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Distribution of Recombination Crossovers and the Origin of Haplotype Blocks: The Interplay of Population History, Recombination, and Mutation

2002; Elsevier BV; Volume: 71; Issue: 5 Linguagem: Inglês

10.1086/344398

1537-6605

Ning Wang, Joshua M. Akey, Kun Zhang, Ranajit Chakraborty, Jin Li,

Evolution and Genetic Dynamics

Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure. Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure. Recently, several studies have proposed that blocklike patterns of linkage disequilibrium (LD), referred to as haplotype blocks, exist throughout the human genome (Daly et al. Daly et al., 2001Daly MJ Rioux JD Schaffner SF Hudson TJ Lander ES High-resolution haplotype structure in the human genome.Nat Genet. 2001; 29: 229-232Crossref PubMed Scopus (1383) Google Scholar; Jefferys et al. Jeffreys et al., 2001Jeffreys AJ Kauppi L Neumann R Intensely punctuate meiotic recombination in the class II region of the major histocompatibility complex.Nat Genet. 2001; 29: 217-222Crossref PubMed Scopus (654) Google Scholar; Reich et al. Reich et al., 2001Reich DE Cargill M Bolk S Ireland J Sabeti PC Richter DJ Lavery T Kouyoumjian R Farhadian SF Ward R Lander ES Linkage disequilibrium in the human genome.Nature. 2001; 411: 199-204Crossref PubMed Scopus (1288) Google Scholar). Understanding the distribution and structure of haplotype blocks may facilitate the identification of complex disease genes via genomewide association studies and, in addition, may provide a comprehensive picture of the apportionment of genetic variation throughout the genome (Collins et al. Collins et al., 1999Collins A Lonjou C Morton NE Genetic epidemiology of single-nucleotide polymorphisms.Proc Natl Acad Sci USA. 1999; 96: 15173-15177Crossref PubMed Scopus (230) Google Scholar; Kruglyak Kruglyak, 1999Kruglyak L Prospects for whole-genome linkage disequilibrium mapping of common disease genes.Nat Genet. 1999; 22: 139-144Crossref PubMed Scopus (1111) Google Scholar; Moffatt et al. Moffatt et al., 2000Moffatt MF Traherne JA Abecasis GR Cookson W Single nucleotide polymorphism and linkage disequilibrium within the TCR α/δ locus.Hum Mol Genet. 2000; 9: 1011-1019Crossref PubMed Google Scholar; Goldstein Goldstein, 2001Goldstein DB Islands of linkage disequilibrium.Nat Genet. 2001; 29: 109-111Crossref PubMed Scopus (225) Google Scholar; Johnson et al. Johnson et al., 2001Johnson GC Esposito L Barratt BJ Smith AN Heward J Genova GD Ueda H Cordell HJ Eaves IA Dudbridge F Twells RC Payne F Hughes W Nutland S Stevens H Carr P Tuomilehto-Wolf E Tuomilehto J Gough SC Clayton DG Todd JA Haplotype tagging for the identification of common disease genes.Nat Genet. 2001; 29: 233-237Crossref PubMed Scopus (999) Google Scholar; Weiss and Clark Weiss and Clark, 2002Weiss KM Clark AG Linkage disequilibrium and the mapping of complex human traits.Trends Genet. 2002; 18: 19-24Abstract Full Text Full Text PDF PubMed Scopus (293) Google Scholar). Although haplotype blocks hold great promise, relatively little is known about the molecular mechanisms and population genetic forces that shape their characteristics. In this report, we propose a novel haplotype block definition based on the distribution of observed recombination crossovers between loci, using an extension of the four-gamete test (FGT; Hudson and Kaplan Hudson and Kaplan, 1985Hudson RR Kaplan NL Statistical properties of the number of recombination events in the history of a sample of DNA sequences.Genetics. 1985; 111: 147-164PubMed Google Scholar). Using this definition, we studied how various population genetic parameters, population history, density of genetic markers, and sample size (number of chromosomes studied) contribute to the distribution of recombination crossovers and, in turn, haplotype block characteristics. Furthermore, through extensive coalescent simulations and published chromosome 21 data, we tested whether recombination hot spots are necessary for the formation of haplotype blocks. In general, haplotype blocks are defined in two different ways. Specifically, one definition of a haplotype block is a contiguous set of markers in which the average D′ (the standardized coefficient of LD) is greater than some predetermined threshold (Reich et al. Reich et al., 2001Reich DE Cargill M Bolk S Ireland J Sabeti PC Richter DJ Lavery T Kouyoumjian R Farhadian SF Ward R Lander ES Linkage disequilibrium in the human genome.Nature. 