The effect that genotyping errors have on the robustness of common linkage-disequilibrium measures

The rapid development of a dense single-nucleotide-polymorphism marker map has stimulated numerous studies attempting to characterize the magnitude and distribution of background linkage disequilibrium (LD) within and between human populations. Although genotyping errors are an inherent problem in all LD studies, there have been few systematic investigations documenting their consequences on estimates of background LD. Therefore, we derived simple deterministic formulas to investigate the effect that genotyping errors have on four commonly used LD measures-D', r, Q, and d-in studies of background LD. We have found that genotyping error rates as small as 3% can have serious affects on these LD measures, depending on the allele frequencies and the assumed error model. Furthermore, we compared the robustness of D', r, Q, and d, in the presence of genotyping errors. In general, Q and d are more robust than D' and r, although exceptions do exist. Finally, through stochastic simulations, we illustrate how genotyping errors can lead to erroneous inferences when measures of LD between two samples are compared.     

Linkage disequilibrium for different scales and applications

Assessing the patterns of linkage disequilibrium (LD) has become an important issue in both evolutionary biology and medical genetics since the rapid accumulation of densely spaced DNA sequence variation data in several organisms. LD deals with the correlation of genetic variation at two or more loci or sites in the genome within a given population. There are a variety of LD measures which range from traditional pairwise LD measures such as D' or r2 to entropy-based multi-locus measures or haplotype-specific approaches. Understanding the evolutionary forces (in particular recombination) that generate the observed variation of LD patterns across genomic regions is addressed by model-based LD analysis. Marker type and its allelic composition also influence the observed LD pattern, microsatellites having a greater power to detect LD in population isolates than SNPs. This review aims to explain basic LD measures and their application properties.     

Haplotype diversity in 11 candidate genes across four populations

Analysis of haplotypes based on multiple single-nucleotide polymorphisms (SNP) is becoming common for both candidate gene and fine-mapping studies. Before embarking on studies of haplotypes from genetically distinct populations, however, it is important to consider variation both in linkage disequilibrium (LD) and in haplotype frequencies within and across populations, as both vary. Such diversity will influence the choice of "tagging" SNPs for candidate gene or whole-genome association studies because some markers will not be polymorphic in all samples and some haplotypes will be poorly represented or completely absent. Here we analyze 11 genes, originally chosen as candidate genes for oral clefts, where multiple markers were genotyped on individuals from four populations. Estimated haplotype frequencies, measures of pairwise LD, and genetic diversity were computed for 135 European-Americans, 57 Chinese-Singaporeans, 45 Malay-Singaporeans, and 46 Indian-Singaporeans. Patterns of pairwise LD were compared across these four populations and haplotype frequencies were used to assess genetic variation. Although these populations are fairly similar in allele frequencies and overall patterns of LD, both haplotype frequencies and genetic diversity varied significantly across populations. Such haplotype diversity has implications for designing studies of association involving samples from genetically distinct populations.     

The estimator of the optimal measure of allelic association: mean, variance and probability distribution when the sample size tends to infinity

The allelic association or linkage disequilibrium between two loci is a parameter of fundamental interest in modern population genetics for evolutionary inference and association mapping studies. Among the many measures available, the optimal measure of allelic association rho presents a strong evolutionary theory basis and is modeled on the physical distance along the chromosome with the Malécot equation for isolation by distance. Moreover, rho is equal to the absolute value of D', the standardized measure of gametic disequilibrium. We studied here the statistical properties of the rho sample estimator. We derived its asymptotic probability distribution and showed that it is neither asymptotically normal nor unbiased when rho=0 or when allelic frequencies are equal at both loci, in contrast to previous claims. This asymptotic study leads to propose a new test for absence of linkage disequilibrium. We compared it to Pearson's Chi2 test for independence in a contingency table and showed by simulations that the range in power of these two tests depends on the sign of D'. The new test outperformed slightly the Chi2 test, when D', polarized with respect to major alleles, is negative. Finally, we derived the asymptotic bias and information of the rho estimator that are due to the experimental sampling and showed by simulation that its bias is large in small samples. The consequences of these findings on applications using the rho measure are then discussed in particular for constructing LD unit maps, and call for a revised statistical treatment.     

