The structure of linkage disequilibrium around a selective sweep

The fixation of advantageous mutations by natural selection has a profound impact on patterns of linked neutral variation. While it has long been appreciated that such selective sweeps influence the frequency spectrum of nearby polymorphism, it has only recently become clear that they also have dramatic effects on local linkage disequilibrium. By extending previous results on the relationship between genealogical structure and linkage disequilibrium, I obtain simple expressions for the influence of a selective sweep on patterns of allelic association. I show that sweeps can increase, decrease, or even eliminate linkage disequilibrium (LD) entirely depending on the relative position of the selected and neutral loci. I also show the importance of the age of the neutral mutations in predicting their degree of association and describe the consequences of such results for the interpretation of empirical data. In particular, I demonstrate that while selective sweeps can eliminate LD, they generate patterns of genetic variation very different from those expected from recombination hotspots.     

The extent and distribution of linkage disequilibrium in a multi-hierarchic outbred canine pedigree

A canine integrated linkage-radiation map has been recently constructed by using microsatellite markers. This map, with a good coverage of the canine genome, allows for a genome-wide search for the extent and distribution of linkage disequilibrium derived from linkage and evolutionary forces. In this study, we genotyped an outbred pedigree between Labrador retriever and Greyhound breeds with a set of microsatellite markers (240) from the canine linkage map. Linkage disequilibrium was measured between all syntenic and nonsyntenic marker pairs. Analysis of syntenic pairs revealed a significant correlation (–0.229, P < 0.001) between linkage disequilibrium and genetic distance (log transformed). Significant linkage disequilibria were observed more frequently between syntenic pairs spaced <40 cM than those paced >40 cM. There is a clear trend for linkage disequilibrium to decline with marker distance. From our results, a genome-wide screen with markers at low to moderate density (1–2 per 10 cM) should take full advantage of linkage disequilibrium for quantitative trait locus mapping in dogs. This study supports the appropriateness of linkage disequilibrium analysis to detect and map quantitative trait loci underlying complex traits in dogs.     

Accuracy of haplotype estimation in a region of low linkage disequilibrium

We compared the accuracy of haplotype inferences at a 6 Mb region on chromosome 7 where significant linkage between a brain oscillation phenotype and a cholinergic muscarinic receptor gene was previously reported. Individual haplotype assignments and haplotype frequencies were estimated using 5, 10, and 14 consecutive Illumina single-nucleotide polymorphisms (SNPs) within the 1-LOD unit support interval of the chromosome 7 linkage peak. Initially, haplotypes were constructed incorporating phase information provided by relatives using the pedigree analysis package MERLIN. Population-based haplotypes were inferred using the haplotype estimation software HAPLO.STATS and PHASE, using unrelated individuals. The 14 SNPs within this region exhibited markedly low linkage disequilibrium, and the average D' estimate between SNPs was 0.18 (range: 0.01-0.97). In comparison to the family-based haplotypes calculated in MERLIN, the computational inferences of individual haplotype assignments were most accurate when considering 5 consecutive SNPs, but decayed dramatically when considering 10 or 14 SNPs in both PHASE and HAPLO.STATS. When comparing the two haplotype inference methods, both PHASE and HAPLO.STATS performed poorly. These analyses underscore the difficulties of haplotype estimation in the presence of low linkage disequilibrium and stress the importance of careful consideration of confidence measures when using estimated haplotype frequencies and individual assignments in biomedical research.     

Efficient mining of haplotype patterns for linkage disequilibrium mapping

Effective identification of disease-causing gene locations can have significant impact on patient management decisions that will ultimately increase survival rates and improve the overall quality of health care. Linkage disequilibrium mapping is the process of finding disease gene locations through comparisons of haplotype frequencies between disease chromosomes and normal chromosomes. This work presents a new method for linkage disequilibrium mapping. The main advantage of the proposed algorithm, called LinkageTracker, is its consistency in producing good predictive accuracy under different conditions, including extreme conditions where the occurrence of disease samples with the mutation of interest is very low and there is presence of error or noise. We compared our method with some leading methods in linkage disequilibrium mapping such as HapMiner, Blade, GeneRecon, and Haplotype Pattern Mining (HPM). Experimental results show that for a substantial class of problems, our method has good predictive accuracy while taking reasonably short processing time. Furthermore, LinkageTracker does not require any population ancestry information about the disease and the genealogy of the haplotypes. Therefore, it is useful for linkage disequilibrium mapping when the users do not have such information about their datasets.     

