Detection and parameter estimation for quantitative trait loci using regression models and multiple markers

A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.     

Detection of loci affecting milk production and health traits in an elite US Holstein population using microsatellite markers

Quantitative trait loci (QTL) affecting health and milk production traits were studied in seven large half-sib US Holstein families by using the granddaughter design. Genotyping for 16 markers was completed and marker allele differences within and pooled-across families were analysed. Potential QTL were identified for somatic cell score (SCS), fat yield, fat percentage, protein yield and protein percentage. Three markers (BM203, BM4505 and BM2078) were associated with significant effects for different traits and, after further analysis, may be useful in marker-assisted selection in specific families. Comparisons between these data and previously identified QTL support the location of a QTL for milk yield and protein yield on chromosome 21.     

Family-based mapping of quantitative trait loci in plant breeding populations with resistance to Fusarium head blight in wheat as an illustration

Traditional quantitative trait loci (QTL) mapping approaches are typically based on early or advanced generation analysis of bi-parental populations. A limitation associated with this methodology is the fact that mapping populations rarely give rise to new cultivars. Additionally, markers linked to the QTL of interest are often not immediately available for use in breeding and they may not be useful within diverse genetic backgrounds. Use of breeding populations for simultaneous QTL mapping, marker validation, marker assisted selection (MAS), and cultivar release has recently caught the attention of plant breeders to circumvent the weaknesses of conventional QTL mapping. The first objective of this study was to test the feasibility of using family-pedigree based QTL mapping techniques generally used with humans and animals within plant breeding populations (PBPs). The second objective was to evaluate two methods (linkage and association) to detect marker-QTL associations. The techniques described in this study were applied to map the well characterized QTL, Fhb1 for Fusarium head blight resistance in wheat (Triticum aestivum L.). The experimental populations consisted of 82 families and 793 individuals. The QTL was mapped using both linkage (variance component and pedigree-wide regression) and association (using quantitative transmission disequilibrium test, QTDT) approaches developed for extended family-pedigrees. Each approach successfully identified the known QTL location with a high probability value. Markers linked to the QTL explained 40–50% of the phenotypic variation. These results show the usefulness of a human genetics approach to detect QTL in PBPs and subsequent use in MAS.     

Quantitative trait locus-by-environment interaction for milk yield traits on Bos taurus autosome 6

Genotype-by-environment interactions for production traits in dairy cattle have often been observed, while QTL analyses have focused on detecting genes with general effects on production traits. In this study, a QTL search for genes with environmental interaction for the traits milk yield, protein yield, and fat yield were performed on Bos taurus autosome 6 (BTA6), also including information about the previously investigated candidate genes ABCG2 and OPN. The animals in the study were Norwegian Red. Eighteen grandsires and 716 sires were genotyped for 362 markers on BTA6. Every marker bracket was regarded as a putative QTL position. The effects of the candidate genes and the putative QTL were modeled as a regression on an environmental parameter (herd year), which is based on the predicted herd-year effect for the trait. Two QTL were found to have environmentally dependent effects on milk yield. These QTL were located 3.6 cM upstream and 9.1 cM downstream from ABCG2. No environmentally dependent QTL was found to significantly affect protein or fat yield.     

Factors Affecting Accuracy From Genomic Selection in Populations Derived From Multiple Inbred Lines: A Barley Case Study

We compared the accuracies of four genomic-selection prediction methods as affected by marker density, level of linkage disequilibrium (LD), quantitative trait locus (QTL) number, sample size, and level of replication in populations generated from multiple inbred lines. Marker data on 42 two-row spring barley inbred lines were used to simulate high and low LD populations from multiple inbred line crosses: the first included many small full-sib families and the second was derived from five generations of random mating. True breeding values (TBV) were simulated on the basis of 20 or 80 additive QTL. Methods used to derive genomic estimated breeding values (GEBV) were random regression best linear unbiased prediction (RR–BLUP), Bayes-B, a Bayesian shrinkage regression method, and BLUP from a mixed model analysis using a relationship matrix calculated from marker data. Using the best methods, accuracies of GEBV were comparable to accuracies from phenotype for predicting TBV without requiring the time and expense of field evaluation. We identified a trade-off between a method's ability to capture marker-QTL LD vs. marker-based relatedness of individuals. The Bayesian shrinkage regression method primarily captured LD, the BLUP methods captured relationships, while Bayes-B captured both. Under most of the study scenarios, mixed-model analysis using a marker-derived relationship matrix (BLUP) was more accurate than methods that directly estimated marker effects, suggesting that relationship information was more valuable than LD information. When markers were in strong LD with large-effect QTL, or when predictions were made on individuals several generations removed from the training data set, however, the ranking of method performance was reversed and BLUP had the lowest accuracy.     