Equilibrium processes cannot explain high levels of short- and medium-range linkage disequilibrium in the domesticated grass Sorghum bicolor

Patterns of linkage disequilibrium (LD) are of interest because they provide evidence of both equilibrium (e.g., mating system or long-term population structure) and nonequilibrium (e.g., demographic or selective) processes, as well as because of their importance in strategies for identifying the genetic basis of complex phenotypes. We report patterns of short and medium range (up to 100 kb) LD in six unlinked genomic regions in the partially selfing domesticated grass, Sorghum bicolor. The extent of allelic associations in S. bicolor, as assessed by pairwise measures of LD, is higher than in maize but lower than in Arabidopsis, in qualitative agreement with expectations based on mating system. Quantitative analyses of the population recombination parameter, rho, however, based on empirical estimates of rates of recombination, mutation, and self-pollination, show that LD is more extensive than expected under a neutral equilibrium model. The disparity between rho and the population mutation parameter, , is similar to that observed in other species whose population history appears to be complex. From a practical standpoint, these results suggest that S. bicolor is well suited for association studies using reasonable numbers of markers, since LD typically extends at least several kilobases but has largely decayed by 15 kb.     

Linkage disequilibrium between STRPs and SNPs across the human genome

Patterns of linkage disequilibrium (LD) reveal the action of evolutionary processes and provide crucial information for association mapping of disease genes. Although recent studies have described the landscape of LD among single nucleotide polymorphisms (SNPs) from across the human genome, associations involving other classes of molecular variation remain poorly understood. In addition to recombination and population history, mutation rate and process are expected to shape LD. To test this idea, we measured associations between short-tandem-repeat polymorphisms (STRPs), which can mutate rapidly and recurrently, and SNPs in 721 regions across the human genome. We directly compared STRP-SNP LD with SNP-SNP LD from the same genomic regions in the human HapMap populations. The intensity of STRP-SNP LD, measured by the average of D', was reduced, consistent with the action of recurrent mutation. Nevertheless, a higher fraction of STRP-SNP pairs than SNP-SNP pairs showed significant LD, on both short (up to 50 kb) and long (cM) scales. These results reveal the substantial effects of mutational processes on LD at STRPs and provide important measures of the potential of STRPs for association mapping of disease genes.     

Characterizing linkage disequilibrium in pig populations

Knowledge of the extent and range of linkage disequilibrium (LD), defined as non-random association of alleles at two or more loci, in animal populations is extremely valuable in localizing genes affecting quantitative traits, identifying chromosomal regions under selection, studying population history, and characterizing/managing genetic resources and diversity. Two commonly used LD measures, r(2) and D', and their permutation based adjustments, were evaluated using genotypes of more than 6,000 pigs from six commercial lines (two terminal sire lines and four maternal lines) at ~4,500 autosomal SNPs (single nucleotide polymorphisms). The results indicated that permutation only partially removed the dependency of D' on allele frequency and that r(2) is a considerably more robust LD measure. The maximum r(2) was derived as a function of allele frequency. Using the same genotype dataset, the extent of LD in these pig populations was estimated for all possible syntenic SNP pairs using r(2) and the ratio of r(2) over its theoretical maximum. As expected, the extent of LD highest for SNP pairs was found in tightest linkage and decreased as their map distance increased. The level of LD found in these pig populations appears to be lower than previously implied in several other studies using microsatellite genotype data. For all pairs of SNPs approximately 3 centiMorgan (cM) apart, the average r(2) was equal to 0.1. Based on the average population-wise LD found in these six commercial pig lines, we recommend a spacing of 0.1 to 1 cM for a whole genome association study in pig populations.     

Linkage disequilibrium and inference of ancestral recombination in 538 single-nucleotide polymorphism clusters across the human genome

The prospect of using linkage disequilibrium (LD) for fine-scale mapping in humans has attracted considerable attention, and, during the validation of a set of single-nucleotide polymorphisms (SNPs) for linkage analysis, a set of data for 4,833 SNPs in 538 clusters was produced that provides a rich picture of local attributes of LD across the genome. LD estimates may be biased depending on the means by which SNPs are first identified, and a particular problem of ascertainment bias arises when SNPs identified in small heterogeneous panels are subsequently typed in larger population samples. Understanding and correcting ascertainment bias is essential for a useful quantitative assessment of the landscape of LD across the human genome. Heterogeneity in the population recombination rate, rho=4Nr, along the genome reflects how variable the density of markers will have to be for optimal coverage. We find that ascertainment-corrected rho varies along the genome by more than two orders of magnitude, implying great differences in the recombinational history of different portions of our genome. The distribution of rho is unimodal, and we show that this is compatible with a wide range of mixtures of hotspots in a background of variable recombination rate. Although rho is significantly correlated across the three population samples, some regions of the genome exhibit population-specific spikes or troughs in rho that are too large to be explained by sampling. This result is consistent with differences in the genealogical depth of local genomic regions, a finding that has direct bearing on the design and utility of LD mapping and on the National Institutes of Health HapMap project.     

The distribution of long range admixture linkage disequilibrium in an African-American population

OBJECTIVES: To better understand the effect of admixture on long range linkage disequilibrium (LD), we characterized extended LD in gene-rich regions of an African-American population. METHODS: Approximately 290 cM of chromosomes 1, 3, 6, 11-17, 20 and 22 were scanned using 109 polymorphic microsatellite markers spaced an average of 3 cM apart. Disequilibrium between loci (D') was based on maximum-likelihood estimates of haplotype frequencies computed for 200 unrelated African Americans. RESULTS: Mean D' values were highest on chromosomes 6p23-p21.3 (D' = 0.33) and 15p22.2-p25.3 (D' = 0.34), and lowest on chromosome 12p11.2-q14 (D' = 0.21). Overall, the variance in LD among chromosomes accounted for approximately two-thirds of the total LD variance. Of the 434 locus pairs spaced between 0.3 and 38.7 cM apart, there was no detectable correlation between LD and recombination distance and a weak negative correlation between LD and physical distance (r(s) = -0.12; p = 0.031). For the 192 intrachromosomal locus pairs where allele frequency data were available from the Centre d'Etude du Polymorphisme humain (CEPH), we found a statistically significant positive correlation between LD and the allelic frequency differences (delta) between the African-American study population and Caucasian reference CEPH population (r(s) = 0.53; p < 0.0001). The correlation between LD and both recombination and physical distance was markedly increased for locus pairs with high delta levels. CONCLUSIONS: Our results suggest that recent Caucasian admixture maintains a high level of long range LD in African Americans on a genomic scale, and selected markers with large African American/Caucasian delta levels may be useful in association studies.     

Increased level of linkage disequilibrium in rural compared with urban communities: a factor to consider in association-study design

Few studies have investigated genetic differentiation within nonisolate European populations, despite the initiation of large national sample collections such as U.K. Biobank. Here, we used short tandem repeat markers to explore fine-scale genetic structure and to examine the extent of linkage disequilibrium (LD) within national subpopulations. We studied 955 unrelated individuals of local ancestry from nine Scottish rural regions and the urban center of Edinburgh, as well as 96 unrelated individuals from the general U.K. population. Despite little overall differentiation on the basis of allele frequencies, there were clear differences among subpopulations in the extent of pairwise LD, measured between a subset of X-linked markers, that reflected presumed differences in the depths of the underlying genealogies within these subpopulations. Therefore, there are strategic advantages in studying rural subpopulations, in terms of increased power and reduced cost, that are lost by sampling across regions or within urban populations. Similar rural-urban contrasts are likely to exist in many other populations with stable rural subpopulations, which could influence the design of genetic association studies and national biobank data collections.     

