Linkage disequilibrium between cystic fibrosis and linked DNA polymorphisms in Italian families: A collaborative study

The locus D7S23 includes a CpG-enriched methylation-free island that maps midway between the markers J3.11 and met and is genetically very close to the mutation causing cystic fibrosis (CF). We have studied the linkage disequilibrium between four polymorphic markers from this locus (KM.19, CS.7, XV-2c, and PT-3) and the CF mutation (CF) in 127 Italian families. Strong linkage disequilibrium is found between KM.19, CS.7, and CF, and weaker but significant disequilibrium is found between XV-2c, PT-3, and CF. The disequilibrium between markers and CF for the Italian population provides additional information on the origin and homogeneity of the CF defect. This panel of probes is sufficiently informative to permit accurate prenatal diagnosis of CF in most families with an affected person, and the disequilibrium also allows indirect carrier detection/exclusion in some cases.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Risks of fetal cystic fibrosis based on linkage disequilibrium data

Summary First-trimester prenatal diagnosis of cystic fibrosis depends on tissues being available from a previous affected child for determination of the phase relationship of DNA markers. If no such tissues are available, it is possible to estimate the risks of a couple producing an affected child from the distribution of haplotypes showing linkage disequilibrium with the cystic fibrosis gene. We have calculated all the fetal risk subsets from the various parental haplotype combinations for the restriction fragment length polymorphisms identified by the KM. 19/PstI and XV-2c/TaqI systems. We conclude that only in a limited number of parental combinations are the fetal risks sufficiently high or sufficiently low to be used in prenatal diagnosis.     

HLA-A confers an HLA-DRB1 independent influence on the risk of multiple sclerosis

A recent high-density linkage screen confirmed that the HLA complex contains the strongest genetic factor for the risk of multiple sclerosis (MS). In parallel, a linkage disequilibrium analysis using 650 single nucleotide polymorphisms (SNP) markers of the HLA complex mapped the entire genetic effect to the HLA-DR-DQ subregion, reflected by the well-established risk haplotype HLA-DRB1*15,DQB1*06. Contrary to this, in a cohort of 1,084 MS patients and 1,347 controls, we show that the HLA-A gene confers an HLA-DRB1 independent influence on the risk of MS (P = 8.4x10(-10)). This supports the opposing view, that genes in the HLA class I region indeed exert an additional influence on the risk of MS, and confirms that the class I allele HLA-A*02 is negatively associated with the risk of MS (OR = 0.63, P = 7x10(-12)) not explained by linkage disequilibrium with class II. The combination of HLA-A and HLA-DRB1 alleles, as represented by HLA-A*02 and HLA-DRB1*15, was found to influence the risk of MS 23-fold. These findings imply complex autoimmune mechanisms involving both the regulatory and the effector arms of the immune system in the triggering of MS.     

Rheumatoid arthritis seropositive for the rheumatoid factor is linked to the protein tyrosine phosphatase nonreceptor 22-620W allele

The protein tyrosine phosphatase nonreceptor type 22 (PTPN22) gene encodes for lymphoid tyrosine phosphatase LYP, involved in the negative regulation of early T-cell activation. An association has recently been reported between the PTPN22-620W functional allele and rheumatoid factor-positive (RF+) rheumatoid arthritis (RA), among other autoimmune diseases. Expected linkage proof for consistency cannot be definitely produced by an affected sib-pair (ASP) analysis. Our aim was therefore to search for linkage evidence with the transmission disequilibrium test. DNA from the French Caucasian population was available for two samples of 100 families with one RA patient and both parents, and for 88 RA index cases from RA ASP families. Genotyping was carried out by PCR-restriction fragment length polymorphism. The analysis was performed using the transmission disequilibrium test, genotype relative risk and ASP-based analysis. The transmission disequilibrium test of the PTPN22-620W allele revealed linkage and association for RF+ RA (61% of transmission, P = 0.037). The genotype relative risk showed the risk allele in 34% of RF+ RA patients and in 24% of controls derived from nontransmitted parental chromosomes (P = 0.047, odds ratio = 1.69, 95% confidence interval = 1.03-2.78). The ASP investigation showed no enriched risk allele in RA multiplex families, resulting in a lack of power of ASP analysis, explaining the published negative results. This study is the first to show linkage of PTPN22 to RF+ RA, consistent with PTPN22 as a new RA gene.     

Linkage Disequilibrium in Growing and Stable Populations

Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with ``starlike' genealogies making significant linkage disequilibrium unlikely.     

