Quantitative trait locus mapping with background control in genetic populations of clonal F1 and double cross

In this study, we considered five categories of molecular markers in clonal F₁ and double cross populations, based on the number of distinguishable alleles and the number of distinguishable genotypes at the marker locus. Using the completed linkage maps, incomplete and missing markers were imputed as fully informative markers in order to simplify the linkage mapping approaches of quantitative trait genes. Under the condition of fully informative markers, we demonstrated that dominance effect between the female and male parents in clonal F₁ and double cross populations can cause the interactions between markers. We then developed an inclusive linear model that includes marker variables and marker interactions so as to completely control additive effects of the female and male parents, as well as the dominance effect between the female and male parents. The linear model was finally used for background control in inclusive composite interval mapping (ICIM) of quantitative trait locus (QTL). The efficiency of ICIM was demonstrated by extensive simulations and by comparisons with simple interval mapping, multiple‐QTL models and composite interval mapping. Finally, ICIM was applied in one actual double cross population to identify QTL on days to silking in maize.     

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

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

Power of tests for QTL detection using replicated progenies derived from a diallel cross

In crop species, most QTL (quantitative trait loci) mapping strategies use segregating populations derived from an initial cross between two lines. However, schemes including more than two parents could also be used. We propose an approach using a high-density restriction fragment length polymorphism (RFLP) map established on six F ₂ populations derived from diallel crosses among four inbred lines and the phenotypic performances of two types of replicated progenies (F ₃ and topcross). The QTL is supposed to be on the marker locus considered. Three linear model tests for the detection of QTL effects (T ₁, T ₂ and T ₃) are described and their power studied for the two types of progeny. T ₁ tests the global genetic effects of the QTL (additivity and dominance) and T ₂ tests only additive effects assuming dominance is absent when it could exist. The models of these two tests assume that the main effects of QTL alleles are constant in different genetic backgrounds. The additive model of test T ₃ considers the six F ₂ populations independently, and T ₃ is the equivalent of the classical mean comparison test if we neglect dominance; it uses only contrasts between the homozygote marker classes. The results show that T ₂ is much more powerful than T ₃. The power of T ₁ and T ₂ depends on the relative sizes of the additive and dominance effects, and their comparison is not easy to establish. Nevertheless, T ₂ seems to be the more powerful in most situations, indicating that it is often more interesting to ignore dominance when testing for a QTL effect. For a given size of genetic effects, the power is affected by the total number of individuals genotyped in F ₂ and the recombination rate between the marker locus and the putative QTL. The approach presented in this paper has some drawbacks but could be easily generalized to other sizes of diallels and different progeny types.     

Prevalence of segregation distortion in diploid alfalfa and its implications for genetics and breeding applications

Segregation distortion (SD) is often observed in plant populations; its presence can affect mapping and breeding applications. To investigate the prevalence of SD in diploid alfalfa (Medicago sativa L.), we developed two unrelated segregating F₁ populations and one F₂ population. We genotyped all populations with SSR markers and assessed SD at each locus in each population. The three maps were syntenic and largely colinear with the Medicago truncatula genome sequence. We found genotypic SD for 24 and 34% of markers in the F₁ populations and 68% of markers in the F₂ population; distorted markers were identified on every linkage group. The smaller percentage of genotypic SD in the F₁ populations could be because they were non-inbred and/or due to non-fully informative markers. For the F₂ population, 60 of 90 mapped markers were distorted, and they clustered into eight segregation distortion regions (SDR). Most SDR identified in the F₁ populations were also identified in the F₂ population. Genotypic SD was primarily due to zygotic rather than allelic distortion, suggesting zygotic not gametic selection is the main cause of SD. On the F₂ linkage map, distorted markers in all SDR except two showed heterozygote excess. The severe SD in the F₂ population likely biased genetic distances among markers and possibly also marker ordering and could affect QTL mapping of agronomic traits. To reduce the effects of SD and non-fully informative markers, we suggest constructing linkage maps and conducting QTL mapping in advanced generation populations.     

