Combined high resolution linkage and association mapping of quantitative trait loci

In this paper, we investigate variance component models of both linkage analysis and high resolution linkage disequilibrium (LD) mapping for quantitative trait loci (QTL). The models are based on both family pedigree and population data. We consider likelihoods which utilize flanking marker information, and carry out an analysis of model building and parameter estimations. The likelihoods jointly include recombination fractions, LD coefficients, the average allele substitution effect and allele dominant effect as parameters. Hence, the model simultaneously takes care of the linkage, LD or association and the effects of the putative trait locus. The models clearly demonstrate that linkage analysis and LD mapping are complementary, not exclusive, methods for QTL mapping. By power calculations and comparisons, we show the advantages of the proposed method: (1) population data can provide information for LD mapping, and family pedigree data can provide information for both linkage analysis and LD mapping; (2) using family pedigree data and a sparse marker map, one may investigate the prior suggestive linkage between trait locus and markers to obtain low resolution of the trait loci, because linkage analysis can locate a broad candidate region; (3) with the prior knowledge of suggestive linkage from linkage analysis, both population and family pedigree data can be used simultaneously in high resolution LD mapping based on a dense marker map, since LD mapping can increase the resolution for candidate regions; (4) models of high resolution LD mappings using two flanking markers have higher power than that of models of using only one marker in the analysis; (5) excluding the dominant variance from the analysis when it does exist would lose power; (6) by performing linkage interval mappings, one may get higher power than by using only one marker in the analysis.     

The consistency of the posterior probability of linkage

When searching for trait loci along the genome, properly incorporating prior genomic information into the analysis will almost certainly increase the chance of success. Recently, we devised a method that utilizes such prior information in the mapping of trait genes for complex disorders (Vieland, 1998; Wang et al . 1999; Vieland et al . 2000). This method uses the posterior probability of linkage (PPL) based on the admixture model as a measure of linkage information. In this paper, we study the consistency of the PPL. It is shown that, as the number of pedigrees increases, the PPL converges in probability to 1 when there is linkage between the marker and a trait locus, and converges to 0 otherwise. This conclusion is shown to be true for general pedigrees and trait models, even when the likelihood functions are based on misspecified trait models. As part of the effort to prove this conclusion, it is shown that when there is no linkage, the maximum likelihood estimator of the recombination fraction in the admixture model is asymptotically 0.5, even when the admixture model misrepresents the true model.     

High resolution linkage and association mapping identifies a novel rheumatoid arthritis susceptibility locus homologous to one linked to two rat models of inflammatory arthritis

Rheumatoid arthritis (RA) is an oligogenic autoimmune disease but, to date, linkage and association to major histocompatibility complex (MHC) has been the only consistent finding in genetic studies. However, MHC is estimated to contribute only 30-40% of the total genetic component to disease susceptibility. Studies in animal models of inflammatory arthritis have identified a number of putative vulnerability loci but the homologous regions in the human genome have not previously been investigated as candidate RA susceptibility loci. We have investigated linkage to five regions homologous to those identified in animal models of inflammatory arthritis in RA affected sibling pair (ASP) families. Linkage to 17q22 syntenic to a susceptibility locus common to two experimental rat models was detected in 200 RA ASP families and replicated in a further 100 RA ASP families. Linkage to additional markers mapping to the area has refined the extent of linkage to a 4 cM region. Association to one of the markers (D17S807) was demonstrated in this cohort using extensions of the transmission disequilibrium test. Association to two 2-marker haplotypes including this marker was detected in an independent cohort of single-case RA families, thus narrowing the region harbouring the aetiological mutation to approximately 1 cM. This is the first time that an arthritis susceptibility locus mapped in experimental animal models of disease has been used to identify a novel RA susceptibility locus in humans. The difficult task of identifying a disease mutation from a linkage result should, in this case at least, be facilitated by the combined use of animal and human based investigations.     

