The detection of linkage disequilibrium between closely linked markers: RFLPs at the AI-CIII apolipoprotein genes.

Study of very closely linked DNA variants at various loci has frequently shown linkage disequilibrium. We studied three closely linked RFLPs at the apolipoprotein AI-CIII locus. Two variants detected by MspI and SstI were in strong linkage disequilibrium; but when conventional statistical tests were used, a third variant (PstI), located between the MspI and SstI markers, appeared to be in linkage equilibrium with these two "outside" markers. Similar discrepancies from the expected monotone relationship between physical distance and linkage disequilibrium have been reported by others. To investigate these discrepancies, the power to detect linkage disequilibrium was calculated. It could be shown that, for the gene frequencies encountered, very large sample sizes would be required to demonstrate negative (i.e., repulsion-phase) linkage disequilibrium. Such numbers are usually very difficult to attain in human studies. Failure to demonstrate linkage disequilibrium by conventional methods therefore does not imply its absence. Appropriate nomograms and tables are provided.     

Modeling linkage disequilibrium in natural populations: the example of the Soay sheep population of St. Kilda, Scotland

The use of linkage disequilibrium to localize the genes underlying quantitative traits has received considerable attention in the livestock genetics community over the past few years. This has resulted in the investigation of linkage disequilibrium structures of several domestic livestock populations to assess their potential use in fine-mapping efforts. However, the linkage disequilibrium structure of free-living populations has been less well investigated. As the direct evaluation of linkage disequilibrium can be both time consuming and expensive the use of simulations that include as many aspects of population history as possible is advocated as an alternative. A simulation of the linkage disequilibrium structure of the Soay sheep population of St. Kilda, Scotland, is provided as an example. The simulated population showed significant decline of linkage disequilibrium with genetic distance and low levels of background linkage disequilibrium, indicating that the Soay sheep population is a viable resource for linkage disequilibrium fine mapping of quantitative trait loci.     

On Models of Quantitative Genetic Variability: A Stabilizing Selection-Balance Model

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.     

Linkage analysis of human leukocyte antigen (HLA) markers in familial psoriasis: strong disequilibrium effects provide evidence for a major determinant in the HLA-B/-C region.

Although psoriasis is strongly associated with certain human leukocyte antigens (HLAs), evidence for linkage to HLA markers has been limited. The objectives of this study were (1) to provide more definitive evidence for linkage of psoriasis to HLA markers in multiplex families; (2) to compare the major HLA risk alleles in these families with those determined by previous case-control studies; and (3) to localize the gene more precisely. By applying the transmission/disequilibrium test (TDT) and parametric linkage analysis, we found evidence for linkage of psoriasis to HLA-C, -B, -DR, and -DQ, with HLA-B and -C yielding the most-significant results. Linkage was detectable by parametric methods only when marker-trait disequilibrium was considered. Case-control association tests and the TDT identified alleles belonging to the EH57.1 ancestral haplotype as the major risk alleles in our sample. Among individuals carrying recombinant ancestral haplotypes involving EH57. 1, the class I markers were retained selectively among affecteds four times more often than among unaffecteds; among the few affected individuals carrying only the class II alleles from the ancestral haplotype, all but one also carried Cw6. These data show that familial and "sporadic" psoriasis share the same risk alleles. They also illustrate that substantial parametric linkage information can be extracted by accounting for linkage disequilibrium. Finally, they strongly suggest that a major susceptibility gene resides near HLA-C.     

Does probabilistic modelling of linkage disequilibrium evolution improve the accuracy of QTL location in animal pedigree?

Background

Since 2001, the use of more and more dense maps has made researchers aware that combining linkage and linkage disequilibrium enhances the feasibility of fine-mapping genes of interest. So, various method types have been derived to include concepts of population genetics in the analyses. One major drawback of many of these methods is their computational cost, which is very significant when many markers are considered. Recent advances in technology, such as SNP genotyping, have made it possible to deal with huge amount of data. Thus the challenge that remains is to find accurate and efficient methods that are not too time consuming. The study reported here specifically focuses on the half-sib family animal design. Our objective was to determine whether modelling of linkage disequilibrium evolution improved the mapping accuracy of a quantitative trait locus of agricultural interest in these populations. We compared two methods of fine-mapping. The first one was an association analysis. In this method, we did not model linkage disequilibrium evolution. Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations. In the second method, the modelling of the evolution of population allele frequencies was derived from a Wright-Fisher model. We simulated a wide range of scenarios adapted to animal populations and compared these two methods for each scenario.

