Bayesian analysis for genetic architecture of dynamic traits

The dissection of the genetic architecture of quantitative traits, including the number and locations of quantitative trait loci (QTL) and their main and epistatic effects, has been an important topic in current QTL mapping. We extend the Bayesian model selection framework for mapping multiple epistatic QTL affecting continuous traits to dynamic traits in experimental crosses. The extension inherits the efficiency of Bayesian model selection and the flexibility of the Legendre polynomial model fitting to the change in genetic and environmental effects with time. We illustrate the proposed method by simultaneously detecting the main and epistatic QTLs for the growth of leaf age in a doubled-haploid population of rice. The behavior and performance of the method are also shown by computer simulation experiments. The results show that our method can more quickly identify interacting QTLs for dynamic traits in the models with many numbers of genetic effects, enhancing our understanding of genetic architecture for dynamic traits. Our proposed method can be treated as a general form of mapping QTL for continuous quantitative traits, being easier to extend to multiple traits and to a single trait with repeat records.     

Simultaneous mapping of epistatic QTL in chickens reveals clusters of QTL pairs with similar genetic effects on growth

We used simultaneous mapping of interacting quantitative trait locus (QTL) pairs to study various growth traits in a chicken F2 intercross. The method was shown to increase the number of detected QTLs by 30 % compared with a traditional method detecting QTLs by their marginal genetic effects. Epistasis was shown to be an important contributor to the genetic variance of growth, with the largest impact on early growth (before 6 weeks of age). There is also evidence for a discrete set of interacting loci involved in early growth, supporting the previous findings of different genetic regulation of early and late growth in chicken. The genotype-phenotype relationship was evaluated for all interacting QTL pairs and 17 of the 21 evaluated QTL pairs could be assigned to one of four clusters in which the pairs in a cluster have very similar genetic effects on growth. The genetic effects of the pairs indicate commonly occurring dominance-by-dominance, heterosis and multiplicative interactions. The results from this study clearly illustrate the increase in power obtained by using this novel method for simultaneous detection of epistatic QTL, and also how visualization of genotype-phenotype relationships for epistatic QTL pairs provides new insights to biological mechanisms underlying complex traits.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

Identification of major QTLs and epistatic interactions for seed protein concentration in soybean under multiple environments based on a high-density map

The concentration of protein in soybean is an important trait that drives successful soybean quality. A recombinant inbred line derived from a cross between the Charleston and Dongnong594 cultivars was planted in one location across 10 years and two locations across 5 years in China (20 environments in total), and the genetic effects were partitioned into additive main effects, epistatic main effects and their environmental interaction effects using composite interval mapping and inclusive composite interval mapping models based on a high-density genetic map. Ten main-effect quantitative trait loci (QTLs) were identified on chromosomes 3, 6, 7, 13, 15 and 20 and detected in more than three environments, with each of the main-effect QTLs contributing a phenotypic variation of around 10 %. Between the intervals of the main-effect QTLs, 93 candidate genes were screened for their involvement in seed protein storage and/or amino acid biosynthesis and metabolism processes based on gene ontology and annotation information. Furthermore, an analysis of epistatic interactions showed that three epistatic QTL pairs were detected, and could explain approximately 50 % of the phenotypic variation. The additive main-effect QTLs and epistatic QTL pairs contributed to high phenotypic variation under multiple environments, and the results were also validated and corroborated with previous research, indicating that marker-assisted selection can be used to improve soybean protein concentrations and that the candidate genes can also be used as a foundation data set for research on gene function.     

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.     

An empirical Bayes method for estimating epistatic effects of quantitative trait loci

Summary .   The genetic variance of a quantitative trait is often controlled by the segregation of multiple interacting loci. Linear model regression analysis is usually applied to estimating and testing effects of these quantitative trait loci (QTL). Including all the main effects and the effects of interaction (epistatic effects), the dimension of the linear model can be extremely high. Variable selection via stepwise regression or stochastic search variable selection (SSVS) is the common procedure for epistatic effect QTL analysis. These methods are computationally intensive, yet they may not be optimal. The LASSO (least absolute shrinkage and selection operator) method is computationally more efficient than the above methods. As a result, it has been widely used in regression analysis for large models. However, LASSO has never been applied to genetic mapping for epistatic QTL, where the number of model effects is typically many times larger than the sample size. In this study, we developed an empirical Bayes method (E-BAYES) to map epistatic QTL under the mixed model framework. We also tested the feasibility of using LASSO to estimate epistatic effects, examined the fully Bayesian SSVS, and reevaluated the penalized likelihood (PENAL) methods in mapping epistatic QTL. Simulation studies showed that all the above methods performed satisfactorily well. However, E-BAYES appears to outperform all other methods in terms of minimizing the mean-squared error (MSE) with relatively short computing time. Application of the new method to real data was demonstrated using a barley dataset.     

