Confidence Intervals in Qtl Mapping by Bootstrapping

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.     

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.     

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).     

On the mapping of quantitative trait loci at marker and non-marker locations

Previous studies have noted that the estimated positions of a large proportion of mapped quantitative trait loci (QTLs) coincide with marker locations and have suggested that this indicates a bias in the mapping methodology. In this study we predict the expected proportion of QTLs with positions estimated to be at the location of a marker and further examine the problem using simulated data. The results show that the higher proportion of putative QTLs estimated to be at marker positions compared with non-marker positions is an expected consequence of the estimation methods. The study initially focused on a single interval with no QTLs and was extended to include multiple intervals and QTLs of large effect. Further, the study demonstrated that the larger proportion of estimated QTL positions at the location of markers was not unique to linear regression mapping. Maximum likelihood produced similar results, although the accumulation of positional estimates at outermost markers was reduced when regions outside the linkage group were also considered. The bias towards marker positions is greatest under the null hypothesis of no QTLs or when QTL effects are small. This study discusses the impact the findings could have on the calculation of thresholds and confidence intervals produced by bootstrap methods.     

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.     

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.     

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.     

Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data.

A novel fine structure mapping method for quantitative traits is presented. It is based on Bayesian modeling and inference, treating the number of quantitative trait loci (QTLs) as an unobserved random variable and using ideas similar to composite interval mapping to account for the effects of QTLs in other chromosomes. The method is introduced for inbred lines and it can be applied also in situations involving frequent missing genotypes. We propose that two new probabilistic measures be used to summarize the results from the statistical analysis: (1) the (posterior) QTL intensity, for estimating the number of QTLs in a chromosome and for localizing them into some particular chromosomal regions, and (2) the locationwise (posterior) distributions of the phenotypic effects of the QTLs. Both these measures will be viewed as functions of the putative QTL locus, over the marker range in the linkage group. The method is tested and compared with standard interval and composite interval mapping techniques by using simulated backcross progeny data. It is implemented as a software package. Its initial version is freely available for research purposes under the name Multimapper at URL http://www.rni.helsinki.fi/mjs.     

Meta - and combined - QTL analysis of different experiments on immune traits in chickens

Meta and/or combined QTL analysis from multiple studies can improve quantitative trait loci (QTL) position estimates compared to the individual experiments. Hereby we present results of a meta-analysis of QTL on chicken chromosome 9, 14 and 18 using data from three separate experiments and joint QTL analysis for chromosome 14 and 18. Meta QTL analysis uses information from multiple QTLs studies. Joint QTL analysis is based on combining raw data from different QTL experimental populations. QTLs under the study were related to specific antibody response to keyhole lymphet hemocyanin (KLH), and natural antibodies to environmental antigens, lipopolisaccharide (LPS) and lipoteichoic acid (LTA). Meta QTL analysis resulted in narrowing down the confidence interval for two QTLs on GGA14. The first one for natural antibodies against LTA and the second one for specific antibody response toward KLH. Also, a confidence interval of a QTL for natural antibodies against LPS located on GGA18 was narrowed down. Combined QTL analysis was successful for two QTLs: for specific antibody response toward KLH on GGA14, and for natural antibodies against LPS on GGA18. The greatest statistical power for QTL detection in joint analysis was achieved when raw data from segregating half–sib families from different populations under the study was used.     

QTL analysis of agronomic traits in barley based on the doubled haploid progeny of two elite North American varieties representing different germplasm groups

A better understanding of the genetics of complex traits, such as yield, may be achieved by using molecular tools. This study was conducted to estimate the number, genome location, effect and allele phase of QTLs determining agronomic traits in the two North American malting barley (Hordeum vulgare L.) quality variety standards. Using a doubled haploid population of 140 lines from the cross of two-rowed Harrington×six-rowed Morex, agronomic phenotypic data sets from nine environments, and a 107-marker linkage map, we performed QTL analyses using simple interval mapping and simplified composite interval mapping procedures. Thirty-five QTLs were associated, either across environments or in individual environments, with five grain and agronomic traits (yield, kernel plumpness, test weight, heading date, and plant height). Significant QTL×environment interaction was detected for all traits. These interactions resulted from both changes in the magnitude of response and changes in the sign of the allelic effect. QTLs for multiple traits were coincident. The vrs1 locus on chromosome 2 (2H), which determines inflorescence row type, was coincident with the largest-effect QTL determining four traits (yield, kernel plumpness, test weight, and plant height). QTL analyses were also conducted separately for each sub-population (six-rowed and two-rowed). Seven new QTLs were detected in the sub-populations. Positive transgressive segregants were found for all traits, but they were more prevalent in the six-rowed sub-population.QTL analysis should be useful for identifying candidate genes and introgressing favorable alleles between germplasm groups. Received: 18 August 2000 / Accepted: 15 December 2000     

A meta–QTL analysis of disease resistance traits of <Emphasis Type="Italic">Theobroma cacao</Emphasis> L.