2001; 411: 199-204Crossref PubMed Scopus (1288) Google Scholar). The second definition is based on the concept of “chromosome coverage,” with a haplotype block containing a minimum number of SNPs that account for a majority of common haplotypes (Patil et al. Patil et al., 2001Patil N Berno AJ Hinds DA Barrett WA Doshi JM Hacker CR Kautzer CR Lee DH Marjoribanks C McDonough DP Nguyen B Norris MC Sheehan JB Shen N Stern D Stokowski RP Thomas DJ Trulson MO Vyas KR Frazer KA Fodor S Cox DR Blocks of limited haplotype diversity revealed by high-resolution scanning of human chromosome 21.Science. 2001; 294: 1719-1723Crossref PubMed Scopus (920) Google Scholar) or a reduced level of haplotype diversity (Daly et al. Daly et al., 2001Daly MJ Rioux JD Schaffner SF Hudson TJ Lander ES High-resolution haplotype structure in the human genome.Nat Genet. 2001; 29: 229-232Crossref PubMed Scopus (1383) Google Scholar). These different haplotype block definitions and reconstruction algorithms, or even the same definition with different subjectively determined thresholds, will lead to varying haplotype block patterns. The ambiguities associated with these haplotype block definitions make it difficult to study the mechanism underlying the formation of haplotype block structure. We therefore propose an alternative approach for haplotype block identification that does not require a threshold. The major steps of this algorithm are outlined in figure 1. Specifically, for a set of m SNPs, our algorithm begins by performing the FGT between each pairwise SNP to identify past recombination events (fig. 1A). In the absence of recurrent and/or backward mutation, the only explanation for observing all four gametes between a pair of loci is the occurrence of at least one historical recombination event. Next, blocks are identified as a set of contiguous and ordered SNP markers in which there is no evidence for recombination. Blocks are searched from the start of the region by sequential addition of the next locus according to the FGT results. This iterative process continues as long as the number of gametes does not exceed three (fig. 1B). When all four gametes are observed between the kth locus with any of previous loci, locus k is regarded as the putative starting point of a new block, and the block size is determined as the sequence length between the start and the end of the block. We compared this searching algorithm with a greedy searching algorithm (Bogart Bogart, 2000Bogart KP Introductory combinatorics. 3rd ed. Harcourt Academic Press, San Diego2000Google Scholar), and, as expected, the results were quite similar, particularly when sample sizes (number of chromosomes studied) are large (data not shown). With this FGT-based definition, it is possible that a true recombination event may not be detected because of limited sample size. The effect of sample size on the average sizes of the inferred haplotype block was investigated, and the results are presented below. The FGT-based algorithm was applied to data simulated under a coalescent framework, to better understand how different population genetic forces affect haplotype block characteristics. The coalescence is a stochastic process that provides a powerful and fast technique for simulating population genetic data (Hudson Hudson, 1983Hudson RR Properties of a neutral allele model with intragenic recombination.Theor Popul Biol. 1983; 23: 183-201Crossref PubMed Scopus (516) Google Scholar; reviewed by Fu and Li Fu and Li, 1999Fu YX Li WH Coalescing into the 21st century: an overview and prospects of coalescent theory.Theor Popul Biol. 1999; 56: 1-10Crossref PubMed Scopus (101) Google Scholar; software available at Hudson Lab home page). The parameters of the simulations were θ=4Neμ (the population mutation rate, where Ne is the effective population size and μ is the mutation rate per locus per generation), R=4Ner (the population recombination rate, where r is the recombination rate), and the sample size (n is the number of chromosomes). Figure 2 shows the effect of recombination rate and effective population size on the average haplotype block size. In this figure, R varies from 0.1θ to 5.0θ, which corresponds to a change in r from 0.25×10−8 to 12.5×10−8 per generation when the mutation rate, μ, is fixed at 10−9 per site per year (Satta et al. Satta et al., 1993Satta Y Ohuigin C Takahata N Klein J The synonymous substitution rate of the major histocompatibility complex loci in primates.Proc Natl Acad Sci USA. 1993; 90: 7480-7484Crossref PubMed Scopus (65) Google Scholar). For a fixed θ, the average haplotype block size decreases with increasing R. Population history also affects the average block size, with small populations (i.e., a small effective population size) exhibiting larger blocks (fig. 2). The effective population size was adjusted by fixing the ratio of R/θ and varying R for different values of θ. The three values of θ considered were 5, 10, and 25, which correspond to Ne of 2,000, 4,000, and 10,000, respectively, for μ=10−9. When R is ∼0.5θ, the average block size decreases from 11.7, 6.1, and 2.6 kb as Ne increases from 2,000, 4,000, and 10,000, respectively, assuming a sample size of 100. Furthermore, we have also investigated the effect of sample size on the inference of haplotype block characteristics. For the same values of θ and R, by changing the sample size from 20 to 50, 100, 200, 400, 600, 800, and 1,000, respectively, figure 3 shows that a smaller sample size exhibits increased block sizes compared with a larger sample size. Specifically, the average haplotype block size increased from 2.95 kb to 4.88 kb as the sample size decreases from 100 to 20. Thus, sample size is an important parameter to consider in designing studies to investigate haplotype block structure. Large sample sizes are necessary to obtain accurate estimates of block boundaries because historic recombination events might not be detected in a small sample. When the sample size is >100, the decrease in average block size becomes much less. Thus, we suggest that a sample size of at least 100 should be used in haplotype block studies. Next, we studied the contribution of θ to haplotype block characteristics by allowing θ to vary for fixed values of R. Practically, the resulting change in θ can be interpreted as a change in either the mutation rate or the SNP density (defined here as the observed number of SNPs per unit distance, irrespective of the underlying mutation rate). For each R in figure 4A, the average block size increases slightly when θ is very small and then decreases until an equilibrium value of θ is reached. A pictorial explanation for why θ affects the average block size is illustrated in figure 4B. A low θ value will lead to a small number of markers in the population and subsequently in the sample, regardless of whether this is due to a low mutation rate or to low SNP density. As a hypothetical example, imagine a genomic region flanked by two sites of recombination (fig. 4B). When θ is small, two markers may be identified, which constitute one block (as shown in panel a of fig. 4B). If θ increases, three markers may be identified, and they form a block whose size is larger compared with (a). As θ continues to increase, enough markers are identified to resolve this genomic region into two block structures (c), whose average block size has now decreased in comparison with (b). Furthermore, the optimal SNP density for haplotype block discovery depends on the local recombination rate. As R increases, the average block size decreases, and thus more markers are required for obtaining accurate estimates of haplotype block boundaries. On the basis of the simulation results, we can cautiously furnish some practical guidelines for SNP density in designing a study. As shown in figure 4A, when the recombination level is low (R=0.4 or r=0.2 cM/Mb in the simulation), a SNP density of 1 SNP/2 kb is sufficient. However, when the recombination level is high (R=2.0 or r=1 cM/Mb in the simulation), a density of at least 2 SNPs/1 kb will be required. Of interest, for values of R>2, the rate of decrease in average block size becomes much less (comparing R=2, 6, 10) and therefore the suggested SNP density of 2 SNPs/1 kb remains valid. Another important question regarding haplotype blocks is what mechanisms are responsible for their formation. Recombination hot spots have been proposed as a mechanism for generating haplotype blocks (Daly et al. Daly et al., 2001Daly MJ Rioux JD Schaffner SF Hudson TJ Lander ES High-resolution haplotype structure in the human genome.Nat Genet. 2001; 29: 229-232Crossref PubMed Scopus (1383) Google Scholar; Goldstein Goldstein, 2001Goldstein DB Islands of linkage disequilibrium.Nat Genet. 2001; 29: 109-111Crossref PubMed Scopus (225) Google Scholar; Gabriel et al. Gabriel et al., 2002Gabriel SB Schaffner SF Nguyen H Moore JM Roy J Blumenstiel B Higgins J Defelice M Lochner A Faggart M Liu-Cordero SN Rotimi C Adeyemo A Cooper R Ward R Lander ES Daly MJ Altshuler D The structure of haplotype blocks in the human genome.Science. 2002; 296: 2225-2229Crossref PubMed Scopus (4531) Google Scholar). In support of this hypothesis, Jeffreys et al. (Jeffreys et al., 2001Jeffreys AJ Kauppi L Neumann R Intensely punctuate meiotic recombination in the class II region of the major histocompatibility complex.Nat Genet. 