Linkage disequilibrium across two different single-nucleotide polymorphism genome scans

Linkage disequilibrium (LD) content was calculated for the Genetic Analysis Workshop 14 Affymetrix and Illumina single-nucleotide polymorphism (SNP) genome scans of the Collaborative Study on the Genetics of Alcoholism samples. Pair-wise LD was measured as both D' and r2 on 505 pedigree founder individuals. The r2 estimates were then used to correct the multipoint identity by descent matrix (MIBD) calculation to account for LD and LOD scores on chromosomes 3 and 18 were calculated for COGA's ttdt3 electrophysiological trait using those MIBDs. Extensive LD was observed throughout both marker sets, and it was higher in Affymetrix's more dense SNP map. However, SNP density did not solely account for Affymetrix's higher LD. MIBD estimation procedures assume linkage equilibrium to construct genotypes of non-genotyped pedigree founder individuals, and dense SNP genotyping maps are likely to contain moderate to high LD between markers. LOD score plots calculated after correction for LD followed the same general pattern as uncorrected ones. Since in our study almost half of the pedigree founders were genotyped, it is possible that LD had a minor impact on the LOD scores. Caution should probably be taken when using high density SNP maps when many non-genotyped founders are present in the study pedigrees.     

Linkage disequilibrium in domestic sheep

The last decade has seen a dramatic increase in the number of livestock QTL mapping studies. The next challenge awaiting livestock geneticists is to determine the actual genes responsible for variation of economically important traits. With the advent of high density single nucleotide polymorphism (SNP) maps, it may be possible to fine map genes by exploiting linkage disequilibrium between genes of interest and adjacent markers. However, the extent of linkage disequilibrium (LD) is generally unknown for livestock populations. In this article microsatellite genotype data are used to assess the extent of LD in two populations of domestic sheep. High levels of LD were found to extend for tens of centimorgans and declined as a function of marker distance. However, LD was also frequently observed between unlinked markers. The prospects for LD mapping in livestock appear encouraging provided that type I error can be minimized. Properties of the multiallelic LD coefficient D' were also explored. D' was found to be significantly related to marker heterozygosity, although the relationship did not appear to unduly influence the overall conclusions. Of potentially greater concern was the observation that D' may be skewed when rare alleles are present. It is recommended that the statistical significance of LD is used in conjunction with coefficients such as D' to determine the true extent of LD.     

Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing

OBJECTIVES: Describe the inflation in nonparametric multipoint LOD scores due to inter-marker linkage disequilibrium (LD) across many markers with varied allele frequencies. METHOD: Using simulated two-generation families with and without parents, we conducted nonparametric multipoint linkage analysis with 2 to 10 markers with minor allele frequencies (MAF) of 0.5 and 0.1. RESULTS: Misspecification of population haplotype frequencies by assuming linkage equilibrium caused inflated multipoint LOD scores due to inter-marker LD when parental genotypes were not included. Inflation increased as more markers in LD were included and decreased as markers in equilibrium were added. When marker allele frequencies were unequal, the r2 measure of LD was a better predictor of inflation than D'. CONCLUSION: This observation strongly supports the evaluation of LD in multipoint linkage analyses, and further suggests that unaccounted for LD may be suspected when two-point and multipoint linkage analyses show a marked disparity in regions with elevated r2 measures of LD. Given the increasing popularity of high-density genome-wide SNP screens, inter-marker LD should be a concern in future linkage studies.     

Marker-inferred relatedness as a tool for detecting heritability in nature

This paper presents a perspective of how inferred relatedness, based on genetic marker data such as microsatellites or amplified fragment length polymorphisms (AFLPs), can be used to demonstrate quantitative genetic variation in natural populations. Variation at two levels is considered: among pairs of individuals within populations, and among pairs of subpopulations within a population. In the former, inferred pairwise relatedness, combined with trait measures, allow estimates of heritability 'in the wild'. In the latter, estimates of QST are obtained, in the absence of known heritabilities, via estimates of pairwise FST. Estimators of relatedness based on the 'Kronecker operator' are given. Both methods require actual variation of relationship, a rarely studied aspect of population structure, and not necessarily present. Some conditions for appropriate population structures in the wild are identified, in part through a review of recent studies.     

