QTL mapping using a memetic algorithm with modifications of BIC as fitness function

The problem of locating quantitative trait loci (QTL) for experimental populations can be approached by multiple regression analysis. In this context variable selection using a modification of the Bayesian Information Criterion (mBIC) has been well established in the past. In this article a memetic algorithm (MA) is introduced to find the model which minimizes the selection criterion. Apart from mBIC also a second modification (mBIC2) is considered, which has the property of controlling the false discovery rate. Given the Bayesian nature of our selection criteria, we are not only interested in finding the best model, but also in computing marker posterior probabilities using all models visited by MA. In a simulation study MA (with mBIC and mBIC2) is compared with a parallel genetic algorithm (PGA) which has been previously suggested for QTL mapping. It turns out that MA in combination with mBIC2 performs best, where determining QTL positions based on marker posterior probabilities yields even better results than using the best model selected by MA. Finally we consider a real data set from the literature and show that MA can also be extended to multiple interval mapping, which potentially increases the precision with which the exact location of QTLs can be estimated.     

Locating multiple interacting quantitative trait Loci using rank-based model selection

In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL mapping, the performance of the mBIC strongly deteriorates when the trait distribution is heavy tailed or when the data contain a significant proportion of outliers. In the present article, we propose a suitable robust version of the mBIC that is based on ranks. We investigate the properties of the resulting method on the basis of theoretical calculations, computer simulations, and a real data analysis. Our simulation results show that for the sample sizes typically used in QTL mapping, the methods based on ranks are almost as efficient as standard techniques when the data are normal and are much better when the data come from some heavy-tailed distribution or include a proportion of outliers.     

大豆昆虫抗性相关QTLs的元分析

大豆虫害严重危害大豆生产。虽然大豆抗虫相关QTLs研究增多, 但由于作图群体不同、同种昆虫抗性QTL的调查性状不同以及数据分析方法存在差异等原因, 使QTL精确性和有效性被降低。因此, 获得相对真实且有效的QTLs位点对于促进分子标记辅助选择有重要意义。文章通过搜集已报道的81个与大豆昆虫抗性相关的QTL, 提取相对有效且可靠的QTLs标记信息, 利用元分析软件BioMercator2.1将这些QTLs映射到大豆公共遗传连锁图谱Soymap2上, 通过单独与联合的两种元分析途径, 利用QTLs的95%的置信区间来推断“真实QTLs”的位置。文章不仅构建了一张大豆昆虫抗性一致性图谱, 而且通过两种元分析途径分别得到12个和14个QTLs位点, 且其中有6个位点QTL的位置一致。它们被定位在9个连锁群上, 主要成簇分布在E、F、H、M等4个连锁群上, 图距由原来平均15 cM缩减到平均3.67 cM。除了一个与大豆食心虫抗性相关的位点外, 其余QTLs都与多种昆虫抗性相关。研究结果明显缩短了原来已报道的QTL置信区间, 为大豆抗虫相关QTL的精细定位以及抗虫相关基因挖掘提供了依据。     

On locating multiple interacting quantitative trait loci in intercross designs

A modified version (mBIC) of the Bayesian Information Criterion (BIC) has been previously proposed for backcross designs to locate multiple interacting quantitative trait loci. In this article, we extend the method to intercross designs. We also propose two modifications of the mBIC. First we investigate a two-stage procedure in the spirit of empirical Bayes methods involving an adaptive (i.e., data-based) choice of the penalty. The purpose of the second modification is to increase the power of detecting epistasis effects at loci where main effects have already been detected. We investigate the proposed methods by computer simulations under a wide range of realistic genetic models, with nonequidistant marker spacings and missing data. In the case of large intermarker distances we use imputations according to Haley and Knott regression to reduce the distance between searched positions to not more than 10 cM. Haley and Knott regression is also used to handle missing data. The simulation study as well as real data analyses demonstrates good properties of the proposed method of QTL detection.     

Fine mapping of multiple QTL using combined linkage and linkage disequilibrium mapping – A comparison of single QTL and multi QTL methods

Two previously described QTL mapping methods, which combine linkage analysis (LA) and linkage disequilibrium analysis (LD), were compared for their ability to detect and map multiple QTL. The methods were tested on five different simulated data sets in which the exact QTL positions were known. Every simulated data set contained two QTL, but the distances between these QTL were varied from 15 to 150 cM. The results show that the single QTL mapping method (LDLA) gave good results as long as the distance between the QTL was large (> 90 cM). When the distance between the QTL was reduced, the single QTL method had problems positioning the two QTL and tended to position only one QTL, i.e. a "ghost" QTL, in between the two real QTL positions. The multi QTL mapping method (MP-LDLA) gave good results for all evaluated distances between the QTL. For the large distances between the QTL (> 90 cM) the single QTL method more often positioned the QTL in the correct marker bracket, but considering the broader likelihood peaks of the single point method it could be argued that the multi QTL method was more precise. Since the distances were reduced the multi QTL method was clearly more accurate than the single QTL method. The two methods combine well, and together provide a good tool to position single or multiple QTL in practical situations, where the number of QTL and their positions are unknown.     

