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.     

Extent and consistency across generations of linkage disequilibrium in commercial layer chicken breeding populations

Recent studies report a surprisingly high degree of marker-to-marker linkage disequilibrium (LD) in ruminant livestock populations. This has important implications for QTL mapping and marker-assisted selection. This study evaluated LD between microsatellite markers in a number of breeding populations of layer chickens using the standardized chi-square (chi(2')) measure. The results show appreciable LD among markers separated by up to 5 cM, decreasing rapidly with increased separation between markers. The LD within 5 cM was strongly conserved across generations and differed among chromosomal regions. Using marker-to-marker LD as an indication for marker-QTL LD, a genome scan of markers spaced 2 cM apart at moderate power would have good chances of uncovering most QTL segregating in these populations. However, of markers showing significant trait associations, only 57% are expected to be within 5 cM of the responsible QTL, and the remainder will be up to 20 cM away. Thus, high-resolution LD mapping of QTL will require dense marker genotyping across the region of interest to allow for interval mapping of the QTL.     

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.     

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.     

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.     

Construction of an RAPD linkage map and localization of QTLs for oleic acid level using recombinant inbreds in mustard (Brassica juncea).

RAPD markers were employed for construction of a linkage map and localization of QTLs for oleic acid level using a set of 94 recombinant inbred lines (RILs) of mustard (Brassica juncea L.) as a mapping population. Only 30% of the 235 random primers used were useful in terms of polymorphism detected and the reproducibility of those patterns. Normal Mendelian segregation was observed for the majority of the 130 markers obtained with 71 informative primers; only 13.1% deviated (P < 0.01) from the expected 1:1 ratio. One-hundred and fourteen markers were assigned to 21 linkage groups (LGs) covering a total length of 790.4 cM with an average distance of 6.93 cM between markers. Two quantitative trait loci (QTL) for oleic acid level were mapped to 14- and 10.6-cM marker intervals on two different LGs. Both loci together explained 32.2% of phenotypic variance. One major QTL explained 28.5% of the trait variance observed in this species.     

A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci

In this article, a unified Markov chain Monte Carlo (MCMC) framework is proposed to identify multiple quantitative trait loci (QTL) for complex traits in experimental designs, based on a composite space representation of the problem that has fixed dimension. The proposed unified approach includes the existing Bayesian QTL mapping methods using reversible jump MCMC algorithm as special cases. We also show that a variety of Bayesian variable selection methods using Gibbs sampling can be applied to the composite model space for mapping multiple QTL. The unified framework not only results in some new algorithms, but also gives useful insight into some of the important factors governing the performance of Gibbs sampling and reversible jump for mapping multiple QTL. Finally, we develop strategies to improve the performance of MCMC algorithms.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

Power of QTL mapping experiments in commercial Atlantic salmon populations, exploiting linkage and linkage disequilibrium and effect of limited recombination in males

Whereas detection and positioning of genes that affect quantitative traits (quantitative trait loci (QTL)) using linkage mapping uses only information from recombinants in the genotyped generations, linkage disequilibrium (LD) mapping uses historical recombinants. Thus, whereas linkage mapping requires large family sizes to detect and accurately position QTL, LD mapping is more dependent on the number of families sampled from the population. In commercial Atlantic salmon breeding programmes, only a small number of individuals per family are routinely phenotyped for traits such as disease resistance and meat colour. In this paper, we assess the power and accuracy of combined linkage disequilibrium linkage analysis (LDLA) to detect QTL in the commercial population using simulation. When 15 half-sib sire families (each sire mated to 30 dams, each dam with 10 progeny) were sampled from the population for genotyping, we were able to detect a QTL explaining 10% of the phenotypic variance in 85% of replicates and position this QTL within 3 cM of the true position in 70% of replicates. When recombination was absent in males, a feature of the salmon genome, power to detect QTL increased; however, the accuracy of positioning the QTL was decreased. By increasing the number of sire families sampled from the population to be genotyped to 30, we were able to increase both the proportion of QTL detected and correctly positioned (even with no recombination in males). QTL with much smaller effect could also be detected. The results suggest that even with the existing recording structure in commercial salmon breeding programmes, there is considerable power to detect and accurately position QTL using LDLA.     