Entropy as a measure for linkage disequilibrium over multilocus haplotype blocks

OBJECTIVE: The presence of linkage disequilibrium (LD) forms the basis for a range of uses, including the fine-mapping of diseases and studies on human genealogy. Recent findings indicate that single nucleotide polymorphisms (SNP) can occur in blocks of limited haplotypic diversity with high degrees of LD. Commonly used measures for LD, such as r(2) and D', consider only two loci and might miss information to appropriately describe LD in larger haplotypic structures. METHODS: We introduce the Normalized Entropy Difference, epsilon, as a new multilocus measure for LD. A related quantity, deltaS, provides an approximate chi(2) test for the significance of LD. The ability of the measure to detect haplotype blocks is investigated using simulated data sets as well as a real data set previously analyzed by Daly et al. (2001). RESULTS: epsilon allows for arbitrary numbers of loci, describes LD with regard to the loci sequence, and can be interpreted as a multilocus extension of r(2). The application of epsilon to the data sets demonstrated the measure's ability to appropriately describe simultaneous multilocus LD and to detect haplotype blocks. CONCLUSIONS: epsilon is a reasonable multilocus LD measure and might be of potential use in the construction of the human haplotype map.     

Assessment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping.

Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.     

The influence of gene conversion on linkage disequilibrium around a selective sweep

In a 2007 article, McVean studied the effect of recombination on linkage disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep. The results demonstrated that two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. In this article, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep.     

Plotting haplotype-specific linkage disequilibrium patterns by extended haplotype homozygosity

Association studies may request more details of a specific haplotype. Haplotype-specific decay of linkage disequilibrium is such a crucial and versatile characteristic. It may be used, e.g. to search for signals of natural selection in a risk haplotype. Here, we present a web-based tool to explore the relationship between population frequency and extended linkage disequilibrium measured as haplotype homozygosity of observed haplotypes within a specified candidate region. AVAILABILITY: The web-tool is available at http://ihg.gsf.de/cgi-bin/mueller/webehh.pl     

Patterns of linkage disequilibrium and haplotype distribution in disease candidate genes

Background

The adequacy of association studies for complex diseases depends critically on the existence of linkage disequilibrium (LD) between functional alleles and surrounding SNP markers.

Results

We examined the patterns of LD and haplotype distribution in eight candidate genes for osteoporosis and/or obesity using 31 SNPs in 1,873 subjects. These eight genes are apolipoprotein E (APOE), type I collagen α1 (COL1A1), estrogen receptor-α (ER-α), leptin receptor (LEPR), parathyroid hormone (PTH)/PTH-related peptide receptor type 1 (PTHR1), transforming growth factor-β1 (TGF-β1), uncoupling protein 3 (UCP3), and vitamin D (1,25-dihydroxyvitamin D₃) receptor (VDR). Yin yang haplotypes, two high-frequency haplotypes composed of completely mismatching SNP alleles, were examined. To quantify LD patterns, two common measures of LD, D' and r², were calculated for the SNPs within the genes. The haplotype distribution varied in the different genes. Yin yang haplotypes were observed only in PTHR1 and UCP3. D' ranged from 0.020 to 1.000 with the average of 0.475, whereas the average r² was 0.158 (ranging from 0.000 to 0.883). A decay of LD was observed as the intermarker distance increased, however, there was a great difference in LD characteristics of different genes or even in different regions within gene.

Conclusion

The differences in haplotype distributions and LD patterns among the genes underscore the importance of characterizing genomic regions of interest prior to association studies.     

The extent of linkage disequilibrium in four populations with distinct demographic histories

The design and feasibility of whole-genome-association studies are critically dependent on the extent of linkage disequilibrium (LD) between markers. Although there has been extensive theoretical discussion of this, few empirical data exist. The authors have determined the extent of LD among 38 biallelic markers with minor allele frequencies >.1, since these are most comparable to the common disease-susceptibility polymorphisms that association studies aim to detect. The markers come from three chromosomal regions-1,335 kb on chromosome 13q12-13, 380 kb on chromosome 19q13.2, and 120 kb on chromosome 22q13.3-which have been extensively mapped. These markers were examined in approximately 1,600 individuals from four populations, all of European origin but with different demographic histories; Afrikaners, Ashkenazim, Finns, and East Anglian British. There are few differences, either in allele frequencies or in LD, among the populations studied. A similar inverse relationship was found between LD and distance in each genomic region and in each population. Mean D' is.68 for marker pairs <5 kb apart and is.24 for pairs separated by 10-20 kb, and the level of LD is not different from that seen in unlinked marker pairs separated by >500 kb. However, only 50% of marker pairs at distances <5 kb display sufficient LD (delta>.3) to be useful in association studies. Results of the present study, if representative of the whole genome, suggest that a whole-genome scan searching for common disease-susceptibility alleles would require markers spaced < or = 5 kb apart.     

