A comparison of regression interval mapping and multiple interval mapping for linked QTL

Regression interval mapping and multiple interval mapping are compared with regard to mapping linked quantitative trait loci (QTL) in inbred-line cross experiments. For that purpose, a simulation study was performed using genetic models with two linked QTL. Data were simulated for F(2) populations of different sizes and with all QTL and marker alleles fixed for alternative alleles in the parental lines. The criteria for comparison are power of QTL identification and the accuracy of the QTL position and effect estimates. Further, the estimates of the relative QTL variance are assessed. There are distinct differences in the QTL position estimates between the two methods. Multiple interval mapping tends to be more powerful as compared to regression interval mapping. Multiple interval mapping further leads to more accurate QTL position and QTL effect estimates. The superiority increased with wider marker intervals and larger population sizes. If QTL are in repulsion, the differences between the two methods are very pronounced. For both methods, the reduction of the marker interval size from 10 to 5 cM increases power and greatly improves QTL parameter estimates. This contrasts with findings in the literature for single QTL scenarios, where a marker density of 10 cM is generally considered as sufficient. The use of standard (asymptotic) statistical theory for the computation of the standard errors of the QTL position and effect estimates proves to give much too optimistic standard errors for regression interval mapping as well as for multiple interval mapping.     

植物数量性状基因的定位与克隆

作物的许多重要农艺性状属于数量性状,鉴定和发掘控制数量性状的基因及其优异的等位变异,并使之快速应用于育种实践是新时期作物科学家和育种学家所面临的重大课题。本文从QTL作图、QTL的精细定位与图位克隆、QTL近等基因系和染色体片断代换系的建立以及基于LD的关联分析等方面对植物数量性状的研究进展进行了讨论,提出了以植物基因组学技术为平台,将QTL作图与关联分析方法相结合,是进行数量性状遗传机理研究同时服务于作物育种实践的有效途径。     

植物数量性状基因的定位与克隆

作物的许多重要农艺性状属于数量性状, 鉴定和发掘控制数量性状的基因及其优异的等位变异, 并使之快速应用于育种实践是新时期作物科学家和育种学家所面临的重大课题。本文从QTL作图、QTL的精细定位与图位克隆、QTL近等基因系和染色体片断代换系的建立以及基于LD的关联分析等方面对植物数量性状的研究进展进行了讨论, 提出了以植物基因组学技术为平台, 将QTL作图与关联分析方法相结合, 是进行数量性状遗传机理研究同时服务于作物育种实践的有效途径。     

Interval Mapping of Multiple Quantitative Trait Loci

The interval mapping method is widely used for the mapping of quantitative trait loci (QTLs) in segregating generations derived from crosses between inbred lines. The efficiency of detecting and the accuracy of mapping multiple QTLs by using genetic markers are much increased by employing multiple QTL models instead of the single QTL models (and no QTL models) used in interval mapping. However, the computational work involved with multiple QTL models is considerable when the number of QTLs is large. In this paper it is proposed to combine multiple linear regression methods with conventional interval mapping. This is achieved by fitting one QTL at a time in a given interval and simultaneously using (part of) the markers as cofactors to eliminate the effects of additional QTLs. It is shown that the proposed method combines the easy computation of the single QTL interval mapping method with much of the efficiency and accuracy of multiple QTL models.     

作物数量性状基因研究进展

分子生物技术的发展对作物数量性状基因（QTL）研究提供了条件,不同的定位群体各有其特点,相继出现的QTL定位也逐步完善。大量的研究揭示了QTL的基本特征,剖析了重要农艺4性状的遗传基础,给作物遗传改良带来了新的策略,不断深入的研究已经完成了特定的QTL的精细定位和克隆。本从QTL的定位群体,定位方法,研究现状,精细定位与克隆,以及QTL利用等方面对作物数量性状基因的研究进行了综述。     

