a, c, and e) and recessive (b, d, and f) settings, for different values of N: plain lines correspond to the equilibrium value of b, dashed lines to a slightly increased N, and dotted lines to a slightly decreased N. The blue lines correspond to W alleles and the red lines correspond to S alleles.

Fig. 7.

a) and b) Average deleterious load in a population as a function of b. The black lines show the equilibrium value of b and the gray line shows the value of b that minimizes the average load. c) and d) Frequency of W and S alleles as a function of b. e) and f) Heterozygosity for W and S alleles as a function of their deleterious effect s for the value of b that minimizes the load. a), c), and e) $h=0.5$. b), d), and f) $h=\mathrm{0.1.}$