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.     

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.     

A Nonparametric Approach for Mapping Quantitative Trait Loci

Genetic mapping of quantitative trait loci (QTLs) is performed typically by using a parametric approach, based on the assumption that the phenotype follows a normal distribution. Many traits of interest, however, are not normally distributed. In this paper, we present a nonparametric approach to QTL mapping applicable to any phenotypic distribution. The method is based on a statistic Z(w), which generalizes the nonparametric Wilcoxon rank-sum test to the situation of whole-genome search by interval mapping. We determine the appropriate significance level for the statistic Z(w), by showing that its asymptotic null distribution follows an Ornstein-Uhlenbeck process. These results provide a robust, distribution-free method for mapping QTLs.     

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).     

Limitations of a two-step moment method for mapping linked multiple QTL

As an alternative to multiple-interval mapping a two-step moment method was recently proposed to map linked multiple quantitative trait loci (QTLs). The advantage of this moment method was supposed to be its simplicity and computational efficiency, especially in detecting closely linked QTLs within a marker bracket, but also in mapping QTLs in different marker intervals. Using simulations it is shown that the two-step moment method may give poor results compared with multiple-interval mapping, irrespective of whether the QTLs are in the same or in different marker intervals, especially if linked QTLs are in repulsion. The criteria of comparison are number of identified QTLs, likelihood ratio test statistics, means and empirical standard errors of the QTL position and QTL effects estimates, and the accuracy of the residual variance estimates. Further, the joint conditional probabilities of QTL genotypes for two putative QTLs within a marker interval were derived and compared with the unmodified approach ignoring the non-independence of the conditional probabilities.     

A comparison of interval mapping procedures including the QTL-cluster mapping

Using the deterministic sampling, patterns of the log-likelihood surfaces expected in some interval mapping procedures for estimating the position of, and the effect for, QTL(s) were investigated for the situations where a single QTL or closely linked QTLs are contained in a chromosome segment bracketed with two markers. The mapping procedures compared were the conventional, likelihood-based interval mapping (IM), the regression interval mapping (RIM), and the QTL-cluster mapping (CM) in which the conditional probabilities of transmission of the whole segment marked by the flanking markers were taken into consideration. The half-sib design was used here, and several cases of the true genetic model were considered, differing in the number of QTLs contained in the marker interval, the linkage phase for the sire, and the magnitude of the QTL(s) effect. For the true genetic models where a single QTL or closely linked QTLs being in coupling phase are contained in the interval, with (R)IM, clear global maxima of the log-likelihood were observed within the range of the marker interval. It was shown that the estimates of the QTL(s) effect at the marked segment level are expected to be unbiased. On the other hand, in a setting where the linkage phase for the linked QTLs located in the interval was different from coupling and repulsion, there was found a ridge along the interval for the log-likelihood surface with (R)IM, indicating the dependency between the estimates of the position of, and the effect for, the putative QTL. For this case, it was found that the position of the putative QTL could be estimated as that of one of the flanking markers, and the estimate of the QTL effect be biased. In contrast, it was revealed that CM is expected to provide the unbiased estimate of the QTL(s)-effect at the segment level for any case of the true genetic models considered here. If the aim is for marker-assisted selection rather than mapping closely linked QTLs individually, then the CM approach is considered to be useful.     

Mapping quantitative trait loci with dominant markers in four-way crosses

 A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families. Received: 16 June 1998 / Accepted: 29 September 1998     

Accuracy of mapping quantitative trait loci in autogamous species

Summary The development of linkage maps with large numbers of molecular markers has stimulated the search for methods to map genes involved in quantitative traits (QTLs). A promising method, proposed by Lander and Botstein (1989), employs pairs of neighbouring markers to obtain maximum linkage information about the presence of a QTL within the enclosed chromosomal segment. In this paper the accuracy of this method was investigated by computer simulation. The results show that there is a reasonable probability of detecting QTLs that explain at least 5% of the total variance. For this purpose a minimum population of 200 backcross or F₂ individuals is necessary. Both the number of individuals and the relative size of the genotypic effect of the QTL are important factors determining the mapping precision. On the average, a QTL with 5% or 10% explained variance is mapped on an interval of 40 or 20 centiMorgans, respectively. Of course, QTLs with a larger genotypic effect will be located more precisely. It must be noted, however, that the interval length is rather variable.     