林木数量性状基因定位中的若干问题

随着ＤＮＡ分子标记技术的迅速发展,ＱＴＬ定位已成为当前生物学研究领域的前沿。迄今已对许多种动、植物定位了许多重要性状的ＱＴＬ。这些研究促进了遗传学的发展,并将作为育种的新策略应用。与作物相比,林木ＱＴＬ定位有其特性。本文详细讨论了林木的生物学特性对ＱＴＬ定位的影响、ＱＴＬ定位的系谱设计和统计分析方法。     

Genetic dissection of grain weight in bread wheat through quantitative trait locus interval and association mapping

Genetic dissection of grain weight in bread wheat was undertaken through both genome-wide quantitative trait locus (QTL) interval mapping and association mapping. QTL interval mapping involved preparation of a framework linkage map consisting of 294 loci {194 simple sequence repeats (SSRs), 86 amplified fragment length polymorphisms (AFLPs) and 14 selective amplifications of microsatellite polymorphic loci (SAMPL)} using a bi-parental recombinant inbred line (RIL) mapping population derived from Rye Selection111 × Chinese Spring. Using the genotypic data and phenotypic data on grain weight (GW) of RILs collected over six environments, genome-wide single locus QTL analysis was conducted to identify main effect QTL. This led to identification of as many as ten QTL including four major QTL (three QTL were stable), each contributing >20% phenotypic variation (PV) for GW. The above study was supplemented with association mapping, which allowed identification of 11 new markers in the genomic regions that were not reported earlier to harbour any QTL for GW. It also allowed identification of closely linked markers for six known QTL, and validation of eight QTL reported earlier. The QTL identified through QTL interval mapping and association mapping may prove useful in marker-assisted selection (MAS) for the development of cultivars with high GW in bread wheat.     

Substitution mapping of Pup1: a major QTL increasing phosphorus uptake of rice from a phosphorus-deficient soil

A major QTL for P uptake had previously been mapped to a 13-cM marker interval on the long arm of chromosome 12. To map that major QTL with higher precision and certainty, a secondary mapping population was developed by backcrossing a near-isogenic line containing the QTL from the donor parent to the recurrent parent of low P uptake. Two different mapping strategies have been followed in this study. A conventional QTL mapping approach was based on individual F(2) RFLP data and the phenotypic evaluation of family means in the F(3). The second strategy employed a substitution-mapping approach. Phenotypic and marker data were obtained for 160 F(3) individuals of six highly informative families that differed in the size of donor chromosomal segments in the region of the putative QTL. QTL mapping showed that close to 80% of the variation between families was due to a single QTL, hereafter referred to as Pup1 (Phosphorus uptake 1). Pup1 was placed in a 3-cM interval flanked by markers S14025 and S13126, which is within 1 cM of the position identified in the original QTL mapping experiment. Other chromosomal regions and epistatic effects were not significant. Substitution mapping revealed that Pup1 co-segregated with marker S13126 and that the flanking markers, S14025 and S13752, were outside the interval containing Pup1. The two mapping strategies therefore yielded almost identical results and, in combining the advantages of both, Pup1 could be mapped with high certainty. The QTL mapping appoach showed that the phenotypic variation between families was due to only one QTL without any additional epistacic interactions, whereas the advantage of substitution mapping was to place clearly defined borders around the QTL.     

On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.     

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.     

植物QTL定位方法的研究进展

本文系统地介绍了QTL定位的单一标记分析法、区间作图法以及复合区间作图法、混合显性模型的分析方法,概述了一些主要定位方法的分析原理、存在的主要优缺点。单一标记分析法可以采用方差分析、回归分析或似然比检验的方法分析。区间作图法和复合区间作图法是基于两个相邻标记的QTL定位方法,可采用回归分析或最大似然法分析。复合区间作图法在模型中包括了与其他QTL连锁的标记,可以提高作图的精度和效率。混合线性模型的QTL定位方法可以包括复杂的遗传效应及QTL与环境的互作效应,具有更广阔的应用前景。 Abstract:QTL mapping methods are reviewed for single-marker mapping,interval mapping,composite interval mapping,and mixed-model based method.Statistical approaches along with their properties are discussed for the mapping methods.ANOVA,regression method and likelihood ratio test can be applied in single-marker mapping.Interval mapping and composite interval mapping can be conducted,based on two interval markers,by regression method and maximum likelihood method.Since markers linked with other QTLs are include in the model,composite interval mapping is more precision and powerful.Mapping QTL by mixed-model approaches is more applicable when complicated QTL effects as well as QTL by environment interaction are analyzed.     

