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.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.     

孙女设计中标记密度对QTL定位精确性的影响

采用蒙特卡罗方法分析了在孙女设计中不同的嫩体结构、性状遗传力、ＱＴＬ效应大小和ＱＴＬ在染色体上的位置中个因素不同水平组合下４种标记密度（标记间隔５ｃＭ,１０ｃＭ,２０ｃＭ、５０ｃＭ对ＱＴＬ定位精确性（以均方误ＭＳＥ为衡量指标）的影响,并从经济学角度探讨了应用于标记辅助选（ＭＡＳ）的ＱＴＬ定位的最佳标记密度。结果表明,一般说来,在各因素水平都较低时,ＭＳＥ随标记密度加大而下降的相对幅度也较 小,反之     

High-density genotyping: an overkill for QTL mapping? Lessons learned from a case study in maize and simulations

High-density genotyping is extensively exploited in genome-wide association mapping studies and genomic selection in maize. By contrast, linkage mapping studies were until now mostly based on low-density genetic maps and theoretical results suggested this to be sufficient. This raises the question, if an increase in marker density would be an overkill for linkage mapping in biparental populations, or if important QTL mapping parameters would benefit from it. In this study, we addressed this question using experimental data and a simulation based on linkage maps with marker densities of 1, 2, and 5 cM. QTL mapping was performed for six diverse traits in a biparental population with 204 doubled haploid maize lines and in a simulation study with varying QTL effects and closely linked QTL for different population sizes. Our results showed that high-density maps neither improved the QTL detection power nor the predictive power for the proportion of explained genotypic variance. By contrast, the precision of QTL localization, the precision of effect estimates of detected QTL, especially for small and medium sized QTL, as well as the power to resolve closely linked QTL profited from an increase in marker density from 5 to 1 cM. In conclusion, the higher costs for high-density genotyping are compensated for by more precise estimates of parameters relevant for knowledge-based breeding, thus making an increase in marker density for linkage mapping attractive.     

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.     

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

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

Selection bias in quantitative trait loci mapping

A simulation study was performed to see whether selection affected quantitative trait loci (QTL) mapping. Populations under random selection, under selection among full-sib families, and under selection within a full-sib family were simulated each with heritability of 0.3, 0.5, and 0.7. They were analyzed with the marker spacing of 10 cM and 20 cM. The accuracy for QTL detection decreased for the populations under selection within full-sib family. Estimates of QTL effects and positions differed (P < .05) from their input values. The problems could be ignored when mapping a QTL for the populations under selection among full-sib families. A large heritability helped reduction of such problems. When the animals were selected within a full-sib family, the QTL was detected for the populations with heritability of 0.5 or larger using the marker spacing of 10 cM, and with heritability of 0.7 using the marker spacing of 20 cM. This study implied that when selection was introduced, the accuracy for QTL detection decreased and the estimates of QTL effects were biased. A caution was warranted on the decision of data (including selected animals to be genotyped) for QTL mapping.     

Interactions between markers can be caused by the dominance effect of quantitative trait loci

F₂ populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F₂ populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F₂ population.     

Optimal haplotype structure for linkage disequilibrium-based fine mapping of quantitative trait loci using identity by descent

A linkage disequilibrium-based method for fine mapping quantitative trait loci (QTL) has been described that uses similarity between individuals' marker haplotypes to determine if QTL alleles are identical by descent (IBD) to model covariances among individuals' QTL alleles for a mixed linear model. Mapping accuracy with this method was found to be sensitive to the number of linked markers that was included in the haplotype when fitting the model at a putative position of the QTL. The objective of this study was to determine the optimal haplotype structure for this IBD-based method for fine mapping a QTL in a previously identified QTL region. Haplotypes consisting of 1, 2, 4, 6, or all 10 available markers were fit as a "sliding window" across the QTL region under ideal and nonideal simulated population conditions. It was found that using haplotypes of 4 or 6 markers as a sliding "window" resulted in the greatest mapping accuracy under nearly all conditions, although the true IBD state at a putative QTL position was most accurately predicted by IBD probabilities obtained using all markers. Using 4 or 6 markers resulted in greater discrimination of IBD probabilities between positions while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Fitting IBD probabilities on the basis of a single marker resulted in the worst mapping accuracy under all conditions because it resulted in poor accuracy of IBD probabilities. In conclusion, for fine mapping using IBD methods, marker information must be used in a manner that results in sensitivity of IBD probabilities to the putative position of the QTL while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Contrary to expectation, use of haplotypes of 4-6 markers to derive IBD probabilities, rather than all available markers, best fits these criteria. Thus for populations similar to those simulated here, optimal mapping accuracy for this IBD-based fine-mapping method is obtained with a haplotype structure including a subset of all available markers.     