Linkage disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle

When a genetic marker and a quantitative trait locus (QTL) are in linkage disequilibrium (LD) in one population, they may not be in LD in another population or their LD phase may be reversed. The objectives of this study were to compare the extent of LD and the persistence of LD phase across multiple cattle populations. LD measures r and r(2) were calculated for syntenic marker pairs using genomewide single-nucleotide polymorphisms (SNP) that were genotyped in Dutch and Australian Holstein-Friesian (HF) bulls, Australian Angus cattle, and New Zealand Friesian and Jersey cows. Average r(2) was approximately 0.35, 0.25, 0.22, 0.14, and 0.06 at marker distances 10, 20, 40, 100, and 1000 kb, respectively, which indicates that genomic selection within cattle breeds with r(2) >or= 0.20 between adjacent markers would require approximately 50,000 SNPs. The correlation of r values between populations for the same marker pairs was close to 1 for pairs of very close markers (<10 kb) and decreased with increasing marker distance and the extent of divergence between the populations. To find markers that are in LD with QTL across diverged breeds, such as HF, Jersey, and Angus, would require approximately 300,000 markers.     

The heterogeneous levels of linkage disequilibrium in white spruce genes and comparative analysis with other conifers

In plants, knowledge about linkage disequilibrium (LD) is relevant for the design of efficient single-nucleotide polymorphism arrays in relation to their use in population and association genomics studies. Previous studies of conifer genes have shown LD to decay rapidly within gene limits, but exceptions have been reported. To evaluate the extent of heterogeneity of LD among conifer genes and its potential causes, we examined LD in 105 genes of white spruce (Picea glauca) by sequencing a panel of 48 haploid megagametophytes from natural populations and further compared it with LD in other conifer species. The average pairwise r(2) value was 0.19 (s.d.=0.19), and LD dropped quickly with a half-decay being reached at a distance of 65 nucleotides between sites. However, LD was significantly heterogeneous among genes. A first group of 29 genes had stronger LD (mean r(2)=0.28), and a second group of 38 genes had weaker LD (mean r(2)=0.12). While a strong relationship was found with the recombination rate, there was no obvious relationship between LD and functional classification. The level of nucleotide diversity, which was highly heterogeneous across genes, was also not significantly correlated with LD. A search for selection signatures highlighted significant deviations from the standard neutral model, which could be mostly attributed to recent demographic changes. Little evidence was seen for hitchhiking and clear relationships with LD. When compared among conifer species, on average, levels of LD were similar in genes from white spruce, Norway spruce and Scots pine, whereas loblolly pine and Douglas fir genes exhibited a significantly higher LD.     

Fine-scale map of encyclopedia of DNA elements regions in the Korean population

The International HapMap Project aims to generate detailed human genome variation maps by densely genotyping single-nucleotide polymorphisms (SNPs) in CEPH, Chinese, Japanese, and Yoruba samples. This will undoubtedly become an important facility for genetic studies of diseases and complex traits in the four populations. To address how the genetic information contained in such variation maps is transferable to other populations, the Korean government, industries, and academics have launched the Korean HapMap project to genotype high-density Encyclopedia of DNA Elements (ENCODE) regions in 90 Korean individuals. Here we show that the LD pattern, block structure, haplotype diversity, and recombination rate are highly concordant between Korean and the two HapMap Asian samples, particularly Japanese. The availability of information from both Chinese and Japanese samples helps to predict more accurately the possible performance of HapMap markers in Korean disease-gene studies. Tagging SNPs selected from the two HapMap Asian maps, especially the Japanese map, were shown to be very effective for Korean samples. These results demonstrate that the HapMap variation maps are robust in related populations and will serve as an important resource for the studies of the Korean population in particular.     

Associations between heterozygosity and morphological variance

Recent studies have contrasted the expression of phenotypic traits, such as variance in morphological characters, with levels of genetic variation (heterozygosity) as determined by electrophoretic analysis of protein-coding loci. The theoretical basis for interpreting significant covariation stems in part from Lerner's work on genetic homeostasis, which predicts that within populations increased heterozygosity will produce decreased morphological variance, owing to a buffering effect of heterosis during development. However, the prediction for the relationship between genic heterozygosity and the variance of morphological traits among populations is unclear. To determine if a relationship existed between heterozygosity and morphological variance, we compared estimates of heterozygosity and morphological variance across 15 population samples of the fox sparrow and 17 samples of the pocket gopher. The estimates of morphological variance included coefficients of variation for each character and the variance of individual scores about the population mean in a principal components analysis. Although several recent studies have reported a significant relationship between heterozygosity and morphological variance, we found that the two measures do not covary significantly.