Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.     

Linear models for joint association and linkage QTL mapping

Background

Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.

Results

We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders'' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.

Conclusion

The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.     

Fine mapping of a quantitative trait locus for twinning rate using combined linkage and linkage disequilibrium mapping

A novel and robust method for the fine-scale mapping of genes affecting complex traits, which combines linkage and linkage-disequilibrium information, is proposed. Linkage information refers to recombinations within the marker-genotyped generations and linkage disequilibrium to historical recombinations before genotyping started. The identity-by-descent (IBD) probabilities at the quantitative trait locus (QTL) between first generation haplotypes were obtained from the similarity of the marker alleles surrounding the QTL, whereas IBD probabilities at the QTL between later generation haplotypes were obtained by using the markers to trace the inheritance of the QTL. The variance explained by the QTL is estimated by residual maximum likelihood using the correlation structure defined by the IBD probabilities. Unlinked background genes were accounted for by fitting a polygenic variance component. The method was used to fine map a QTL for twinning rate in cattle, previously mapped on chromosome 5 by linkage analysis. The data consisted of large half-sib families, but the method could also handle more complex pedigrees. The likelihood of the putative QTL was very small along most of the chromosome, except for a sharp likelihood peak in the ninth marker bracket, which positioned the QTL within a region <1 cM in the middle part of bovine chromosome 5. The method was expected to be robust against multiple genes affecting the trait, multiple mutations at the QTL, and relatively low marker density.     

The role of pedigree information in combined linkage disequilibrium and linkage mapping of quantitative trait loci in a general complex pedigree

Combined linkage disequilibrium and linkage (LDL) mapping can exploit historical as well as recent and observed recombinations in a recorded pedigree. We investigated the role of pedigree information in LDL mapping and the performance of LDL mapping in general complex pedigrees. We compared using complete and incomplete genotypic data, spanning 5 or 10 generations of known pedigree, and we used bi- or multiallelic markers that were positioned at 1- or 5-cM intervals. Analyses carried out with or without pedigree information were compared. Results were compared with linkage mapping in some of the data sets. Linkage mapping or LDL mapping with sparse marker spacing ( approximately 5 cM) gave a poorer mapping resolution without considering pedigree information compared to that with considering pedigree information. The difference was bigger in a pedigree of more generations. However, LDL mapping with closely linked markers ( approximately 1 cM) gave a much higher mapping resolution regardless of using pedigree information. This study shows that when marker spacing is dense and there is considerable linkage disequilibrium generated from historical recombinations between flanking markers and QTL, the loss of power due to ignoring pedigree information is negligible and mapping resolution is very high.     

Genetic Structure,Linkage Disequilibrium and Association Mapping of Verticillium Wilt Resistance in Elite Cotton (Gossypium hirsutum L.) Germplasm Population

Understanding the population structure and linkage disequilibrium in an association panel can effectively avoid spurious associations and improve the accuracy in association mapping. In this study, one hundred and fifty eight elite cotton (Gossypium hirsutum L.) germplasm from all over the world, which were genotyped with 212 whole genome-wide marker loci and phenotyped with an disease nursery and greenhouse screening method, were assayed for population structure, linkage disequilibrium, and association mapping of Verticillium wilt resistance. A total of 480 alleles ranging from 2 to 4 per locus were identified from all collections. Model-based analysis identified two groups (G1 and G2) and seven subgroups (G1a–c, G2a–d), and differentiation analysis showed that subgroup having a single origin or pedigree was apt to differentiate with those having a mixed origin. Only 8.12% linked marker pairs showed significant LD (P<0.001) in this association panel. The LD level for linked markers is significantly higher than that for unlinked markers, suggesting that physical linkage strongly influences LD in this panel, and LD level was elevated when the panel was classified into groups and subgroups. The LD decay analysis for several chromosomes showed that different chromosomes showed a notable change in LD decay distances for the same gene pool. Based on the disease nursery and greenhouse environment, 42 marker loci associated with Verticillium wilt resistance were identified through association mapping, which widely were distributed among 15 chromosomes. Among which 10 marker loci were found to be consistent with previously identified QTLs and 32 were new unreported marker loci, and QTL clusters for Verticillium wilt resistanc on Chr.16 were also proved in our study, which was consistent with the strong linkage in this chromosome. Our results would contribute to association mapping and supply the marker candidates for marker-assisted selection of Verticillium wilt resistance in cotton.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Mapping multiple QTL using linkage disequilibrium and linkage analysis information and multitrait data