Merino sheep: a further look at quantitative trait loci for wool production

A quantitative trait loci (QTL) analysis of wool traits from experimental half-sib data of Merino sheep is presented. A total of 617 animals distributed in 10 families were genotyped for 36 microsatellite markers on four ovine chromosomes OAR1, OAR3, OAR4 and OAR11. The markers covering OAR3 and OAR11 were densely spaced, at an average distance of 2.8 and 1.2 cM, respectively. Body weight and wool traits were measured at first and second shearing. Analyses were conducted under three hypotheses: (i) a single QTL controlling a single trait (for multimarker regression models); (ii) two linked QTLs controlling a single trait (using maximum likelihood techniques) and (iii) a single QTL controlling more than one trait (also using maximum likelihood techniques). One QTL was identified for several wool traits on OAR1 (average curvature of fibre at first and second shearing, and clean wool yield measured at second shearing) and on OAR11 (weight and staple strength at first shearing, and coefficient of variation of fibre diameter at second shearing). In addition, one QTL was detected on OAR4 affecting weight measured at second shearing. The results of the single trait method and the two-QTL hypotheses showed an additional QTL segregating on OAR11 (for greasy fleece weight at first shearing and clean wool yield trait at second shearing). Pleiotropic QTLs (controlling more than one trait) were found on OAR1 (clean wool yield, average curvature of fibre, clean and greasy fleece weightand staple length, all measured at second shearing).     

Genome-wide scan for bovine twinning rate QTL using linkage disequilibrium

Twinning is a complex trait with negative impacts on health and reproduction, which cause economic loss in dairy production. Several twinning rate quantitative trait loci (QTL) have been detected in previous studies, but confidence intervals for QTL location are broad and many QTL are unreplicated. To identify genomic regions or genes associated with twinning rate, QTL analysis based on linkage combined with linkage disequilibrium (LLD) and individual marker associations was conducted across the genome using high-throughput single nucleotide polymorphism (SNP) genotypes. A total of 9919 SNP markers were genotyped with 200 sires and sons in 19 half-sib North American Holstein dairy cattle families. After SNPs were genotyped, informative markers were selected for genome-wide association tests and QTL searches. Evidence for twinning rate QTL was found throughout the genome. Thirteen markers significantly associated with twinning rate were detected on chromosomes 2, 5 and 14 ( P  < 2.3 × 10⁻⁵). Twenty-six regions on fourteen chromosomes were identified by LLD analysis at P  < 0.0007. Seven previously reported ovulation or twinning rate QTL were supported by results of single marker association or LLD analyses. Single marker association analysis and LLD mapping were complementary tools for the identification of putative QTL in this genome scan.     

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.     

Use of a novel outbred by inbred F1 cross to detect genetic markers for growth

A unique outbred by inbred F1 resource population was established. The population structure facilitated the unique opportunity of examining gene by genetic background interaction through crossing two modern broiler sires with dams from two unrelated inbred lines, with no selection for growth rate, to produce about 600 F1 chicks. Pools of DNA were generated from the phenotypic extremes (20% high and low) for 8-week body weight for each of the four combinations of sire and dam line. For one sire family, pools were also separately generated for each sex. The pools were genoyped with 25 informative (segregating) microsatellites. This unique F1 cross between outbred and inbred populations allowed use of the inbred alleles as an 'internal control' for polymerase chain reaction amplification quality in DNA pools. Ten microsatellites showed marked differences (P < 0.05) in allele frequencies between high and low pools, suggesting an association between marker and quantitative trait loci (QTL). These differences were verified using selective genotyping. For many markers, differences in allele frequencies between the high and the low pools, or marker effect, varied between the two dam lines and the two sexes, suggesting an interaction between some genes and the genetic background as represented by different dam lines or sexes. The suggestive marker-QTL associations identified in this F1 population demonstrate the efficiency of this population design while different QTL effects in different genetic line crosses and sexes highlight the importance of gene by genetic background interaction in QTL detection.     

