Linkage Disequilibrium between STRPs and SNPs across the Human Genome

STRP Genotyping and Selection of SNPs

STRPs for genotyping were from Marshfield 5 cM genomic linkage screening sets (see Web Resources). These markers were chosen to be uniformly spaced, highly informative, and easy to type accurately.⁴¹ Genotyping was performed in the Mammalian Genotyping Service as previously described.⁴²

We determined the genomic positions of 721 autosomal STRPs from the screening sets by BLATing the consensus sequence to the human genome sequence at the UCSC website (hg17; Build 35). Of these 721 STRPs, 51 were dinucleotide repeats, 149 were trinucleotide repeats, 511 were tetranucleotide repeats, and 10 were pentanucleotide repeats. For phased analyses, genotypes of all SNPs within 50kb of each microsatellite were downloaded from the HapMap website (public release 21). To conduct longer-range, unphased analyses, the cM position of each STRP was estimated using the high-density STRP human genetic map.⁴³ Two hundred seventy three of the STRPs were directly placed on this map; the cM position of each remaining STRP was estimated as the position of the closest mapped STRP in the sequence. The sequence positions of mapped STRPs nearest to 2 cM on either side of each STRP, assuming a constant recombination rate in each region (but allowing rates to vary among regions), were used to delineate a window of approximately 4 cM in size centered on each STRP. All SNPs falling within these windows were obtained from the HapMap website.

Analyses

Individuals from the CHB (Han Chinese individuals living in Beijing, China) and JPT (Japanese individuals living in Tokyo, Japan) populations were combined (denoted hereafter as “CHB+JPT”) for purposes of this study.¹⁴ The CEU, YRI (individuals from the Yoruba population in Ibadan, Nigeria), and CHB+JPT populations were considered separately in all analyses. Autosomal haplotypes including each STRP and all non-singleton SNPs within 50 kb were computationally phased using PHASE v.2.1.^44,45 This distance was selected based on average haplotype block sizes reported for the SNP-dense ENCODE regions in these individuals¹⁴ and computational constraints associated with phasing. PHASE assumes an infinite-sites model for SNPs and a symmetrical, one-step stepwise-mutation model for STRPs. For the CEU and YRI populations, genotypes from children were used in haplotype reconstruction.⁴⁶ All genotypes that departed from Mendelian transmission were re-coded as missing. If a genotype was absent in one or both parents, the genotype of the corresponding child was also re-coded as missing. One CEU parent was not genotyped for STRPs and the matching parent and child were removed prior to all analyses. For each individual, the haplotype pair with the highest posterior probability estimated by PHASE was used for subsequent analyses. All genomic regions except two in CEU and three in YRI were successfully phased. The remaining 719, 718, and 721 autosomal regions (in CEU, YRI, and CHB+JPT, respectively) were the focus of our analyses. We analyzed an additional 31 X-linked STRPs in males only, where haplotypes were directly observed, to investigate LD in the absence of phasing. All LD analyses involved only unrelated individuals: 58 parents from CEU trios, 60 parents from YRI trios, and 90 (45+45) CHB+JPT individuals.

For phased haplotypes, D′ ⁴⁷ was estimated for each pair of alleles from each STRP-SNP (designated as D′_ind) or SNP-SNP combination. For each STRP-SNP combination, the multi-allelic, average D′ (designated as D′ _avg) was also estimated as

(ref. ⁴⁸) with the Haploxt program in the GOLD package.⁴⁹ Statistical evidence for association was measured with contingency tables of haplotype counts. p values for SNP-SNP associations (2 × 2 tables) were estimated with Fisher's Exact Test (FET). p values for STRP-SNP associations were also estimated with FET, but the null distribution was obtained from 10,000 randomized tables because the number of STRP alleles was large.

To evaluate long-range LD, composite genotypic disequilibrium (CGD)^50–52 between STRPs and all SNPs within 2 cM was calculated with the use of unphased diploid genotypes. CGD between the SNP closest to each STRP and all remaining SNPs in the window was estimated for comparison. Statistical significance was measured with a χ² test. CGD analyses were restricted to alleles with at least 5% frequency to minimize departures from the asymptotic χ² approximation caused by sparse contingency tables. The CGD approach directly uses unphased diploid genotypes, obviating the need for phasing (which can be very difficult at larger recombinational distances) and thus avoiding effects of phasing error. These analyses were implemented with an R script kindly provided by Daniel Schaid.⁵⁰