A multi-locus QTL mapping method is presented, which combines linkage and linkage disequilibrium (LD) information and uses multitrait data. The method assumed a putative QTL at the midpoint of each marker bracket. Whether the putative QTL had an effect or not was sampled using Markov chain Monte Carlo (MCMC) methods. The method was tested in dairy cattle data on chromosome 14 where the DGAT1 gene was known to be segregating. The DGAT1 gene was mapped to a region of 0.04 cM, and the effects of the gene were accurately estimated. The fitting of multiple QTL gave a much sharper indication of the QTL position than a single QTL model using multitrait data, probably because the multi-locus QTL mapping reduced the carry over effect of the large DGAT1 gene to adjacent putative QTL positions. This suggests that the method could detect secondary QTL that would, in single point analyses, remain hidden under the broad peak of the dominant QTL. However, no indications for a second QTL affecting dairy traits were found on chromosome 14.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

A mammary gland EST showing linkage disequilibrium to a milk production QTL on bovine Chromosome 14

As part of a genome scan, ESTs derived from mammary gland tissue of a lactating cow were used as candidate genes for quantitative trait loci (QTL), affecting milk production traits. Resource families were genotyped with 247 microsatellite markers and 4 polymorphic ESTs. It was shown by linkage analysis that one of these ESTs, KIEL_E8, mapped to the centromeric region of bovine Chromosome (Chr) 14. Regression analysis revealed the presence of a QTL, with significant effect on milk production, in this chromosome region, and analysis of variance showed no significant interaction of marker genotype and family. The estimated significant differences between homozygous marker genotypes were 140 kg milk, −5.02 kg fat yield, and 2.58 kg protein yield for the first 100 days of lactation. Thus, there was strong evidence for a complete or nearly complete linkage disequilibrium between KIEL_E8 and the QTL. To identify the biological function of KIEL_E8, we extended the sequence for 869 bp by 5′-RACE. A 560-bp fragment of this shows a 90.9% similarity to a gene encoding a cysteine- and histidine-rich cytoplasmic protein in mouse. Although such a protein may have a regulatory function for lactation and a linkage disequilibrium between the EST marker and the QTL has been observed, it remains to be elucidated whether they are identical or not. Nevertheless, KIEL_E8 will be an efficient marker to perform marker-assisted selection in the Holstein-Friesian population. Received 20 October 2000 / Accepted: 11 April 2001     

人类复杂遗传疾病QTL分析方法的理论探讨

利用连锁不平衡理论,人类遗传学家已能把影响人类疾病的质量基因定位在小至1cM区域内,有些基因已被克隆出来。罗泽伟等进一步发展统计分析方法检测及估算分子标记与QTL之间的连锁不平衡系数,从而提出了人类复杂遗传病高解析度基因定位的理论策略。以此为基础,进一步探讨了供试群体在双亲基因频率存在差异时检测QTL和检测QTL互作的方法,给出了有关的理论结果。     

Simultaneous mining of linkage and linkage disequilibrium to fine map quantitative trait loci in outbred half-sib pedigrees: revisiting the location of a quantitative trait locus with major effect on milk production on bovine chromosome 14

A maximum-likelihood QTL mapping method that simultaneously exploits linkage and linkage disequilibrium and that is applicable in outbred half-sib pedigrees is described. The method is applied to fine map a QTL with major effect on milk fat content in a 3-cM marker interval on proximal BTA14. This proximal location is confirmed by applying a haplotype-based association method referred to as recombinant ancestral haplotype analysis. The origin of the discrepancy between the QTL position derived in this work and that of a previous analysis is examined and shown to be due to the existence of distinct marker haplotypes associated with QTL alleles having large substitution effects.     

The importance of identity-by-state information for the accuracy of genomic selection

Background

It is commonly assumed that prediction of genome-wide breeding values in genomic selection is achieved by capitalizing on linkage disequilibrium between markers and QTL but also on genetic relationships. Here, we investigated the reliability of predicting genome-wide breeding values based on population-wide linkage disequilibrium information, based on identity-by-descent relationships within the known pedigree, and to what extent linkage disequilibrium information improves predictions based on identity-by-descent genomic relationship information.

