Multitrait least squares for quantitative trait loci detection

A multiple-trait QTL mapping method using least squares is described. It is presented as an extension of a single-trait method for use with three-generation, outbred pedigrees. The multiple-trait framework allows formal testing of whether the same QTL affects more than one trait (i.e., a pleiotropic QTL) or whether more than one linked QTL are segregating. Several approaches to the testing procedure are presented and their suitability discussed. The performance of the method is investigated by simulation. As previously found, multitrait analyses increase the power to detect a pleiotropic QTL and the precision of its location estimate. With enough information, discrimination between alternative genetic models is possible.     

Bayes factors for detection of Quantitative Trait Loci

A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor.     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

An empirical Bayes method for updating inferences in analysis of quantitative trait loci using information from related genome scans

Individual genome scans for quantitative trait loci (QTL) mapping often suffer from low statistical power and imprecise estimates of QTL location and effect. This lack of precision yields large confidence intervals for QTL location, which are problematic for subsequent fine mapping and positional cloning. In prioritizing areas for follow-up after an initial genome scan and in evaluating the credibility of apparent linkage signals, investigators typically examine the results of other genome scans of the same phenotype and informally update their beliefs about which linkage signals in their scan most merit confidence and follow-up via a subjective-intuitive integration approach. A method that acknowledges the wisdom of this general paradigm but formally borrows information from other scans to increase confidence in objectivity would be a benefit. We developed an empirical Bayes analytic method to integrate information from multiple genome scans. The linkage statistic obtained from a single genome scan study is updated by incorporating statistics from other genome scans as prior information. This technique does not require that all studies have an identical marker map or a common estimated QTL effect. The updated linkage statistic can then be used for the estimation of QTL location and effect. We evaluate the performance of our method by using extensive simulations based on actual marker spacing and allele frequencies from available data. Results indicate that the empirical Bayes method can account for between-study heterogeneity, estimate the QTL location and effect more precisely, and provide narrower confidence intervals than results from any single individual study. We also compared the empirical Bayes method with a method originally developed for meta-analysis (a closely related but distinct purpose). In the face of marked heterogeneity among studies, the empirical Bayes method outperforms the comparator.     

Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis

A novel multitrait fine-mapping method is presented. The method is implemented by a model that treats QTL effects as random variables. The covariance matrix of allelic effects is proportional to the IBD matrix, where each element is the probability that a pair of alleles is identical by descent, given marker information and QTL position. These probabilities are calculated on the basis of similarities of marker haplotypes of individuals of the first generation of genotyped individuals, using "gene dropping" (linkage disequilibrium) and transmission of markers from genotyped parents to genotyped offspring (linkage). A small simulation study based on a granddaughter design was carried out to illustrate that the method provides accurate estimates of QTL position. Results from the simulation also indicate that it is possible to distinguish between a model postulating one pleiotropic QTL affecting two traits vs. one postulating two closely linked loci, each affecting one of the traits.     

Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model

Variance component analysis of quantitative trait loci (QTL) is an important strategy of genetic mapping for complex traits in humans. The method is robust because it can handle an arbitrary number of alleles with arbitrary modes of gene actions. The variance component method is usually implemented using the proportion of alleles with identity-by-descent (IBD) shared by relatives. As a result, information about marker linkage phases in the parents is not required. The method has been studied extensively under either the maximum-likelihood framework or the sib-pair regression paradigm. However, virtually all investigations are limited to normally distributed traits under a single QTL model. In this study, we develop a Bayes method to map multiple QTL. We also extend the Bayesian mapping procedure to identify QTL responsible for the variation of complex binary diseases in humans under a threshold model. The method can also treat the number of QTL as a parameter and infer its posterior distribution. We use the reversible jump Markov chain Monte Carlo method to infer the posterior distributions of parameters of interest. The Bayesian mapping procedure ends with an estimation of the joint posterior distribution of the number of QTL and the locations and variances of the identified QTL. Utilities of the method are demonstrated using a simulated population consisting of multiple full-sib families.     

Experimental designs for reliable detection of linkage disequilibrium in unstructured random population association studies

A method is given for design of experiments to detect associations (linkage disequilibrium) in a random population between a marker and a quantitative trait locus (QTL), or gene, with a given strength of evidence, as defined by the Bayes factor. Using a version of the Bayes factor that can be linked to the value of an F-statistic with an existing deterministic power calculation makes it possible to rapidly evaluate a comprehensive range of scenarios, demonstrating the feasibility, or otherwise, of detecting genes of small effect. The Bayes factor is advocated for use in determining optimal strategies for selecting candidate genes for further testing or applications. The prospects for fine-scale mapping of QTL are reevaluated in this framework. We show that large sample sizes are needed to detect small-effect genes with a respectable-sized Bayes factor, and to have good power to detect a QTL allele at low frequency it is necessary to have a marker with similar allele frequency near the gene.     