High resolution mapping of quantitative trait loci by linkage disequilibrium analysis

Two methods, linkage analysis and linkage disequilibrium (LD) mapping or association study, are usually utilised for mapping quantitative trait loci (QTL). Linkage mapping is appropriate for low resolution mapping to localise trait loci to broad chromosome regions within a few cM (<10 cM), and is based on family data. Linkage disequilibrium mapping, on the other hand, is useful in high resolution or fine mapping, and is based on both population and family data. Using only one marker, one may carry out single-point linkage analysis and linkage disequilibrium mapping. Using two or more markers, it is possible to flank the QTL by multipoint analysis. The development and thus availability of dense marker maps, such as single nucleotide polymorphisms (SNP) in human genome, presents a tremendous opportunity for multipoint fine mapping. In this article, we propose a regression approach of mapping QTL by linkage disequilibrium mapping based on population data. Assuming that two marker loci flank one quantitative trait locus, a two-point linear regression is proposed to analyse population data. We derive analytical formulas of parameter estimations, and non-centrality parameters of appropriate tests of genetic effects and linkage disequilibrium coefficients. The merit of the method is shown by the power calculation and comparison. The two-point regression model can capture much more linkage and linkage disequilibrium information than that derived when only one marker is used. For a complex disease with heritability h(2)> or =0.15, a study with sample size of 250 can provide high power for QTL detection under moderate linkage disequilibria.     

Counselling under genetic heterogeneity: a practical approach

Hereditary diseases due to mutation at different gene loci may be indistinguishable phenotypically. In these situations genetic risk predictions using polymorphic markers may be hampered if an individual family is not sufficiently informative to permit it to be assigned to one or the other linkage group. To provide the most usefull estimates of risk, the probability of linkage to a particular chromosome region should be determined prior to calculating risk estimates using the marker system. The probability can be calculated directly using the lod score generated for the family. The individual carrier risk is then the average of the carrier risks determined for linkage to different genetic loci, weighted by the probability of linkage to each group. Several examples are provided.     

Linkage analysis in multiple sclerosis of chromosomal regions syntenic to experimental autoimmune disease loci.

Multiple sclerosis is a demyelinating disorder of the central nervous system with a putative autoimmune aetiology in which several genes are thought to be involved. Four published genomic screens have confirmed that a gene influencing MS resides within or close to the HLA class II region in 6p21. Still, this locus is likely to confer only a part of the genetic susceptibility in MS. Further, all four studies identified a number of other regions with possible linkage. We have investigated eight chromosomal intervals syntenic to loci of importance for experimental autoimmune model diseases in the rat in 74 Swedish MS families. Possible linkage (a non-parametric linkage NPL score of 1.16 by GENEHUNTER computer package) was observed with markers in 12p13.3, a region syntenic to the rat Oia2 locus which is importance for oil induced arthritis (OIA). Four markers in the T cell receptor beta chain gene region in 7q35 showed possible linkage (highest NPL score of 1.16). This locus is syntenic to the rat Cia3 locus (collagen induced arthritis). These two loci at least partially overlap with chromosomal regions showing indicative evidence for linkage in the previous MS genomic screens. Indeed, both Oia2 and Cia3 were recently found to be linked also with experimental autoimmune encephalomyelitis, a commonly used model for MS. Markers in 2p12, 3p25, 10q11.23, 17q21-25, 19q13.1, and 22q12-13 failed to provide evidence for linkage. We conclude that evidence is amounting that 12p13-12 and 7q34-36 may harbour genes with an importance for MS. The synteny with experimental loci may eventually facilitate their identification.     

A CORRECTION TO TDT STATISTICS FOR MAPPING QUANTITATIVE TRAIT LOCI

Xiong et al. (1998) proposed a general transmission disequilibrium test (TDT) for quantitative traits. Their TDT for quantitative traits permits more than one child and more than one heterozygous parent per family. This TDT is also appropriate for the situation where the trait and marker loci are at varying degrees of linkage and linkage disequilibrium. Their generalized TDT statistic for a multi-allele marker locus may be more useful in practice. However, there are several mistakes in their mathematical presentation for this generalized TDT statistic for a multi-allele marker locus, and it confuses readers. Here, we present a corrected TDT statistic for a multi-allele marker locus with a clearer presentation. We hope that this new presentation will remove some confusion for readers.     

