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.     

Multipoint identity-by-descent prediction using dense markers to map quantitative trait loci and estimate effective population size

A novel multipoint method, based on an approximate coalescence approach, to analyze multiple linked markers is presented. Unlike other approximate coalescence methods, it considers all markers simultaneously but only two haplotypes at a time. We demonstrate the use of this method for linkage disequilibrium (LD) mapping of QTL and estimation of effective population size. The method estimates identity-by-descent (IBD) probabilities between pairs of marker haplotypes. Both LD and combined linkage and LD mapping rely on such IBD probabilities. The method is approximate in that it considers only the information on a pair of haplotypes, whereas a full modeling of the coalescence process would simultaneously consider all haplotypes. However, full coalescence modeling is computationally feasible only for few linked markers. Using simulations of the coalescence process, the method is shown to give almost unbiased estimates of the effective population size. Compared to direct marker and haplotype association analyses, IBD-based QTL mapping showed clearly a higher power to detect a QTL and a more realistic confidence interval for its position. The modeling of LD could be extended to estimate other LD-related parameters such as recombination rates.     

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background

In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation.

Methods

For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers.

Results

The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers.

Conclusions

The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritability.     

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.     

植物QTL分析的理论研究进展

数量性状的表型是由数量性状基因座 ( Quantitative trait locus,QTL)和环境效应共同作用的结果。传统的数量遗传学采用统计学的方法由一级统计量和二级统计量描述处理 QTL的复合作用 ,估计各种遗传参数 (例如遗传力、遗传相关、遗传进度、有效因子数等 ) ,用于指导遗传育种实践。然而 ,在传统的数量遗传学分析中 ,往往假设数量性状受微效多基因控制 ,这些基因具有相同的并且是较微小的效应 ,所估计的遗传参数反映的是数量性状多基因系统的整体特征 ,其理论方法不能用于追踪研究和描述单个数量性状基因的作用。近年来 ,由于分子生物学技…     

Fine mapping quantitative trait loci affecting milk production traits on bovine chromosome 6 in a Chinese Holstein population

To fine map the previously detected quantitative trait loci （QTLs） affecting milk production traits on bovine chromosome 6 （BTA6）, 15 microsatellite markers situated within an interval of 14.3 cM spanning from BMS690 to BM4528 were selected and 918 daughters of 8 sires were genotyped. Two mapping approaches, haplotype sharing based LD mapping and single marker regression mapping, were used to analyze the data. Both approaches revealed a quantitative trait locus （QTL） with significant effects on milk yield, fat yield and protein yield located in the segment flanked by markers BMS483 and MNB209, which spans a genetic distance of 0.6 cM and a physical distance of 1.5 Mb. In addition, the single marker regression mapping also revealed a QTL affecting fat percentage and protein percentage at marker DIK2291. Our fine mapping work will facilitate the cloning of candidate genes underlying the QTLs for milk production traits.     

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.     

Interactions between markers can be caused by the dominance effect of quantitative trait loci

F₂ populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F₂ populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F₂ population.     

Accuracy of marker-assisted selection with single markers and marker haplotypes in cattle

A key question for the implementation of marker-assisted selection (MAS) using markers in linkage disequilibrium with quantitative trait loci (QTLs) is how many markers surrounding each QTL should be used to ensure the marker or marker haplotypes are in sufficient linkage disequilibrium (LD) with the QTL. In this paper we compare the accuracy of MAS using either single markers or marker haplotypes in an Angus cattle data set consisting of 9323 genome-wide single nucleotide polymorphisms (SNPs) genotyped in 379 Angus cattle. The extent of LD in the data set was such that the average marker-marker r2 was 0.2 at 200 kb. The accuracy of MAS increased as the number of markers in the haplotype surrounding the QTL increased, although only when the number of markers in the haplotype was 4 or greater did the accuracy exceed that achieved when the SNP in the highest LD with the QTL was used. A large number of phenotypic records (>1000) were required to accurately estimate the effects of the haplotypes.     

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.     

Durability of marker-quantitative trait loci haplotypes in structured populations

Given the relative ease of identifying genetic markers linked to QTL (compared to finding the loci themselves), it is natural to ask whether linked markers can be used to address questions concerning the contemporary dynamics and recent history of the QTL. In particular, can a marker allele found associated with a QTL allele in a QTL mapping study be used to track population dynamics or the history of the QTL allele? For this strategy to succeed, the marker-QTL haplotype must persist in the face of recombination over the relevant time frame. Here we investigate the dynamics of marker-QTL haplotype frequencies under recombination, population structure, and divergent selection to assess the potential utility of linked markers for a population genetic study of QTL. For two scenarios, described as "secondary contact" and "novel allele," we use both deterministic and stochastic methods to describe the influence of gene flow between habitats, the strength of divergent selection, and the genetic distance between a marker and the QTL on the persistence of marker-QTL haplotypes. We find that for most reasonable values of selection on a locus (s < or = 0.5) and migration (m > 1%) between differentially selected populations, haplotypes of typically spaced markers (5 cM) and QTL do not persist long enough (>100 generations) to provide accurate inference of the allelic state at the QTL.     