Power and precision of alternate methods for linkage disequilibrium mapping of quantitative trait loci

Linkage disequilibrium (LD) analysis in outbred populations uses historical recombinations to detect and fine map quantitative trait loci (QTL). Our objective was to evaluate the effect of various factors on power and precision of QTL detection and to compare LD mapping methods on the basis of regression and identity by descent (IBD) in populations of limited effective population size (N(e)). An 11-cM region with 6-38 segregating single-nucleotide polymorphisms (SNPs) and a central QTL was simulated. After 100 generations of random mating with N(e) of 50, 100, or 200, SNP genotypes and phenotypes were generated on 200, 500, or 1000 individuals with the QTL explaining 2 or 5% of phenotypic variance. To detect and map the QTL, phenotypes were regressed on genotypes or (assumed known) haplotypes, in comparison with the IBD method. Power and precision to detect QTL increased with sample size, marker density, and QTL effect. Power decreased with N(e), but precision was affected little by N(e). Single-marker regression had similar or greater power and precision than other regression models, and was comparable to the IBD method. Thus, for rapid initial screening of samples of adequate size in populations in which drift is the primary force that has created LD, QTL can be detected and mapped by regression on SNP genotypes without recovering haplotypes.     

Mapping of rat Chromosome 2 markers generated from chromosome-sorted DNA

A quantitative trait locus (QTL) for blood pressure has recently been mapped to a region of roughly 30 cM on rat Chromosome (Chr) 2 by linkage and by the use of congenic strains. For further fine mapping of the QTL, however, closely linked chromosome markers residing in this 30-cM region are required. In the current work, 36 new markers were generated by screening rat Chr 2-sorted DNA libraries and subsequently mapped using five F₂ populations. Combining new and existing markers, the marker density for the 30-cM region approaches, on average, one marker per 1.1 cM. Received: 11 April 1997 / Accepted: 12 May 1997     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

QTL linkage analysis of connected populations using ancestral marker and pedigree information

The common assumption in quantitative trait locus (QTL) linkage mapping studies that parents of multiple connected populations are unrelated is unrealistic for many plant breeding programs. We remove this assumption and propose a Bayesian approach that clusters the alleles of the parents of the current mapping populations from locus-specific identity by descent (IBD) matrices that capture ancestral marker and pedigree information. Moreover, we demonstrate how the parental IBD data can be incorporated into a QTL linkage analysis framework by using two approaches: a Threshold IBD model (TIBD) and a Latent Ancestral Allele Model (LAAM). The TIBD and LAAM models are empirically tested via numerical simulation based on the structure of a commercial maize breeding program. The simulations included a pilot dataset with closely linked QTL on a single linkage group and 100 replicated datasets with five linkage groups harboring four unlinked QTL. The simulation results show that including parental IBD data (similarly for TIBD and LAAM) significantly improves the power and particularly accuracy of QTL mapping, e.g., position, effect size and individuals’ genotype probability without significantly increasing computational demand.     

Bias of allele-sharing linkage statistics in the presence of intermarker linkage disequilibrium

Current genome-wide linkage-mapping single-nucleotide polymorphism (SNP) panels with densities of 0.3 cM are likely to have increased intermarker linkage disequilibrium (LD) compared to 5-cM microsatellite panels. The resulting difference in haplotype frequencies versus that predicted may affect multipoint linkage analysis with ungenotyped founders; a common haplotype may be assumed to be rare, leading to inflation of identical-by-descent (IBD) allele-sharing estimates and evidence for linkage. Using data simulated for the Genetic Analysis Workshop 14, we assessed bias in allele-sharing measures and nonparametric linkage (NPL all) and Kong and Cox LOD (KC-LOD) scores in a targeted analysis of regions with and without LD and with and without genes. Using over 100 replicates, we found that if founders were not genotyped, multipoint IBD estimates and delta parameters were modestly inflated and NPL all and KC-LOD scores were biased upwards in the region with LD and no gene; rather than centering on the null, the mean NPL all and KC-LOD scores were 0.51 +/- 0.91 and 0.19 +/- 0.38, respectively. Reduction of LD by dropping markers reduced this upward bias. These trends were not seen in the non-LD region with no gene. In regions with genes (with and without LD), a slight loss in power with dropping markers was suggested. These results indicate that LD should be considered in dense scans; removal of markers in LD may reduce false-positive results although information may also be lost. Methods to address LD in a high-throughput manner are needed for efficient, robust genomic scans with dense SNPs.     

