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.     

Linkage disequilibrium mapping of quantitative trait loci under truncation selection

As a dense map of single nucleotide polymorphism (SNP) markers are available, population-based linkage disequilibrium (LD) mapping or association study is becoming one of the major tools for identifying quantitative trait loci (QTL) and for fine gene mapping. However, in many cases, LD between the marker and trait locus is not very strong. Approaches that maximize the potential of detecting LD will be essential for the success of LD mapping of QTL. In this paper, we propose two strategies for increasing the probability of detecting LD: (1) phenotypic selection and (2) haplotype LD mapping. To provide the foundations for LD mapping of QTL under selection, we develop analytic tools for assessing the impact of phenotypic selection on allele and haplotype frequencies, and LD under three trait models: single trait locus, two unlinked trait loci, and two linked trait loci with or without epistasis. In addition to a traditional chi(2) test, which compares the difference in allele or haplotype frequencies in the selected sample and population sample, we present multiple regression methods for LD mapping of QTL, and investigate which methods are effective in employing phenotypic selection for QTL mapping. We also develop a statistical framework for investigating and comparing the power of the single marker and multilocus haplotype test for LD mapping of QTL. Finally, the proposed methods are applied to mapping QTL influencing variation in systolic blood pressure in an isolated Chinese population.     

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.     

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.     

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.     

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.     

An entropy-based measure for QTL mapping using extreme samples of population

Quantitative trait locus (QTL) mapping can be accomplished through the method of selective genotyping, which is based on the differences of frequencies between an upper sample and a lower sample in population. However, amplifying the differences in marker allele frequencies in extreme samples may increase the probability for QTL mapping. Shannon entropy, which is a nonlinear function of allele frequencies, can be used to amplify the differences in marker allele frequencies. In this paper, we present a novel measure for linkage disequilibrium (LD) between a marker and single QTL, that is based on the comparison of the entropy and conditional entropy in a marker in extreme samples of population. This measure of LD between the marker and the trait locus can be used when the marker allele frequencies are known in the extreme samples of a population. We investigate the mapping performance in both analytic and simulation scenarios of a single QTL linked to a single marker. Our results show that the measure has very reasonable performance. In addition, a simulation study is performed on the basis of the haplotype frequencies of 10 SNPs of angiotensin-I converting enzyme (ACE) genes.     

From QTL to QTN identification in livestock--winning by points rather than knock-out: a review

Many quantitative trait loci (QTL) affecting economic traits in livestock have now been identified. However, the confidence interval (CI) of individual QTL as determined by linkage analysis often spans tens of map units, containing hundreds of genes. Linkage disequilibrium (LD) mapping can reduce the CI to individual map units, but this reduced interval will still contain tens of genes. Methods suitable for model animals to find and validate specific quantitative trait nucleotides (QTN) underlying the QTL cannot be easily applied to livestock species because of their long generation intervals, the cost of maintaining each animal and the difficulty of producing transgenics or 'knock-outs'. Considering these limitations, we review successful approaches for identifying QTN in livestock and outline a schematic strategy for QTN determination and verification. In addition to linkage and LD mapping, the methods include positional cloning, selection of candidate genes, DNA sequencing and statistical analyses. Concordance determination and functional assays are the critical tests for validation of a QTN; we provide a generalized formula for the probability of concordance by chance. Three genes that meet the burden of proof for QTN identification--DGAT1 in cattle, IGF2 in swine and GDF8 in sheep--are discussed in detail. The genetic and economic ramifications of identified QTN and the horizon for selection and introgression are also considered.     

Variations and Transmission of QTL Alleles for Yield and Fiber Qualities in Upland Cotton Cultivars Developed in China

Cotton is the world’s leading cash crop, and genetic improvement of fiber yield and quality is the primary objective of cotton breeding program. In this study, we used various approaches to identify QTLs related to fiber yield and quality. Firstly, we constructed a four-way cross (4WC) mapping population with four base core cultivars, Stoneville 2B, Foster 6, Deltapine 15 and Zhongmiansuo No.7 (CRI 7), as parents in Chinese cotton breeding history and identified 83 QTLs for 11 agronomic and fiber quality traits. Secondly, association mapping of agronomical and fiber quality traits was based on 121 simple sequence repeat (SSR) markers using a general linear model (GLM). For this, 81 Gossypium hirsutum L. accessions including the four core parents and their derived cultivars were grown in seven diverse environments. Using these approaches, we successfully identified 180 QTLs significantly associated with agronomic and fiber quality traits. Among them were 66 QTLs that were identified via linkage disequilibrium (LD) and 4WC family-based linkage (FBL) mapping and by previously published family-based linkage (FBL) mapping in modern Chinese cotton cultivars. Twenty eight and 44 consistent QTLs were identified by 4WC and LD mapping, and by FBL and LD mapping methods, respectively. Furthermore, transmission and variation of QTL-alleles mapped by LD association in the three breeding periods revealed that some could be detected in almost all Chinese cotton cultivars, suggesting their stable transmission and some identified only in the four base cultivars and not in the modern cultivars, suggesting they were missed in conventional breeding. These results will be useful to conduct genomics-assisted breeding effectively using these existing and novel QTL alleles to improve yield and fiber qualities in cotton.     