Linkage analysis of the nevoid basal cell carcinoma syndrome

Twelve pedigrees were informative for linkage between the gene locus for the nevoid basal cell carcinoma syndrome and the ABO, MNS, Rh, P, Kell, Lewis, Ddy, and Kidd blood group marker loci. Linkage with a recombination fraction less than θ= 0.1 was unlikely for any marker locus. The most favourable of the possible loose linkages, that between the syndrome locus and Rh locus, showed a 12% probability of linkage when the prior odds against two autosomel loci being on the same chromosome were taken into account. The other marker loci manifested probabilities averaging about 3%.     

Extensive genome-wide linkage disequilibrium in cattle

A genome-wide linkage disequilibrium (LD) map was generated using microsatellite genotypes (284 autosomal microsatellite loci) of 581 gametes sampled from the dutch black-and-white dairy cattle population. LD was measured between all marker pairs, both syntenic and nonsyntenic. Analysis of syntenic pairs revealed surprisingly high levels of LD that, although more pronounced for closely linked marker pairs, extended over several tens of centimorgan. In addition, significant gametic associations were also shown to be very common between nonsyntenic loci. Simulations using the known genealogies of the studied sample indicate that random drift alone is likely to account for most of the observed disequilibrium. No clear evidence was obtained for a direct effect of selection ("Bulmer effect"). The observation of long range disequilibrium between syntenic loci using low-density marker maps indicates that LD mapping has the potential to be very effective in livestock populations. The frequent occurrence of gametic associations between nonsyntenic loci, however, encourages the combined use of linkage and linkage disequilibrium methods to avoid false positive results when mapping genes in livestock.     

Pedigree linkage disequilibrium mapping of quantitative trait loci

In this paper, we propose to use pedigrees of any size and any types of relatives in joint high-resolution linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) by variance component models. Two or multiple markers can be simultaneously used in modeling association with the trait locus, instead of using one marker a time in the analysis. The proposed method can provide a unified result by using two or multiple markers in the modeling. This may avoid the complications of different results obtained from the separate analysis of marker by marker. The models simultaneously incorporate both linkage and LD information. The measures of LD are modeled by mean coefficients, and linkage information is modeled by variance-covariance matrix. Using analytical formulas to calculate the regression coefficients, the genetic effects are shown to be decomposed into additive and dominance components. The noncentrality parameter approximations of test statistics of LD are provided to make power calculations. Power and type I error rates are explored to investigate the merit of the proposed method by both the analytical formulas and simulations. Comparing with the association between-family and association within-family ('AbAw') approach of Fulker and Abecasis et al, it is evident that the method proposed in this article is more powerful. The method is applied to investigate the relation between polymorphisms in the angiotensin 1-converting enzyme (ACE) genes and circulating ACE levels, with a better result than that of the 'AbAw' approach. Moreover, two markers I/D and 4656(CT)3/2 can fully interpret association with the trait locus at a 0.01 significance level, which provides a unique result for the ACE data.     

TDT statistics for mapping quantitative trait loci

The original transmission disequilibrium test (TDT), was introduced to test for linkage between a marker and a disease-susceptibility locus (Spielman et al . 1993). Allison (1997) extended the TDT procedure to quantitative traits. Allison's test, however, is restrictive in that it requires family trios consisting of one heterozygous parent, one homozygous parent and one child, and considers only the situation where the marker locus is analogous to the quantitative trait locus itself. In this paper, we propose, investigate and apply a general TDT for quantitative traits that permits more than one child per family, does not require only one parent to be heterozygous, and allows for the fact that the various alleles at the marker and trait loci may be at varying degree of linkage disequilibrium. We also show that this TDT for quantitative traits is still a valid test of linkage in the presence of population substructure. To provide guidelines for study design, we develop analytic formulae for calculation of the power of the TDT for mapping quantitative trait loci and investigate the impact of various factors on the power. Power calculations show that the proposed TDT for quantitative traits is more powerful than Allison's basic test statistic and the extreme discordant sib pair linkage method. The proposed TDT statistic for quantitative traits is applied to systolic blood pressure variation in the Rochester Family Heart Study using an extremely discordant sibling pair design.     