Power analysis for quantitative trait locus mapping in populations derived by multiple backcrosses

 Populations derived by multiple backcrosses are potentially useful for quantitative trait locus (QTL) mapping studies. Comparisons of relative power to detect QTL using populations derived by multiple back-crosses are needed to make decisions when mapping projects are initiated. The objective of this study was to theoretically compare the power to detect QTL in populations derived by multiple backcrosses relative to mapping in a recombinant inbred population of equal size. Backcrossing results in a reduction in genetic variance with each generation and also results in an increasing frequency of the recurrent parent marker genotype. The relevant outcome for QTL mapping is a reduction in genetic variance to partition between marker genotype classes and increasing unbalance of the number of individuals contributing to the mean of the marker genotypes. Both of these factors lead to a decrease in the power to detect a QTL as the number of backcross generations increases. Experimental error was held constant with the populations compared. From a theoretical standpoint, backcross-derived populations offer few advantages for QTL detection. If, however, a backcrossing approach is the most efficient method to achieve a desired breeding objective and if QTL detection is an objective of equal or less importance, backcross-derived populations are a reasonable approach to QTL detection. Received: 4 August 1996 / Accepted: 4 April 1997     

Linkage disequilibrium mapping of quantitative trait loci under truncation selection

As a dense map of single nucleotide polymorphism (SNP) markers are available, population-based linkage disequilibrium (LD) mapping or association study is becoming one of the major tools for identifying quantitative trait loci (QTL) and for fine gene mapping. However, in many cases, LD between the marker and trait locus is not very strong. Approaches that maximize the potential of detecting LD will be essential for the success of LD mapping of QTL. In this paper, we propose two strategies for increasing the probability of detecting LD: (1) phenotypic selection and (2) haplotype LD mapping. To provide the foundations for LD mapping of QTL under selection, we develop analytic tools for assessing the impact of phenotypic selection on allele and haplotype frequencies, and LD under three trait models: single trait locus, two unlinked trait loci, and two linked trait loci with or without epistasis. In addition to a traditional chi(2) test, which compares the difference in allele or haplotype frequencies in the selected sample and population sample, we present multiple regression methods for LD mapping of QTL, and investigate which methods are effective in employing phenotypic selection for QTL mapping. We also develop a statistical framework for investigating and comparing the power of the single marker and multilocus haplotype test for LD mapping of QTL. Finally, the proposed methods are applied to mapping QTL influencing variation in systolic blood pressure in an isolated Chinese population.     

Fine mapping of quantitative trait loci using linkage disequilibria with closely linked marker loci

A multimarker linkage disequilibrium mapping method was developed for the fine mapping of quantitative trait loci (QTL) using a dense marker map. The method compares the expected covariances between haplotype effects given a postulated QTL position to the covariances that are found in the data. The expected covariances between the haplotype effects are proportional to the probability that the QTL position is identical by descent (IBD) given the marker haplotype information, which is calculated using the genedropping method. Simulation results showed that a QTL was correctly positioned within a region of 3, 1.5, or 0.75 cM in 70, 62, and 68%, respectively, of the replicates using markers spaced at intervals of 1, 0.5, and 0.25 cM, respectively. These results were rather insensitive to the number of generations since the QTL occurred and to the effective population size, except that 10 generations yielded rather poor estimates of the QTL position. The position estimates of this multimarker disequilibrium mapping method were more accurate than those from a single marker transmission disequilibrium test. A general approach for identifying QTL is suggested, where several stages of disequilibrium mapping are used with increasingly dense marker spacing.     

Fine-mapping of quantitative trait loci in half-sib families using current recombinations

Two groups of methods are being developed to fine-map quantitative trait loci (QTLs): identity-by-descent methods or methods using historical recombinations, and genetic chromosome dissection methods or methods utilizing current recombinations. Here we propose two methods that fall into the second group: contrast mapping and substitution mapping. A QTL has previously been detected via linkage mapping in a half-sib design (granddaughter or daughter design), and sires (grandsires) likely to be heterozygous at the QTL have been identified. A sire (grandsire) and its recombinant offspring are then genotyped for a series of ordered markers spanning the initial marker interval. Offspring are grouped by paternal multi-marker haplotype with haplotypes differing in the location of the recombination event. In the contrast method, contrasts between the phenotypic averages of haplotypes or offspring groups are calculated which correspond to marker intervals within the original interval. The expected value of the contrast for the true QTL interval is always maximum, hence the interval with maximum observed contrast is assumed to contain the QTL. Alternative statistics for determining the interval most likely to contain a QTL are presented for contrast mapping, as well as a bootstrap estimation of the probability of having identified the correct interval. For an initial marker bracket of 20 cM and 10 additional equidistant markers, the probability of assigning the QTL to the correct 2 cM marker interval or to a combined 4 cM interval was calculated. For substitution effects of 0.093, 0.232, 0.464, 0.696 and 0.928 (in additive genetic SD), power values near 0.14, 0.26, 0.48, 0.67 and 0.80 (0.25, 0.53, 0.86, 0.97 and 0.99) are achieved for a family of 200 (1000) sons, respectively. In substitution mapping, QTL segregation status of recombinant sons must be determined using daughter genotyping. Combinations of two haplotypes with their segregation status are required to assign the QTL to an interval. Probabilities of correct QTL assignment were calculated assuming absence of the mutant QTL allele in dams of sons. For a 2 cM interval and a QTL at the midpoint of an interval, power near 0.95 (0.90) is reached when the number of recombinant sons is 70 (60), or total number of sons is 424 (363). For QTL positions away from the midpoint, power decreases but can be improved by combining marker intervals. For a QTL located halfway to the midpoint, and 182 sons in a family resulting in 30 recombinant sons, probability is 0.94 for assignment to either a 2 cM or a combined 4 cM interval. Effect of type I and type II errors in segregation status determination on power of QTL assignment was found to be small. Errors in segregation status due to QTL segregation in dams have an impact if the frequency of the mutant QTL allele is intermediate to high.     