Whole-Genome Quantitative Trait Locus Mapping Reveals Major Role of Epistasis on Yield of Rice

Although rice yield has been doubled in most parts of the world since 1960s, thanks to the advancements in breeding technologies, the biological mechanisms controlling yield are largely unknown. To understand the genetic basis of rice yield, a number of quantitative trait locus (QTL) mapping studies have been carried out, but whole-genome QTL mapping incorporating all interaction effects is still lacking. In this paper, we exploited whole-genome markers of an immortalized F₂ population derived from an elite rice hybrid to perform QTL mapping for rice yield characterized by yield per plant and three yield component traits. Our QTL model includes additive and dominance main effects of 1,619 markers and all pair-wise interactions, with a total of more than 5 million possible effects. The QTL mapping identified 54, 5, 28 and 4 significant effects involving 103, 9, 52 and 7 QTLs for the four traits, namely the number of panicles per plant, the number of grains per panicle, grain weight, and yield per plant. Most identified QTLs are involved in digenic interactions. An extensive literature survey of experimentally characterized genes related to crop yield shows that 19 of 54 effects, 4 of 5 effects, 12 of 28 effects and 2 of 4 effects for the four traits, respectively, involve at least one QTL that locates within 2 cM distance to at least one yield-related gene. This study not only reveals the major role of epistasis influencing rice yield, but also provides a set of candidate genetic loci for further experimental investigation.     

Effects of missing marker and segregation distortion on QTL mapping in F2 populations

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.     

A quantitative trait locus for cold tolerance at the booting stage on rice chromosome 8

A quantitative trait locus (QTL) for cold tolerance at the booting stage of a cold-tolerant rice breeding line, Hokkai-PL9, was analyzed. A total of 487 simple sequence repeat (SSR) markers distributed throughout the genome were used to survey for polymorphism between Hokkai-PL9 and a cold-sensitive breeding line, Hokkai287, and 54 markers were polymorphic. Single marker analysis revealed that markers on chromosome 8 are associated with cold tolerance. By interval mapping using an F₂ population between Hokkai-PL9 and Hokkai287, a QTL for cold tolerance was detected on the short arm of chromosome 8. The QTL explains 26.6% of the phenotypic variance, and its additive effect is 11.4%. Substitution mapping suggested that the QTL is located in a 193-kb interval between SSR markers RM5647 and PLA61. We tentatively designated the QTL as qCTB8 (quantitative trait locus for cold tolerance at the booting stage on chromosome 8).     

More about quantitative trait locus mapping with diallel designs

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.     

QTL analysis: a simple ‘marker-regression’ approach

A method to locate quantitative trait loci (QTL) on a chromosome and to estimate their additive and dominance effects is described. It applies to generations derived from an F₁ by selfing or backcrossing and to doubled haploid lines, given that marker genotype information (RFLP, RAPD, etc.) and quantitative trait data are available. The method involves regressing the additive difference between marker genotype means at a locus against a function of the recombination frequency between that locus and a putative QTL. A QTL is located, as by other regression methods, at that point where the residual mean square is minimised. The estimates of location and gene effects are consistent and as reliable as conventional flanking-marker methods. Further applications include the ability to test for the presence of two, or more, linked QTL and to compare different crosses for the presence of common QTL. Furthermore, the technique is straightforward and may be programmed using standard pc-based statistical software.     

Comparing linkage disequilibrium-based methods for fine mapping quantitative trait loci

Recently, a method for fine mapping quantitative trait loci (QTL) using linkage disequilibrium was proposed to map QTL by modeling covariance between individuals, due to identical-by-descent (IBD) QTL alleles, on the basis of the similarity of their marker haplotypes under an assumed population history. In the work presented here, the advantage of using marker haplotype information for fine mapping QTL was studied by comparing the IBD-based method with 10 markers to regression on a single marker, a pair of markers, or a two-locus haplotype under alternative population histories. When 10 markers were genotyped, the IBD-based method estimated the position of the QTL more accurately than did single-marker regression in all populations. When 20 markers were genotyped for regression, as single-marker methods do not require knowledge of haplotypes, the mapping accuracy of regression in all populations was similar to or greater than that of the IBD-based method using 10 markers. Thus for populations similar to those simulated here, the IBD-based method is comparable to single-marker regression analysis for fine mapping QTL.     