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.     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

New properties of the two-locus partial selfing model with selection

Analytic solutions are obtained for the equilibria of a simple two-locus, heterotic selection model with mixed selfing and random outcrossing. Two general phenomena are possible, depending upon the viabilities and the degree of selfing: (1) Negative disequilibrium potential, under which only gametic disequilibrium is possible; and (2) positive disequilibrium potential, which can result in permanent gametic disequilibrium provided that linkage is sufficiently tight. Under random mating (s = 0), these two situations correspond to negative and positive additive epistasis, respectively. With partial self-fertilization, however, this is no longer true, and a more appropriate measure of gametc disequilibrium potential, Δ(s), is introduced. A numerically aided examination of the model results in the discovery of two new properties of partial selfing with selection: (1) With negative disequilibrium potential (Δ(s) < 0), the equilibrium mean fitness increases with increasing recombination. With positive disequilibrium potential (Δ(s) > 0), the opposite is true. (2) Gametic disequilibrium can increase or decrease as the degree of selfing is increased. Therefore, it is apparent that partial selfing and linkage are not analogous as regards the maintenance of disequilibrium.     

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.     

Significant admixture linkage disequilibrium across 30 cM around the FY locus in African Americans

Scientists, to understand the importance of allelic polymorphisms on phenotypes that are quantitative and environmentally interacting, are now turning to population-association screens, especially in instances in which pedigree analysis is difficult. Because association screens require linkage disequilibrium between markers and disease loci, maximizing the degree of linkage disequilibrium increases the chances of discovering functional gene-marker associations. One theoretically valid approach-mapping by admixture linkage disequilibrium (MALD), using recently admixed African Americans-is empirically evaluated here by measurement of marker associations with 15 short tandem repeats (STRs) and an insertion/deletion polymorphism of the AT3 locus in a 70-cM segment at 1q22-23, around the FY (Duffy) locus. The FY polymorphism (-46T-->C) disrupts the GATA promoter motif, specifically blocking FY erythroid expression and has a nearly fixed allele-frequency difference between European Americans and native Africans that is likely a consequence of a selective advantage of FY-/- in malaria infections. Analysis of linkage disequilibrium around the FY gene has indicated that there is strong and consistent linkage disequilibrium between FY and three flanking loci (D1S303, SPTA1, and D1S484) spanning 8 cM. We observed significant linkage-disequilibrium signals over a 30-cM region from -4.4 to 16.3 cM (from D1S2777 to D1S196) for STRs and at 26.4 cM (AT3), which provided quantitative estimates of centimorgan limits, by MALD assessment in African American population-association analyses, of 5-10 cM.     

Linkage disequilibrium patterns vary with chromosomal location: a case study from the von Willebrand factor region.

Linkage disequilibrium analysis has been used as a tool for analyzing marker order and locating disease genes. Under appropriate circumstances, disequilibrium patterns reflect recombination events that have occurred throughout a population's history. As a result, disequilibrium mapping may be useful in genomic regions of < 1 cM where the number of informative meioses needed to detect recombinant individuals within pedigrees is exceptionally high. Its utility for refining target areas for candidate disease genes before initiating chromosomal walks and cloning experiments will be enhanced as the relationship between linkage disequilibrium and physical distance is better understood. To address this issue, we have characterized linkage disequilibrium in a 144-kb region of the von Willebrand factor gene on chromosome 12. Sixty CEPH and 12 von Willebrand disease families were genotyped for five PCR-based markers, which include two microsatellite repeats and three single-base-pair substitutions. Linkage disequilibrium and physical distance between polymorphisms are highly correlated (rm = -.76; P < .05) within this region. None of the five markers showed significant disequilibrium with the von Willebrand disease phenotype. The linkage disequilibrium/physical distance relationship was also analyzed as a function of chromosomal location for this and eight previously characterized regions. This analysis revealed a general trend in which linkage disequilibrium dissipates more rapidly with physical distance in telomeric regions than in centromeric regions. This trend is consistent with higher recombination rates near telomeres.     