Results

Our results indicated that the improvement produced by probabilistic modelling of linkage disequilibrium evolution was not significant. Both methods led to similar results concerning the location accuracy of quantitative trait loci which appeared to be mainly improved by using four flanking markers instead of two.

Conclusions

Therefore, in animal half-sib designs, modelling linkage disequilibrium evolution using a Wright-Fisher model does not significantly improve the accuracy of the QTL location when compared to a simpler method assuming complete and constant linkage between the QTL and the marker alleles. Finally, given the high marker density available nowadays, the simpler method should be preferred as it gives accurate results in a reasonable computing time.     

Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM).

A population association has consistently been observed between insulin-dependent diabetes mellitus (IDDM) and the "class 1" alleles of the region of tandem-repeat DNA (5'' flanking polymorphism [5''FP]) adjacent to the insulin gene on chromosome 11p. This finding suggests that the insulin gene region contains a gene or genes contributing to IDDM susceptibility. However, several studies that have sought to show linkage with IDDM by testing for cosegregation in affected sib pairs have failed to find evidence for linkage. As means for identifying genes for complex diseases, both the association and the affected-sib-pairs approaches have limitations. It is well known that population association between a disease and a genetic marker can arise as an artifact of population structure, even in the absence of linkage. On the other hand, linkage studies with modest numbers of affected sib pairs may fail to detect linkage, especially if there is linkage heterogeneity. We consider an alternative method to test for linkage with a genetic marker when population association has been found. Using data from families with at least one affected child, we evaluate the transmission of the associated marker allele from a heterozygous parent to an affected offspring. This approach has been used by several investigators, but the statistical properties of the method as a test for linkage have not been investigated. In the present paper we describe the statistical basis for this "transmission test for linkage disequilibrium" (transmission/disequilibrium test [TDT]). We then show the relationship of this test to tests of cosegregation that are based on the proportion of haplotypes or genes identical by descent in affected sibs. The TDT provides strong evidence for linkage between the 5''FP and susceptibility to IDDM. The conclusions from this analysis apply in general to the study of disease associations, where genetic markers are usually closely linked to candidate genes. When a disease is found to be associated with such a marker, the TDT may detect linkage even when haplotype-sharing tests do not.     

Amino Acid Covariation in a Functionally Important Human Immunodeficiency Virus Type 1 Protein Region Is Associated With Population Subdivision

The frequently reported amino acid covariation of the highly polymorphic human immunodeficiency virus type 1 (HIV-1) exterior envelope glycoprotein V3 region has been assumed to reflect fitness epistasis between residues. However, nonrandom association of amino acids, or linkage disequilibrium, has many possible causes, including population subdivision. If the amino acids at a set of sequence sites differ in frequencies between subpopulations, then analysis of the whole population may reveal linkage disequilibrium even if it does not exist in any subpopulation. HIV-1 has a complex population structure, and the effects of this structure on linkage disequilibrium were investigated by estimating within- and among-subpopulation components of variance in linkage disequilibrium. The amino acid covariation previously reported is explained by differences in amino acid frequencies among virus subpopulations in different patients and by nonsystematic disequilibrium among patients. Disequilibrium within patients appears to be entirely due to differences in amino acid frequencies among sampling time points and among chemokine coreceptor usage phenotypes of virus particles, but not source tissues. Positive selection explains differences in allele frequencies among time points and phenotypes, indicating that these differences are adaptive rather than due to genetic drift. However, the absence of a correlation between linkage disequilibrium and phenotype suggests that fitness epistasis is an unlikely cause of disequilibrium. Indeed, when population structure is removed by analyzing sequences from a single time point and phenotype, no disequilibrium is detectable within patients. These results caution against interpreting amino acid covariation and coevolution as evidence for fitness epistasis.     