For both phased and unphased LD analyses, the overall (genomic) proportion of tests for which the null hypothesis of no association was rejected (m₁/m) was estimated from the pooled distribution of p values with the use of a false-discovery-rate approach^53–55 implemented in Storey's Qvalue package in R. Values of m₁/m were estimated separately for different data subsets (STRP versus SNP tests, STRP repeat types, etc.). Because SNP-SNP FET p value distributions were noncontinuous with a peak at 1 (a feature of FET⁵⁶), we used the bootstrap method (rather than the smoother method) to estimate m₁/m.⁵⁵

For each STRP, polymorphism summary statistics, including expected heterozygosity and variance in repeat number, were calculated separately for each population with Microsatellite Analyzer.⁵⁷

Genomic Distributions of STRP-SNP LD

To measure LD between STRPs and SNPs, we genotyped 721 autosomal and 31 X-linked STRPs in 268 individuals from the HapMap project.¹⁴ These individuals had already been genotyped at more than 3.1 million SNPs. The STRPs were approximately uniformly spaced along each of the chromosomes.⁴¹

We first analyzed D′ between autosomal STRPs and SNPs separated by less than 50 kb on haplotypes reconstructed with the use of PHASE.^44,45 Genomic distributions of D′ between STRPs and SNPs were characterized by several patterns (Figure 1). First, many locus pairs were perfectly associated, with D′ values of 1. Second, a substantial fraction of tests yielded D′ values less than 1, consistent with the action of recombination or recurrent mutation. This pattern was observed in D′ distributions among individual pairs of alleles (D′ _ind) and was considerably stronger in distributions of D′ averaged across allele pairs (D′ _avg) (Figure 1), suggesting substantial heterogeneity among alleles within individual STRPs. Comparisons with D′ among SNP pairs drawn from the same genomic regions indicated that: (1) STRP-SNP D′ _ind was similar to but lower than SNP-SNP D′ (Mann-Whitney U test; p < 10⁻¹⁵ in all populations), and (2) STRP-SNP D′ _avg was considerably lower than SNP-SNP D′ (p < 10⁻¹⁵ in all populations). STRP-SNP D′ distributions differed among populations (Kruskal-Wallis test; p < 10⁻¹⁵) (Figure 1). In particular, YRI showed lower D′ _avg values (median: YRI = 0.43; CEU = 0.49; CHB+JPT = 0.47), in agreement with patterns of SNP-SNP LD (International HapMap Consortium, 2005) and presumably reflecting the larger effective size of the Yoruban population.

D′ levels among STRPs and SNPs separated by up to 50 kb are likely to have been reduced by both recombination and recurrent mutation during the history of the population samples. To further gauge the contribution of recurrent mutation, we examined D′ between the subset of loci located less than 5 kb apart (Figure 2), where effects of recombination should be less visible. STRP-SNP D′ was increased relative to the 50 kb regions (compare to Figure 1) (median: CEU = 0.65; YRI = 0.57; CHB+JPT = 0.66), revealing the effects of tighter linkage. However, both D′_ind and D′ _avg were still reduced in comparison to SNP-SNP pairs (p < 10⁻¹⁵ in all tests), demonstrating that recurrent mutation had significantly shaped STRP-SNP LD.

Because repeat types mutate at different rates,^20,58 we also compared D′ distributions among repeat types (excluding pentanucleotides, for which only ten loci were available) (Figure 3). Significant variation in D′ among repeat types was observed in each population (Kruskal-Wallis test; p < 10⁻¹⁵ in all tests), with dinucleotides (D′_avg median: CEU = 0.59; YRI = 0.52; CHB+JPT = 0.58) and trinucleotides (D′_avg median: CEU = 0.62; YRI = 0.53; CHB+JPT = 0.61) showing higher D′_avg than that of tetranucleotides (D′_avg median: CEU = 0.44; YRI = 0.40; CHB+JPT = 0.43). Comparisons to D′ among SNP-SNP pairs from the corresponding genomic regions confirmed that STRP-SNP D′_avg was reduced in each repeat class (p < 10⁻¹⁵ in all tests).

Although D′ describes the intensity of LD in useful ways, it does not measure statistical significance. We used Fisher's Exact Test to calculate p values for the tables of haplotype counts from all two-locus pairs located in the 50 kb intervals. Then, we separately estimated the genomic fractions of STRP-SNP and SNP-SNP tests for which the null hypothesis of no association was rejected (m₁/m) by using a false-discovery-rate approach.^53–55 This method accounts for the performance of multiple tests by considering the full distribution of p values.