Investigation of the Ability of Haplotype Association and Logistic Regression to Identify Associated Susceptibility Loci

While finely spaced markers are increasingly being used in case‐control association studies in attempts to identify susceptibility loci, not enough is yet known as to the optimal spacing of such markers, their likely power to detect association, the relative merits of single marker versus multimarker analysis, or which methods of analysis may be optimal. Some investigations of these issues have used markers simulated under different theoretical models of population evolution. However the HapMap project and other sources provide real datasets which can be used to obtain a more realistic view of the performance of these approaches. SNPs around APOE and from two HapMap regions were used to obtain information regarding linkage disequilibrium (LD) relationships between polymorphisms, and these real patterns of LD were used to simulate datasets such as would be obtained in case‐control studies were these SNPs to influence susceptibility to disease. The datasets obtained were analysed using tests for heterogeneity of estimated haplotype frequencies and using logistic regression analyses in which only main effects from each marker were considered. All markers surrounding the putative susceptibility locus were analysed, using sets of either 1, 2, 3 or 4 markers at a time. Some markers within 150 kb of the susceptibility locus were able to detect association. At distances less than 100 kb there was no correlation between the distance from the susceptibility locus and the strength of evidence for association. When the average inter‐locus spacing is 25 kb many loci would not be detected, while when the spacing is as low as 2 kb one can be fairly confident that at least one marker will be in strong enough LD with the susceptibility locus to enable association to be detected, if the susceptibility locus has a strong enough effect relative to the sample size. With an inter‐locus spacing of 4 kb some susceptibility loci did not have a marker locus in strong LD, potentially undermining the ability to detect association. There was little difference in the performance of haplotype‐based analysis compared with logistic regression considering effects of each marker as separate. Multimarker analysis on occasion produced results which were much more highly significant than single marker analysis, but only very rarely. Our results support the view that if markers are randomly selected then a spacing as low as 2 kb is desirable. Multimarker analysis can sometimes be more powerful than single marker analysis so both should be performed. However, because it is rare for multimarker analysis to be much more highly significant than single marker analysis one should strongly suspect that when such results occur they may be due to mistakes in genotyping or through some other artefact. Haplotype analysis may be more prone to such problems than logistic regression, suggesting that the latter method might be preferred.     

An extended transmission/disequilibrium test (TDT) for multi-allele marker loci

The transmission/disequilibrium test (TDT) was recently introduced by Spielman et al. (1993) as a test for linkage and linkage disequilibrium. The test is based on the unequal probability of transmission of two different marker alleles from parents to affected offspring, when the marker locus and the hypothetical disease locus are linked and are in linkage disequilibrium. The probabilities of marker allele transmission to affected offspring conditional on parental genotype have been derived by Ott (1989) for a biallelic marker and a recessive disorder with no phenocopies. Here, we derive the transmission probabilities for a multi-allele marker locus and a generalized single locus disease model in a random sample of affected individuals from a randomly mating population. The form of these transmission probabilities suggests an extension of the TDT to multi-allele marker loci, in which the alternative hypothesis is restricted to take account of the likely pattern of unequal transmission when the recombination fraction is near 0. We show how our extended TDT can be implemented by standard software for logistic regression, although we have also written our own program which is available on request. We have evaluated the approximate power of the test under a range of realistic assumptions, and it appears that the test will often have good power when linkage disequilibrium is strong and if the disease is recessive.     

The linkage detection problem

Linkage data in man are usually analysed on families lacking a full set of grandparents on the assumption that there is one locus relating to an abnormal phenotype, the test locus. The basic problems of establishing linkage of this locus to another locus, the marker locus, with a defined likelihood and of estimating the recombination fraction were resolved by Morton(1955). However, the likelihood ratio derived after estimating the most likely recombination fraction is widely misunderstood to be a direct measure of the likelihood of linkage while the bias of estimates conditional on some likelihood criterion derived from the same data is usually ignored. Since data are limited this tolerance of excessive confidence in detecting linkages and a consistent tendency to underestimate recombination fractions is justified but the expected errors are not small and they are readily magnified when multiple loci are involved.
Multiple markers provide further opportunities for detecting false linkages although the corrections required are known. The problems imposed by multiple loci at which mutations lead to a common phenotype have so far had little consideration. As most proteins are multimers whose units are not necessarily coded for by neighbouring loci, and as disturbances to any of several enzymes acting in series may lead to similar consequences, the assumption of a one-to-one relationship between a locus and a phenotype will usually be wrong.     