Mapping of rat Chromosome 2 markers generated from chromosome-sorted DNA

A quantitative trait locus (QTL) for blood pressure has recently been mapped to a region of roughly 30 cM on rat Chromosome (Chr) 2 by linkage and by the use of congenic strains. For further fine mapping of the QTL, however, closely linked chromosome markers residing in this 30-cM region are required. In the current work, 36 new markers were generated by screening rat Chr 2-sorted DNA libraries and subsequently mapped using five F₂ populations. Combining new and existing markers, the marker density for the 30-cM region approaches, on average, one marker per 1.1 cM. Received: 11 April 1997 / Accepted: 12 May 1997     

胚乳性状数量基因的定位方法

将三倍体胚乳性状的数量遗传模型和二倍体性状数量基因（QTL）图构建方法相结合,导出双侧标记基因型下有关胚乳性状QTL的遗传组成、平均数和遗传方差分量,据之提出以某一区间双侧标记基因型胚乳性状的平均值为依变数,以该区间内任一点假定存在的QTL的加性效应d、显性效应h1和／或h2的系数为自变数,进行有重复观察值的多元线性回归分析,根据多元线性回归的显著性测验该点是否存在QTL,并估计出QTL的遗传效应。给定区间内任一点,皆可以此进行分析,从而可在整条染色体上作图,并以之确定QTL的数目和最可能位置,同时,在检测某一区间时,利用多元线性回归方法将该区间外可能存在的QTL的干扰进行统计控制,以提高QTL检测的精度。此外,还讨论了如何将之推广应用于其他类型的DNA不对应资料以及具复杂遗传模型的胚乳性状资料。     

Genetic analysis of rice CMS-WA fertility restoration based on QTL mapping

 The inheritance of fertility restoration of rice cytoplasmic male sterility of the wild abortive type was studied by means of QTL mapping. The two segregating populations examined showed high frequencies of highly sterile and highly fertile progenies, but a low frequency of partially sterile and partially fertile progenies. The distributions suggested that fertility restoration was mainly controlled by major genes. Based on a linkage map constructed with 57 RFLP and 61 AFLP markers on a B₁F₁ population, composite interval mapping (CIM) revealed that the fertility was restored by the additive effects of two restorer loci located on chromosome 10. One QTL, tightly linked to RFLP marker C1361 in the middle of the long arm of chromosome 10, explained 71.5% of the phenotypic variance. The second QTL was located between RFLP markers R2309 and RG257 on the short arm and explained 27.3% of the phenotypic variance. Similar results were obtained using the simple interval mapping (SIM) methods. Recived: 8 January 1998/Accepted: 22 April 1998     

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.     

Multiple regression for molecular-marker,quantitative trait data from large F2 populations

Molecular marker-quantitative trait associations are important for breeders to recognize and understand to allow application in selection. This work was done to provide simple, intuitive explanations of trait-marker regression for large samples from an F₂ and to examine the properties of the regression estimators. Beginning with a(- 1,0,1) coding of marker classes and expected frequencies in the F₂, expected values, variances, and covariances of marker variables were calculated. Simple linear regression and regression of trait values on two markers were computed. The sum of coefficient estimates for the flanking-marker regression is asymptotically unbiased for an included additive effect with complete interference, and is only slightly biased with no interference and moderately close (15 cM) marker spacing. The variance of the sum of regression coefficients is much more stable for small recombination distances than variances of individual coefficients. Multiple regression of trait variables on coded marker variables can be interpreted as the product of the inverse of the marker correlation matrix R and the vector a of simple linear regression estimators for each marker. For no interference, elements of the correlation matrix R can be written as products of correlations between adjacent markers. The inverse of R is displayed and used to illustrate the solution vector. Only markers immediately flanking trait loci are expected to have non-zero values and, with at least two marker loci between each trait locus, the solution vector is expected to be the sum of solutions for each trait locus. Results of this work should allow breeders to test for intervals in which trait loci are located and to better interpret results of the trait-marker regression.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.     