Estimates of Linkage Disequilibrium and the Recombination Parameter Determined from Segregating Nucleotide Sites in the Alcohol Dehydrogenase Region of Drosophila Pseudoobscura

The alcohol dehydrogenase (Adh) region of Drosophila pseudoobscura, which includes the two genes Adh and Adh-Dup, was used to examine the pattern and organization of linkage disequilibrium among pairs of segregating nucleotide sites. A collection of 99 strains from the geographic range of D. pseudoobscura were nucleotide-sequenced with polymerase chain reaction-mediated techniques. All pairs of the 359 polymorphic sites in the 3.5-kb Adh region were tested for significant linkage disequilibrium with Fisher's exact test. Of the 74,278 pairwise comparisons of segregating sites, 127 were in significant linkage disequilibrium at the 5% level. The distribution of five linkage disequilibrium estimators D(ij), D(2), r(ij), r(2) and Dij were compared to theoretical distributions. The observed distributions of D(ij), D(2), r(ij) and r(2) were consistent with the theoretical distribution given an infinite sites model. The observed distribution of Dij differed from the theoretical distribution because of an excess of values at -1 and 1. No spatial pattern was observed in the linkage disequilibrium pattern in the Adh region except for two clusters of sites nonrandomly associated in the adult intron and intron 2 of Adh. The magnitude of linkage disequilibrium decreases significantly as nucleotide distance increases, or a distance effect. Adh-Dup had a larger estimate of the recombination parameter, 4Nc, than Adh, where N is the effective population size and c is the recombination rate. A comparison of the mutation and recombination parameters shows that 7-17 recombination events occur for each mutation event. The heterogeneous estimates of the recombination parameter and the inverse relationship between linkage disequilibrium and nucleotide distance are no longer significant when the two clusters of Adh intron sites are excluded from analyses. The most likely explanation for the two clusters of linkage disequilibria is epistatic selection between sites in the cluster to maintain pre-mRNA secondary structure.     

Linkage disequilibrium predicts physical distance in the adenomatous polyposis coli region.

To test the reliability of linkage-disequilibrium analysis for gene mapping, we compared physical distance and linkage disequilibrium among seven polymorphisms in the adenomatous polyposis coli (APC) region on chromosome 5. Three of them lie within the APC gene, and two lie within the nearby MCC (mutated in colon cancer) gene. One polymorphism lies between the two genes, and one is likely to be 5' of MCC. Five of these polymorphisms are newly reported. All polymorphisms were typed in the CEPH kindreds, yielding 179-205 unrelated two-locus haplotypes. Linkage disequilibrium between each pair of polymorphisms is highly correlated with physical distance in this 550-kb region (correlation coefficient -.80, P < .006). This result is replicated in both the Utah and non-Utah CEPH kindreds. There is a tendency for greater disequilibrium among pairs of polymorphisms located within the same gene than among other pairs of polymorphisms. Trigenic, quadrigenic, three-locus, and four-locus disequilibrium measures were also estimated, but these measures revealed much less disequilibrium than did the two-locus disequilibrium measures. A review of 19 published disequilibrium studies, including this one, shows that linkage disequilibrium nearly always correlates significantly with physical distance in genomic regions > 50-60 kb but that it does not do so in smaller genomic regions. We show that this agrees with theoretical predictions. This finding helps to resolve controversies regarding the use of disequilibrium for inferring gene order. Disequilibrium mapping is unlikely to predict gene order correctly in regions < 50-60 kb in size but can often be applied successfully in regions of 50-500 kb or so in size. It is convenient that this is the range in which other mapping techniques, including chromosome walking and linkage mapping, become difficult.     

Decomposing multilocus linkage disequilibrium

We present a mathematically precise formulation of total linkage disequilibrium between multiple loci as the deviation from probabilistic independence and provide explicit formulas for all higher-order terms of linkage disequilibrium, thereby combining J. Dausset et al.'s 1978 definition of linkage disequilibrium with H. Geiringer's 1944 approach. We recursively decompose higher-order linkage disequilibrium terms into lower-order ones. Our greatest simplification comes from defining linkage disequilibrium at a single locus as allele frequency at that locus. At each level, decomposition of linkage disequilibrium is mathematically equivalent to number theoretic compositions of positive integers; i.e., we have converted a genetic decomposition into a mathematical decomposition.     

Vitiligo: complex segregation and linkage disequilibrium analyses with respect to microsatellite loci spanning the HLA