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.     

Optimal use of regression models in genome-wide association studies

The performance of linear regression models in genome-wide association studies is influenced by how marker information is parameterized in the model. Considering the impact of parameterization is especially important when using information from multiple markers to test for association. Properties of the population, such as linkage disequilibrium (LD) and allele frequencies, will also affect the ability of a model to provide statistical support for an underlying quantitative trait locus (QTL). Thus, for a given location in the genome, the relationship between population properties and model parameterization is expected to influence the performance of the model in providing evidence for the position of a QTL. As LD and allele frequencies vary throughout the genome and between populations, understanding the relationship between these properties and model parameterization is of considerable importance in order to make optimal use of available genomic data. Here, we evaluate the performance of regression-based association models using genotype and haplotype information across the full spectrum of allele frequency and LD scenarios. Genetic marker data from 200 broiler chickens were used to simulate genomic conditions by selecting individual markers to act as surrogate QTL (sQTL) and then investigating the ability of surrounding markers to estimate sQTL genotypes and provide statistical support for their location. The LD and allele frequencies of markers and sQTL are shown to have a strong effect on the performance of models relative to one another. Our results provide an indication of the best choice of model parameterization given certain scenarios of marker and QTL LD and allele frequencies. We demonstrate a clear advantage of haplotype-based models, which account for phase uncertainty over other models tested, particularly for QTL with low minor allele frequencies. We show that the greatest advantage of haplotype models over single-marker models occurs when LD between markers and the causal locus is low. Under these situations, haplotype models have a greater accuracy of predicting the location of the QTL than other models tested.     

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.     

The effect of an imprecise map on interval mapping QTLs

The statistical analysis of quantitative trait locus (QTL) experiments relies on the use of a linkage map of the markers genotyped. Such a map is, at best, a good estimate of the true map. Resources might be diverted into developing better marker maps or improved maps become available after the analysis, raising concerns over the original analysis. It is therefore important to understand the sensitivity of QTL analysis to map inaccuracy. We have used simulation methods to investigate the consequences of an incorrect map on the results of a QTL analysis using interval mapping. Backcross data sets were generated with a particular map and then analysed with both the correct map and incorrect maps. If the incorrect maps maintained the true linkage groups (i.e. no markers were incorrectly assigned to another linkage group), the accuracy of the map had little or no impact on the ability to detect QTLs, the true significance levels of the tests or the relative placement of QTLs. When a marker was incorrectly placed on another linkage group, there was a small increase in the level of the test. After adjusting for this increase, there was a decrease in power to detect a QTL near the misplaced marker. This decrease was of a similar magnitude to that found when using a single-marker analysis compared with interval mapping. These results mean that QTL analyses can proceed without the need for very accurate marker maps, and that estimated QTL positions can be translated onto updated maps without the need for reanalysis.     

Modeling of identity-by-descent processes along a chromosome between haplotypes and their genotyped ancestors

Identity-by-descent probabilities are important for many applications in genetics. Here we propose a method for modeling the transmission of the haplotypes from the closest genotyped relatives along an entire chromosome. The method relies on a hidden Markov model where hidden states correspond to the set of all possible origins of a haplotype within a given pedigree. Initial state probabilities are estimated from average genetic contribution of each origin to the modeled haplotype while transition probabilities are computed from recombination probabilities and pedigree relationships between the modeled haplotype and the various possible origins. The method was tested on three simulated scenarios based on real data sets from dairy cattle, Arabidopsis thaliana, and maize. The mean identity-by-descent probabilities estimated for the truly inherited parental chromosome ranged from 0.94 to 0.98 according to the design and the marker density. The lowest values were observed in regions close to crossing over or where the method was not able to discriminate between several origins due to their similarity. It is shown that the estimated probabilities were correctly calibrated. For marker imputation (or QTL allele prediction for fine mapping or genomic selection), the method was efficient, with 3.75% allelic imputation error rates on a dairy cattle data set with a low marker density map (1 SNP/Mb). The method should prove useful for situations we are facing now in experimental designs and in plant and animal breeding, where founders are genotyped with relatively high markers densities and last generation(s) genotyped with a lower-density panel.     

Quantitative trait loci for yield components in oil palm (Elaeis guineensis Jacq.)