The Statistical Power of Inclusive Composite Interval Mapping in Detecting Digenic Epistasis Showing Common F2 Segregation Ratios

Epistasis is a commonly observed genetic phenomenon and an important source of variation of complex traits,which could maintain additive variance and therefore assure the long-term genetic gain in breeding.Inclusive composite interval mapping（ICIM） is able to identify epistatic quantitative trait loci（QTLs） no matter whether the two interacting QTLs have any additive effects.In this article,we conducted a simulation study to evaluate detection power and false discovery rate（FDR） of ICIM epistatic mapping,by considering F₂ and doubled haploid（DH） populations,different F₂ segregation ratios and population sizes.Results indicated that estimations of QTL locations and effects were unbiased,and the detection power of epistatic mapping was largely affected by population size,heritability of epistasis,and the amount and distribution of genetic effects.When the same likelihood of odd（LOD） threshold was used,detection power of QTL was higher in F₂ population than power in DH population;meanwhile FDR in F₂ was also higher than that in DH.The increase of marker density from 10 cM to 5 cM led to similar detection power but higher FDR.In simulated populations,ICIM achieved better mapping results than multiple interval mapping（MIM） in estimation of QTL positions and effect.At the end,we gave epistatic mapping results of ICIM in one actual population in rice（Oryza sativa L.）.     

Study of strategies for selecting quantitative trait locus mapping procedures by computer simulation

Along with the development and integration of molecular genetics and quantitative genetics, many quantitative trait locus (QTL) mapping studies have been conducted using different mapping populations in various crop species. Existing QTLs can be used for marker-assisted breeding and map-based cloning, whereas the false-positive QTLs are no use. The purpose of this study is to evaluate the suitability of different mapping procedures for data from different genetic models. In this study, four types of recombinant inbred lines (RILs) with different genetic models, viz. additive QTLs (Model I), additive and epistatic QTLs (Model II), additive QTLs and QTL × environment interaction (Model III), additive, epistatic QTLs and QTL × environment interaction (Model IV), were simulated by computer. Six types of QTL mapping procedures, viz. CIM, MIMF, MIMR, ICIM, MQM and NWIM, on four kinds of QTL mapping software, viz. WinQTL Cartographer Version 2.5, IciMapping Version 2.0, MapQTL Version 5.0 and QTLnetwork Version 2.0, were used for screening QTLs of the simulated RILs. The results showed that different mapping procedures have different suitability for different genetic models. CIM and MQM can only screen Model I data. MIMR, MIMF and ICIM can only screen Model I and Model II data. NWIM can screen all four models’ data. It can be concluded that different genetic models’ data have different most suitable mapping procedures. In practical experiments where the genetic model of the data is unknown, a multiple model mapping strategy should be used, that is a full model scanning with complex model procedure followed by verification with other procedures corresponding to the scanning results.     

Mapping QTLs with epistatic effects and QTL×environment interactions for plant height using a doubled haploid population in cultivated wheat

Quantitative trait loci (QTLs) for plant height in wheat (Triticum aestivum L.) were studied using a set of 168 doubled haploid (DH) lines, which were derived from the cross Huapei 3/Yumai 57. A genetic linkage map was constructed using 283 SSR and 22 EST-SSR markers. The DH population and the parents were evaluated for wheat plant height in 2005 and 2006 in Tai'an and 2006 in Suzhou. QTL analyses were performed using the software of QTLNetwork version 2.0 based on the mixed linear model. Four additive QTLs and five pairs of epistatic effects were detected, which were distributed on chromosomes 3A, 4B, 4D, 5A, 6A, 7B, and 7D. Among them, three additive QTLs and three pairs of epistatic QTLs showed QTLxenvironment interactions (QEs). Two major QTLs, QphAB and Qph4D, which accounted for 14.51 % and 20.22% of the phenotypic variation, were located similar to the reported locations of the dwarfing genes Rhtl and Rht2, respectively. The Qph3A-2 with additive effect was not reported in previous linkage mapping studies. The total QTL ef fects detected for the plant height explained 85.04% of the phenotypic variation, with additive effects 46.07%, epistatic effects 19.89%, and QEs 19.09%. The results showed that both additive effects and epistatic effects were important genetic bases of wheat plant height, which were subjected to environmental modifications, and caused dramatic changes in phenotypic effects. The information obtained in this study will be useful for manipulating the QTLs for wheat plant height by molecular marker-assisted selection (MAS).     

