Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses

ABSTRACT: BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.     

Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genomewide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F(2) intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses.     

Mapping quantitative trait loci with epistatic effects

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.     

Bayesian quantitative trait loci mapping for multiple traits

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.     

遗传基因组学(Genetical genomics)的研究进展

遗传基因组学(geneticalgenomics)是将微阵列技术和数量性状座位(QTL)分析结合起来,全基因组水平上定位基因表达的QTL(eQTL).它为研究复杂性状的分子机理和调控网络提供全新的手段.遗传基因组这个概念和研究策略在2001年由Janson和Nap首先提出,到目前为止,遗传基因组学已应用于酵母、老鼠、人以及玉米等植物.研究结果表明:基因表达水平的差异是可遗传的复杂性状;eQTL可以分为顺式作用eQTL和反式作用eQTL,顺式作用eQTL就是某个基因的eQTL定位到该基因所在的基因组区域,表明可能是该基因本身的差别引起mRNA水平的差别,反式作用就是eQTL定位到其他基因组区域,表明其他基因的差别控制该基因mRNA水平的差异.将eQTL结果、基因功能注解以及多种统计分析方法相结合,不仅能更准确地鉴别控制复杂性状及其相关基因表达的候选基因,而且能构建相应的基因调控网络.     

Sequential elimination of major-effect contributors identifies additional quantitative trait loci conditioning high-temperature growth in yeast

Several quantitative trait loci (QTL) mapping strategies can successfully identify major-effect loci, but often have poor success detecting loci with minor effects, potentially due to the confounding effects of major loci, epistasis, and limited sample sizes. To overcome such difficulties, we used a targeted backcross mapping strategy that genetically eliminated the effect of a previously identified major QTL underlying high-temperature growth (Htg) in yeast. This strategy facilitated the mapping of three novel QTL contributing to Htg of a clinically derived yeast strain. One QTL, which is linked to the previously identified major-effect QTL, was dissected, and NCS2 was identified as the causative gene. The interaction of the NCS2 QTL with the first major-effect QTL was background dependent, revealing a complex QTL architecture spanning these two linked loci. Such complex architecture suggests that more genes than can be predicted are likely to contribute to quantitative traits. The targeted backcrossing approach overcomes the difficulties posed by sample size, genetic linkage, and epistatic effects and facilitates identification of additional alleles with smaller contributions to complex traits.     

Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.     

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.     

Genetical genomics in livestock: potentials and pitfalls

Genetical genomics combines gene mapping and gene expression approaches to identify loci controlling gene expression (eQTLs) that may underlie functional trait variation. The combination of genomic tools has great potential to facilitate dissection of complex traits, but studies need careful design and interpretation. Here we explore both the potential and the pitfalls of this approach with illustrations from actual studies. There are now an appreciable number of studies in model species and even humans demonstrating the feasibility of genetical genomics. However, most studies are too limited in size and design to unlock the full potential of the approach. Limited statistical power of studies exacerbates the problem of detection of false-positive eQTL and some reported results should be interpreted with caution. As one approach to more successful implementation of genetical genomics, we propose to combine expression studies with fine mapping of functional trait loci. This synergistic approach facilitates the implementation of genetical genomics for species without inbred resources but is equally applicable to model species. These properties make it particularly suitable for livestock populations where many QTL are already in the public domain and potentially very large pedigreed populations can be accessed.     

Genetic complexity and quantitative trait loci mapping of yeast morphological traits

Functional genomics relies on two essential parameters: the sensitivity of phenotypic measures and the power to detect genomic perturbations that cause phenotypic variations. In model organisms, two types of perturbations are widely used. Artificial mutations can be introduced in virtually any gene and allow the systematic analysis of gene function via mutants fitness. Alternatively, natural genetic variations can be associated to particular phenotypes via genetic mapping. However, the access to genome manipulation and breeding provided by model organisms is sometimes counterbalanced by phenotyping limitations. Here we investigated the natural genetic diversity of Saccharomyces cerevisiae cellular morphology using a very sensitive high-throughput imaging platform. We quantified 501 morphological parameters in over 50,000 yeast cells from a cross between two wild-type divergent backgrounds. Extensive morphological differences were found between these backgrounds. The genetic architecture of the traits was complex, with evidence of both epistasis and transgressive segregation. We mapped quantitative trait loci (QTL) for 67 traits and discovered 364 correlations between traits segregation and inheritance of gene expression levels. We validated one QTL by the replacement of a single base in the genome. This study illustrates the natural diversity and complexity of cellular traits among natural yeast strains and provides an ideal framework for a genetical genomics dissection of multiple traits. Our results did not overlap with results previously obtained from systematic deletion strains, showing that both approaches are necessary for the functional exploration of genomes.     