Optimal haplotype structure for linkage disequilibrium-based fine mapping of quantitative trait loci using identity by descent

A linkage disequilibrium-based method for fine mapping quantitative trait loci (QTL) has been described that uses similarity between individuals' marker haplotypes to determine if QTL alleles are identical by descent (IBD) to model covariances among individuals' QTL alleles for a mixed linear model. Mapping accuracy with this method was found to be sensitive to the number of linked markers that was included in the haplotype when fitting the model at a putative position of the QTL. The objective of this study was to determine the optimal haplotype structure for this IBD-based method for fine mapping a QTL in a previously identified QTL region. Haplotypes consisting of 1, 2, 4, 6, or all 10 available markers were fit as a "sliding window" across the QTL region under ideal and nonideal simulated population conditions. It was found that using haplotypes of 4 or 6 markers as a sliding "window" resulted in the greatest mapping accuracy under nearly all conditions, although the true IBD state at a putative QTL position was most accurately predicted by IBD probabilities obtained using all markers. Using 4 or 6 markers resulted in greater discrimination of IBD probabilities between positions while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Fitting IBD probabilities on the basis of a single marker resulted in the worst mapping accuracy under all conditions because it resulted in poor accuracy of IBD probabilities. In conclusion, for fine mapping using IBD methods, marker information must be used in a manner that results in sensitivity of IBD probabilities to the putative position of the QTL while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Contrary to expectation, use of haplotypes of 4-6 markers to derive IBD probabilities, rather than all available markers, best fits these criteria. Thus for populations similar to those simulated here, optimal mapping accuracy for this IBD-based fine-mapping method is obtained with a haplotype structure including a subset of all available markers.     

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.     

Approximating identity-by-descent matrices using multiple haplotype configurations on pedigrees

Identity-by-descent (IBD) matrix calculation is an important step in quantitative trait loci (QTL) analysis using variance component models. To calculate IBD matrices efficiently for large pedigrees with large numbers of loci, an approximation method based on the reconstruction of haplotype configurations for the pedigrees is proposed. The method uses a subset of haplotype configurations with high likelihoods identified by a haplotyping method. The new method is compared with a Markov chain Monte Carlo (MCMC) method (Loki) in terms of QTL mapping performance on simulated pedigrees. Both methods yield almost identical results for the estimation of QTL positions and variance parameters, while the new method is much more computationally efficient than the MCMC approach for large pedigrees and large numbers of loci. The proposed method is also compared with an exact method (Merlin) in small simulated pedigrees, where both methods produce nearly identical estimates of position-specific kinship coefficients. The new method can be used for fine mapping with joint linkage disequilibrium and linkage analysis, which improves the power and accuracy of QTL mapping.     

Population structure and linkage disequilibrium unravelled in tetraploid potato

Association mapping is considered to be an important alternative strategy for the identification of quantitative trait loci (QTL) as compared to traditional QTL mapping. A necessary prerequisite for association analysis to succeed is detailed information regarding hidden population structure and the extent of linkage disequilibrium. A collection of 430 tetraploid potato cultivars, comprising two association panels, has been analysed with 41 AFLP^® and 53 SSR primer combinations yielding 3364 AFLP fragments and 653 microsatellite alleles, respectively. Polymorphism information content values and detected number of alleles for the SSRs studied illustrate that commercial potato germplasm seems to be equally diverse as Latin American landrace material. Genome-wide linkage disequilibrium (LD)—reported for the first time for tetraploid potato—was observed up to approximately 5 cM using r ² higher than 0.1 as a criterion for significant LD. Within-group LD, however, stretched on average twice as far when compared to overall LD. A Bayesian approach, a distance-based hierarchical clustering approach as well as principal coordinate analysis were adopted to enquire into population structure. Groups differing in year of market release and market segment (starch, processing industry and fresh consumption) were repeatedly detected. The observation of LD up to 5 cM is promising because the required marker density is not likely to disable the possibilities for association mapping research in tetraploid potato. Population structure appeared to be weak, but strong enough to demand careful modelling of genetic relationships in subsequent marker-trait association analyses. There seems to be a good chance that linkage-based marker-trait associations can be identified at moderate marker densities.     

Association mapping of agronomic traits on chromosome 2A of wheat

Association mapping is a method to test the association between molecular markers and quantitative trait loci (QTL) based on linkage disequilibrium (LD). In this study, the collection of 108 wheat germplasm accessions form China were evaluated for their plant heights, spike length, spikelets per spike, grains per spike, thousand kernel weight and spikelets density in 3 years at three locations. And they were genotyped with 85 SSR markers and 40 EST-SSR markers. The population structure was inferred on the basis of unlinked 48 SSR markers and 40 EST-SSR markers. The extent of LD on chromosome 2A was 2.3 cM. Association of 37 SSR loci on chromosomes 2A with six agronomic traits was analysed with a mixed linear model. A total of 14 SSR loci were significantly associated with agronomic traits. Some of the associated markers were located in the QTL region detected in previous linkage mapping analysis. Our results demonstrated that association mapping can enhance QTL information and achieves higher resolution with short LD extent.