Mapping QTLs with epistatic effects and QTL×environment interactions for plant height using a doubled haploid population in cultivated wheat

Quantitative trait loci (QTLs) for plant height in wheat (Triticum aestivum L.) were studied using a set of 168 doubled haploid (DH) lines, which were derived from the cross Huapei 3/Yumai 57. A genetic linkage map was constructed using 283 SSR and 22 EST-SSR markers. The DH population and the parents were evaluated for wheat plant height in 2005 and 2006 in Tai’an and 2006 in Suzhou. QTL analyses were performed using the software of QTLNetwork version 2.0 based on the mixed linear model. Four additive QTLs and five pairs of epistatic effects were detected, which were distributed on chromosomes 3A, 4B, 4D, 5A, 6A, 7B, and 7D. Among them, three additive QTLs and three pairs of epistatic QTLs showed QTL×environment interactions (QEs). Two major QTLs, Qph4B and Qph4D, which accounted for 14.51% and 20.22% of the phenotypic variation, were located similar to the reported locations of the dwarfing genes Rht1 and Rht2, respectively. The Qph3A-2 with additive effect was not reported in previous linkage mapping studies. The total QTL effects detected for the plant height explained 85.04% of the phenotypic variation, with additive effects 46.07%, epistatic effects 19.89%, and QEs 19.09%. The results showed that both additive effects and epistatic effects were important genetic bases of wheat plant height, which were subjected to environmental modifications, and caused dramatic changes in phenotypic effects. The information obtained in this study will be useful for manipulating the QTLs for wheat plant height by molecular marker-assisted selection (MAS).     

小麦幼苗耐热性的QTL定位分析

以小麦DH群体(‘旱选10号’ב鲁麦14’)为材料,在高温(热胁迫)及常温(对照)两种条件下考察小麦幼苗的根干重、苗干重、幼苗生物量、叶片叶绿素含量、叶绿素荧光参数及其耐热指数,并应用基于混合线性模型的复合区间作图法分析幼苗性状及其耐热指数QTL的数量、染色体分布及表达情况,以及QTL与环境的互作效应。结果显示:(1)亲本‘旱选10号’的耐热性明显优于‘鲁麦14’,且杂交后代的耐热性出现超亲分离。(2)控制幼苗耐热相关性状的QTL位点在染色体2D、6B、3A、4A、5A和7A上分布较多,而控制幼苗性状耐热指数的QTL在染色体6A、6B、3A、2D、5A和7A上分布较多,QTL位点在染色体上的分布有区域化的趋势。(3)控制幼苗性状的单个加性QTL和上位性QTL解释的表型变异分别平均为2.48%和2.65%;而控制耐热指数的单个加性QTL和上位性QTL解释的表型变异分别平均为8.84%和1.98%。(4)在热胁迫和对照条件下共检测到与幼苗性状及其耐热指数有关的加性效应QTL 13个和上位性效应QTL 28对,分布在除4D和6D以外的19条染色体上。研究表明,控制幼苗性状的QTL以上位性效应为主,而其耐热指数的QTL以加性效应为主。     

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 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.     

玉米开花期相关性状的QTL分析

利用玉米强优势组合(Mo17×黄早四)自交衍生的191个F_2单株构建了由SSR和AFLP标记组成的分子连锁图谱,用F2进一步自交产生的184个F_(2:3)家系调查散粉期、吐丝期和开花-吐丝间隔期(ASI)的表型值,采用基于混合线性模型的复合区间作图法和相应的作图软件QTLmapper/V2.0,在两个生长环境下定位了与散粉期、吐丝期和ASI相关的QTL数目分别为13、7和5个,检测到3对控制散粉期、17对控制吐丝期和5对控制ASI的上位性效应位点;同时发现了与环境存在显著互作的3个散粉期、3个吐丝期和2个ASI单位点标记区域以及1对散粉期、3对吐丝期和2对ASI上位性效应区域.对玉米散粉期、吐丝期和ASI遗传基础中遗传因素相对作用大小分析表明,加性效应、部分显性效应和上位性效应是玉米开花期相关性状的重要遗传基础.     

Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

植物QTL分析的理论研究进展

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

Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations

It has long been recognized that epistasis or interactions between non-allelic genes plays an important role in the genetic control and evolution of quantitative traits. However, the detection of epistasis and estimation of epistatic effects are difficult due to the complexity of epistatic patterns, insufficient sample size of mapping populations and lack of efficient statistical methods. Under the assumption of additivity of QTL effects on the phenotype of a trait in interest, the additive effect of a QTL can be completely absorbed by the flanking marker variables, and the epistatic effect between two QTL can be completely absorbed by the four marker-pair multiplication variables between the two pairs of flanking markers. Based on this property, we proposed an inclusive composite interval mapping (ICIM) by simultaneously considering marker variables and marker-pair multiplications in a linear model. Stepwise regression was applied to identify the most significant markers and marker-pair multiplications. Then a two-dimensional scanning (or interval mapping) was conducted to identify QTL with significant digenic epistasis using adjusted phenotypic values based on the best multiple regression model. The adjusted values retain the information of QTL on the two current mapping intervals but exclude the influence of QTL on other intervals and chromosomes. Epistatic QTL can be identified by ICIM, no matter whether the two interacting QTL have any additive effects. Simulated populations and one barley doubled haploids (DH) population were used to demonstrate the efficiency of ICIM in mapping both additive QTL and digenic interactions.     

Mapping QTLs with epistatic effects and QTL×environment interactions by mixed linear model approaches

A new methodology based on mixed linear models was developed for mapping QTLs with digenic epistasis and QTL×environment (QE) interactions. Reliable estimates of QTL main effects (additive and epistasis effects) can be obtained by the maximum-likelihood estimation method, while QE interaction effects (additive×environment interaction and epistasis×environment interaction) can be predicted by the-best-linear-unbiased-prediction (BLUP) method. Likelihood ratio and t statistics were combined for testing hypotheses about QTL effects and QE interactions. Monte Carlo simulations were conducted for evaluating the unbiasedness, accuracy, and power for parameter estimation in QTL mapping. The results indicated that the mixed-model approaches could provide unbiased estimates for both positions and effects of QTLs, as well as unbiased predicted values for QE interactions. Additionally, the mixed-model approaches also showed high accuracy and power in mapping QTLs with epistatic effects and QE interactions. Based on the models and the methodology, a computer software program (QTLMapper version 1.0) was developed, which is suitable for interval mapping of QTLs with additive, additive×additive epistasis, and their environment interactions. Received: 23 October 1998 / Accepted: 11 May 1999     

水稻株高构成因素的QTL剖析

利用水稻籼粳杂交 (圭 6 30× 0 2 42 8) F1 的花药离体培养建立的一个含 81个 DH家系的作图群体 ,对水稻株高构成因素 (穗长、第 1节间长、……、第 5节间长 )进行基因定位。DH群体中株高构成因素均呈正态分布。相邻的构成因素间呈极显著的正相关 ,而相距较远的构成因素间的相关较弱或不显著。采用 QTL(Quantitative trait lo-cus)分析 ,定位了影响株高构成因素的 6个 QTL:qtl7同时影响穗长和第 1、2、3节间长 ,qtl1 和 qtl2 同时影响第 4和第 5节间长 ,qtl1 0 a和 qtl1 0 b仅影响第 1节间长 ,qtl3 仅影响第 3节间长。采用 QTL 互作分析 ,检测到 19对显著的互作 ,每个构成因素受 2个或 2个以上的 QTL 互作对的影响。并且还发现 ,同一个 QTL 互作对可能影响不同的性状 ,以及一个 QTL 可以分别与不同的 QTL 产生互作而影响同一个性状或影响不同的性状 ,但总的看来 ,加性效应是主要的。这些结果揭示了株高构成因素间相关的遗传基础 ,在水稻育种中运用这些 QTL 将有助于对株高 ,以及对穗长和上部节间长度进行精细的遗传调控。     

Precision Mapping of Quantitative Trait Loci

Adequate separation of effects of possible multiple linked quantitative trait loci (QTLs) on mapping QTLs is the key to increasing the precision of QTL mapping. A new method of QTL mapping is proposed and analyzed in this paper by combining interval mapping with multiple regression. The basis of the proposed method is an interval test in which the test statistic on a marker interval is made to be unaffected by QTLs located outside a defined interval. This is achieved by fitting other genetic markers in the statistical model as a control when performing interval mapping. Compared with the current QTL mapping method (i.e., the interval mapping method which uses a pair or two pairs of markers for mapping QTLs), this method has several advantages. (1) By confining the test to one region at a time, it reduces a multiple dimensional search problem (for multiple QTLs) to a one dimensional search problem. (2) By conditioning linked markers in the test, the sensitivity of the test statistic to the position of individual QTLs is increased, and the precision of QTL mapping can be improved. (3) By selectively and simultaneously using other markers in the analysis, the efficiency of QTL mapping can be also improved. The behavior of the test statistic under the null hypothesis and appropriate critical value of the test statistic for an overall test in a genome are discussed and analyzed. A simulation study of QTL mapping is also presented which illustrates the utility, properties, advantages and disadvantages of the method.