QTL fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium at a series of linked marker loci in extreme samples of populations

It has recently been demonstrated that fine-scale mapping of a susceptibility locus for a complex disease can be accomplished on the basis of deviations from Hardy-Weinberg (HW) equilibrium at closely linked marker loci among affected individuals. We extend this theory to fine-scale localization of a quantitative-trait locus (QTL) from extreme individuals in populations, by means of HW and linkage-disequilibrium (LD) analyses. QTL mapping and/or linkage analyses can establish a large genomic region ( approximately 30 cM) that contains a QTL. The QTL can be fine mapped by examination of the degree of deviation from HW and LD at a series of closely linked marker loci. The tests can be performed for samples of individuals belonging to either high or low percentiles of the phenotype distribution or for combined samples of these extreme individuals. The statistical properties (the power and the size) of the tests of this fine-mapping approach are investigated and are compared extensively, under various genetic models and parameters for the QTL and marker loci. On the basis of the results, a two-stage procedure that uses extreme samples and different tests (for HW and LD) is suggested for QTL fine mapping. This two-step procedure is economic and powerful and can accurately narrow a genomic region containing a QTL from approximately 30-1 cM, a range that renders physical mapping feasible for identification of the QTL. In addition, the relationship between parameterizations of complex diseases, by means of penetrance, and those of complex quantitative traits, by means of genotypic values, is outlined. This means that many statistical genetic methods developed for searching for susceptibility loci of complex diseases can be directly adopted and/or extended to QTL mapping for quantitative traits.     

作物数量性状研究进展

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

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

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

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.     

Optimum design of family structure and allocation of resources in association mapping with lines from multiple crosses

Family mapping is based on multiple segregating families and is becoming increasingly popular because of its advantages over population mapping. Athough much progress has been made recently, the optimum design and allocation of resources for family mapping remains unclear. Here, we addressed these issues using a simulation study, resample model averaging and cross-validation approaches. Our results show that in family mapping, the predictive power and the accuracy of quatitative trait loci (QTL) detection depend greatly on the population size and phenotyping intensity. With small population sizes or few test environments, QTL results become unreliable and are hampered by a large bias in the estimation of the proportion of genotypic variance explained by the detected QTL. In addition, we observed that even though good results can be achieved with low marker densities, no plateau is reached with our full marker complement. This suggests that higher quality results could be achieved with greater marker densities or sequence data, which will be available in the near future for many species.     

Disequilibrium mapping of a quantitative-trait locus in an expanding population.

Linkage disequilibrium (LD) mapping can be successful if there is strong nonrandom association between marker alleles and an allele affecting a trait of interest. The principles of LD mapping of dichotomous traits are well understood, but less is known about LD mapping of a quantitative-trait locus (QTL). It is shown in this report that selective genotyping can increase the power to detect and map a rare allele of large effect at a QTL. Two statistical tests of the association between an allele and a quantitative character are proposed. These tests are approximately independent, so information from them can be combined. Analytic theory is developed to show that these two tests are effective in detecting the presence of a low-frequency allele with a relatively large effect on the character when the QTL is either already a candidate locus or closely linked to a marker locus that is in strong LD with the QTL. The latter situation is expected in a rapidly growing population in which the allele of large effect was present initially in one copy. Therefore, the proposed tests are useful under the same conditions as those for successful LD mapping of a dichotomous trait or disease. Simulations show that, for detection of the presence of a QTL, these tests are more powerful than a simple t-test. The tests also provide a basis for defining a measure of association, gamma, between a low-frequency allele at a putative QTL and a low-frequency allele at a marker locus.     

Comparison of biometrical approaches for QTL detection in multiple segregating families

Detection of QTL in multiple segregating families possesses many advantages over the classical QTL mapping in biparental populations. It has thus become increasingly popular, and different biometrical approaches are available to analyze such data sets. We empirically compared an approach based on linkage mapping methodology with an association mapping approach. To this end, we used a large population of 788 elite maize lines derived from six biparental families genotyped with 857 SNP markers. In addition, we constructed genetic maps with reduced marker densities to assess the dependency of the performance of both mapping approaches on the marker density. We used cross-validation and resample model averaging and found that while association mapping performed better under high marker densities, this was reversed under low marker densities. In addition to main effect QTL, we also detected epistatic interactions. Our results suggest that both approaches will profit from a further increase in marker density and that a cross-validation should be applied irrespective of the biometrical approach.