Multi-QTL mapping for quantitative traits using distorted markers

Marker segregation distortion is a common natural phenomenon. However, relatively little is known about utilizing distorted markers for detecting quantitative trait loci (QTL). Therefore, in this study we proposed a multi-QTL mapping approach that uses distorted markers. First, the information from all markers, including distorted markers, was used to detect segregation distortion loci (SDL). Second, the information from the detected SDL was used to correct the conditional probabilities of the QTL genotypes conditional on marker information, and these corrected probabilities were then incorporated into a multi-QTL mapping methodology. Finally, the proposed approach was validated by both Monte Carlo simulation studies and real data analysis. The results from the simulation studies show that as long as one or two SDL are placed around the simulated QTL, there are no differences between the new method and the ordinary interval mapping method in terms of the power of QTL detection or the estimates of the position and dominant effects of the QTL. However, the power of QTL detection is higher under the dominant genetic model of SDL than under the additive genetic model, and the estimate for the additive effect of QTL using the new method is significantly different from the estimate obtained using ordinary interval mapping. The above results were further confirmed by the detection of QTL for dried soymilk in 222 F_2:4 families in soybean.     

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.     

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/).     

Dimension reduction for mapping mRNA abundance as quantitative traits

The advent of sophisticated genomic techniques for gene mapping and microarray analysis has provided opportunities to map mRNA abundance to quantitative trait loci (QTL) throughout the genome. Unfortunately, simple mapping of each individual mRNA trait on the scale of a typical microarray experiment is computationally intensive, subject to high sample variance, and therefore underpowered. However, this problem can be addressed by capitalizing on correlation among the large number of mRNA traits. We present a method to reduce the dimensionality for mapping gene expression data as quantitative traits. We used a blind method, principal components, and a sighted method, hierarchical clustering seeded by disease relevant traits, to define new traits composed of a small collection of promising mRNAs. We validated the principle of our approach by mapping the expression levels of metabolism genes in a population of F(2)-ob/ob mice derived from the BTBR and C57BL/6J strains. We found that lipogenic and gluconeogenic mRNAs, which are known targets of insulin action, were closely associated with the insulin trait. Multiple interval mapping and Bayesian interval mapping of this new trait revealed significant linkages to chromosome regions that were contained in loci associated with type 2 diabetes in this same mouse sample. As a further statistical refinement, we show that principal component analysis also effectively reduced dimensions for mapping phenotypes composed of mRNA abundances.     

Bayesian functional mapping of dynamic quantitative traits

Without consideration of other linked QTLs responsible for dynamic trait, original functional mapping based on a single QTL model is not optimal for analyzing multiple dynamic trait loci. Despite that composite functional mapping incorporates the effects of genetic background outside the tested QTL in mapping model, the arbitrary choice of background markers also impact on the power of QTL detection. In this study, we proposed Bayesian functional mapping strategy that can simultaneously identify multiple QTL controlling developmental patterns of dynamic traits over the genome. Our proposed method fits the change of each QTL effect with the time by Legendre polynomial and takes the residual covariance structure into account using the first autoregressive equation. Also, Bayesian shrinkage estimation was employed to estimate the model parameters. Especially, we specify the gamma distribution as the prior for the first-order auto-regressive coefficient, which will guarantee the convergence of Bayesian sampling. Simulations showed that the proposed method could accurately estimate the QTL parameters and had a greater statistical power of QTL detection than the composite functional mapping. A real data analysis of leaf age growth in rice is used for the demonstration of our method. It shows that our Bayesian functional mapping can detect more QTLs as compared to composite functional mapping.     