Values of m₁/m for STRP-SNP pairs exceeded those for SNP-SNP pairs from corresponding genomic regions in all populations (Figure 4). The contrast was especially strong in the YRI population. Proportions of locus pairs showing significant LD differed substantially among STRP repeat types (Figure 4). In agreement with analyses of D′, dinucleotides and trinucleotides showed more evidence for LD than did tetranucleotides.

Paired Comparisons between STRP-SNP and SNP-SNP LD

In addition to comparing the full distributions of STRP-SNP LD and SNP-SNP LD, we sought to test whether STRPs and SNPs located near each other differed in the ability to detect LD with the same SNPs. We conducted paired comparisons in which each (target) SNP within 50 kb of a genotyped STRP was considered with (1) the STRP and (2) the SNP located nearest the STRP. The average distances between STRPs and the closest SNPs were 589 bp (CEU), 518 bp (YRI), and 621 bp (CHB+JPT). Loci from such paired tests probably had identical genealogical histories and shared all properties of the target SNPs. As a result, variation in recombination rate and target-SNP allele frequency could not contribute to observed differences between STRPs and SNPs.

STRP-SNP and SNP-SNP D′ values were positively correlated (Spearman's ρ: CEU = 0.43; YRI = 0.40; CHB+JPT = 0.48; p < 10⁻¹⁵ in all populations), reflecting shared genealogical histories. Nevertheless, D′ values were lower for STRPs than for SNPs (Wilcoxon matched-pairs signed-rank test; p < 10⁻¹⁵ in all populations), and STRP p values were lower than SNP p values (p < 10⁻¹⁵ in all populations). These patterns confirmed that the lower D′ and stronger statistical significance of LD involving STRPs inferred from the full distributions (above) was not caused by differences in recombination rate, target-SNP allele frequency, or other factors that vary among genomic regions. STRP-SNP D′_avg showed a slightly weaker relationship with physical distance (Spearman's ρ: CEU = −0.22; YRI = −0.19; CHB+JPT = −0.25) than did SNP-SNP D′ (CEU = −0.30; YRI = −0.27; CHB+JPT = −0.33).

Differences in LD patterns at STRPs and SNPs could be primarily attributable to the larger number of alleles at STRPs. Although individual SNPs only harbor two alleles, neighboring SNPs can be combined to capture more diversity. To compare STRP and SNP LD for markers with similar amounts of variation, we (1) selected contiguous SNPs that mapped closest to each STRP, (2) combined these SNPs to generate multi-SNP haplotypes, and (3) calculated LD between multi-SNP haplotypes and all remaining SNPs in the 50 kb regions. Seven-SNP haplotypes were used for these analyses because the average numbers of 7SNP haplotypes were similar to the average numbers of STRP alleles. Paired comparisons between 7SNP-SNP and STRP-SNP loci revealed lower p values at 7SNP-SNP combinations than at both 1SNP-SNP and STRP-SNP markers (Wilcoxon matched-pairs signed-rank test; p < 10⁻¹⁵ in all populations). These results suggested that the increased statistical significance of LD at STRPs was largely driven by greater diversity.

Effects of Allele Frequency

Levels of LD depend on allele frequency, both for statistical reasons⁴⁸ and because alleles with higher frequencies tend to be older and are more likely to have experienced recombination. This phenomenon can be seen clearly in genomic SNP-SNP LD patterns.^7,13–15 We found that STRP-SNP D′_avg was also strongly influenced by SNP allele frequency, with clear reductions at higher minor-allele frequencies (Figure 5). This pattern probably reflected not only the increased recombination but also the higher probability of multiple mutations at STRP alleles paired with older SNPs.

Differences in frequency spectra between STRPs and SNPs could also contribute to observed patterns. STRPs harbor more rare alleles than do SNPs in human populations, and this difference is especially pronounced in the HapMap samples, where SNPs were ascertained to exhibit uniform frequency spectra.^14,59,60 To examine the cumulative effects of low-frequency alleles on relative patterns of LD, we repeated all analyses after removing STRP and SNP alleles with frequencies of less than 5%. In this filtered dataset, p values were slightly decreased for both STRP-SNP and SNP-SNP pairs. p values for SNP-SNP pairs were more similar to p values for STRP-SNP pairs than had occurred in unfiltered analyses. However, STRPs still retained a higher fraction of significant tests than did SNPs in all populations (results not shown).