Multivariate whole genome average interval mapping: QTL analysis for multiple traits and/or environments

A major aim in some plant-based studies is the determination of quantitative trait loci (QTL) for multiple traits or across multiple environments. Understanding these QTL by trait or QTL by environment interactions can be of great value to the plant breeder. A whole genome approach for the analysis of QTL is presented for such multivariate applications. The approach is an extension of whole genome average interval mapping in which all intervals on a linkage map are included in the analysis simultaneously. A random effects working model is proposed for the multivariate (trait or environment) QTL effects for each interval, with a variance-covariance matrix linking the variates in a particular interval. The significance of the variance-covariance matrix for the QTL effects is tested and if significant, an outlier detection technique is used to select a putative QTL. This QTL by variate interaction is transferred to the fixed effects. The process is repeated until the variance-covariance matrix for QTL random effects is not significant; at this point all putative QTL have been selected. Unlinked markers can also be included in the analysis. A simulation study was conducted to examine the performance of the approach and demonstrated the multivariate approach results in increased power for detecting QTL in comparison to univariate methods. The approach is illustrated for data arising from experiments involving two doubled haploid populations. The first involves analysis of two wheat traits, α-amylase activity and height, while the second is concerned with a multi-environment trial for extensibility of flour dough. The method provides an approach for multi-trait and multi-environment QTL analysis in the presence of non-genetic sources of variation.     

Fine-mapping QTL for mastitis resistance on BTA9 in three Nordic red cattle breeds

A QTL affecting clinical mastitis and/or somatic cell score (SCS) has been reported previously on chromosome 9 from studies in 16 families from the Swedish Red and White (SRB), Finnish Ayrshire (FA) and Danish Red (DR) breeds. In order to refine the QTL location, 67 markers were genotyped over the whole chromosome in the 16 original families and 18 additional half-sib families. This enabled linkage disequilibrium information to be used in the analysis. Data were analysed by an approach that combines information from linkage and linkage disequilibrium, which allowed the QTL affecting clinical mastitis to be mapped to a small interval (<1 cM) between the markers BM4208 and INRA084 . This QTL showed a pleiotropic effect on SCS in the DR and SRB breeds. Haplotypes associated with variations in mastitis resistance were identified. The haplotypes were predictive in the general population and can be used in marker-assisted selection. Pleiotropic effects of the mastitis QTL were studied for three milk production traits and eight udder conformation traits. This QTL was also associated with yield traits in DR but not in FA or SRB. No QTL were found for udder conformation traits on chromosome 9.     

Detection of QTL affecting fatty acid composition in the pig

We present a QTL genome scan for fatty acid composition in pigs. An F₂ cross between Iberian × Landrace pigs and a regression approach fitting the carcass weight as a covariate for QTL identification was used. Chromosomes (Chrs) 4, 6, 8, 10, and 12 showed highly significant effects. The Chr 4 QTL influenced the linoleic content and both the fatty acid double-bond index and peroxidability index. In Chr 6 we found significant associations with the double-bond index and the unsaturated index of fatty acids. Chr 8 showed clear effects on the percentages of palmitic and palmitoleic fatty acids as well as the average chain length of fatty acids. In Chr 10 we detected a significant QTL for the percentage of myristic fatty acid, with an F value that was slightly above the genomewide threshold. The percentage of linolenic fatty acid was affected by a region on Chr 12. A nearly significant QTL for the content of gadoleic fatty acid was also detected in Chr 12. We also analyzed the genomic QTL distribution by a regression model that fits the backfat thickness as a covariate. Some of the QTL that were detected in our analysis could not be detected when the data were corrected by backfat thickness. This work shows how critical the selection of a covariate can be in the interpretation of results. This is the first report of a genome scan detection of QTL directly affecting fatty acid composition in pigs.     

A model for quantitative trait loci mapping,linkage phase,and segregation pattern estimation for a full-sib progeny

Quantitative trait loci (QTL) mapping is an important approach for the study of the genetic architecture of quantitative traits. For perennial species, inbred lines cannot be obtained due to inbreed depression and a long juvenile period. Instead, linkage mapping can be performed by using a full-sib progeny. This creates a complex scenario because both markers and QTL alleles can have different segregation patterns as well as different linkage phases between them. We present a two-step method for QTL mapping using full-sib progeny based on composite interval mapping (i.e., interval mapping with cofactors), considering an integrated genetic map with markers with different segregation patterns and conditional probabilities obtained by a multipoint approach. The model is based on three orthogonal contrasts to estimate the additive effect (one in each parent) and dominance effect. These estimatives are obtained using the EM algorithm. In the first step, the genome is scanned to detect QTL. After, segregation pattern and linkage phases between QTL and markers are estimated. A simulated example is presented to validate the methodology. In general, the new model is more effective than existing approaches, because it can reveal QTL present in a full-sib progeny that segregates in any pattern present and can also identify dominance effects. Also, the inclusion of cofactors provided more statistical power for QTL mapping.     