Ghost QTL and hotspots in experimental crosses: novel approach for modeling polygenic effects

Ghost quantitative trait loci (QTL) are the false discoveries in QTL mapping, that arise due to the “accumulation” of the polygenic effects, uniformly distributed over the genome. The locations on the chromosome that are strongly correlated with the total of the polygenic effects depend on a specific sample correlation structure determined by the genotypes at all loci. The problem is particularly severe when the same genotypes are used to study multiple QTL, e.g. using recombinant inbred lines or studying the expression QTL. In this case, the ghost QTL phenomenon can lead to false hotspots, where multiple QTL show apparent linkage to the same locus. We illustrate the problem using the classic backcross design and suggest that it can be solved by the application of the extended mixed effect model, where the random effects are allowed to have a nonzero mean. We provide formulas for estimating the thresholds for the corresponding t-test statistics and use them in the stepwise selection strategy, which allows for a simultaneous detection of several QTL. Extensive simulation studies illustrate that our approach eliminates ghost QTL/false hotspots, while preserving a high power of true QTL detection.     

QTL analysis: unreliability and bias in estimation procedures

Several statistical methods which employ multiple marker data are currently available for the analysis of quantitative trait loci (QTL) in experimental populations. Although comparable estimates of QTL location and effects have been obtained by these methods, using simulated and real data sets, their accuracy and reliability have not been extensively investigated. The present study specifically examines the merit of using F₂ and doubled haploid populations for locating QTL and estimating their effects. Factors which may affect accuracy and reliability of QTL mapping, such as the number and position of the markers available, the accuracy of the marker locations and the size of the experimental population used, are considered. These aspects are evaluated for QTL of differing heritabilities and locations along the chromosome.A population of 300 F₂ individuals and 150 doubled haploid lines gave estimates of QTL position and effect which were comparable, albeit extremely unreliable. Even for a QTL of high heritability (10%), the confidence interval was 35 cM. There was little increase in reliability to be obtained from using 300, rather than 200, F₂ individuals and 100 doubled haploid lines gave similar results to 150. QTL estimates were not significantly improved either by using the expected, rather than the observed, marker positions or by using a dense map of markers rather than a sparse map. A QTL which was asymmetrically located in the linkage group resulted in inaccurate estimates of QTL position which were seriously biassed at low heritability of the QTL. In a population of 300 F₂ individuals the bias increased from 4 cM to 20 cM, for a QTL with 10% and 2% heritability respectively.     

小麦苗期水分利用效率及其相关性状的QTL分析

以小麦DH群体(旱选10号×鲁麦14)为研究材料,采用复合区间作图法,对小麦幼苗在水分胁迫及非胁迫条件下的水分利用效率(WUE)及其相关性状的QTL进行定位,并对比分析QTL的加性效应.两种水分条件下共检测到14个具显著加性效应的QTL,分布在2A、3A、4A、5A、6A、7A、1B、3B、3D染色体上,可解释表型变异的范围在6.36%～19.73%.其中,非胁迫(对照)条件下检测到10个QTL,包括2个单株WUE的QTL,5个地上部WUE的QTL,1个根系WUE的QTL及2个总耗水量的QTL;水分胁迫条件下上述性状各检测到1个QTL.对于同一性状没有检测到在两种水分条件下均位于同一标记区间的QTL,表明不同水分环境条件下同一性状的QTL表达模式是不同的.论文也讨论了可能用于标记辅助选择的QTL及其分子标记.     

玉米杂交种掖单13号的SSR连锁图谱构建与叶夹角和叶向值的QTL定位与分析

为了增加单位面积产量, 玉米育种者已经开始了更密植更紧凑株型的选育。叶夹角和叶向值是评价玉米株型的重要指标。本研究以掖478×丹340的500个F2单株为作图群体, 构建了具有138个位点的SSR标记连锁图谱, 图谱总长度为1 394.9 cM, 平均间距10.1 cM。利用397个F2：3家系对叶夹角和叶向值进行QTL定位分析, 结果表明: 叶夹角和叶向值分别检测到6和8个QTL, 累计解释表型变异41.0%和60.8%, 单个QTL的贡献率在2.9%~13.6%之间。与叶夹角和叶向值有关的基因主要作用方式为加性和部分显性。此外两个性状共检测到9对上位性互作位点, 表明上位性互作在叶夹角和叶向值的遗传中也起较重要的作用。     