Detection of putative quantitative trait loci in line crosses under infinitesimal genetic models

Quantitative trait locus (QTL) mapping studies often employ segregating generations derived from a cross between genetically divergent inbred lines. In the analysis of such data it is customary to fit a single QTL and use a null hypothesis which assumes that the genomic region under study contributes no genetic variance. To explore the situation in which multiple linked genes contribute to the genetic variance, we simulated an F₂-mapping experiment in which the genetic difference between the two original inbred strains was caused by a large number of loci, each having equal effect on the quantitative trait. QTLs were either in coupling, dispersion or repulsion phase in the base population of inbred lines, with the expected F₂ genetic variance explained by the QTLs being equivalent in the three models. Where QTLs were in coupling phase, one inbred line was fixed for all plus alleles, and the other line was fixed for minus alleles. Where QTLs were in dispersion phase, they were assumed to be randomly fixed for one or other allele (as if the inbred lines had evolved from a common ancestor by random drift). Where QTLs were in repulsion phase alleles within an inbred line were alternating plus and minus at adjacent loci, and alternative alleles were fixed in the two inbred lines. In all these genetic models a standard interval mapping test statistic used to determine whether there is a QTL of large effect segregating in the population was inflated on average. Furthermore, the use of a threshold for QTL detection derived under the assumption that no QTLs were segregating would often lead to spurious conclusions regards the presence of genes of large effects (i.e. type I errors). The employment of an alternative model for the analysis, including linked markers as cofactors in the analysis of a single interval, reduced the problem of type I error rate, although test statistics were still inflated relative to the case of no QTLs. It is argued that in practice one should take into account the difference between the strains or the genetic variance in the F₂ population when setting significance thresholds. In addition, tests designed to probe the adequacy of a single-QTL model or of an alternative infinitesimal coupling model are described. Such tests should be applied in QTL mapping studies to help dissect the true nature of genetic variation.     

Empirical Bayesian elastic net for multiple quantitative trait locus mapping

In multiple quantitative trait locus (QTL) mapping, a high-dimensional sparse regression model is usually employed to account for possible multiple linked QTLs. The QTL model may include closely linked and thus highly correlated genetic markers, especially when high-density marker maps are used in QTL mapping because of the advancement in sequencing technology. Although existing algorithms, such as Lasso, empirical Bayesian Lasso (EBlasso) and elastic net (EN) are available to infer such QTL models, more powerful methods are highly desirable to detect more QTLs in the presence of correlated QTLs. We developed a novel empirical Bayesian EN (EBEN) algorithm for multiple QTL mapping that inherits the efficiency of our previously developed EBlasso algorithm. Simulation results demonstrated that EBEN provided higher power of detection and almost the same false discovery rate compared with EN and EBlasso. Particularly, EBEN can identify correlated QTLs that the other two algorithms may fail to identify. When analyzing a real dataset, EBEN detected more effects than EN and EBlasso. EBEN provides a useful tool for inferring high-dimensional sparse model in multiple QTL mapping and other applications. An R software package ‘EBEN'' implementing the EBEN algorithm is available on the Comprehensive R Archive Network (CRAN).     

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…     

Quantitative Trait Loci for Light Sensitivity,Body Weight,Body Size,and Morphological Eye Parameters in the Bumblebee,Bombus terrestris

Bumblebees such as Bombus terrestris are essential pollinators in natural and managed ecosystems. In addition, this species is intensively used in agriculture for its pollination services, for instance in tomato and pepper greenhouses. Here we performed a quantitative trait loci (QTL) analysis on B. terrestris using 136 microsatellite DNA markers to identify genes linked with 20 traits including light sensitivity, body size and mass, and eye and hind leg measures. By composite interval mapping (IM), we found 83 and 34 suggestive QTLs for 19 of the 20 traits at the linkage group wide significance levels of p = 0.05 and 0.01, respectively. Furthermore, we also found five significant QTLs at the genome wide significant level of p = 0.05. Individual QTLs accounted for 7.5-53.3% of the phenotypic variation. For 15 traits, at least one QTL was confirmed with multiple QTL model mapping. Multivariate principal components analysis confirmed 11 univariate suggestive QTLs but revealed three suggestive QTLs not identified by the individual traits. We also identified several candidate genes linked with light sensitivity, in particular the Phosrestin-1-like gene is a primary candidate for its phototransduction function. In conclusion, we believe that the suggestive and significant QTLs, and markers identified here, can be of use in marker-assisted breeding to improve selection towards light sensitive bumblebees, and thus also the pollination service of bumblebees.     