Linkage disequilibrium analyses and restriction mapping of four RFLPs at the proα2(I) collagen locus: lack of correlation between linkage disequilibrium and physical distance

Summary Restriction fragment length polymorphisms (RRLPs) located at short distances may demonstrate linkage disequilibrium. Under the assumption that the distances between the loci of the RFLPs are inversely related to the linkage disequilibria, gene order may be deduced. However, if the assumption is invalid, the results may be incorrect. We have studied four different DNA polymorphisms at the COLIA2 locus in 180 unrelated Norwegian individuals. Observed frequencies (presence/absence) for the different polymorphic sites were as follows: site A (EcoRI) 0.30/0.70, site B (MspI) 0.83/0.16, site C (StuI) 0.86/0.14, and site D (RsaI) 0.66/0.34. Of 16 possible haplotypes 12 were demonstrated, and 2 additional were deduced to be present. Restriction mapping of the four polymorphic sites gave the following order of the sites from the 5 to the 3 of the gene: A-D-B-C. Linkage disequilibrium was not found between the sites A and D; strong disequilibrium was found between sites A and C, and B and C; and less strong, between A and B, B and D, and C and D. Analysis of linkage disequilibrium coefficients between all pairs of loci demonstrated that there is no consistent relationship between linkage disequilibrium and physical distance (=-0.07). These results suggest that for a small region of the genome, factors such as deviating mutation rate and gene conversion may add significantly to rearrangements by recombination. Thus, a deduced gene order from linkage disequilibrium data has to be regarded with great caution.     

Significant linkage disequilibrium between the Huntington disease gene and the loci D4S10 and D4S95 in the Dutch population.

Significant linkage disequilibrium has been found between the Huntington disease (HD) gene and DNA markers located around D4S95 and D4S98. The linkage-disequilibrium studies favor the proximal location of the HD gene, in contrast to the conflicting results of recombination analyses. We have analyzed 45 Dutch HD families with 19 DNA markers and have calculated the strength of linkage disequilibrium. Highly significant linkage disequilibrium has been detected with D4S95, consistent with the studies in other populations. In contrast with most other studies, however, the area of linkage disequilibrium extends from D4S10 proximally to D4S95, covering 1,100 kb. These results confirm that the HD gene most likely maps near D4S95.     

Linkage disequilibrium for DNA haplotypes near the cystic fibrosis locus in two South European populations

Summary Three polymorphic DNA marker loci (INT1L1, D7S23 and D7S399) map to a chromosomal region that is very close to the cystic fibrosis (CF) locus in terms of genetic distance. These marker loci have been used to analyse the linkage disequilibrium in 137CF families from two South European countries (Italy and Spain). The markers can be analysed for differences in linkage disequilibrium more easily in these populations than in North Europeans, in whom the disequilibrium between the allelic systems defined by the probes and CF is much greater and on a plateau through the genetic region. The different levels of disequilibrium found in the studied populations suggest that D7S399 and D7S23 are both closer to CF than INT1L1, and provide additional information on the origins and homogeneity of the CF defect.     

A sibship test for linkage in the presence of association: the sib transmission/disequilibrium test.

Linkage analysis with genetic markers has been successful in the localization of genes for many monogenic human diseases. In studies of complex diseases, however, tests that rely on linkage disequilibrium (the simultaneous presence of linkage and association) are often more powerful than those that rely on linkage alone. This advantage is illustrated by the transmission/disequilibrium test (TDT). The TDT requires data (marker genotypes) for affected individuals and their parents; for some diseases, however, data from parents may be difficult or impossible to obtain. In this article, we describe a method, called the "sib TDT" (or "S-TDT"), that overcomes this problem by use of marker data from unaffected sibs instead of from parents, thus allowing application of the principle of the TDT to sibships without parental data. In a single collection of families, there might be some that can be analyzed only by the TDT and others that are suitable for analysis by the S-TDT. We show how all the data may be used jointly in one overall TDT-type procedure that tests for linkage in the presence of association. These extensions of the TDT will be valuable for the study of diseases of late onset, such as non-insulin-dependent diabetes, cardiovascular diseases, and other diseases associated with aging.     

Linkage disequilibrium in the human insulin/insulin-like growth factor II region of human chromosome II.