Methods

The study was performed on milk, fat, and protein yield, using genotype data on 35 706 SNP and deregressed proofs of 1086 Italian Brown Swiss bulls. Genome-wide breeding values were predicted using a genomic identity-by-state relationship matrix and a genomic identity-by-descent relationship matrix (averaged over all marker loci). The identity-by-descent matrix was calculated by linkage analysis using one to five generations of pedigree data.

Results

We showed that genome-wide breeding values prediction based only on identity-by-descent genomic relationships within the known pedigree was as or more reliable than that based on identity-by-state, which implicitly also accounts for genomic relationships that occurred before the known pedigree. Furthermore, combining the two matrices did not improve the prediction compared to using identity-by-descent alone. Including different numbers of generations in the pedigree showed that most of the information in genome-wide breeding values prediction comes from animals with known common ancestors less than four generations back in the pedigree.

Conclusions

Our results show that, in pedigreed breeding populations, the accuracy of genome-wide breeding values obtained by identity-by-descent relationships was not improved by identity-by-state information. Although, in principle, genomic selection based on identity-by-state does not require pedigree data, it does use the available pedigree structure. Our findings may explain why the prediction equations derived for one breed may not predict accurate genome-wide breeding values when applied to other breeds, since family structures differ among breeds.     

人类混血群体连锁不平衡的遗传学模型与基因定位

人类混血群体可以说是混合群体的一种特例．在无选择、无突变、无限随机交配群体的假定前提下,研究了亲本群体的基因频率对混血群体及其衍生后代群体连锁不平衡结构的影响,导出了各群体连锁不平衡值的表达式,建立了一个估计基因间重组率的简便方法;同时, 采用估算分子标记与QTL之间连锁不平衡系数的统计分析方法,分析了人类混血群体及其衍生后代群体QTL检测与估计的关系,建立了该关系的系列理论公式．研究结果表明,本方法不仅适用于人类疾病(包括复杂遗传疾病)基因定位,而且适合于人类正常基因的定位,同时也适用于人类普通多基因性状的QTL分析．     

Methods for linkage disequilibrium mapping in crops

Linkage disequilibrium (LD) mapping in plants detects and locates quantitative trait loci (QTL) by the strength of the correlation between a trait and a marker. It offers greater precision in QTL location than family-based linkage analysis and should therefore lead to more efficient marker-assisted selection, facilitate gene discovery and help to meet the challenge of connecting sequence diversity with heritable phenotypic differences. Unlike family-based linkage analysis, LD mapping does not require family or pedigree information and can be applied to a range of experimental and non-experimental populations. However, care must be taken during analysis to control for the increased rate of false positive results arising from population structure and variety interrelationships. In this review, we discuss how suitable the recently developed alternative methods of LD mapping are for crops.     

Fine mapping of quantitative trait loci using linkage disequilibria with closely linked marker loci

A multimarker linkage disequilibrium mapping method was developed for the fine mapping of quantitative trait loci (QTL) using a dense marker map. The method compares the expected covariances between haplotype effects given a postulated QTL position to the covariances that are found in the data. The expected covariances between the haplotype effects are proportional to the probability that the QTL position is identical by descent (IBD) given the marker haplotype information, which is calculated using the genedropping method. Simulation results showed that a QTL was correctly positioned within a region of 3, 1.5, or 0.75 cM in 70, 62, and 68%, respectively, of the replicates using markers spaced at intervals of 1, 0.5, and 0.25 cM, respectively. These results were rather insensitive to the number of generations since the QTL occurred and to the effective population size, except that 10 generations yielded rather poor estimates of the QTL position. The position estimates of this multimarker disequilibrium mapping method were more accurate than those from a single marker transmission disequilibrium test. A general approach for identifying QTL is suggested, where several stages of disequilibrium mapping are used with increasingly dense marker spacing.     