Multi-environment mapping and meta-analysis of 100-seed weight in soybean

100-Seed weight (100-SW) of soybean is an important but complicated quantitative trait to yield. This study was focus on the quantitative trait loci (QTLs) of soybean 100-SW from 2006 to 2010, using recombination inbred lines population that was derived from a cross between Charleston and Dongnong 594. A total of 23 QTLs for 100-SW were detected in the linkage group C2, D1a, F, G and O. Nine QTLs were identified by composite interval mapping including one QTL with the minimum confidence interval (CI) of 1.3?cM, while 14 QTLs by multiple interval mapping. Furthermore, 94 reported QTLs of 100-SW were integrated with our QTL mapping results using BioMercator. As a result, 15 consensus QTLs and their corresponding markers were identified. The minimum CI was reduced to 1.52?cM by the combination of meta-analysis. These findings may merit fine-mapping of these QTL in soybean.     

Maximum Likelihood Mapping of Quantitative Trait Loci Using Full-Sib Families

A maximum likelihood method is presented for the detection of quantitative trait loci (QTL) using flanking markers in full-sib families. This method incorporates a random component for common family effects due to additional QTL or the environment. Simulated data have been used to investigate this method. With a fixed total number of full sibs power of detection decreased substantially with decreasing family size. Increasing the number of alleles at the marker loci (i.e., polymorphism information content) and decreasing the interval size about the QTL increased power. Flanking markers were more powerful than single markers. In testing for a linked QTL the test must be made against a model which allows for between family variation (i.e., including an unlinked QTL or a between family variance component) or the test statistic may be grossly inflated. Mean parameter estimates were close to the simulated values in all situations when fitting the full model (including a linked QTL and common family effect). If the common family component was omitted the QTL effect was overestimated in data in which additional genetic variance was simulated and when compared with an unlinked QTL model there was reduced power. The test statistic curves, reflecting the likelihood of the QTL at each position along the chromosome, have discontinuities at the markers caused by adjacent pairs of markers providing different amounts of information. This must be accounted for when using flanking markers to search for a QTL in an outbred population.     

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.     

Multiple Trait Analysis of Genetic Mapping for Quantitative Trait Loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.     

与偏分离位点连锁的QTL作图的统计方法

提出了一种统计方法,可以估计与偏分离位点连锁的QTL的位置和效应。该方法利用回交群体中呈现偏分离的分子标记,首先用最大似然法对偏分离位点与标记位点之间的重组率和配子存活率进行估计,然后用区间作图法估计加性-显性模型下QTL的位置和效应参数。该方法可用于对常规作图研究中表现偏分离的标记进行分析,以帮助我们发现新的偏分离基因（或不育基因）和数量性状位点。     

Pooled analysis of data from multiple quantitative trait locus mapping populations