作物数量性状研究进展

作物主要农艺性状和经济性状大多属于数量性状。传统数量遗传学采用数理统计方法,把控制数量性状的多基因系统作为一个整体进行研究。DNA分子标记技术的出现和发展,为数量性状研究提供了重要工具。自20世纪80年代以来,QTL定位的统计分析方法发展很快,先后提出单标记分析法、区间作图法及复合区间作图法等。目前,作物QTL研究取得了重要进展,一些重要作物、重要农艺性状的主效QTL基因已被相继克隆成功,作物数量性状的研究已经成为一个具有勃勃生机的热门领域。     

Conditional QTL mapping of protein content in wheat with respect to grain yield and its components

Grain protein content in wheat (Triticum aestivum L.) is generally considered a highly heritable character that is negatively correlated with grain yield and yield-related traits. Quantitative trait loci (QTL) for protein content was mapped using data on protein content and protein content conditioned on the putatively interrelated traits to evaluate possible genetic interrelationships between protein content and yield, as well as yield-related traits. Phenotypic data were evaluated in a recombinant inbred line population with 302 lines derived from a cross between the Chinese cultivar Weimai 8 and Luohan 2. Inclusive composite interval mapping using IciMapping 3.0 was employed for mapping unconditional and conditional QTL with additives. A strong genetic relationship was found between protein content and grain yield, and yield-related traits. Unconditional QTL mapping analysis detected seven additive QTL for protein content, with additive effects ranging in absolute size from 0.1898% to 0.3407% protein content, jointly accounting for 43.45% of the trait variance. Conditional QTL mapping analysis indicated two QTL independent from yield, which can be used in marker-assisted selection for increasing yield without affecting grain protein content. Three additional QTL with minor effects were identified in the conditional mapping. Of the three QTLs, two were identified when protein content was conditioned on yield, which had pleiotropic effects on those two traits. Conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the individual QTL level for closely correlated traits. Further, conditional QTL mapping can reveal additional QTL with minor effects that are undetectable in unconditional mapping.     

Improving QTL Mapping Resolution Based on Genotypic Sampling—a Case Using a RIL Population

The QTL mapping results were compared with the genotypically selected and random samples of the same size on the base of a RIL population. The results demonstrated that there were no obvious differences in the trait distribution and marker segregation distortion between the genotypically selected and random samples with the same population size. However, a significant increase in QTL detection power, sensitivity, specificity, and QTL resolution in the genotypically selected samples were observed. Moreover, the highly significant effect was detected in small size of genotypically selected samples. In QTL mapping, phenotyping is a more sensitive limiting factor than genotyping so that the selection of samples could be an attractive strategy for increasing genome-wide QTL mapping resolution. The efficient selection of samples should be more helpful for QTL maker assistant selection, fine mapping, and QTL cloning.     