2001; 29: 217-222Crossref PubMed Scopus (654) Google Scholar) experimentally demonstrated that recombination was clustered into three hot spots in the major histocompatibility complex class II region, and these hot spots corresponded to haplotype block boundaries. However, haplotype blocks may also arise by stochastic variation in models assuming that recombination is randomly distributed (Subrahmanyan et al. Subrahmanyan et al., 2001Subrahmanyan L Eberle MA Clark AG Kruglyak L Nickerson DA Sequence variation and linkage disequilibrium in the human T-cell receptor β (TCRB) locus.Am J Hum Genet. 2001; 69: 381-395Abstract Full Text Full Text PDF PubMed Scopus (47) Google Scholar). Results from the coalescent simulations presented above clearly demonstrate that a model of randomly distributed recombination can lead to the formation of haplotype blocks (figs. Figure 2, Figure 4). To better understand whether empirical data are consistent with a random or hot spot model of recombination, we applied our FGT-based haplotype block identification algorithm to published chromosome 21 data (Patil et al. Patil et al., 2001Patil N Berno AJ Hinds DA Barrett WA Doshi JM Hacker CR Kautzer CR Lee DH Marjoribanks C McDonough DP Nguyen B Norris MC Sheehan JB Shen N Stern D Stokowski RP Thomas DJ Trulson MO Vyas KR Frazer KA Fodor S Cox DR Blocks of limited haplotype diversity revealed by high-resolution scanning of human chromosome 21.Science. 2001; 294: 1719-1723Crossref PubMed Scopus (920) Google Scholar) and compared it with the coalescent simulation results. In total, Patil et al. (Patil et al., 2001Patil N Berno AJ Hinds DA Barrett WA Doshi JM Hacker CR Kautzer CR Lee DH Marjoribanks C McDonough DP Nguyen B Norris MC Sheehan JB Shen N Stern D Stokowski RP Thomas DJ Trulson MO Vyas KR Frazer KA Fodor S Cox DR Blocks of limited haplotype diversity revealed by high-resolution scanning of human chromosome 21.Science. 2001; 294: 1719-1723Crossref PubMed Scopus (920) Google Scholar) genotyped 35,989 SNPs from 10 individuals across 32.4 Mb on human chromosome 21 (average 1.1 SNP/kb). The average mutation rate of the whole region can be estimated as 0.3×10−9 per site per year. To match the real data, this mutation rate was used in the simulations. Since there are many undetermined nucleotides in the real data (denoted as “N”), the true sample size is actually <20. Therefore, we set the sample size (number of chromosomes) to 14 in the simulations, which is the approximate average number of observations across all loci. In addition, we considered two recombination rates, r=1.0×10−8 and r=4.0×10−8. The distribution of haplotype block sizes for the real and simulated data is summarized in figure 5A. Although the average block sizes for the real data (8.73 kb) are similar to the ones obtained in the simulated data with r=1.0×10−8 (9.01 kb) and with r=4.0×10−8 (4.75 kb), the distributions of block sizes are different (Kolmogorov-Smirnov test, P<10−3 for each pairwise comparison). However, a closer inspection of figure 5A shows that for small block sizes, the real data are more consistent with the simulated data when r=4.0×10−8, whereas for larger block sizes the real data are more consistent with the simulated data when r=1.0×10−8. Therefore, we hypothesize that a randomly distributed recombination model (i.e., no hot spots) with a varying recombination rate across the chromosome can explain the empirical data. The distinction between the varying and hot spot recombination models is that in the hot spot model, recombination is heterogeneous both within a given stretch of DNA and across the genome. By contrast, in the varying–recombination rate model, recombination rate is homogeneous within a given stretch of DNA but heterogeneous across the genome. In other words, within a defined genomic region, recombination is uniformly distributed, but the recombination rate can vary across the genome. Supporting this hypothesis, Lynn et al. (Lynn et al., 2000Lynn A Kashuk C Petersen MB Bailey JA Cox DR Antonarakis SE Chakravarti A Patterns of meiotic recombination on the long arm of human chromosome 21.Genome Res. 2000; 10: 1319-1332Crossref PubMed Scopus (45) Google Scholar) studied patterns of recombination, using 187 microsatellite markers spanning chromosome 21, and concluded that the rate of recombination is not uniformly distributed across the chromosome. To further test our hypothesis, we performed additional simulations and compared the real data with a mixture model in which r=1.0×10−8 for 50% of the simulation replicates and r=4.0×10−8 for the remaining 50% of simulation replicates (fig. 5B). The simulated data are again qualitatively similar to the real data. Our point here is not to exhaustively search the parameter space of recombination rates to match the empirical data but rather to illustrate how a simple composition of different recombination rates can lead to haplotype block patterns observed in real data. Furthermore, we emphasize that our hypothesis does not preclude the existence of recombination hot spots (which have been demonstrated to exist; see Jeffreys et al. [Jeffreys et al., 2001Jeffreys AJ Kauppi L Neumann R Intensely punctuate meiotic recombination in the class II region of the major histocompatibility complex.Nat Genet. 