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

Causal mutations and their intra- and inter-locus interactions play a critical role in complex trait variation. It is often not easy to detect epistatic quantitative trait loci (QTL) due to complicated population structure requirements for detecting epistatic effects in linkage analysis studies and due to main effects often being hidden by interaction effects. Mapping their positions is even harder when they are closely linked. The data structure requirement may be overcome when information on linkage disequilibrium is used. We present an approach using a mixed linear model nested in an empirical Bayesian approach, which simultaneously takes into account additive, dominance and epistatic effects due to multiple QTL. The covariance structure used in the mixed linear model is based on combined linkage disequilibrium and linkage information. In a simulation study where there are complex epistatic interactions between QTL, it is possible to simultaneously map interacting QTL into a small region using the proposed approach. The estimated variance components are accurate and less biased with the proposed approach compared with traditional models.     

Quantifying evidence for candidate gene polymorphisms: Bayesian analysis combining sequence-specific and quantitative trait loci colocation information

We calculate posterior probabilities for candidate genes as a function of genomic location. Posterior probabilities for quantitative trait loci (QTL) presence in a small interval are calculated using a Bayesian model-selection approach based on the Bayesian information criterion (BIC) and used to combine QTL colocation information with sequence-specific evidence, e.g., from differential expression and/or association studies. Our method takes into account uncertainty in estimation of number and locations of QTL and estimated map position. Posterior probabilities for QTL presence were calculated for simulated data with n = 100, 300, and 1200 QTL progeny and compared with interval mapping and composite-interval mapping. Candidate genes that mapped to QTL regions had substantially larger posterior probabilities. Among candidates with a given Bayes factor, those that map near a QTL are more promising for further investigation with association studies and functional testing or for use in marker-aided selection. The BIC is shown to correspond very closely to Bayes factors for linear models with a nearly noninformative Zellner prior for the simulated QTL data with n > or = 100. It is shown how to modify the BIC to use a subjective prior for the QTL effects.     

An 11-bp insertion in Zea mays fatb reduces the palmitic acid content of fatty acids in maize grain

The ratio of saturated to unsaturated fatty acids in maize kernels strongly impacts human and livestock health, but is a complex trait that is difficult to select based on phenotype. Map-based cloning of quantitative trait loci (QTL) is a powerful but time-consuming method for the dissection of complex traits. Here, we combine linkage and association analyses to fine map QTL-Pal9, a QTL influencing levels of palmitic acid, an important class of saturated fatty acid. QTL-Pal9 was mapped to a 90-kb region, in which we identified a candidate gene, Zea mays fatb (Zmfatb), which encodes acyl-ACP thioesterase. An 11-bp insertion in the last exon of Zmfatb decreases palmitic acid content and concentration, leading to an optimization of the ratio of saturated to unsaturated fatty acids while having no effect on total oil content. We used three-dimensional structure analysis to explain the functional mechanism of the ZmFATB protein and confirmed the proposed model in vitro and in vivo. We measured the genetic effect of the functional site in 15 different genetic backgrounds and found a maximum change of 4.57 mg/g palmitic acid content, which accounts for ～20-60% of the variation in the ratio of saturated to unsaturated fatty acids. A PCR-based marker for QTL-Pal9 was developed for marker-assisted selection of nutritionally healthier maize lines. The method presented here provides a new, efficient way to clone QTL, and the cloned palmitic acid QTL sheds lights on the genetic mechanism of oil biosynthesis and targeted maize molecular breeding.     

A two-phase procedure for QTL mapping with regression models

It is typical in QTL mapping experiments that the number of markers under investigation is large. This poses a challenge to commonly used regression models since the number of feature variables is usually much larger than the sample size, especially, when epistasis effects are to be considered. The greedy nature of the conventional stepwise procedures is well known and is even more conspicuous in such cases. In this article, we propose a two-phase procedure based on penalized likelihood techniques and extended Bayes information criterion (EBIC) for QTL mapping. The procedure consists of a screening phase and a selection phase. In the screening phase, the main and interaction features are alternatively screened by a penalized likelihood mechanism. In the selection phase, a low-dimensional approach using EBIC is applied to the features retained in the screening phase to identify QTL. The two-phase procedure has the asymptotic property that its positive detection rate (PDR) and false discovery rate (FDR) converge to 1 and 0, respectively, as sample size goes to infinity. The two-phase procedure is compared with both traditional and recently developed approaches by simulation studies. A real data analysis is presented to demonstrate the application of the two-phase procedure.     