基于基因型选择提高QTL作图的精度——以一个RIL群体为例

以PCR为基础的分子标记以及其他检测技术的发展,使得大规模的标记分析成为现实。这也为通过大群体标记分析,然后基于基因型选择挑选合适的小群体,从而提高QTL定位准确性和精度提供了可能。以一个包含294个家系的重组自交系（RIL）群体为例,通过基因型选择和随机选择的办法产生了一系列大小不等的亚群体,比较了两类群体QTL定位的结果。分析表明：相同大小的基因型选择群体与随机群体相比性状的表型分布都符合正态分布;标记的偏分离情况也没有明显的差别,都随着群体大小的增大,偏分离的比例也逐渐增大。但同等大小的基因型选择群体比随机群体的交换富集率（CE）要大,且随着选择强度的增大不断增大,如群体大小为270时,CE=1．04,群体大小为30时,CE=1．45。总体上,随着群体大小的增加,不管是随机群体还是选择群体,其QTL检测能力、灵敏性和特异性也随之增加,但选择群体的检测能力、灵敏性和特异性总体上要好于随机群体。当群体大于或等于240时,其QTL检测能力基本没有差别;群体大小大于或等于210时,其QTL检测的灵敏性和特异性也没有什么差别。这也说明：选择强度越大,效果越明显。以QTLI—LOD区间作为衡量QTL精度的一个指标,结果显示所有基因型选择群体都比相同大小随机群体的QTL定位精度高。目前QTL定位研究中,基因型数据较表型数据而言更容易准确获得,因此通过基因型选择可以更好的优化群体结构,减少田间实验的工作量,提高全基因组水平QTL作图的精度,为随后的QTL辅助选择和精细定位以及克隆提供帮助。     

Some ways to improve QTL mapping accuracy

In this paper, we review some approaches for QTL mapping developed by our research group in collaboration with, following the recommendation of, or under inspiration of Moshe Soller. Specifically, we explain at a simple intuitive level the main principles and ideas of: (a) QTL mapping by fractioned DNA pooling, (b) increasing the detection power of QTL mapping (in the case of individual genotyping) by multiple-trait analysis, and (c) the role of variance-covariance effects in QTL mapping. On each of these themes we had long and deep discussions with Soller on the statistical aspects of the proposed procedures. We hope that together we made important contributions towards making QTL mapping procedures easier and more effective.     

家畜抗性等级性状的QTL定位方法

在广义线性模型的框架内模拟研究了家畜抗性等级性状的QTL定位方法,QTL参数的估计采用最大似然方法,比较了阈模型方法与一般线性方法的QTL定位效率,并对影响等级性状QTL定位效率的主要因素（QTL效应、性状的遗传力）进行了模拟研究,实验设计为多个家系的女儿设计,资源群体大小为500头。研究结果表明：在QTL位置参数估计及检验功效方面,阈模型方法具有一定的优势,对抗性等级性状QTL定位的功效也高于线性方法。另外,性状遗传力和QTL效应的大小对QTL定位的准确度也有直接的影响,随着性状遗传力QTL效应的     

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.     

Robust Bayesian mapping of quantitative trait loci using Student-t distribution for residual

In most quantitative trait loci (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection, leading to detection of false positive QTL. To improve the robustness of QTL mapping methods, we replace the normal distribution assumption for residuals in a multiple QTL model with a Student-t distribution that is able to accommodate residual outliers. A Robust Bayesian mapping strategy is proposed on the basis of the Bayesian shrinkage analysis for QTL effects. The simulations show that Robust Bayesian mapping approach can substantially increase the power of QTL detection when the normality assumption does not hold and applying it to data already normally distributed does not influence the result. The proposed QTL mapping method is applied to mapping QTL for the traits associated with physics–chemical characters and quality in rice. Similarly to the simulation study in the real data case the robust approach was able to detect additional QTLs when compared to the traditional approach. The program to implement the method is available on request from the first or the corresponding author. Xin Wang and Zhongze Piao contributed equally to this study.     

离散性状QTL区间定位的最大似然方法

采用最大似然区间定位法对阈模型与一般线性模型的QTL定位效率进行了比较,并对影响离散性状QTL检测效率的主要因素（QTL效应、性状的遗传力和表型发生率）进行了模拟研究,实验设计为多个家系的女儿设计．资源群体大小为500头。研究结果表明：在QTL参数估计及检验功效方面,阈模型方法具有较大的优势,对离散性状QTL定位的效率明显高于LM（Linear Model）方法,定位的准确性也较高。另外,性状遗传力、QTL效应的大小和性状表型发生率对QTL定位的准确度也有直接的影响,随着性状遗传力和表型发生率的提高,随着QTL效应的增大,QTL定位的效率也进一步提高。