Mapping quantitative trait loci controlling variation in forage quality traits in barley

Barley forage quality has a direct relationship to animal performance, but forage quality traits are often neglected or not accessible to the plant breeders. Doubled haploid lines (145) from the cross Steptoe × Morex were grown in 2 years of trails under irrigated conditions to evaluate the variation in forage quality characteristics, identify quantitative trait loci (QTL) for these traits and determine if variation in forage quality characteristics among barley lines is heritable. Forage quality traits were determined at plant anthesis and at peak forage yield stages. A total of 32 QTL were identified that conditioned forage traits at anthesis stage, and 10 QTLs were identified at peak forage yield. At anthesis, forage traits were highly to moderate heritablely, while at peak forage yield, all traits were weakly heritable, indicating that selection progress for these traits will be effective at early stages of maturity. This research has identified and mapped QTL for barley forage quality and will allow deployment of genes for improved forage quality via marker-assisted selection.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Bayesian mapping of genome-wide epistatic imprinted loci for quantitative traits

Genomic imprinting, an epigenetic phenomenon of parent-of-origin-specific gene expression, has been widely observed in plants, animals, and humans. To detect imprinting genes influencing quantitative traits, the least squares and maximum likelihood approaches for fitting a single quantitative trait locus (QTL) and Bayesian methods for simultaneously modeling multiple QTL have been adopted, respectively, in various studies. However, most of these studies have only estimated imprinting main effects and thus ignored imprinting epistatic effects. In the presence of extremely complex genomic imprinting architectures, we introduce a Bayesian model selection method to analyze the multiple interacting imprinted QTL (iQTL) model. This approach will greatly enhance the computational efficiency through setting the upper bound of the number of QTLs and performing selective sampling for QTL parameters. The imprinting types of detected main-effect QTLs can be estimated from the Bayes factor statistic formulated by the posterior probabilities for the genetic effects being compared. The performance of the proposed method is demonstrated by several simulation experiments. Moreover, this method is applied to dissect the imprinting genetic architecture for body weight in mouse and fruit weight in tomato. Matlab code for implementing this approach will be available from the authors upon request.     

Genetic mapping of quantitative phenotypic traits in Saccharomyces cerevisiae

Saccharomyces cerevisiae has become a favorite production organism in industrial biotechnology presenting new challenges to yeast engineers in terms of introducing advantageous traits such as stress tolerances. Exploring subspecies diversity of S. cerevisiae has identified strains that bear industrially relevant phenotypic traits. Provided that the genetic basis of such phenotypic traits can be identified inverse engineering allows the targeted modification of production strains. Most phenotypic traits of interest in S. cerevisiae strains are quantitative, meaning that they are controlled by multiple genetic loci referred to as quantitative trait loci (QTL). A straightforward approach to identify the genetic basis of quantitative traits is QTL mapping which aims at the allocation of the genetic determinants to regions in the genome. The application of high-density oligonucleotide arrays and whole-genome re-sequencing to detect genetic variations between strains has facilitated the detection of large numbers of molecular markers thus allowing high-resolution QTL mapping over the entire genome. This review focuses on the basic principle and state of the art of QTL mapping in S. cerevisiae. Furthermore we discuss several approaches developed during the last decade that allow down-scaling of the regions identified by QTL mapping to the gene level. We also emphasize the particular challenges of QTL mapping in nonlaboratory strains of S. cerevisiae.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.     

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.     

Large-scale in silico mapping of complex quantitative traits in inbred mice

Understanding the genetic basis of common disease and disease-related quantitative traits will aid in the development of diagnostics and therapeutics. The processs of gene discovery can be sped up by rapid and effective integration of well-defined mouse genome and phenome data resources. We describe here an in silico gene-discovery strategy through genome-wide association (GWA) scans in inbred mice with a wide range of genetic variation. We identified 937 quantitative trait loci (QTLs) from a survey of 173 mouse phenotypes, which include models of human disease (atherosclerosis, cardiovascular disease, cancer and obesity) as well as behavioral, hematological, immunological, metabolic, and neurological traits. 67% of QTLs were refined into genomic regions <0.5 Mb with approximately 40-fold increase in mapping precision as compared with classical linkage analysis. This makes for more efficient identification of the genes that underlie disease. We have identified two QTL genes, Adam12 and Cdh2, as causal genetic variants for atherogenic diet-induced obesity. Our findings demonstrate that GWA analysis in mice has the potential to resolve multiple tightly linked QTLs and achieve single-gene resolution. These high-resolution QTL data can serve as a primary resource for positional cloning and gene identification in the research community.     