Linkage disequilibrium on the bovine X chromosome: characterization and use in quantitative trait locus mapping

We herein demonstrate that in the Holstein-Friesian dairy cattle population, microsatellites are as polymorphic on the X chromosome as on the autosomes but that the level of linkage disequilibrium between these markers is higher on the X chromosome than on the autosomes. The latter observation is not compatible with the small male-to-female ratio that prevails in this population and results in a higher gonosomal than autosomal effective population size. It suggests that the X chromosome undergoes distinct selective or mutational forces. We describe and characterize a novel Markovian approach to exploit this linkage disequilibrium to compute the probability that two chromosomes are identical-by-descent conditional on flanking marker data. We use the ensuing probabilities in a restricted maximum-likelihood approach to search for quantitative trait loci (QTL) affecting 48 traits of importance to the dairy industry and provide evidence for the presence of QTL affecting 5 of these traits on the bovine X chromosome.     

Molecular dissection of a quantitative trait locus: a phenylalanine-to-tyrosine substitution in the transmembrane domain of the bovine growth hormone receptor is associated with a major effect on milk yield and composition

We herein report on our efforts to improve the mapping resolution of a QTL with major effect on milk yield and composition that was previously mapped to bovine chromosome 20. By using a denser chromosome 20 marker map and by exploiting linkage disequilibrium using two distinct approaches, we provide strong evidence that a chromosome segment including the gene coding for the growth hormone receptor accounts for at least part of the chromosome 20 QTL effect. By sequencing individuals with known QTL genotype, we identify an F to Y substitution in the transmembrane domain of the growth hormone receptor gene that is associated with a strong effect on milk yield and composition in the general population.     

A transmission/disequilibrium test approach to screen for quantitative trait loci in two selected lines of large white pigs

Pedigree and marker data from a multiple-generation pig selection experiment have been analysed to screen for loci affecting quantitative traits (QTL). Pigs from a base population were selected either for low backfat thickness at fixed live weight (L-line) or high live weight at fixed age (F-line). Selection was based on single-trait own performance and DNA was available on selected individuals only. Genotypes for three marker loci with known positions on chromosome 4 were available. The transmission/disequilibrium test (TDT) was originally described in human genetics to test for linkage between a genetic marker and a disease-susceptibility locus, in the presence of association. Here, we adapt the TDT to test for linkage between a marker and QTL favoured by selection, and for linkage disequilibrium between them in the base population. The a priori unknown distribution of the test statistic under the null hypothesis, no linkage, was obtained via Monte Carlo simulation. Significant TDT statistics were found for markers AFABP and SW818 in the F-line, indicating the presence of a closely linked QTL affecting growth performance. In the L-line, none of the markers studied showed significance. This study emphasizes the potential of the TDT as a quick and simple approach to screen for QTL in situations where marker genotypes are available on selected individuals. The results suggest that previously identified QTL in crosses of genetically diverse breeds may also segregate in commercial selection lines.     

Linkage disequilibrium mapping of a<Emphasis Type="Italic"> Verticillium dahliae</Emphasis> resistance quantitative trait locus in tetraploid potato (<Emphasis Type="Italic">Solanum tuberosum</Emphasis>) through a candidate gene approach

We have used the linkage disequilibrium mapping method to test for an association between a candidate gene marker and resistance to Verticillium dahliae in tetraploid potato. A probe derived from the tomato Verticillium resistance gene (Ve1) identified homologous sequences (StVe1) in potato, which in a diploid population map to chromosome 9, in a position analogous to that of the tomato resistance gene. When a molecular marker closely linked (1.5 cM) to the homologues was used as a candidate gene marker on 137 tetraploid potato genotypes (mostly North American cultivars), the association between the marker and resistance was confirmed (P<0.001). The amount of phenotypic variation in resistance explained by the allele of the STM1051 marker was greater than 10% and 25% in two subpopulations that were inferred from coancestry data matrix. Cloning of homologues from the highly resistant potato cv. Reddale indicates that the resistance quantitative trait locus (QTL) comprises at least an eleven-member family, encoding plant-specific leucine-rich repeat proteins highly similar to the tomato Ve genes. The sequence analysis shows that all homologues are uninterrupted open reading frames and thus represent putative functional resistance genes. This is the first time that the linkage disequilibrium method has been used to find an association between a resistance gene and a candidate gene marker in tetraploid potato. We have shown that it is possible to map QTL directly on already available potato cultivars, without developing a new mapping population.Communicated by F. SalaminiAn erratum to this article can be found at