A simulation study on the accuracy of position and effect estimates of linked QTL and their asymptotic standard deviations using multiple interval mapping in an F2 scheme

Approaches like multiple interval mapping using a multiple-QTL model for simultaneously mapping QTL can aid the identification of multiple QTL, improve the precision of estimating QTL positions and effects, and are able to identify patterns and individual elements of QTL epistasis. Because of the statistical problems in analytically deriving the standard errors and the distributional form of the estimates and because the use of resampling techniques is not feasible for several linked QTL, there is the need to perform large-scale simulation studies in order to evaluate the accuracy of multiple interval mapping for linked QTL and to assess confidence intervals based on the standard statistical theory. From our simulation study it can be concluded that in comparison with a monogenetic background a reliable and accurate estimation of QTL positions and QTL effects of multiple QTL in a linkage group requires much more information from the data. The reduction of the marker interval size from 10 cM to 5 cM led to a higher power in QTL detection and to a remarkable improvement of the QTL position as well as the QTL effect estimates. This is different from the findings for (single) interval mapping. The empirical standard deviations of the genetic effect estimates were generally large and they were the largest for the epistatic effects. These of the dominance effects were larger than those of the additive effects. The asymptotic standard deviation of the position estimates was not a good criterion for the accuracy of the position estimates and confidence intervals based on the standard statistical theory had a clearly smaller empirical coverage probability as compared to the nominal probability. Furthermore the asymptotic standard deviation of the additive, dominance and epistatic effects did not reflect the empirical standard deviations of the estimates very well, when the relative QTL variance was smaller/equal to 0.5. The implications of the above findings are discussed.     

大豆油份含量QTL的定位

以大豆杂交组合皖82-178×通山薄皮黄豆甲衍生的重组自交系群体(RIL)为材料, 以该群体所构建的遗传连锁图谱为基础, 以2004和2005年油份含量为指标, 利用软件Cartgrapher(V. 2.0)采用复合区间作图法进行了QTL分析, 结果表明, 利用两年资料对油份含量QTL的定位结果基本一致。两年资料所检测到的QTL均位于wt-11连锁群的satt331附近, 分别可以解释13.95%和15.01%遗传变异。此外, 利用软件QTL Mapper 1.6, 采用复合区间作图法直接对两年的油份含量进行QTL联合分析, 结果表明, 控制油份的QTL也位于wt-11连锁群的satt331附近。     

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.     

Mapping of QTLs for Oral Alcohol Self-Administration in B6.C and B6.I Quasi-Congenic RQI Strains

One strategy to identify neurochemical pathways of addiction is to map the relevant genes. In the present study we used 43 B6.C and 35 B6.I inbred RQI mouse strains, carrying <3% donor genome on C57BL/6ByJ background, for gene mapping. The strains were phenotyped for consumption of alcohol (12% v/v) in a two-bottle-choice paradigm, and genotyped for 396 microsatellite markers. The current mapping study extends our earlier experiment scanning five mouse chromosomes (Vadasz et al. (2000) Scanning of five chromosomes for alcohol consumption loci. Alcohol 22:25–34) to a whole-genome study, and discusses the differences and limitations. Data were analyzed with composite interval (CIM) and multiple interval (MIM) QTL mapping methods. CIM of B6.C strains detected significant QTLs on chrs. 6 and 12. A suggestive, but not significant, locus was detected in the B6.I strains on chr. 12. The best MIM model for B6.C strains confirmed one QTL on chr. 6 and one QTL on chr. 12, while the MIM model for the B6.I strains confirmed the suggestive locus on chr. 12. Some of the QTLs for alcohol consumption are new, while others confirm previously reported QTLs for alcohol preference, and alcohol acceptance.     

Controlling the Type I and Type II Errors in Mapping Quantitative Trait Loci

Although the interval mapping method is widely used for mapping quantitative trait loci (QTLs), it is not very well suited for mapping multiple QTLs. Here, we present the results of a computer simulation to study the application of exact and approximate models for multiple QTLs. In particular, we focus on an automatic two-stage procedure in which in the first stage ``important' markers are selected in multiple regression on markers. In the second stage a QTL is moved along the chromosomes by using the pre-selected markers as cofactors, except for the markers flanking the interval under study. A refined procedure for cases with large numbers of marker cofactors is described. Our approach will be called MQM mapping, where MQM is an acronym for ``multiple-QTL models' as well as for ``marker-QTL-marker.' Our simulation work demonstrates the great advantage of MQM mapping compared to interval mapping in reducing the chance of a type I error (i.e., a QTL is indicated at a location where actually no QTL is present) and in reducing the chance of a type II error (i.e., a QTL is not detected).     