Quantitative trait locus (QTL) analysis on pooled data from multiple populations (pooled analysis) provides a means for evaluating, as a whole, evidence for existence of a QTL from different studies and examining differences in gene effect of a QTL among different populations. Objectives of this study were to: (1) develop a method for pooled analysis and (2) conduct pooled analysis on data from two soybean mapping populations. Least square interval mapping was extended for pooled analysis by inclusion of populations and cofactor markers as indicator variables and covariate variables separately in the multiple linear models. The general linear test approach was applied for detecting a QTL. Single population-based and pooled analyses were conducted on data from two F_2:3 mapping populations, Hamilton (susceptible) × PI 90763 (resistant) and Magellan (susceptible) × PI 404198A (resistant), for resistance to soybean cyst nematode (SCN) in soybean. It was demonstrated that where a QTL was shared among populations, pooled analysis showed increased LOD values on the QTL candidate region over single population analyses. Where a QTL was not shared among populations, however, the pooled analysis showed decreased LOD values on the QTL candidate region over single population analyses. Pooled analysis on data from genetically similar populations may have higher power of QTL detection than single population-based analyses. QTLs were identified by pooled analysis on linkage groups (LGs) G, B1 and J for resistance to SCN race 2 whereas QTLs on LGs G, B1 and E for resistance to SCN race 5 in soybean PI 90763 and PI 404198A. QTLs on LG G and B1 were identified in both PI 90763 and PI 404198A whereas QTLs on LG E and J were identified in PI 90763 only. QTLs on LGs G and B1 for resistance to race 2 may be the same or closely linked with QTLs on LG G and B1 for resistance to race 5, respectively. It was further demonstrated that QTLs on G and B1 carried by PI 90763 were not significantly different in gene effect from QTLs on LGs G and B1 in PI 404198A, respectively.     

Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping

The aim of this study was to explore, by computer simulation, the mapping of QTLs in a realistic but complex situation of many (linked) QTLs with different effects, and to compare two QTL mapping methods. A novel method to dissect genetic variation on multiple chromosomes using molecular markers in backcross and F₂ populations derived from inbred lines was suggested, and its properties tested using simulations. The rationale for this sequential testing method was to explicitly test for alternative genetic models. The method consists of a series of four basic statistical tests to decide whether variance was due to a single QTL, two QTLs, multiple QTLs, or polygenes, starting with a test to detect genetic variance associated with a particular chromosome. The method was able to distinguish between different QTL configurations, in that the probability to `detect' the correct model was high, varying from 0.75 to 1. For example, for a backcross population of 200 and an overall heritability of 50%, in 78% of replicates a polygenic model was detected when that was the underlying true model. To test the method for multiple chromosomes, QTLs were simulated on 10 chromosomes, following a geometric series of allele effects, assuming positive alleles were in coupling in the founder lines For these simulations, the sequential testing method was compared to the established Multiple QTL Mapping (MQM) method. For a backcross population of 400 individuals, power to detect genetic variance was low with both methods when the heritability was 0.40. For example, the power to detect genetic variation on a chromosome on which 6 QTLs explained 12.6% of the genetic variance, was less than 60% for both methods. For a large heritability (0.90), the power of MQM to detect genetic variance and to dissect QTL configurations was generally better, due to the simultaneous fitting of markers on all chromosomes. It is concluded that when testing different QTL configurations on a single chromosome using the sequential testing procedure, regions of other chromosomes which explain a significant amount of variation should be fitted in the model of analysis. This study reinforces the need for large experiments in plants and other species if the aim of a genome scan is to dissect quantitative genetic variation.     

Mapping of quantitative trait loci (QTLs) for oil yield using SSRs and gene-based markers in African oil palm (<Emphasis Type="Italic">Elaeis guineensis</Emphasis> Jacq.)

The identification of quantitative trait loci (QTLs) based on anchor markers, especially candidate genes that control a trait of interest, has been noted to increase the power of QTL detection. Since these markers can be scored as co-dominant data, they are also valuable for comparing and integrating the QTL linkage maps from diverse mapping populations. To estimate the position and effects of QTLs linked to oil yield traits in African oil palm, co-dominant microsatellites (SSR) and candidate gene-based sequence polymorphisms were applied to construct a linkage map for a progeny showing large differences in oil yield components. The progeny was genotyped for 97 SSR markers, 93 gene-linked markers, and 12 non-gene-linked SNP markers. From these, 190 segregating loci could be arranged into 31 linkage groups while 12 markers remained unmapped. Using the single marker linkage, interval mapping and multiple QTL methods, 16 putative QTLs on seven linkage groups affecting important oil yield related traits such as fresh fruit bunch yield (FFB), ratio of oil per fruit (OF), oil per bunch (OB), fruit per bunch (FB) and wet mesocarp per fruit (WMF) could be identified in the segregating population with estimated values for explained variance ranging from 12.4 % to 54.5 %. Markers designed from some candidate genes involved in lipid biosynthesis were found to be mapped near significant QTLs for various economic yield traits. Associations between QTLs and potential candidate genes are discussed.