Theobroma cacao, is a tropical understorey tree that is a major economic resource to several tropical countries. However, the crop is under increased threat from several diseases that are responsible for 30% loss of harvest globally. Although QTL data related to the genetic determinism of disease resistance exist in cocoa, QTL mapping experiments are heterogeneous, thus making comparative QTL mapping essential for marker assisted selection (MAS). Sixteen QTL experiments were analysed, and the 76 QTLs detected were projected on a progressively established consensus map. Several hot spots, with QTLs related to different Phytophthora species and other diseases, were observed. The likely number of “real” QTLs was estimated by using a meta-analysis implemented in BioMercator software. There was a twofold reduction in average confidence interval observed when compared to the confidence interval of individual QTLs. This alternative approach confirms the existence of several sources of resistance to different diseases of cocoa which could be cumulated in new varieties to increase the sustainability of cocoa resistance using MAS strategies.     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

亚麻主要农艺与品质相关性状的QTL定位

为了全面了解亚麻产量和品质相关性状的遗传基础,为亚麻基因克隆和分子标记辅助育种提供理论依据,在已构建SNP连锁遗传图谱的基础上,以LH-89为父本,R43为母本构建F2:3家系QTL定位群体,用R/QTL软件采用复合区间作图法对13个农艺和品质性状进行QTL定位。结果表明:(1)该研究共检测出35个QTL位点,与粗脂肪及其组成成分相关的QTL有20个,与农艺性状相关的QTL有15个;其中:亚油酸和粗脂肪各5个,亚麻酸、千粒重各4个,棕榈酸、株高、工艺长度各3个,硬脂酸、分枝数各2个,单株果数、果粒数、单株粒重、油酸各1个。(2)共有18个QTL的表型贡献率超10%(主效基因),其中农艺性状定位8个主效基因,品质性状定位10个主效基因。     

Non-parametric interval mapping in half-sib designs: use of midranks to account for ties

In QTL analysis of non-normally distributed phenotypes, non-parametric approaches have been proposed as an alternative to the use of parametric tests on mathematically transformed data. The non-parametric interval mapping test uses random ranking to deal with ties. Another approach is to assign to each tied individual the average of the tied ranks (midranks). This approach is implemented and compared to the random ranking approach in terms of statistical power and accuracy of the QTL position. Non-normal phenotypes such as bacteria counts showing high numbers of zeros are simulated (0-80% zeros). We show that, for low proportions of zeros, the power estimates are similar but, for high proportions of zeros, the midrank approach is superior to the random ranking approach. For example, with a QTL accounting for 8% of the total phenotypic variance, a gain from 8% to 11% of power can be obtained. Furthermore, the accuracy of the estimated QTL location is increased when using midranks. Therefore, if non-parametric interval mapping is chosen, the midrank approach should be preferred. This test might be especially relevant for the analysis of disease resistance phenotypes such as those observed when mapping QTLs for resistance to infectious diseases.     

Accounting for variability in the use of permutation testing to detect quantitative trait loci

Locating quantitative trait loci (QTL), or genomic regions associated with known molecular markers, is of increasing interest in a wide variety of applications ranging from human genetics to agricultural genetics. The hope of locating QTL (or genes) affecting a quantitative trait is that it will lead to characterization and possible manipulations of these genes. However, the complexity of both statistical and genetic issues surrounding the location of these regions calls into question the asymptotic statistical results supplying the distribution of the test statistics employed. Coupled with the power of current-day computing, permutation theory was reintroduced for the purpose of estimating the distribution of any test statistic used to test for the location of QTL. Permutation techniques have offered an attractive alternative to significance measures based on asymptotic theory. The ideas of permutation testing are extended in this application to include confidence intervals for the thresholds and p-values estimated in permutation testing procedures. The confidence intervals developed account for the Monte Carlo error associated with practical applications of permutation testing and lead to an effective method of determining an efficient permutation sample size.     

Identification of QTLs controlling tissue-culture traits in barley ( Hordeum vulgare L.)

