Genet. Res., Camb. (1994), 63, pp. 213-227 With 3 text-figures Copyright © 1994 Cambridge University Press 213 The effect of background selection against deleterious mutations on weakly selected, linked variants BRIAN CHARLESWORTH Department of Ecology and Evolution, The University of Chicago, 1101 E. 57th St., Chicago, IL 60637-1573, USA (Received 21 October 1993 and in revised form 11 January 1994) Summary This paper analyses the effects of selection against deleterious alleles maintained by mutation (' background selection') on rates of evolution and levels of genetic diversity at weakly selected, completely linked, loci. General formulae are derived for the expected rates of gene substitution and genetic diversity, relative to the neutral case, as a function of selection and dominance coefficients at the loci in question, and of the frequency of gametes that are free of deleterious mutations with respect to the loci responsible for background selection. As in the neutral case, most effects of background selection can be predicted by considering the effective size of the population to be multiplied by the frequency of mutation-free gametes. Levels of genetic diversity can be sharply reduced by background selection, with the result that values for sites under selection approach those for neutral variants subject to the same regime of background selection. Rates of fixation of slightly deleterious mutations are increased by background selection, and rates of fixation of advantageous mutations are reduced. The properties of sex-linked and autosomal loci in random-mating populations are compared, and the effects of background selection on asexual and self-fertilizing populations are considered. The implications of these results for the interpretation of studies of molecular evolution and variation are discussed. would be expected to show a smaller but significant 1. Introduction reduction in variation than in selfing or asexual In regions of the genome where recombination is populations, since they make up only a fraction of the infrequent, the amount of genetic variability at neutral total genome and so are subject to a lower rate of sites can be reduced by selection against linked input of deleterious mutation (Charlesworth et al. deleterious alleles, maintained in the population by 1993). The process of background selection provides recurrent mutation at many loci. This process was a possible explanation for observations of reduced called 'background selection' by Charlesworth, levels of DNA sequence variability in asexual Morgan & Charlesworth (1993), who showed that its and self-fertilizing taxa, and in regions of the magnitude depends on the total mutation rate to Drosophila genome where recombination is restricted deleterious alleles for the genomic region in question (Charlesworth et al. 1993). and the frequency of recombination in that region. The neutral model of molecular evolution (Kimura, Given the fact that the mutation rate to alleles with 1983) may be viewed as a useful null model, whose detectable deleterious effects on fitness may be as high statistical predictions can be tested against observed as an average of one or more new mutations per patterns of molecular evolution and variation zygote per generation in higher organisms (Mukai (Kreitman, 1991; McDonald & Kreitman, 1991). et al. 1972; Crow & Simmons, 1983; Kondrashov, There is still considerable controversy concerning the 1988; Houle et al. 1992), background selection may extent to which nucleotide site variants are subject to severely reduce neutral genetic variation in asexual or natural selection, particularly for substitutions causing highly self-fertilizing species, in which there is effect- amino-acid replacements (Kimura, 1983; Gillespie, ively little or no recombination across the entire 1991; McDonald & Kreitman, 1991). It is thus genome. The telomeric and centromeric regions of important to determine whether background selection many randomly mating species also show greatly distorts the predictions of selective versus neutral restricted recombination. Neutral sites in such regions models. Downloaded from https://www.cambridge.org/core. IP address: 170.106.40.40, on 23 Sep 2021 at 10:25:55, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0016672300032365 B. Charlesworth 214 In addition, if background selection operates each locus and equal effects on the two sexes, together differently on sites subject to different kinds of with multiplicative fitness interactions between del- evolutionary forces, differences in patterns of mol- eterious alleles at different background loci, are ecular evolution and variation between taxa or assumed. The value of /„ depends on the mating genomic regions subject to different levels of back- system and mode of inheritance e.g. with autosomal ground selection could shed light on the nature of the inheritance and random-mating, we have /„ = evolutionary forces affecting molecular variation. It is exp(—U/2hs), whereas with sex-linkage /„ = intuitively fairly obvious that both background selec- exp(-3U/2s[2h + l]) (Charlesworth, etal. 1993). For tion and the related process of hitch-hiking of variants chromosome regions of comparable physical size and by linked selectively favourable alleles (Maynard map length, we would therefore expect larger values Smith & Haigh, 1974; Ohta & Kimura, 1975; of/0 for X-linked loci, given that deleterious alleles are Thomson, 1977; Birky & Walsh, 1988; Kaplan, generally partly recessive (Crow & Simmons, 1983). Hudson & Langley, 1989; Stephan, Wiehe & Lenz, An approximate /„ value of 0-2 seems reasonable for 1992; Wiehe & Stephan, 1993) are analogous to a an autosomal centromeric region in D. melanogaster, reduction in the effective population number for the 0-6 for the centromeric region of the X, and 008 for a region of the genome concerned. We would ac- highly selfing species (Charlesworth et al. 1993). cordingly expect the level of variability for both A general formula for the rate of substitution of neutral and selected variants to be reduced by weakly selected mutations in a genome influenced by background selection, although the extent of this background selection will be given first, followed by a reduction will depend on the mode and strength of formula for the expected nucleotide-site diversity selection. If effective population number is greatly which they contribute during their sojourn in the reduced, the behaviour of weakly selected and neutral population, under the infinite-sites model of molecular sites will become indistinguishable. The rate of variation (Kimura, 1969, 1971). Selection on the substitution of favourable variants should thus be mutations studied in this way is assumed to be much reduced by background selection and hitch-hiking, weaker than on the background loci subject to whereas that for deleterious variants will be increased, recurrent deleterious mutations. This is probably and neutral variants will be unaffected. Birky & Walsh (1988) have previously shown this to be true, but did not provide any explicit formulae for the size of the Table 1. Definitions of some quantities introduced in effects. the text The main purpose of this paper is to investigate the expected effects of background selection under differ- U Mean number of new deleterious mutations ent assumptions about breeding system and mode of per individual per generation, at loci inheritance. Complete linkage is assumed throughout, responsible for background selection as this enables explicit formulae to be developed and (background loci) f0 Equilibrium frequency of gametes free of provides an upper bound to the effect of background mutations at background loci selection. Sex-linked as well as autosomal loci will be i Selection coefficient against homozygous considered, as both play a prominent role in empirical mutations at background loci work on Drosophila. h Dominance coefficient for fitness effect of a background locus v, Rate of germline mutation per nucleotide site in females 2. A general model vm Rate of germline mutation per nucleotide site in males (i) General considerations a Selection coefficient on homozygote for a Background selection is assumed to operate by the weakly selected variant 6 Dominance coefficient for fitness effect elimination of new mutations at the loci of interest if of a weakly selected variant they arise in gametes that carry one or more deleterious S Product of a and effective population number mutations (the loci in question will be referred to as K Rate of substitution of variants under background loci). Under equilibrium between selection background selection, relative to the and mutation in a large population, the frequency of neutral value ft Nucleotide site diversity under background gametes free of deleterious mutations is/0, where/„ is selection, relative to the neutral value a function of the diploid mutation rate per genome to without background selection deleterious alleles (U), and of the selection coefficient n* Nucleotide site diversity under background and dominance coefficient for a single deleterious selection, relative to the neutral value mutant allele at a background locus. These are denoted under background selection Q Ratio of substitution rate to nucleotide by s and h respectively, where s is the reduction in site diversity, both measured relative fitness to a mutant homozygote and sh is the reduction to their neutral values under background in fitness