Familial clustering and linkage disequilibrium studies suggest that genetic factors predispose to vitiligo, although a clear transmission pattern and cosegregation of vitiligo with specific mutations have not been demonstrated. We collected pedigree data on vitiligo from a set of 56 multigeneration families belonging to the Paisa community from Antioquia, Colombia, with the goal of applying the unified model of complex segregation and linkage disequilibrium analyses to test the hypotheses of the existence of a major gene predisposing to vitiligo and that allelic or haplotype polymorphisms of microsatellite loci at 6p21.3-21.4 spanning HLA (D6S276, D6S265, D6S273, and D6S291) are associated with this predisposition. Minimum sibship sample size to discriminate dominant and recessive inheritance models was largely accomplished. Between the 15 models of complex segregation used, the one that best fitted the data was that of a major dominant gene and the existence of strong environmental effects acting on the recessive genotype. The penetrance and risk estimations discriminated two sets of vitiligo patients: those with early onset of vitiligo cosegregating with a dominant mode of inheritance without environmental effects, and those with late onset of vitiligo cosegregating with the recessive genotype and being influenced by environmental effects. After establishing the normal distribution of allelic frequencies and performing multiple comparisons correction, the linkage disequilibrium analysis suggested that a major genetic factor could be located at 6p21.3-21.4, because we detected significant case-control differences for allele 122 at D6S265 ( Pc=0.0264) and significant linkage disequilibrium between loci D6S276 and D6S273 in the cases but not in the controls. We cannot explain these results as a consequence of evolutionary forces or as genetic stratification acting differentially on cases and controls, because there was neither deviation from the Hardy-Weinberg expectations nor genetic subdivision between cases and controls, as theta; (non-biased F(ST)) was not significantly different from 0.     

Linkage disequilibrium and modification of risk for Huntington disease.

The major limitation in performing predictive testing for Huntington disease (HD) is the unavailability of DNA from crucial family members. In our program approximately 20% (36/183) of persons have been excluded from predictive testing because of this reason. The major aim of this study was to examine whether data derived from linkage disequilibrium could modify risk analysis for persons at risk for HD. As a first step, we assessed whether the previously reported linkage disequilibrium between alleles recognized by probe pBS674E-D at locus D4S95 remained significant in a much larger data set. A total of 1,150 chromosomes from 622 individuals--200 affected and 422 unaffected--from 118 families were assessed. Significant haplotype association was detected with AccI and MboI RFLPs at the locus D4S95, with all the families (P = .00003), as well as for a subset from the United Kingdom (P = .0037). Data derived from linkage disequilibrium studies using D4S95 modifies the risk for HD, especially in persons of U.K. descent. Utilization of this approach for risk modification of HD awaits both validation of these data and additional information concerning ethnic-specific alleles at the D4S95 locus.     

Some additional results about polymorphisms in models of an additive quantitative trait under stabilizing selection

 The existence of two stable, symmetric (allelic frequency 0.5 in each locus) polymorphic states is demonstrated for a two-locus model of an additive quantitative trait under strong Gaussian selection. Linkage disequilibrium at one of the states is negative whereas it is positive at the other state. For a three-locus model, it is shown that in order to maintain a stable polymorphism in all three loci, selection must be sufficiently but not exces- sively strong relative to recombination. Also, positive linkage disequilibrium can be maintained in a three-locus model under stabilizing selection that is not very strong. Received 15 July 1995     

A method for estimating the mutation,gene conversion and recombination parameters in small multigene families

A simple two-locus gene conversion model is considered to investigate the amounts of DNA variation and linkage disequilibrium in small multigene families. The exact solutions for the expectations and variances of the amounts of variation within and between two loci are obtained. It is shown that gene conversion increases the amount of variation within each locus and decreases the amount of variation between two loci. The expectation and variance of the amount of linkage disequilibrium are also obtained. Gene conversion generates positive linkage disequilibrium and the degree of linkage disequilibrium decreases as the recombination rate is increased. Using the theoretical results, a method for estimating the mutation, gene conversion, and recombination parameters is developed and applied to the data of the Amy multigene family in Drosophila melanogaster. The gene conversion rate is estimated to be approximately 60-165 times higher than the mutation rate for synonymous sites.     

Disequilibrium Pattern Analysis. I. Theory

We have developed a method, disequilibrium pattern analysis, for examining the disequilibrium distribution of the entire array of two locus multiallelic haplotypes in a population. It is shown that a selected haplotype will produce a distinct pattern of linkage disequilibrium values for all generations while the selection is acting. This pattern will also presumably be maintained for many generations after the selection event, until the disequilibrium pattern is eventually broken down by genetic drift and recombination. Related haplotypes, sharing an allele with a selected haplotype, assume a value of linkage disequilibrium proportional to the frequency of the unshared allele and have a single negative value of the normalized linkage disequilibrium. The analysis assumes zero linkage disequilibrium for all allelic combinations initially. The same basic results continue to apply if the selection involves a new mutant, the occurrence of which creates linkage disequilibrium for some haplotypes. The disequilibrium pattern predicted under selection is robust with respect to the influence of migration and random genetic drift. This method is applicable to population data having linked polymorphic loci including that determined from protein or DNA sequencing.