Different models of genetic variation and their effect on genomic evaluation

Background

The theory of genomic selection is based on the prediction of the effects of quantitative trait loci (QTL) in linkage disequilibrium (LD) with markers. However, there is increasing evidence that genomic selection also relies on "relationships" between individuals to accurately predict genetic values. Therefore, a better understanding of what genomic selection actually predicts is relevant so that appropriate methods of analysis are used in genomic evaluations.

Methods

Simulation was used to compare the performance of estimates of breeding values based on pedigree relationships (Best Linear Unbiased Prediction, BLUP), genomic relationships (gBLUP), and based on a Bayesian variable selection model (Bayes B) to estimate breeding values under a range of different underlying models of genetic variation. The effects of different marker densities and varying animal relationships were also examined.

Results

This study shows that genomic selection methods can predict a proportion of the additive genetic value when genetic variation is controlled by common quantitative trait loci (QTL model), rare loci (rare variant model), all loci (infinitesimal model) and a random association (a polygenic model). The Bayes B method was able to estimate breeding values more accurately than gBLUP under the QTL and rare variant models, for the alternative marker densities and reference populations. The Bayes B and gBLUP methods had similar accuracies under the infinitesimal model.

Conclusions

Our results suggest that Bayes B is superior to gBLUP to estimate breeding values from genomic data. The underlying model of genetic variation greatly affects the predictive ability of genomic selection methods, and the superiority of Bayes B over gBLUP is highly dependent on the presence of large QTL effects. The use of SNP sequence data will outperform the less dense marker panels. However, the size and distribution of QTL effects and the size of reference populations still greatly influence the effectiveness of using sequence data for genomic prediction.     

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.     

Fatty acid synthase effects on bovine adipose fat and milk fat

A quantitative trait locus (QTL) was identified by linkage analysis on bovine Chromosome 19 that affects the fatty acid, myristic acid (C14:0), in subcutaneous adipose tissue of pasture-fed beef cattle (99% level: experiment-wise significance). The QTL was also shown to have significant effects on ten fatty acids in the milk fat of pasture-fed dairy cattle. A positional candidate gene for this QTL was identified as fatty acid synthase (FASN), which is a multifunctional enzyme with a central role in the metabolism of lipids. Five single nucleotide polymorphisms (SNPs) were identified in the bovine FASN gene, and animals were genotyped for FASN SNPs in three different cattle resource populations. Linkage and association mapping results using these SNPs were consistent with FASN being the gene underlying the QTL. SNP substitution effects for C14:0 percentage were found to have an effect in the opposite direction in adipose fat to that in milk fat. It is concluded that SNPs in the bovine FASN gene are associated with variation in the fatty acid composition of adipose fat and milk fat.     

Identification of pleiotropic genes and gene sets underlying growth and immunity traits: a case study on Meishan pigs

Both growth and immune capacity are important traits in animal breeding. The animal quantitative trait loci (QTL) database is a valuable resource and can be used for interpreting the genetic mechanisms that underlie growth and immune traits. However, QTL intervals often involve too many candidate genes to find the true causal genes. Therefore, the aim of this study was to provide an effective annotation pipeline that can make full use of the information of Gene Ontology terms annotation, linkage gene blocks and pathways to further identify pleiotropic genes and gene sets in the overlapping intervals of growth-related and immunity-related QTLs. In total, 55 non-redundant QTL overlapping intervals were identified, 1893 growth-related genes and 713 immunity-related genes were further classified into overlapping intervals and 405 pleiotropic genes shared by the two gene sets were determined. In addition, 19 pleiotropic gene linkage blocks and 67 pathways related to immunity and growth traits were discovered. A total of 343 growth-related genes and 144 immunity-related genes involved in pleiotropic pathways were also identified, respectively. We also sequenced and genotyped 284 individuals from Chinese Meishan pigs and European pigs and mapped the single nucleotide polymorphisms (SNPs) to the pleiotropic genes and gene sets that we identified. A total of 971 high-confidence SNPs were mapped to the pleiotropic genes and gene sets that we identified, and among them 743 SNPs were statistically significant in allele frequency between Meishan and European pigs. This study explores the relationship between growth and immunity traits from the view of QTL overlapping intervals and can be generalized to explore the relationships between other traits.