Responses to drought and flooding in tropical forage grasses

Seasonal drought and flooding severely limit pasture growth in tropical savannas. The objective of this study is to analyze and compare yield, biomass allocation, leaf growth rate and nutrient concentration of four important perennial C₄ forage grasses to short term flooding and moderate drought under controlled conditions. The grasses studied were the tufted Andropogon gayanus (CIAT 621) and Hyparrhenia rufa and the stoloniferous Echinochloa polystachya and Brachiaria mutica. All grasses were able to adjust their growth and development in response to flooding and drought: leaf growth and total biomass decreased under both treatments but the specific responses to these treatments differed markedly. Considering only total yield and leaf area, A. gayanus and H. rufa were relatively more tolerant to and less affected by drought whereas B. mutica and E. polystachya were more flood tolerant. In A. gayanus and H. rufa, both treatments reduced the proportion of assimilates devoted to roots and culms while increasing that of leaves decreasing the root/shoot ratio. In contrast, in B. mutica and E. polystachya only the proportion devoted to culms or stolons increased under flooding but the root/shoot ratio remained relatively stable under both treatments. All grasses produced adventitious rootlets except A. gayanus which was the most affected by flooding. Waterlogging decreased leaf nutrient concentration in all grasses which contributed to growth reduction. All species were relatively tolerant to both stresses. The results confirm the empirical observation that stoloniferous species B. mutica and E. polystachya are more tolerant to flooding thanks to adaptations typical of wetland plants such as hollow stolons which enhance oxygen diffusion to the roots and the development of adventitious rootlets that promotes water and nutrient absorption.     

Mixed linear model approach for mapping quantitative trait loci underlying crop seed traits

The crop seed is a complex organ that may be composed of the diploid embryo, the triploid endosperm and the diploid maternal tissues. According to the genetic features of seed characters, two genetic models for mapping quantitative trait loci (QTLs) of crop seed traits are proposed, with inclusion of maternal effects, embryo or endosperm effects of QTL, environmental effects and QTL-by-environment (QE) interactions. The mapping population can be generated either from double back-cross of immortalized F₂ (IF₂) to the two parents, from random-cross of IF₂ or from selfing of IF₂ population. Candidate marker intervals potentially harboring QTLs are first selected through one-dimensional scanning across the whole genome. The selected candidate marker intervals are then included in the model as cofactors to control background genetic effects on the putative QTL(s). Finally, a QTL full model is constructed and model selection is conducted to eliminate false positive QTLs. The genetic main effects of QTLs, QE interaction effects and the corresponding P-values are computed by Markov chain Monte Carlo algorithm for Gaussian mixed linear model via Gibbs sampling. Monte Carlo simulations were performed to investigate the reliability and efficiency of the proposed method. The simulation results showed that the proposed method had higher power to accurately detect simulated QTLs and properly estimated effect of these QTLs. To demonstrate the usefulness, the proposed method was used to identify the QTLs underlying fiber percentage in an upland cotton IF₂ population. A computer software, QTLNetwork-Seed, was developed for QTL analysis of seed traits.     

Bayesian multiple quantitative trait loci mapping for complex traits using markers of the entire genome

A Bayesian methodology has been developed for multiple quantitative trait loci (QTL) mapping of complex binary traits that follow liability threshold models. Unlike most QTL mapping methods where only one or a few markers are used at a time, the proposed method utilizes all markers across the genome simultaneously. The outperformance of our Bayesian method over the traditional single-marker analysis and interval mapping has been illustrated via simulations and real data analysis to identify candidate loci associated with colorectal cancer.     