Assignment of a gene locus involved in craniosynostosis to chromosome 5qter

Craniosynostosis, the abnormal development of the calvarialsutures, occurs as an autosomal dominant trait in many clinicallydistinct syndromes. We performed linkage analysis of a provisionallynovel type of autosomal dominant craniosynostosis in a largethree generational family. Linkage was established between thecraniosynostotic locus and D5S211, a locus defined by the shorttandem repeat polymorphism (STRP) marker Mfd 154 in distal 5q.The maximum LOD score, Z_max, was 4.8 at a recombination fractionof zero. No significant linkage was found with markers located30 cM and more proximal to D5S211. The findings assign the craniosynostoticlocus in this family to a telomeric region in the long arm ofchromosome 5. Linkage analysis with Mfd 154 in other autosomaldominant craniosynostotic syndromes should reveal whether thesedisorders are caused by mutations of genes at the same or atdifferent loci.     

Genetic control of susceptibility to UV-induced immunosuppression by interacting quantitative trait loci

Ultraviolet B radiation (290-320 nm) initiates a dose and wavelength dependent down-regulation of cell-mediated immunity which is critical in experimental ultraviolet radiation (UV) carcinogenesis, preventing immune attack on highly antigenic UV-induced tumors. UV-induced immunosuppression has been demonstrated in humans and may be a risk factor for skin cancer. In this study, we have investigated genetic linkage of the autosomal loci controlling this trait. Previously, we had derived a model describing control of susceptibility to UV-induced immunosuppression in inbred mice by unlinked interacting autosomal and X-linked loci. A genome-wide scan using MIT microsatellite markers was carried out on 100 backcross (BALB/c x (BALB/c x C57BL/6) F1) mice derived from the inbred strains BALB/c (low susceptibility) and C57BL/6 (high susceptibility) and tested for systemic UV-induced immunosuppression of a contact hypersensitivity response. The values for % suppression for each animal and the genotype data were used to investigate genetic linkage by multiple regression analysis. Significance was assessed using the permutation test. Both main effects and interactive effects were investigated, first with each genotype marker singly, and secondly, in a novel approach using markers pairwise. A joint model was derived in which all loci and pairs of loci identified were included simultaneously in a multiple regression model. This model indicates four quantitative trait loci (QTLs) with significant main effects, one on chromosome 10 which decreased susceptibility to UV-induced immunosuppression and QTLs on chromosomes 6, 17 and 1 which increased susceptibility. Additionally, loci on chromosomes 14 and 19 showed significant interaction with the locus on chromosome 1. Further investigation indicated a potential three-way interaction involving the loci on chromosomes 1, 14 and 19.     

Development of pachytene FISH maps for six maize chromosomes and their integration with other maize maps for insights into genome structure variation