Combining data from multiple inbred line crosses improves the power and resolution of quantitative trait loci mapping

Rodent inbred line crosses are widely used to map genetic loci associated with complex traits. This approach has proven to be powerful for detecting quantitative trait loci (QTL); however, the resolution of QTL locations, typically approximately 20 cM, means that hundreds of genes are implicated as potential candidates. We describe analytical methods based on linear models to combine information available in two or more inbred line crosses. Our strategy is motivated by the hypothesis that common inbred strains of the laboratory mouse are derived from a limited ancestral gene pool and thus QTL detected in multiple crosses are likely to represent shared ancestral polymorphisms. We demonstrate that the combined-cross analysis can improve the power to detect weak QTL, can narrow support intervals for QTL regions, and can be used to separate multiple QTL that colocalize by chance. Moreover, combined-cross analysis can establish the allelic states of a QTL among a set of parental lines, thus providing critical information for narrowing QTL regions by haplotype analysis.     

Incorporating pleiotropic quantitative trait loci in dissection of complex traits: seed yield in rapeseed as an example

Key message

A comprehensive linkage atlas for seed yield in rapeseed.

Abstract

Most agronomic traits of interest for crop improvement (including seed yield) are highly complex quantitative traits controlled by numerous genetic loci, which brings challenges for comprehensively capturing associated markers/genes. We propose that multiple trait interactions underlie complex traits such as seed yield, and that considering these component traits and their interactions can dissect individual quantitative trait loci (QTL) effects more effectively and improve yield predictions. Using a segregating rapeseed (Brassica napus) population, we analyzed a large set of trait data generated in 19 independent experiments to investigate correlations between seed yield and other complex traits, and further identified QTL in this population with a SNP-based genetic bin map. A total of 1904 consensus QTL accounting for 22 traits, including 80 QTL directly affecting seed yield, were anchored to the B. napus reference sequence. Through trait association analysis and QTL meta-analysis, we identified a total of 525 indivisible QTL that either directly or indirectly contributed to seed yield, of which 295 QTL were detected across multiple environments. A majority (81.5%) of the 525 QTL were pleiotropic. By considering associations between traits, we identified 25 yield-related QTL previously ignored due to contrasting genetic effects, as well as 31 QTL with minor complementary effects. Implementation of the 525 QTL in genomic prediction models improved seed yield prediction accuracy. Dissecting the genetic and phenotypic interrelationships underlying complex quantitative traits using this method will provide valuable insights for genomics-based crop improvement.

     

Multiple-interval mapping for quantitative trait loci controlling endosperm traits

Endosperm traits are trisomic inheritant and are of great economic importance because they are usually directly related to grain quality. Mapping for quantitative trait loci (QTL) underlying endosperm traits can provide an efficient way to genetically improve grain quality. As the traditional QTL mapping methods (diploid methods) are usually designed for traits under diploid control, they are not the ideal approaches to map endosperm traits because they ignore the triploid nature of endosperm. In this article, a statistical method considering the triploid nature of endosperm (triploid method) is developed on the basis of multiple-interval mapping (MIM) to map for the underlying QTL. The proposed triploid MIM method is derived to broadly use the marker information either from only the maternal plants or from both the maternal plants and their embryos in the backcross and F2 populations for mapping endosperm traits. Due to the use of multiple intervals simultaneously to take multiple QTL into account, the triploid MIM method can provide better detection power and estimation precision, and as shown in this article it is capable of analyzing and searching for epistatic QTL directly as compared to the traditional diploid methods and current triploid methods using only one (or two) interval(s). Several important issues in endosperm trait mapping, such as the relation and differences between the diploid and triploid methods, variance components of genetic variation, and the problems if effects are present and ignored, are also addressed. Simulations are performed to further explore these issues, to investigate the relative efficiency of different experimental designs, and to evaluate the performance of the proposed and current methods in mapping endosperm traits. The MIM-based triploid method can provide a powerful tool to estimate the genetic architecture of endosperm traits and to assist the marker-assisted selection for the improvement of grain quality in crop science. The triploid MIM FORTRAN program for mapping endosperm traits is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Enhanced efficiency of quantitative trait loci mapping analysis based on multivariate complexes of quantitative traits

An approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F(2)/F(3) mapping population of tetraploid wheat (Triticum durum x T. dicoccoides) is provided.     