Caucasian (N = 128) and Chinese (N = 84) subjects were typed for RFLPs in the insulin (INS)/insulin-like growth factor II (IGF2) region of chromosome 11. Both the analysis of extended haplotypes and the pairwise measures of linkage disequilibrium among the RFLPs indicate that there is extensive linkage disequilibrium in the INS/IGF2 region. The disequilibrium extends across the hypervariable region (HVR) located just 5' to the INS gene and encompasses a region of at least 40 kbp. Previous studies had suggested that linkage disequilibrium in the INS region was negligible and that this region may therefore contain a "recombinational hotspot" (Chakravarti et al. 1986). However, results of this and another recent study (Thompson et al. 1988) highlight the importance of the frequencies of associated alleles in the ability to detect linkage disequilibrium. Thus, the previous failure to detect disequilibrium in the INS region may have reflected a lack of power, rather than a true absence of disequilibrium in this region.     

A locus on chromosome 11p with multiple restriction site polymorphisms.

We have discovered and characterized a new polymorphic locus on chromosome 11p, D11S12, defined by an arbitrary genomic DNA segment cloned in the plasmid pADJ762. Four different polymorphic restriction sites with minor allele frequencies greater than 5% are revealed by Southern hybridization of this probe and its derivatives to digests of human DNAs. These include two MspI sites, a TaqI site, and a BclI site. The frequencies of the common haplotypes at this locus have been determined in a Utah population. Significant linkage disequilibrium has been demonstrated to exist between some pairs of polymorphic sites. A molecular map of this region has been determined, and the polymorphic sites have been localized. Comparison of physical separation with degree of linkage disequilibrium reveals an interesting case where an MspI site and a TaqI site that are separated by 6.8 kilobases (kb) show a greater degree of disequilibrium with each other than they do with two polymorphic sites located between them. One of the two interior sites is a BclI site that is approximately 0.2 kb away from the TaqI site but shows the same degree of disequilibrium with the TaqI site as with the MspI site 6.7 kb away. Although there is significant linkage disequilibrium at this locus, there are four major haplotypes with frequencies of 5% or greater, and the polymorphic information content (PIC) of this locus is .64.     

Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans

We develop predictions for the correlation of heterozygosity and for linkage disequilibrium between two loci using a simple model of population structure that includes migration among local populations, or demes. We compare the results for a sample of size two from the same deme (a single-deme sample) to those for a sample of size two from two different demes (a scattered sample). The correlation in heterozygosity for a scattered sample is surprisingly insensitive to both the migration rate and the number of demes. In contrast, the correlation in heterozygosity for a single-deme sample is sensitive to both, and the effect of an increase in the number of demes is qualitatively similar to that of a decrease in the migration rate: both increase the correlation in heterozygosity. These same conclusions hold for a commonly used measure of linkage disequilibrium (r(2)). We compare the predictions of the theory to genomic data from humans and show that subdivision might account for a substantial portion of the genetic associations observed within the human genome, even though migration rates among local populations of humans are relatively large. Because correlations due to subdivision rather than to physical linkage can be large even in a single-deme sample, then if long-term migration has been important in shaping patterns of human polymorphism, the common practice of disease mapping using linkage disequilibrium in "isolated" local populations may be subject to error.     

Linkage disequilibrium and fingerprinting in sugar beet

It has been suggested that map information for molecular markers can be used to strengthen finterprinting analyses. The success of this strategy depends on the distribution of linkage disequilibrium over the genome. Using 451 mapped AFLP markers, we investigated the occurrence of linkage disequilibrium in nine sugar beet breeding lines. A low but significant level of linkage disequilibrium was found for unlinked markers. Only for very tigthly linked (<3 cM) markers was this level substantially higher. This implies that little is gained in utilising the map position of the markers in fingerprinting applications. Received: 25 May 1999 / Accepted: 18 Oktober 1999     

The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

Expected Linkage Disequilibrium for a Neutral Locus Linked to a Chromosomal Arrangement

The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.     

The relative contributions of recombination and point mutation to the diversification of bacterial clones

Low levels of recombination in bacterial species have often been inferred from the presence of linkage disequilibrium between the alleles at different loci in the population. However, significant linkage disequilibrium is inevitable in organisms that divide by binary fission, and recombinational replacements must be very frequent, compared to point mutation, to dissipate disequilibrium. Recent studies using data from multilocus sequence typing indicate that, in many species, recombinational replacements contribute more greatly to clonal diversification than do point mutations and, in some species, recombination has been sufficient to eliminate any phylogenetic signal from gene trees. Recent efforts to improve understanding of the extent and impact of homologous recombination in the diversification of bacterial clones are discussed.     

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.