Copyright 2000 by the Genetics Society of America Joint Effects of Genetic Hitchhiking and Background Selection on Neutral Variation Yuseob Kim and Wolfgang Stephan Department of Biology, University of Rochester, Rochester, New York 14627 Manuscript received December 7, 1999 Accepted for publication March 20, 2000 ABSTRACT Due to relatively high rates of strongly selected deleterious mutations, directional selection on favorable alleles (causing hitchhiking effects on linked neutral polymorphisms) is expected to occur while a deleteri- ous mutation-selection balance is present in a population. We analyze this interaction of directional selection and background selection and study their combined effects on neutral variation, using a three- locus model in which each locus is subjected to either deleterious, favorable, or neutral mutations. Average heterozygosity is measured by simulations (1) at the stationary state under the assumption of recurrent hitchhiking events and (2) as a transient level after a single hitchhiking event. The simulation results are compared to theoretical predictions. It is shown that known analytical solutions describing the hitchhiking effect without background selection can be modi®ed such that they accurately predict the joint effects of hitchhiking and background on linked, neutral variation. Generalization of these results to a more appro- priate multilocus model (such that background selection can occur at multiple sites) suggests that, in regions of very low recombination rates, stationary levels of nucleotide diversity are primarily determined by hitchhiking, whereas in regions of high recombination, background selection is the dominant force. The implications of these results on the identi®cation and estimation of the relevant parameters of the model are discussed. T has been suggested that the ªhitchhiking effectº of a similarly good ®t has been obtained when the hitchhik- I strongly selected allele on the frequencies of neutral ing model alone is applied to the same data set (Ste- DNA polymorphisms at linked loci may play an im- phan 1995). Other studies supported hitchhiking over portant role in determining the patterns of genetic vari- background selection for explaining patterns of genetic ation across eukaryotic genomes (Maynard Smith and variation at (mostly) individual loci (SchloÈtterer et Haigh 1974; Ohta and Kimura 1975; Kaplan et al. al. 1997; Nurminsky et al. 1998; Stephan et al. 1998; 1989; Stephan et al. 1992; Gillespie 1994; Barton Benassi et al. 1999), whereas in some cases background 1998). Furthermore, it has been shown that, on the selection was thought to be suf®cient in explaining the basis of the observed patterns of variation, the relevant results. Thus, it appears that the relative importance of parameters of the underlying selective process can be hitchhiking and background selection in determining estimated (Wiehe and Stephan 1993; Stephan 1995). the level of genetic variation remains essentially un- As predicted by the theory of hitchhiking (Birky and known. Walsh 1988, and references above), the level of genetic Previous studies of the hitchhiking effect used a model variation is usually positively correlated with the rate of in which recurrent deleterious mutations at linked loci recombination, but divergence between closely related are not included. However, since the rate of deleterious species is nearly unaffected by recombination (Begun mutations is believed to be high (Keightley and Eyre- and Aquadro 1992). On the other hand, the theory Walker 1999), hitchhiking events are likely to occur of ªbackground selectionº (leading to a reduction of in chromosomal regions where the standing level of effective population size by recurrent deleterious muta- variation is already reduced by background selection tions) proposed by Charlesworth et al. (1993) makes (Charlesworth 1996). Therefore, the effect of back- qualitatively similar predictions (Hudson and Kaplan ground selection on the process of hitchhiking should 1995; Nordborg et al. 1996). Hudson and Kaplan be investigated to assess the relative importance of these (1995) and Charlesworth (1996) showed that back- two forces. ground selection can explain genome-wide patterns in Peck (1994) and Barton (1995) studied the reduc- Drosophila melanogaster polymorphism data. However, a tion of the ®xation probability of strongly selected al- leles due to background selection. Stephan et al. (1999) derived results for the effect of background selection on the nucleotide diversity and ®xation probability at Corresponding author: Yuseob Kim, Department of Biology, University of Rochester, Rochester, NY 14627. a partially linked, weakly selected locus. But genetic E-mail: [email protected] variation at a