Fine mapping a QTL qCTB7 for cold tolerance at the booting stage on rice chromosome 7 using a near-isogenic line

Low temperature at the booting stage is a serious abiotic stress in rice, and cold tolerance is a complex trait controlled by many quantitative trait loci (QTL). A QTL for cold tolerance at the booting stage in cold-tolerant near-isogenic rice line ZL1929-4 was analyzed. A total of 647 simple sequence repeat (SSR) markers distributed across 12 chromosomes were used to survey for polymorphisms between ZL1929-4 and the cold-sensitive japonica cultivar Towada, and nine were polymorphic. Single marker analysis revealed that markers on chromosome 7 were associated with cold tolerance. By interval mapping using an F₂ population from ZL1929-4 × Towada, a QTL for cold tolerance was detected on the long arm of chromosome 7. The QTL explained 9 and 21% of the phenotypic variances in the F₂ and F₃ generations, respectively. Recombinant plants were screened for two flanking markers, RM182 and RM1132, in an F₂ population with 2,810 plants. Two-step substitution mapping suggested that the QTL was located in a 92-kb interval between markers RI02905 and RM21862. This interval was present in BAC clone AP003804. We designated the QTL as qCTB7 (quantitative trait locus for cold tolerance at the booting stage on chromosome 7), and identified 12 putative candidate genes.     

High-resolution association mapping of quantitative trait loci: a population-based approach

In this article, population-based regression models are proposed for high-resolution linkage disequilibrium mapping of quantitative trait loci (QTL). Two regression models, the "genotype effect model" and the "additive effect model," are proposed to model the association between the markers and the trait locus. The marker can be either diallelic or multiallelic. If only one marker is used, the method is similar to a classical setting by Nielsen and Weir, and the additive effect model is equivalent to the haplotype trend regression (HTR) method by Zaykin et al. If two/multiple marker data with phase ambiguity are used in the analysis, the proposed models can be used to analyze the data directly. By analytical formulas, we show that the genotype effect model can be used to model the additive and dominance effects simultaneously; the additive effect model takes care of the additive effect only. On the basis of the two models, F-test statistics are proposed to test association between the QTL and markers. By a simulation study, we show that the two models have reasonable type I error rates for a data set of moderate sample size. The noncentrality parameter approximations of F-test statistics are derived to make power calculation and comparison. By a simulation study, it is found that the noncentrality parameter approximations of F-test statistics work very well. Using the noncentrality parameter approximations, we compare the power of the two models with that of the HTR. In addition, a simulation study is performed to make a comparison on the basis of the haplotype frequencies of 10 SNPs of angiotensin-1 converting enzyme (ACE) genes.     

A two‐step approach to map quantitative trait loci for meat quality in connected porcine F2 crosses considering main and epistatic effects

The aim of this study was to map QTL for meat quality traits in three connected porcine F₂ crosses comprising around 1000 individuals. The three crosses were derived from the founder breeds Chinese Meishan, European Wild Boar and Pietrain. The animals were genotyped genomewide for approximately 250 genetic markers, mostly microsatellites. They were phenotyped for seven meat quality traits (pH at 45 min and 24 h after slaughter, conductivity at 45 min and 24 h after slaughter, meat colour, drip loss and rigour). QTL mapping was conducted using a two‐step procedure. In the first step, the QTL were mapped using a multi‐QTL multi‐allele model that was tailored to analyse multiple connected F₂ crosses. It considered additive, dominance and imprinting effects. The major gene RYR1:g.1843C>T affecting the meat quality on SSC6 was included as a cofactor in the model. The mapped QTL were tested for pairwise epistatic effects in the second step. All possible epistatic effects between additive, dominant and imprinting effects were considered, leading to nine orthogonal forms of epistasis. Numerous QTL were found. The most interesting chromosome was SSC6. Not all genetic variance of meat quality was explained by RYR1:g.1843C>T. A small confidence interval was obtained, which facilitated the identification of candidate genes underlying the QTL. Epistasis was significant for the pairwise QTL on SSC12 and SSC14 for pH24 and for the QTL on SSC2 and SSC5 for rigour. Some evidence for additional pairwise epistatic effects was found, although not significant. Imprinting was involved in epistasis.