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 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.     

Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.     

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.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence

Summary A Bayesian method was developed for identifying genetic markers linked to quantitative trait loci (QTL) by analyzing data from daughter or granddaughter designs and single markers or marker pairs. Traditional methods may yield unrealistic results because linkage tests depend on number of markers and QTL gene effects associated with selected markers are overestimated. The Bayesian or posterior probability of linkage combines information from a daughter or granddaughter design with the prior probability of linkage between a marker locus and a QTL. If the posterior probability exceeds a certain quantity, linkage is declared. Upon linkage acceptance, Bayesian estimates of marker-QTL recombination rate and QTL gene effects and frequencies are obtained. The Bayesian estimates of QTL gene effects account for different amounts of information by shrinking information from data toward the mean or mode of a prior exponential distribution of gene effects. Computation of the Bayesian analysis is feasible. Exact results are given for biallelic QTL, and extensions to multiallelic QTL are suggested.     

Advances in Statistical Methods to Map Quantitative Trait Loci in Outbred Populations

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.     

Mapping of QTL for Body Conformation and Behavior in Cattle

Genome scans for quantitative trait loci (QTL) in farm animals have concentrated on primary production and health traits, and information on QTL for other important traits is rare. We performed a whole genome scan in a granddaughter design to detect QTL affecting body conformation and behavior in dairy cattle. The analysis included 16 paternal half-sib families of the Holstein breed with 872 sons and 264 genetic markers. The markers were distributed across all 29 autosomes and the pseudoautosomal region of the sex chromosomes with average intervals of 13.9 cM and covering an estimated 3155.5 cM. All families were analyzed jointly for 22 traits using multimarker regression and significance thresholds determined empirically by permutation. QTL that exceeded the experiment-wise significance threshold (5% level) were detected on chromosome 6 for foot angle, teat placement, and udder depth, and on chromosome 29 for temperament. QTL approaching experiment-wise significance (10% level) were located on chromosome 6 for general quality of feet and legs and general quality of udder, on chromosome 13 for teat length, on chromosome 23 for general quality of feet and legs, and on chromosome 29 for milking speed. An additional 51 QTL significant at the 5% chromosome-wise level were distributed over 21 chromosomes. This study provides the first evidence for QTL involved in behavior of dairy cattle and identifies QTL for udder conformation on chromosome 6 that could form the basis of recently reported QTL for clinical mastitis.     

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 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.     

Methods for the detection of multiple linked QTL applied to a mixture of full and half sib families

A new multiple trait strategy based on discriminant analysis was studied for efficient detection of linked QTL in outbred sib families, in comparison with a multivariate likelihood technique. The discriminant analysis technique describes the segregation of a linear combination of the traits in a univariate likelihood. This combination is calculated for each pair of positions depending on the inheritance of the pairs of QTL haplotypes in the progeny. The gains in power and accuracy for position estimations of multiple trait methods in grid searches were evaluated in reference to single trait detections of linked QTL. The methods were applied to simulated designs with two correlated traits submitted to various effects from the linked QTL. Multiple trait strategies were generally more powerful and accurate than the single trait technique. Linked QTL were distinguished when they were separated enough to identify informative recombinations: at least two genetic markers and 25 cM between the QTL under the simulated conditions. Except in a particular case, discriminant analysis was at least as powerful as the multivariate technique and its implementation was five times faster. Combining the advantages from both methodologies, we finally propose a complete strategy for rapid and efficient systematic multivariate detections in outbred populations.     

Quantitative trait loci affecting lactose and total solids on chromosome 6 in Brazilian Gir dairy cattle

Fourteen Brazilian Gir sire families with 657 daughters were analyzed for quantitative trait loci (QTL) on chromosome 6 affecting lactose and total solids. Cows and sires were genotyped with 27 microsatellites with a mean spacing between markers of 4.9 cM. We used a 1% chromosome-wide threshold for QTL qualification. A QTL for lactose yield was found close to marker MNB66 in three families. A QTL for total solid yield was identified close to marker BMS2508 in three families. A QTL for lactose percentage, close to marker DIK1182, was identified in two families. A QTL for total solid percentage, close to marker MNB208, was identified in four families. These QTLs could be used for selection of animals in dairy production systems.