Polymorphisms in cinnamoyl CoA reductase (CCR) are associated with variation in microfibril angle in Eucalyptus spp

Linkage disequilibrium (LD) mapping using natural populations results in higher resolution of marker-trait associations compared to family-based quantitative trait locus (QTL) studies. Depending on the extent of LD, it is possible to identify alleles within candidate genes associated with a trait. Analysis of a natural mutant in Arabidopsis has shown that mutations in cinnamoyl CoA reductase (CCR), a key lignin gene, affect physical properties of the secondary cell wall such as stiffness and strength. Using this gene, we tested whether LD mapping could identify alleles associated with microfibril angle (MFA), a wood quality trait affecting stiffness and strength of wood. We identified 25 common single-nucleotide polymorphism (SNP) markers in the CCR gene in Eucalyptus nitens. Using single-marker and haplotype analyses in 290 trees from a E. nitens natural population, two haplotypes significantly associated with MFA were found. These results were confirmed in two full-sib families of E. nitens and Eucalyptus globulus. In an effort to understand the functional significance of the SNP markers, we sequenced the cDNA clones and identified an alternatively spliced variant from the significant haplotype region. This study demonstrates that LD mapping can be used to identify alleles associated with wood quality traits in natural populations of trees.     

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.     

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL

Effectiveness of marker-assisted selection (MAS) and quantitative trait loci (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTL depends on the extent of LD and how it declines with distance in a population. Because marker-QTL LD cannot be observed directly, the objective of this study was to evaluate alternative measures of observable LD between multi-allelic markers as predictors of usable LD of multi-allelic markers with presumed biallelic QTL. Observable LD between marker pairs was evaluated using eight existing measures and one new measure. These consisted of two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy-Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. In simulated populations with a range of LD generated by drift and a range of marker polymorphism, marker-marker LD measured by a standardized chi-square statistic (denoted chi(2')) was found to be the best predictor of useable marker-QTL LD for a group of multi-allelic markers. Estimates of the level and decline of marker-marker LD with distance obtained from chi(2') were linearly and highly correlated with usable LD of those markers with QTL across population structures and marker polymorphism. Corresponding relationships were poorer for the other marker-marker LD measures. Therefore, when LD is generated by drift, chi(2') is recommended to quantify the amount and extent of usable LD in a population for QTL mapping and MAS based on multi-allelic markers.     

Linkage disequilibrium in related breeding lines of chickens

High-density genotyping of single-nucleotide polymorphisms (SNPs) enables detection of quantitative trait loci (QTL) by linkage disequilibrium (LD) mapping using LD between markers and QTL and the subsequent use of this information for marker-assisted selection (MAS). The success of LD mapping and MAS depends on the extent of LD in the populations of interest and the use of associations across populations requires LD between loci to be consistent across populations. To assess the extent and consistency of LD in commercial broiler breeding populations, we used genotype data for 959 and 398 SNPs on chromosomes 1 and 4 on 179-244 individuals from each of nine commercial broiler chicken breeding lines. Results show that LD measured by r(2) extends over shorter distances than reported previously in other livestock breeding populations. The LD at short distance (within 1 cM) tended to be consistent across related populations; correlations of LD measured by r for pairs of lines ranged from 0.17 to 0.94 and closely matched the line relationships based on marker allele frequencies. In conclusion, LD-based correlations are good estimates of line relationships and the relationship between a pair of lines a good predictor of LD consistency between the lines.     