2001; 29: 217-222Crossref PubMed Scopus (654) Google Scholar]) but simply predicts that a randomly distributed recombination model can explain the majority of haplotype block characteristics. Ultimately, the relative contribution of the hot spot and random recombination models in shaping patterns of LD will have to be determined empirically (Jeffreys et al. Jeffreys et al., 2001Jeffreys AJ Kauppi L Neumann R Intensely punctuate meiotic recombination in the class II region of the major histocompatibility complex.Nat Genet. 2001; 29: 217-222Crossref PubMed Scopus (654) Google Scholar). Currently, there is tremendous interest in constructing a haplotype block map of the human genome and in applying it to identify genes underlying complex disease (Daly et al. Daly et al., 2001Daly MJ Rioux JD Schaffner SF Hudson TJ Lander ES High-resolution haplotype structure in the human genome.Nat Genet. 2001; 29: 229-232Crossref PubMed Scopus (1383) Google Scholar; Goldstein Goldstein, 2001Goldstein DB Islands of linkage disequilibrium.Nat Genet. 2001; 29: 109-111Crossref PubMed Scopus (225) Google Scholar; Johnson et al. Johnson et al., 2001Johnson G Esposito L Barratt BJ Smith AN Heward J Genova GD Ueda H Cordell HJ Eaves IA Dudbridge F Twells R Payne F Hughes W Nutland S Stevens H Carr P Tuomilehto-Wolf E Tuomilehto J Gough S Clayton DG Todd JA Haplotype tagging for the identification of common disease genes.Nat Genet. 2001; 29: 233-237Crossref PubMed Scopus (893) Google Scholar; Gabriel et al. Gabriel et al., 2002Gabriel SB Schaffner SF Nguyen H Moore JM Roy J Blumenstiel B Higgins J Defelice M Lochner A Faggart M Liu-Cordero SN Rotimi C Adeyemo A Cooper R Ward R Lander ES Daly MJ Altshuler D The structure of haplotype blocks in the human genome.Science. 2002; 296: 2225-2229Crossref PubMed Scopus (4531) Google Scholar). An important and unresolved question about haplotype blocks in the context of disease gene studies is to what extent block boundaries are conserved across populations. If recombination hot spots are the predominant mechanism underlying the formation of haplotype blocks, then it is likely that blocks will generally be shared across populations, unless population-specific mechanisms of recombination exist. However, our results show that even in the absence of recombination hot spots, randomly distributed recombination events can also lead to the formation of haplotype blocks, and that population genetic parameters combined with demographic history affect block characteristics. Therefore, populations with different demographic histories will likely have different block structures, which suggests that a reference haplotype map may be of limited value in disease gene studies. Recently, Gabriel et al. (Gabriel et al., 2002Gabriel SB Schaffner SF Nguyen H Moore JM Roy J Blumenstiel B Higgins J Defelice M Lochner A Faggart M Liu-Cordero SN Rotimi C Adeyemo A Cooper R Ward R Lander ES Daly MJ Altshuler D The structure of haplotype blocks in the human genome.Science. 2002; 296: 2225-2229Crossref PubMed Scopus (4531) Google Scholar) concluded that block boundaries are largely shared across populations, which supports the recombination hot spot hypothesis. However, this study focused on common SNPs (minor allele frequency ⩾20%) and common haplotypes (⩾5%), and thus one would expect a high conservation of block structure, given their antiquity. Clearly, empirical studies of relatively less common SNPs and haplotypes need to be conducted and the degree of block sharing across populations reassessed. In summary, we have presented an objective and stringent haplotype block identification algorithm based on the FGT to investigate the origin of haplotype blocks and to examine the effects of various population genetics forces on haplotype block patterns. Our primary conclusions are that (1) population demographic history, recombination, and mutation jointly dictate haplotype block characteristics, and (2) haplotype blocks can arise in the absence of recombination hot spots. More generally, our results demonstrate that haplotype block structure and characteristics are dictated by individual as well as interactive effects of multiple evolutionary forces (e.g., mutation, recombination, and population history). This work was supported by National Institutes of Health grants to R.C. and L.J. K.Z. was also supported by the Hite Foundation.