Quantitative trait loci (QTLs) controlling callus growth (CG), subsequent shoot differentiation ratio (SD) and green shoot ratio (GS) in immature embryo culture were identified in barley. A base map was developed from 99 recombinant inbred lines (RILs) of 'Azumamugi' 2 'Kanto Nakate Gold'. The tissue-culture traits were evaluated at the F₇ and F₁₀ generations of the RILs. The RILs showed wide and continuous variations in each of the three tissue-culture traits. Three QTLs for CG, three QTLs for SD and two QTLs for GS were detected by using composite interval mapping. A QTL for SD on chromosome 3H had a large effect, and 'Kanto Nakate Gold', which has a high differentiation ability, contributed to this QTL. The location of this QTL is identical to, or very close to, the uzu locus. We discuss the relationships between tissue-culture loci in 'Azumamugi' 2 'Kanto Nakate Gold' and those in other mapping populations.     

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。     

The effect of an imprecise map on interval mapping QTLs

The statistical analysis of quantitative trait locus (QTL) experiments relies on the use of a linkage map of the markers genotyped. Such a map is, at best, a good estimate of the true map. Resources might be diverted into developing better marker maps or improved maps become available after the analysis, raising concerns over the original analysis. It is therefore important to understand the sensitivity of QTL analysis to map inaccuracy. We have used simulation methods to investigate the consequences of an incorrect map on the results of a QTL analysis using interval mapping. Backcross data sets were generated with a particular map and then analysed with both the correct map and incorrect maps. If the incorrect maps maintained the true linkage groups (i.e. no markers were incorrectly assigned to another linkage group), the accuracy of the map had little or no impact on the ability to detect QTLs, the true significance levels of the tests or the relative placement of QTLs. When a marker was incorrectly placed on another linkage group, there was a small increase in the level of the test. After adjusting for this increase, there was a decrease in power to detect a QTL near the misplaced marker. This decrease was of a similar magnitude to that found when using a single-marker analysis compared with interval mapping. These results mean that QTL analyses can proceed without the need for very accurate marker maps, and that estimated QTL positions can be translated onto updated maps without the need for reanalysis.     

Using the mixed model for interval mapping of quantitative trait loci in outbred line crosses

Interval mapping by simple regression is a powerful method for the detection of quantitative trait loci (QTLs) in line crosses such as F2 populations. Due to the ease of computation of the regression approach, relatively complex models with multiple fixed effects, interactions between QTLs or between QTLs and fixed effects can easily be accommodated. However, polygenic effects, which are not targeted in QTL analysis, cannot be treated as random effects in a least squares analysis. In a cross between true inbred lines this is of no consequence, as the polygenic effect contributes just to the residual variance. In a cross between outbred lines, however, if a trait has high polygenic heritability, the additive polygenic effect has a large influence on variation in the population. Here we extend the fixed model for the regression interval mapping method to a mixed model using an animal model. This makes it possible to use not only the observations from progeny (e.g. F2), but also those from the parents (F1) to evaluate QTLs and polygenic effects. We show how the animal model using parental observations can be applied to an outbred cross and so increase the power and accuracy of QTL analysis. Three estimation methods, i.e. regression and an animal model either with or without parental observations, are applied to simulated data. The animal model using parental observations is shown to have advantages in estimating QTL position and additive genotypic value, especially when the polygenic heritability is large and the number of progeny per parent is small.     

Mapping Mendelian Factors Underlying Quantitative Traits Using RFLP Linkage Maps

The advent of complete genetic linkage maps consisting of codominant DNA markers [typically restriction fragment length polymorphisms (RFLPs)] has stimulated interest in the systematic genetic dissection of discrete Mendelian factors underlying quantitative traits in experimental organisms. We describe here a set of analytical methods that modify and extend the classical theory for mapping such quantitative trait loci (QTLs). These include: (i) a method of identifying promising crosses for QTL mapping by exploiting a classical formula of SEWALL WRIGHT; (ii) a method (interval mapping) for exploiting the full power of RFLP linkage maps by adapting the approach of LOD score analysis used in human genetics, to obtain accurate estimates of the genetic location and phenotypic effect of QTLs; and (iii) a method (selective genotyping) that allows a substantial reduction in the number of progeny that need to be scored with the DNA markers. In addition to the exposition of the methods, explicit graphs are provided that allow experimental geneticists to estimate, in any particular case, the number of progeny required to map QTLs underlying a quantitative trait.