Coalescence with Background and Balancing Selection in Systems with Bi- and Uniparental Reproduction: Contrasting Partial Asexuality and Selfing

Abstract

Uniparental reproduction in diploids, via asexual reproduction or selfing, reduces the independence with which separate loci are transmitted across generations. This is expected to increase the extent to which a neutral marker is affected by selection elsewhere in the genome. Such effects have previously been quantified in coalescent models involving selfing. Here we examine the effects of background selection and balancing selection in diploids capable of both sexual and asexual reproduction (i.e., partial asexuality). We find that the effect of background selection on reducing coalescent time (and effective population size) can be orders of magnitude greater when rates of sex are low than when sex is common. This is because asexuality enhances the effects of background selection through both a recombination effect and a segregation effect. We show that there are several reasons that the strength of background selection differs between systems with partial asexuality and those with comparable levels of uniparental reproduction via selfing. Expectations for reductions in Ne via background selection have been verified using stochastic simulations. In contrast to background selection, balancing selection increases the coalescence time for a linked neutral site. With partial asexuality, the effect of balancing selection is somewhat dependent upon the mode of selection (e.g., heterozygote advantage vs. negative frequency-dependent selection) in a manner that does not apply to selfing. This is because the frequency of heterozygotes, which are required for recombination onto alternative genetic backgrounds, is more dependent on the pattern of selection with partial asexuality than with selfing.

Keywords: asexual reproduction; background selection; balancing selection; coalescence; effective population size; self-fertilization.

Figure 1

The direct effect of uniparental reproduction via asexuality or selfing on the scaled coalescence time (E[T]/2N). Partial asexuality has a negligible direct effect unless the rate of sex (σ) is on the order of the reciprocal of the population size; here N = 10⁵. High selfing reduces N_e to 50% of N.

Figure 2

The scaled coalescence time (E[T]/2N or, equivalently, N_e/N) as a function of the recombination distance between the focal neutral locus and the selected locus in the background selection model with partial asexuality. (A) The reduction in coalescence times with low rates of sex is particularly strong at higher rates of recombination; hs = 0.005. (B) The effects of background selection are larger with weak selection when recombination is low. Mutation rate: µ = 10⁻⁶.

Figure 3

Genome-wide background selection in systems with sexual and asexual reproduction. (A) The background selection coefficient B as a function of the rate of sex, considering mutations across the entire genome. Results for genomes with relatively short and long maps (L = 2 Morgans vs. 20 Morgans) are shown. The longer map implies lower gene density as the mutation rate is held constant (U = 0.1); mutations are assumed to be uniformly distributed across the genome. (B) The background selection coefficient for different genomic regions (tightly linked, loosely linked, and unlinked sites) as well as the total. Parameters are L = 10, hs = 0.005, and U = 0.1. Tightly linked loci make the largest contribution to background selection when rates of sex are very high but unlinked loci make the largest contribution when sex is rare.

Figure 4

Simulation comparisons of background selection. (A) Simulation results (symbols) and analytical approximations (lines) of B = N_e/N as a function of the rate of sex. Parameters are N = 10⁴, U = 0.02, s = 0.02, h = 0.25, and L = 1 (solid symbols and line) or L = 10 (shaded symbols and dashed line). Bars on simulation symbols represent 95% confidence intervals. (B) Background selection effect for σ = 0.01 as a function of the population size. Parameters are U = 0.02, s = 0.02, h = 0.25, and L = 10. The horizontal shaded line is the theoretical expectation given with Equation 9. (C) Same as B but for σ = 0.001.

Figure 5

Background selection in systems with different forms of uniparental reproduction (asexuality and selfing). The background selection coefficient B is shown for systems with sexual and asexual reproduction (solid symbols and line) and systems with outcrossing and selfing (shaded symbols and lines). Analytical approximations (lines) are contrasted with simulation results (symbols; error bars are 95% confidence intervals. The analytical approximation for selfing is based on an extension of (14) and is given in Kamran-Disfani and Agrawal (2014). Parameters: U = 0.02, s =0.02, h = 0.25, L = 10 (N = 10⁴ for simulations).

Figure 6

Coalescence times near a site under balancing selection. The expected time to coalescence (scaled to 2N generations) is shown as a function of the distance (in base pairs) from a site under balancing selection via heterozygote advantage (W_1/1 = W_2/2 = 1 – s and W_1/2 = 1). The population is assumed to be fully sexual and outcrossing (Equation 17, σ = 1; thick shaded line), mostly asexual (Equation 17, σ = 0.01; solid line), or mostly selfing (Equation 19b, o = 0.01; thin shaded line). Symbols represent the expected coalescence time based on simulations (see File S3). Error bars are 95% confidence intervals; in some cases error bars are too small to be visible. We assume r = ρd, where d is the distance in base pairs from the selected site. For the partial asexual case, results are shown with and without gene conversion. For gene conversion, the model of Andolfatto and Nordborg (1998) is used: γ = gd/L for d < L and γ = g for d ≥ L, where L is the length of gene conversion tracts. For the fully sexual case, the results with gene conversion are visually indistinguishable from those with γ = 0 for the parameter values used here. The selfing case assumes no gene conversion, but gene conversion is not expected to affect coalescence in selfers (see Discussion); simulations including gene conversion support this conjecture (File S3). The selfing line asymptotes at 1/2 rather than 1 because of the direct effect of selfing on coalescence (Figure 1). These results ignore mutation at the selected site and thus overestimate the coalescence time for extremely tightly linked sites (e.g., d << 100 if µ = 10⁻⁹, see text). Parameter values: s = 0.1, N = 5 × 10⁴, ρ = 2 × 10⁻⁸ (Ashburner 1989), g = 2 × 10⁻⁶ (N. P. Sharp and A. F. Agrawal, unpublished results), and L = 1400 (Preston and Engels 1996).