To further account for potential effects of allele frequency on LD, we compared pairs of alleles matched by frequency. We chose the SNP closest to each STRP and then selected the STRP allele with the most similar frequency to that SNP. Then, we measured D′ between these alleles and all SNPs within 50 kb. The result was a paired set of tests with very similar allele frequencies at both loci and physical distances between them. On average, STRP and SNP alleles with frequency differences of less than 0.1 differed in D′_ind by 0.17 (CEU), 0.16 (YRI), and 0.17 (CHB+JPT) when considered with the same SNPs. These matched STRP-and-SNP D′ distributions were significantly different (Wilcoxon matched-pairs signed-rank test; p < 10⁻¹⁵ for all tests), demonstrating that the reduction in D′ observed at STRP-SNP pairs was not caused by allele-frequency differences.

Effects of STRP-Polymorphism Levels

Markers with greater levels of variation are expected to detect LD with stronger statistical significance. This prediction was supported by negative correlations between p values and (1) STRP variance in allele size (Spearman's ρ: CEU = −0.26; YRI = −0.24; CHB+JPT = −0.24; p < 10⁻¹⁵ in all populations) and (2) expected heterozygosity (CEU = −0.14; YRI = −0.19; CHB+JPT = −0.12; p < 10⁻¹⁵ in all populations). Similarly, positive correlations between D′ and (1) variance in allele size (CEU = 0.31; YRI = 0.30; CHB+JPT = 0.28; p < 10⁻¹⁵ in all populations) and (2) expected heterozygosity (CEU = 0.17; YRI = 0.23; CHB+JPT = 0.11; p < 10⁻¹⁵ in all populations) were observed.

Effects of Haplotype Phasing

We assumed that haplotypes were reconstructed without error, as in other large-scale analyses of LD in humans.^13–15,46 Although PHASE is expected to be highly accurate at the physical scale and SNP densities considered here,⁴⁶ especially in the CEU and YRI populations for which trios were used, there are reasons to suspect that phasing errors affected observed patterns of LD. First, the posterior probabilities of haplotype pairs provided evidence of uncertainty. Although many haplotype pairs had high posterior probabilities, some regions in some individuals had low probabilities. Use of the haplotype pairs with the highest probabilities ignored that uncertainty. Second, to infer haplotypes involving STRPs is a challenging task. These loci harbor many low-frequency alleles and sometimes mutate in ways that are inconsistent with the stepwise-mutation model assumed in PHASE. A heuristic measure of phasing uncertainty, the (across-individual) average of the highest posterior probabilities of haplotype pairs, was negatively correlated with STRP-SNP D′_avg (Spearman's rho: CEU = −0.13; YRI = −0.14; CHB+JPT = −0.31; p < 10⁻¹⁵ in all populations), suggesting that LD estimates might have been biased by the phasing process.

We conducted two additional sets of analyses to address the effects of phasing error on the STRP-SNP LD patterns we observed. First, we estimated LD for 31 X-linked regions in males, in which phases were known without error. X-linked and autosomal D′ distributions were similar (median: CEU X = 0.54, CEU autosomes = 0.49; YRI X = 0.48, YRI autosomes = 0.43; CHB+JPT X = 0.49, CHB+JPT autosomes = 0.47) (Figure 6), although D′ levels were significantly higher on the X chromosome (Mann-Whitney U test: CEU = p < 10⁻¹⁵; YRI = p < 10⁻¹³; CHB+JPT = p < 10⁻¹⁵). Because the smaller effective population size of the X chromosome and the lack of recombination in males should lead to greater LD among X-linked loci, the similarity in D′ distributions suggests that phasing error was not a major contributor to observed LD patterns. As a further precaution against the effects of phasing error, we also estimated LD with the use of unphased genotypes.

Long-range LD among Unphased Genotypes

We used composite genotypic disequilibrium (CGD)^50–52 to study LD between loci separated by larger distances. We used the high-density human genetic map⁴³ to define windows with similar recombinational sizes and then calculated CGD between each STRP and every SNP within 2 cM. We also calculated CGD between the SNP closest to each STRP and every SNP within 2 cM. This design allowed us to directly compare the decay of LD in STRP-SNP and SNP-SNP pairs.

Table 1 shows the fractions of significant tests (m₁/m) in different cM intervals, separated by repeat type. STRPs detected significant LD more often than did SNPs across most cM scales and populations. Consistent with patterns observed in the shorter-scale phased analyses, dinucleotides and trinucleotides showed stronger statistical significance than did tetranucleotides. Paired comparisons of STRP-SNP and SNP-SNP tests revealed similar results. STRP-SNP p values were significantly lower than SNP-SNP p values across the 2 cM intervals (Wilcoxon matched-pairs signed-rank test; p < 10⁻¹⁰ in all populations).