Integrated cytogenetic pachytene fluorescence in situ hybridization (FISH) maps were developed for chromosomes 1, 3, 4, 5, 6, and 8 of maize using restriction fragment length polymorphism marker-selected Sorghum propinquum bacterial artificial chromosomes (BACs) for 19 core bin markers and 4 additional genetic framework loci. Using transgenomic BAC FISH mapping on maize chromosome addition lines of oats, we found that the relative locus position along the pachytene chromosome did not change as a function of total arm length, indicative of uniform axial contraction along the fibers during mid-prophase for tested loci on chromosomes 4 and 5. Additionally, we cytogenetically FISH mapped six loci from chromosome 9 onto their duplicated syntenic regions on chromosomes 1 and 6, which have varying amounts of sequence divergence, using sorghum BACs homologous to the chromosome 9 loci. We found that successful FISH mapping was possible even when the chromosome 9 selective marker had no counterpart in the syntenic block. In total, these 29 FISH-mapped loci were used to create the most extensive pachytene FISH maps to date for these six maize chromosomes. The FISH-mapped loci were then merged into one composite karyotype for direct comparative analysis with the recombination nodule-predicted cytogenetic, genetic linkage, and genomic physical maps using the relative marker positions of the loci on all the maps. Marker colinearity was observed between all pair-wise map comparisons, although marker distribution patterns varied widely in some cases. As expected, we found that the recombination nodule-based predictions most closely resembled the cytogenetic map positions overall. Cytogenetic and linkage map comparisons agreed with previous studies showing a decrease in marker spacing in the peri-centromeric heterochromatin region on the genetic linkage maps. In fact, there was a general trend with most loci mapping closer towards the telomere on the linkage maps than on the cytogenetic maps, regardless of chromosome number or maize inbred line source, with just some of the telomeric loci exempted. Finally and somewhat surprisingly, we observed considerable variation between the relative arm positions of loci when comparing our cytogenetic FISH map to the B73 genomic physical maps, even where comparisons were to a B73-derived cytogenetic map. This variation is more evident between different chromosome arms, but less so within a given arm, ruling out any type of inbred-line dependent global features of linear deoxyribonucleic acid compared with the meiotic fiber organization. This study provides a means for analyzing the maize genome structure by producing new connections for integrating the cytogenetic, linkage, and physical maps of maize.     

Extensive conservation of sex chromosome organization between cat and human revealed by parallel radiation hybrid mapping

A radiation hybrid (RH)-derived physical map of 25 markers on the feline X chromosome (including 19 Type I coding loci and 6 Type II microsatellite markers) was compared to homologous marker order on the human and mouse X chromosome maps. Complete conservation of synteny and marker order was observed between feline and human X chromosomes, whereas the same markers identified a minimum of seven rearranged syntenic segments between mouse and cat/human X chromosome marker order. Within the blocks, the feline, human, and mouse marker order was strongly conserved. Similarly, Y chromosome locus order was remarkably conserved between cat and human Y chromosomes, with only one marker (SMCY) position rearranged between the species. Tight linkage and a conserved gene order for a segment encoding three genes, DFFRY-DBY-UTY in human, mouse, and cat Y chromosomes, coupled with demonstrated deletion effects of these genes on reproductive impairment in both human and mouse, implicates the region as critical for Y-mediated sperm production.     

Linkage of multilocus components of variance to polymorphic markers

Haseman & Elston (1972) introduced a sib pair method using classical regression analysis to detect linkage between a polymorphic marker locus and any quantitative trait locus. Most of the diseases mapped to date follow simple Mendelian, single locus transmission. But there are many familial diseases that do not follow simple Mendelian segregation, for example diabetes, several forms of cancer, etc. In this paper, we extend Haseman and Elston's sib pair method to two unlinked quantitative trait loci each linked to one of two unlinked polymorphic marker loci. For the two-locus epistatic model, we give a general formulation of the complete regression model and details of the regression coefficients in terms of variance components.     

Identification of a sixth locus for autosomal dominant retinitis pigmentosa on chromosome 19

We report the mapping of a sixth locus for autosomal dominantretinitis pigmentosa (adRP) to 19q13.4. After a total genomelinkage search using over 300 markers in a single large pedigree,marker loci on the long arm of chromosome 19 showed significantlinkage with the disease locus. Since the mapping informationfor the marker loci used in this study was derived from twodifferent genome maps, we established genetic distances betweenrelevant marker loci so that linkage information could be combinedfrom both maps. A conventional three point analysis betweenthe adRP phenotype and markers D19S180 and D19S214 gave a maximumlod score of 4.87. Combining data from these and other markers,we used the recently described multiple two point programmeFASTMAP to simulate a multipoint analysis of the full data set.This gave a lod score of 5.34 in the Interval between markersD19S180 and D19S214. Recently this laboratory has also reportedthe linkage of another form of retinal degeneration known ascone-rod dystrophy (CRD) to a genetically different set of markersfrom 19q. Linkage data presented here clearly supports the existenceof two separate retinal genes in this part of the genome.