Tests of candidate genes in breed cross populations for QTL mapping in livestock

In recent years, several F₂ crosses between outbred lines of livestock have been developed to identify quantitative trait loci (QTL). These populations are valuable for further genetic analysis, including positional candidate gene loci (CGL). Analysis of CGL in F₂ populations is, however, hindered by extensive between-breed linkage disequilibrium (LD). The objectives here were to develop and evaluate three tests for CGL in simulated F₂ breed-cross populations. 1) A standard association test, based on the fixed effect of CGL genotype. This test was significant for CGL at considerable distances from the QTL. 2) A marker-assisted association test, based on a test at the CGL of the fixed effect of CGL genotype in a breed-cross QTL interval mapping model. This removed the impact of between-breed LD, but was not powerful in detecting CGL closely linked to the QTL, unless the CGL was the QTL. 3) An F-drop test, comparing F ratios for a QTL at the CGL with and without the CGL included as fixed effect. It had low power to distinguish close from distant CGL. Power to distinguish two CGL within 10 cM from the QTL was limited and little improved by including QTL effects associated with markers to remove between-breed LD, although the power was greater when one of the CGL was the causative mutation. Therefore, while we conclude that candidate gene tests in QTL mapping populations must be interpreted with caution, we now have a clearer picture of the value of candidate gene tests in these populations.     

关联分析及其在植物遗传学研究中的应用

植物的很多重要经济性状均属于复杂性状。基于连锁分析的QTL作图是研究复杂性状的有效手段,但其尚存在一定的局限性。随着现代生物学的发展,一种基于连锁不平衡的新剖分复杂性状方法——关联分析法,开始应用于植物遗传学研究。与QTL作图法相比,应用关联分析法具有不需要构建特殊的群体,可同时对多个等位基因进行分析,定位QTL精度可达到单基因水平等优势。该文介绍了关联分析方法学的基础和特性,简述了其在植物遗传学研究中的进展情况,并对其未来发展和在植物遗传学研究中的应用进行了展望。     

Comparative LD mapping using single SNPs and haplotypes identifies QTL for plant height and biomass as secondary traits of drought tolerance in maize

Drought often delays developmental events so that plant height and above-ground biomass are reduced, resulting in yield loss due to inadequate photosynthate. In this study, plant height and biomass measured by the Normalized Difference Vegetation Index (NDVI) were used as criteria for drought tolerance. A total of 305 lines representing temperate, tropical and subtropical maize germplasm were genotyped using two single nucleotide polymorphism (SNP) chips each containing 1536 markers, from which 2052 informative SNPs and 386 haplotypes each constructed with two or more SNPs were used for linkage disequilibrium (LD) or association mapping. Single SNP- and haplotype-based LD mapping identified two significant SNPs and three haplotype loci [a total of four quantitative trait loci (QTL)] for plant height under well-watered and water-stressed conditions. For biomass, 32 SNPs and 12 haplotype loci (30 QTL) were identified using NDVIs measured at seven stages under the two water regimes. Some significant SNP and haplotype loci for NDVI were shared by different stages. Comparing significant loci identified by single SNP- and haplotype-based LD mapping, we found that six out of the 14 chromosomal regions defined by haplotype loci each included at least one significant SNP for the same trait. Significant SNP haplotype loci explained much higher phenotypic variation than individual SNPs. Moreover, we found that two significant SNPs (two QTL) and one haplotype locus were shared by plant height and NDVI. The results indicate the power of comparative LD mapping using single SNPs and SNP haplotypes with QTL shared by plant height and biomass as secondary traits for drought tolerance in maize.     

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.     

Multiple Trait Analysis of Genetic Mapping for Quantitative Trait Loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.     

Fine mapping of quantitative trait loci for mastitis resistance on bovine chromosome 11

Quantitative trait loci (QTL) affecting clinical mastitis (CM) and somatic cell score (SCS) were mapped on bovine chromosome 11. The mapping population consisted of 14 grandsire families belonging to three Nordic red cattle breeds: Finnish Ayrshire (FA), Swedish Red and White (SRB) and Danish Red. The families had previously been shown to segregate for udder health QTL. A total of 524 progeny tested bulls were included in the analysis. A linkage map including 33 microsatellite and five SNP markers was constructed. We performed combined linkage disequilibrium and linkage analysis (LDLA) using the whole data set. Further analyses were performed for FA and SRB separately to study the origin of the identified QTL/haplotype and to examine if it was common in both populations. Finally, different two-trait models were fitted. These postulated either a pleiotropic QTL affecting both traits; two linked QTL, each affecting one trait; or one QTL affecting a single trait. A QTL affecting CM was fine-mapped. In FA, a haplotype having a strong association with a high negative effect on mastitis resistance was identified. The mapping precision of an earlier detected SCS-QTL was not improved by the LDLA analysis because of lack of linkage disequilibrium between the markers used and the QTL in the region.     

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.