Measuring the extent of linkage disequilibrium in commercial pig populations

To evaluate the extent of linkage disequilibrium in domestic pigs, we genotyped 33 and 44 unrelated individuals from two commercial populations for 29 and five microsatellite markers located on chromosomes 15 and 2 respectively. A high proportion of marker pairs up to 40 cM apart exhibited significant linkage disequilibrium in both populations. Pair-wise r(2) values averaged between 0.15 and 0.50 (depending on chromosome and population) for markers <1 cM apart and declined to values of 0.05 for more distant syntenic markers. Our results suggest that both populations underwent a bottleneck approximately 20 generations ago, which reduced the effective population size from thousands to <200 animals.     

Assessing the performance of the haplotype block model of linkage disequilibrium

Several recent studies have suggested that linkage disequilibrium (LD) in the human genome has a fundamentally "blocklike" structure. However, thus far there has been little formal assessment of how well the haplotype block model captures the underlying structure of LD. Here we propose quantitative criteria for assessing how blocklike LD is and apply these criteria to both real and simulated data. Analyses of several large data sets indicate that real data show a partial fit to the haplotype block model; some regions conform quite well, whereas others do not. Some improvement could be obtained by genotyping higher marker densities but not by increasing the number of samples. Nonetheless, although the real data are only moderately blocklike, our simulations indicate that, under a model of uniform recombination, the structure of LD would actually fit the block model much less well. Simulations of a model in which much of the recombination occurs in narrow hotspots provide a much better fit to the observed patterns of LD, suggesting that there is extensive fine-scale variation in recombination rates across the human genome.     

A haplotype and linkage disequilibrium analysis of the hereditary hemochromatosis gene region

Hereditary hemochromatosis is a recessive disease of iron metabolism widely distributed among people of European descent. Most patients have inherited the causative mutation from a single ancestor. In the course of cloning the hemochromatosis gene, genotypes were generated for these samples at 43 microsatellite repeat markers that span the 6.5-Mb hemochromatosis gene region. The data used to reconstruct the ancestral haplotype across the hemochromatosis gene region are presented in this paper. Portions of the ancestral haplotype were present on 85% of patient chromosomes in this sample and ranged in size from approximately 500 kb to greater than 6.5 Mb. Only one marker, D6S2239, was identical by descent on all of the patient chromosomes containing the ancestral mutation. In contrast, only 3 of the 128 control chromosomes, or 2.3%, carried the ancestral mutation and the surrounding ancestral haplotype. To test new methods for gene finding using linkage disequilibrium we analyzed the genotypic data with a multilocus maximum likelihood method (DISMULT) and a single point method (DISLAMB), both written to analyze data generated from multi-allelic markers. The maximum value from DISLAMB analysis occurred at marker D6S2239, which is less than 20 kb from the hemochromatosis gene HFE, consistent with the haplotype analysis. The peak of the multi-point analysis was 700 kb from HFE, possibly due to the nonuniform recombination rates within this large region. The recombination rate appears to be lower than expected centromeric of the HFE gene. Received: 10 June 1997 / Accepted: 4 December 1997     

Accounting for decay of linkage disequilibrium in haplotype inference and missing-data imputation

Although many algorithms exist for estimating haplotypes from genotype data, none of them take full account of both the decay of linkage disequilibrium (LD) with distance and the order and spacing of genotyped markers. Here, we describe an algorithm that does take these factors into account, using a flexible model for the decay of LD with distance that can handle both "blocklike" and "nonblocklike" patterns of LD. We compare the accuracy of this approach with a range of other available algorithms in three ways: for reconstruction of randomly paired, molecularly determined male X chromosome haplotypes; for reconstruction of haplotypes obtained from trios in an autosomal region; and for estimation of missing genotypes in 50 autosomal genes that have been completely resequenced in 24 African Americans and 23 individuals of European descent. For the autosomal data sets, our new approach clearly outperforms the best available methods, whereas its accuracy in inferring the X chromosome haplotypes is only slightly superior. For estimation of missing genotypes, our method performed slightly better when the two subsamples were combined than when they were analyzed separately, which illustrates its robustness to population stratification. Our method is implemented in the software package PHASE (v2.1.1), available from the Stephens Lab Web site.     