neutral locus that is partially linked to Genetics 155: 1415±1427 ( July 2000) 1416 Y. Kim and W. Stephan both a locus under strong positive selection and a locus TABLE 1 under background selection has not been investigated. De®nitions of parameters In the latter case, the dynamics of favorable and deleteri- ous alleles may interfere with each other, making it N Diploid population size dif®cult to predict the outcome of this interaction by N1, N2 Effective population size at the Fav and the Neu analyzing these processes individually. In this article, locus, respectively we investigate this problem using simulations based on s, t Selection coef®cients of favorable and deleteri- three-locus, two-allele models. We measure heterozygos- ous alleles, respectively ity at a neutral locus using two different models of ge- r1, r2 Recombination fraction between Del and Fav and between Fav and Neu, respectively netic hitchhiking. In the ®rst model, we analyze the ␣ Strength of directional selection ϭ 2Ns stationary level of heterozygosity caused by background u Rate of deleterious mutations per generation per selection and recurrent hitchhiking events; in the sec- locus ond one, we study the effect of background selection uf Rate of favorable mutations per generation per and a single hitchhiking event on heterozygosity. The population results of this analysis have signi®cant implications for ␮ Rate of neutral mutations per generation per our understanding of selective processes in natural pop- locus (nucleotide) ⌸ Reduction factor of the ®xation probability of ulations and for the identi®cation and estimation of favorable mutations relevant parameters of these processes. ⌽ Fixation probability of favorable mutations fH, fB Reduction factors of the stationary level of het- erozygosity due to recurrent hitchhiking STATIONARY LEVEL OF HETEROZYGOSITY CAUSED events and background selection, respectively BY BACKGROUND SELECTION AND RECURRENT h Reduction of heterozygosity due to a single hitch- HITCHHIKING EVENTS (MODEL 1) hiking event ␲ Heterozygosity per nucleotide In this section, we investigate the stationary level of ␪ Expected heterozygosity without hitchhiking heterozygosity determined by recurrent substitutions of (ϭ 4N2␮) favorable alleles and continuous removal of deleterious H Cumulative heterozygosity of one trajectory of a alleles by background selection. We use a simple dis- neutral allele crete-generation model of a diploid population of size pa, pB Allele frequencies of a and B, respectively N. (Note that a list of parameters is provided in Table ␳ Recombination rate per nucleotide per genera- 1.) Since we assume that the ®tness effects of alleles tion ␶ Number of generations until the last hitchhiking within a locus combine multiplicatively, this model is event equivalent to that of a haploid population of size 2N that ␯ Number of advantageous substitutions per gen- undergoes random conjugation and recombination. We eration per nucleotide consider a three-locus model such that the three loci are located on a chromosome in the following order: The ®rst locus (Del) experiences recurrent deleterious mutations. The mutation of the wild-type allele (A)to changes of eight haplotype frequencies. It is straightfor- a deleterious allele (a) with selective disadvantage t oc- ward to derive a set of equations describing the deter- curs at a rate u (per gene per generation). That is, as ministic change of haplotype frequencies by selection, in Stephan et al. (1999), background selection acts at recombination, and deleterious mutations (appendix a single locus. The second locus (Fav) is under positive a). When one copy of B or M is introduced in the selection such that a favorable allele (B) with selection population, haplotype frequencies are changed accord- coef®cient s is introduced as described below. Mutation ingly before they are subjected to selection. To incorpo- from an ancestral (m) to a derived neutral allele (M) rate the effects of ®nite population size, multinomial occurs at the third locus (Neu). The genetic background sampling of different haplotypes was simulated after (haplotype) on which the mutations to B and to M occur their frequencies were changed according to the deter- is chosen randomly in proportion to its frequency. The ministic equations. We used the random binomial num- recombination fractions between Del and Fav and be- ber generator of Press et al. (1992) with some modi®ca- tween Fav and Neu are r1 and r2, respectively. The two tion. other possibilities of gene order, i.e., Del-Neu-Fav and Each simulation starts with a population of Abm and Fav-Del-Neu, were also studied. For all three gene orders, abm haplotypes. The initial frequency of a is given as the simulation and theoretical methods are