Interval mapping of quantitative trait loci with selective DNA pooling data

Selective DNA pooling is an efficient method to identify chromosomal regions that harbor quantitative trait loci (QTL) by comparing marker allele frequencies in pooled DNA from phenotypically extreme individuals. Currently used single marker analysis methods can detect linkage of markers to a QTL but do not provide separate estimates of QTL position and effect, nor do they utilize the joint information from multiple markers. In this study, two interval mapping methods for analysis of selective DNA pooling data were developed and evaluated. One was based on least squares regression (LS-pool) and the other on approximate maximum likelihood (ML-pool). Both methods simultaneously utilize information from multiple markers and multiple families and can be applied to different family structures (half-sib, F2 cross and backcross). The results from these two interval mapping methods were compared with results from single marker analysis by simulation. The results indicate that both LS-pool and ML-pool provided greater power to detect the QTL than single marker analysis. They also provide separate estimates of QTL location and effect. With large family sizes, both LS-pool and ML-pool provided similar power and estimates of QTL location and effect as selective genotyping. With small family sizes, however, the LS-pool method resulted in severely biased estimates of QTL location for distal QTL but this bias was reduced with the ML-pool.     

玉米和水稻重要性状QTL的比较研究

在构建玉米分子标记连锁图和对重要性状进行QTL定位的基础上,以玉米和水稻的分子标记比较图谱为桥梁,分析了控制玉米和水稻F2：3群体重要农艺和产量性状QTL的共线性关系。研究结果表明：在玉米和水稻共线性的染色体区段,控制玉米株高、行数和行粒数的QTL与控制水稻株高、单株有效穗和每穗实粒数的QTL存在广泛的对应关系;在已定位的影响玉米株高等5个性状的45个QTL中,有16个与水稻“汕优63”群体中5个相同或相似性状所定位的38个QTL中的12个具有共线性关系。这一结果为利用水稻的基因组数据来定位、分离和克隆玉米重要性状的QTL提供了有益信息。同时发现,控制水稻某一个性状的QTL常常与控制玉米同一性状的两个QTL相对应,这一结果为玉米染色体是由水稻染色体加倍而来的理论假设提供了支持。研究还发现,不管是玉米还是水稻在染色体上都存在QTL的富集区域,而这些富集区域常常存在于相同的共线性区域,暗示着玉米和水稻控制相同或相似性状的QTL可能有着相同的起源。基于性状的比较基因组研究不但有助于新基因或QTL的发现、克隆和利用,同时还有助于研究不同物种间染色体的演变和进化规律。     

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

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

油菜硫甙性状QTL 区间的加密和整合

目的:加密油菜控制硫甙性状QTL区间,并进行QTL整合预测候选基因。方法:利用生物信息学方法根据已知测序的白菜BAC序列信息设计引物,在油菜TN DH群体中进行多态性扩增和定位,并根据加密后构建的遗传连锁图重新检测QTL,进行QTL整合。结果:将根据白菜BAC设计的3对多态性标记成功定位到油菜控制硫甙性状QTL区间,进行QTL整合后将QTL置信区间进一步缩小,并判定了初步的候选基因。结论:充分利用白菜已测序的BAC或者基因组信息,将能加快油菜基础研究的步伐。     

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.     

Fine-Scale Mapping of Quantitative Trait Loci Using Historical Recombinations

With increasing popularity of QTL mapping in economically important animals and experimental species, the need for statistical methodology for fine-scale QTL mapping becomes increasingly urgent. The ability to disentangle several linked QTL depends on the number of recombination events. An obvious approach to increase the recombination events is to increase sample size, but this approach is often constrained by resources. Moreover, increasing the sample size beyond a certain point will not further reduce the length of confidence interval for QTL map locations. The alternative approach is to use historical recombinations. We use analytical methods to examine the properties of fine QTL mapping using historical recombinations that are accumulated through repeated intercrossing from an F(2) population. We demonstrate that, using the historical recombinations, both simple and multiple regression models can reduce significantly the lengths of support intervals for estimated QTL map locations and the variances of estimated QTL map locations. We also demonstrate that, while the simple regression model using historical recombinations does not reduce the variances of the estimated additive and dominant effects, the multiple regression model does. We further determine the power and threshold values for both the simple and multiple regression models. In addition, we calculate the Kullback-Leibler distance and Fisher information for the simple regression model, in the hope to further understand the advantages and disadvantages of using historical recombinations relative to F(2) data.