The extent of linkage disequilibrium in beef cattle breeds using high-density SNP genotypes

Background

The extent of linkage disequilibrium (LD) between molecular markers impacts genome-wide association studies and implementation of genomic selection. The availability of high-density single nucleotide polymorphism (SNP) genotyping platforms makes it possible to investigate LD at an unprecedented resolution. In this work, we characterised LD decay in breeds of beef cattle of taurine, indicine and composite origins and explored its variation across autosomes and the X chromosome.

Findings

In each breed, LD decayed rapidly and r² was less than 0.2 for marker pairs separated by 50 kb. The LD decay curves clustered into three groups of similar LD decay that distinguished the three main cattle types. At short distances between markers (< 10 kb), taurine breeds showed higher LD (r² = 0.45) than their indicine (r² = 0.25) and composite (r² = 0.32) counterparts. This higher LD in taurine breeds was attributed to a smaller effective population size and a stronger bottleneck during breed formation. Using all SNPs on only the X chromosome, the three cattle types could still be distinguished. However for taurine breeds, the LD decay on the X chromosome was much faster and the background level much lower than for indicine breeds and composite populations. When using only SNPs that were polymorphic in all breeds, the analysis of the X chromosome mimicked that of the autosomes.

Conclusions

The pattern of LD mirrored some aspects of the history of breed populations and showed a sharp decay with increasing physical distance between markers. We conclude that the availability of the HD chip can be used to detect association signals that remained hidden when using lower density genotyping platforms, since LD dropped below 0.2 at distances of 50 kb.     

Comparison of linkage disequilibrium and haplotype diversity on macro- and microchromosomes in chicken

Background

Toll like receptors (TLR) play the central role in the recognition of pathogen associated molecular patterns (PAMPs). Mutations in the TLR1, TLR2 and TLR4 genes may change the ability to recognize PAMPs and cause altered responsiveness to the bacterial pathogens.

Results

The study presents association between TLR gene mutations and increased susceptibility to Mycobacterium avium subsp. paratuberculosis (MAP) infection. Novel mutations in TLR genes (TLR1- Ser150Gly and Val220Met; TLR2 – Phe670Leu) were statistically correlated with the hindrance in recognition of MAP legends. This correlation was confirmed subsequently by measuring the expression levels of cytokines (IL-4, IL-8, IL-10, IL-12 and IFN-γ) in the mutant and wild type moDCs (mocyte derived dendritic cells) after challenge with MAP cell lysate or LPS. Further in silico analysis of the TLR1 and TLR4 ectodomains (ECD) revealed the polymorphic nature of the central ECD and irregularities in the central LRR (leucine rich repeat) motifs.

Conclusion

The most critical positions that may alter the pathogen recognition ability of TLR were: the 9^th amino acid position in LRR motif (TLR1–LRR10) and 4^th residue downstream to LRR domain (exta-LRR region of TLR4). The study describes novel mutations in the TLRs and presents their association with the MAP infection.     

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

The extent of linkage disequilibrium caused by selection on G6PD in humans

The gene coding for glucose-6-phosphate dehydrogenase (G6PD) is subject to positive selection by malaria in some human populations. The G6PD A- allele, which is common in sub-Saharan Africa, is associated with deficient enzyme activity and protection from severe malaria. To delimit the impact of selection on patterns of linkage disequilibrium (LD) and nucleotide diversity, we resequenced 5.1 kb at G6PD and approximately 2-3 kb at each of eight loci in a 2.5-Mb region roughly centered on G6PD in a diverse sub-Saharan African panel of 51 unrelated men (including 20 G6PD A-, 11 G6PD A+, and 20 G6PD B chromosomes). The signature of selection is evident in the absence of genetic variation at G6PD and at three neighboring loci within 0.9 Mb from G6PD among all individuals bearing G6PD A- alleles. A genomic region of approximately 1.6 Mb around G6PD was characterized by long-range LD associated with the A- alleles. These patterns of nucleotide variability and LD suggest that G6PD A- is younger than previous age estimates and has increased in frequency in sub-Saharan Africa due to strong selection (0.1 < s < 0.2). These results also show that selection can lead to nonrandom associations among SNPs over great physical and genetic distances, even in African populations.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.