Complexities in the genetic dissection of quantitative trait loci

The analysis of complex traits, including those involved in many common diseases, has encountered significant difficulties, and, despite major efforts during the past decade, has had little success. Current advances in genomics, however, promise to change this. Recently, Steinmetz et al. used a new technique to produce the first complete quantitative trait locus (QTL) analysis of a complex trait from phenotype to gene to be published entirely in a single report. This marks a significant advance over previous QTL analyses, which took several years. The work exemplifies some of the complexities of QTL mapping and demonstrates a novel method to resolve the underlying genetic architecture of QTLs in yeast. Here we discuss this work in the general context of genetic dissection of complex traits and QTLs.     

Major quantitative trait loci affect resistance to infectious pancreatic necrosis in Atlantic salmon (Salmo salar)

Infectious pancreatic necrosis (IPN) is a viral disease currently presenting a major problem in the production of Atlantic salmon (Salmon salar). IPN can cause significant mortality to salmon fry within freshwater hatcheries and to smolts following transfer to seawater, although challenged populations show clear genetic variation in resistance. To determine whether this genetic variation includes loci of major effect, a genomewide quantitative trait loci (QTL) scan was performed within 10 full-sib families that had received a natural seawater IPN challenge. To utilize the large difference between Atlantic salmon male and female recombination rates, a two-stage mapping strategy was employed. Initially, a sire-based QTL analysis was used to detect linkage groups with significant effects on IPN resistance, using two to three microsatellite markers per linkage group. A dam-based analysis with additional markers was then used to confirm and position any detected QTL. Two genomewide significant QTL and one suggestive QTL were detected in the genome scan. The most significant QTL was mapped to linkage group 21 and was significant at the genomewide level in both the sire and the dam-based analyses. The identified QTL can be applied in marker-assisted selection programs to improve the resistance of salmon to IPN and reduce disease-related mortality.     

Quantitative trait loci mapping in dairy cattle: review and meta-analysis

From an extensive review of public domain information on dairy cattle quantitative trait loci (QTL), we have prepared a draft online QTL map for dairy production traits. Most publications (45 out of 55 reviewed) reported QTL for the major milk production traits (milk, fat and protein yield, and fat and protein concentration (%)) and somatic cell score. Relatively few QTL studies have been reported for more complex traits such as mastitis, fertility and health. The collated QTL map shows some chromosomal regions with a high density of QTL, as well as a substantial number of QTL at single chromosomal locations. To extract the most information from these published records, a meta-analysis was conducted to obtain consensus on QTL location and allelic substitution effect of these QTL. This required modification and development of statistical methodologies. The meta-analysis indicated a number of consensus regions, the most striking being two distinct regions affecting milk yield on chromosome 6 at 49 cM and 87 cM explaining 4.2 and 3.6 percent of the genetic variance of milk yield, respectively. The first of these regions (near marker BM143) affects five separate milk production traits (protein yield, protein percent, fat yield, fat percent, as well as milk yield).     

On the generalized poisson regression mixture model for mapping quantitative trait loci with count data

Statistical methods for mapping quantitative trait loci (QTL) have been extensively studied. While most existing methods assume normal distribution of the phenotype, the normality assumption could be easily violated when phenotypes are measured in counts. One natural choice to deal with count traits is to apply the classical Poisson regression model. However, conditional on covariates, the Poisson assumption of mean-variance equality may not be valid when data are potentially under- or overdispersed. In this article, we propose an interval-mapping approach for phenotypes measured in counts. We model the effects of QTL through a generalized Poisson regression model and develop efficient likelihood-based inference procedures. This approach, implemented with the EM algorithm, allows for a genomewide scan for the existence of QTL throughout the entire genome. The performance of the proposed method is evaluated through extensive simulation studies along with comparisons with existing approaches such as the Poisson regression and the generalized estimating equation approach. An application to a rice tiller number data set is given. Our approach provides a standard procedure for mapping QTL involved in the genetic control of complex traits measured in counts.