Revisiting variation in leaf magnesium concentrations in forage grasses for improved animal health

Plant and Soil - An Italian ryegrass cultivar (Lolium multiflorum Lam. cv. Bb2067), selected and bred for increased leaf magnesium (Mg) concentration in the 1970s, reduced the incidence of...     

Bayesian mapping of genotype x expression interactions in quantitative and qualitative traits

A novel Bayesian gene mapping method, which can simultaneously utilize both molecular marker and gene expression data, is introduced. The approach enables a quantitative or qualitative phenotype to be expressed as a linear combination of the marker genotypes, gene expression levels, and possible genotype x gene expression interactions. The interaction data, given as marker-gene pairs, contains possible in cis and in trans effects obtained from earlier allelic expression studies, genetical genomics studies, biological hypotheses, or known pathways. The method is presented for an inbred line cross design and can be easily generalized to handle other types of populations and designs. The model selection is based on the use of effect-specific variance components combined with Jeffreys' non-informative prior--the method operates by adaptively shrinking marker, expression, and interaction effects toward zero so that non-negligible effects are expected to occur only at very few positions. The estimation of the model parameters and the handling of missing genotype or expression data is performed via Markov chain Monte Carlo sampling. The potential of the method including heritability estimation is presented using simulated examples and novel summary statistics. The method is also applied to a real yeast data set with known pathways.     

The development of highly transferable intron-spanning markers for temperate forage grasses

DNA markers have the potential to be a powerful tool for the molecular study and breeding of agronomic traits of temperate forage grasses, but some of these grasses have only limited sequence information available. We aimed to design highly transferable primer sets by using the abundant sequence information available for related crop species such as wheat and rice. The degree of similarity between the primer sequences of the wheat PCR-based landmark unique gene (PLUG) primer set and the corresponding sequences of rice orthologs was designated as the ??universality index?? (UI). We classified 359 PLUG primer pairs based on their UI values and found that primer pairs with high UI values showed higher successful amplification rates in Festuca and Lolium species than those with low UI values. Based on these results, we designed new primer sets, designated Conserved Three-prime-End Region (COTER) primers, with complete similarity to rice orthologs for eight bases at the 3?? end of each primer. COTER primer sets developed from both tall fescue and wheat showed high transferability in six temperate grasses (mean amplification rates of 95% for tall fescue primers; 79% for wheat primers). This strategy and primer information could also be useful for developing DNA markers for other grass species with little genome information available.     

Bayesian mapping of multiple traits in maize: the importance of pleiotropic effects in studying the inheritance of quantitative traits

Pleiotropy has played an important role in understanding quantitative traits. However, the extensiveness of this effect in the genome and its consequences for plant improvement have not been fully elucidated. The aim of this study was to identify pleiotropic quantitative trait loci (QTLs) in maize using Bayesian multiple interval mapping. Additionally, we sought to obtain a better understanding of the inheritance, extent and distribution of pleiotropic effects of several components in maize production. The design III procedure was used from a population derived from the cross of the inbred lines L-14-04B and L-08-05F. Two hundred and fifty plants were genotyped with 177 microsatellite markers and backcrossed to both parents giving rise to 500 backcrossed progenies, which were evaluated in six environments for grain yield and its components. The results of this study suggest that mapping isolated traits limits our understanding of the genetic architecture of quantitative traits. This architecture can be better understood by using pleiotropic networks that facilitate the visualization of the complexity of quantitative inheritance, and this characterization will help to develop new selection strategies. It was also possible to confront the idea that it is feasible to identify QTLs for complex traits such as grain yield, as pleiotropy acts prominently on its subtraits and as this "trait" can be broken down and predicted almost completely by the QTLs of its components. Additionally, pleiotropic QTLs do not necessarily signify pleiotropy of allelic interactions, and this indicates that the pervasive pleiotropy does not limit the genetic adaptability of plants.