The development of an oil palm RFLP marker map has enabled marker-based QTL mapping studies to be undertaken. Information from 153 RFLP markers was used in combination with phenotypic data from an F₂ population to estimate the position and effects of quantitative trait loci (QTLs) for traits including yield of fruit and its components and measures of vegetative growth. The mapping population consisted of 84 palms segregating for the major gene influencing shell thickness. Marker data were analysed to produce a linkage map consisting of 22 linkage groups. The QTL mapping analysis was carried out by interval mapping and single-marker analysis for the unlinked markers; significance thresholds were generated by permutation. Using both single-marker and interval-mapping analysis significant marker associated QTL effects were found for 11 of the 13 traits analysed. The results of interval-mapping analysis of fruit weight, petiole cross section and rachis length, and ratios of shell:fruit, mesocarp:fruit and kernel:fruit indicated significant (P<0.05) QTLs at the genome-wide threshold. The putative QTLs were associated with between 8.2% and 44.0% of the phenotypic variation, with an average of 27% for the single-marker analysis and 19% for the interval-mapping analysis. The higher percentage of phenotypic variation explained in the single-marker analysis, when compared to the interval-mapping analysis, is likely to be due to the lower stringency associated with the single-marker analysis. Large dominance deviations were associated with a sizeable proportion of the putative QTLs. The ultimate objective of mapping QTLs in commercial populations is to utilise novel breeding strategies such as marker-assisted selection (MAS). The potential impact of MAS in oil palm breeding programmes is discussed. Received: 26 June 2000 / Accepted: 24 October 2000     

Performance of single nucleotide polymorphisms versus haplotypes for genome-wide association analysis in barley

Genome-wide association studies (GWAS) may benefit from utilizing haplotype information for making marker-phenotype associations. Several rationales for grouping single nucleotide polymorphisms (SNPs) into haplotype blocks exist, but any advantage may depend on such factors as genetic architecture of traits, patterns of linkage disequilibrium in the study population, and marker density. The objective of this study was to explore the utility of haplotypes for GWAS in barley (Hordeum vulgare) to offer a first detailed look at this approach for identifying agronomically important genes in crops. To accomplish this, we used genotype and phenotype data from the Barley Coordinated Agricultural Project and constructed haplotypes using three different methods. Marker-trait associations were tested by the efficient mixed-model association algorithm (EMMA). When QTL were simulated using single SNPs dropped from the marker dataset, a simple sliding window performed as well or better than single SNPs or the more sophisticated methods of blocking SNPs into haplotypes. Moreover, the haplotype analyses performed better 1) when QTL were simulated as polymorphisms that arose subsequent to marker variants, and 2) in analysis of empirical heading date data. These results demonstrate that the information content of haplotypes is dependent on the particular mutational and recombinational history of the QTL and nearby markers. Analysis of the empirical data also confirmed our intuition that the distribution of QTL alleles in nature is often unlike the distribution of marker variants, and hence utilizing haplotype information could capture associations that would elude single SNPs. We recommend routine use of both single SNP and haplotype markers for GWAS to take advantage of the full information content of the genotype data.     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

Mapping quantitative trait loci using the experimental designs of recombinant inbred populations

In the data collection of the QTL experiments using recombinant inbred (RI) populations, when individuals are genotyped for markers in a population, the trait values (phenotypes) can be obtained from the genotyped individuals (from the same population) or from some progeny of the genotyped individuals (from the different populations). Let Fu be the genotyped population and Fv (v>or=u) be the phenotyped population. The experimental designs that both marker genotypes and phenotypes are recorded on the same populations can be denoted as (Fu/Fv, u=v) designs and that genotypes and phenotypes are obtained from the different populations can be denoted as (Fu/Fv, v>u) designs. Although most of the QTL mapping experiments have been conducted on the backcross and F2(F2/F2) designs, the other (Fu/Fv, v>or=u) designs are also very popular. The great benefits of using the other (Fu/Fv, v>or=u) designs in QTL mapping include reducing cost and environmental variance by phenotyping several progeny for the genotyped individuals and taking advantages of the changes in population structures of other RI populations. Current QTL mapping methods including those for the (Fu/Fv, u=v) designs, mostly for the backcross or F2/F2 design, and for the F2/F3 design based on a one-QTL model are inadequate for the investigation of the mapping properties in the (Fu/Fv, uor=u) designs. In addition, the QTL mapping properties of the proposed and approximate methods in different designs are discussed. Simulations were performed to evaluate the performance of the proposed and approximate methods. The proposed method is proven to be able to correct the problems of the approximate and current methods for improving the resolution of genetic architecture of quantitative traits and can serve as an effective tool to explore the QTL mapping study in the system of RI populations.