Multi-QTL Mapping for Quantitative Traits Using Epistatic Distorted Markers

The interaction between segregation distortion loci (SDL) has been often observed in all kinds of mapping populations. However, little has been known about the effect of epistatic SDL on quantitative trait locus (QTL) mapping. Here we proposed a multi-QTL mapping approach using epistatic distorted markers. Using the corrected linkage groups, epistatic SDL was identified. Then, these SDL parameters were used to correct the conditional probabilities of QTL genotypes, and these corrections were further incorporated into the new QTL mapping approach. Finally, a set of simulated datasets and a real data in 304 mouse F₂ individuals were used to validate the new method. As compared with the old method, the new one corrects genetic distance between distorted markers, and considers epistasis between two linked SDL. As a result, the power in the detection of QTL is higher for the new method than for the old one, and significant differences for estimates of QTL parameters between the two methods were observed, except for QTL position. Among two QTL for mouse weight, one significant difference for QTL additive effect between the above two methods was observed, because epistatic SDL between markers C66 and T93 exists (P = 2.94e-4).     

Quantitative trait locus mapping can benefit from segregation distortion

Segregation distortion is a phenomenon that has been observed in many experimental systems. How segregation distortion among markers arises and its impact on mapping studies are the focus of this work. Segregation distortion of markers can be considered to arise from segregation distortion loci (SDL). I develop a theory of segregation distortion and show that the presence of only a few SDL can cause the entire chromosome to distort from Mendelian segregation. Segregation distortion is detrimental to the power of detecting quantitative trait loci (QTL) with dominance effects, but it is not always a detriment to QTL mapping for additive effects. When segregation distortion of a locus is a random event, the SDL is beneficial to QTL mapping ~44% of the time. If SDL are present and ignored, power loss can be substantial. A dense marker map can be used to ameliorate the situation, and if dense marker information is incorporated, power loss is minimal. However, other situations are less benign. A method that can simultaneously map QTL and SDL is discussed, maximizing both use of mapping resources and use by agricultural and evolutionary biologists.     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

A model for quantitative trait loci mapping,linkage phase,and segregation pattern estimation for a full-sib progeny

Quantitative trait loci (QTL) mapping is an important approach for the study of the genetic architecture of quantitative traits. For perennial species, inbred lines cannot be obtained due to inbreed depression and a long juvenile period. Instead, linkage mapping can be performed by using a full-sib progeny. This creates a complex scenario because both markers and QTL alleles can have different segregation patterns as well as different linkage phases between them. We present a two-step method for QTL mapping using full-sib progeny based on composite interval mapping (i.e., interval mapping with cofactors), considering an integrated genetic map with markers with different segregation patterns and conditional probabilities obtained by a multipoint approach. The model is based on three orthogonal contrasts to estimate the additive effect (one in each parent) and dominance effect. These estimatives are obtained using the EM algorithm. In the first step, the genome is scanned to detect QTL. After, segregation pattern and linkage phases between QTL and markers are estimated. A simulated example is presented to validate the methodology. In general, the new model is more effective than existing approaches, because it can reveal QTL present in a full-sib progeny that segregates in any pattern present and can also identify dominance effects. Also, the inclusion of cofactors provided more statistical power for QTL mapping.     

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.     

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.     

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。     

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.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

The covariance between relatives conditional on genetic markers

The development of molecular genotyping techniques makes it possible to analyze quantitative traits on the basis of individual loci. With marker information, the classical theory of estimating the genetic covariance between relatives can be reformulated to improve the accuracy of estimation. In this study, an algorithm was derived for computing the conditional covariance between relatives given genetic markers. Procedures for calculating the conditional relationship coefficients for additive, dominance, additive by additive, additive by dominance, dominance by additive and dominance by dominance effects were developed. The relationship coefficients were computed based on conditional QTL allelic transmission probabilities, which were inferred from the marker allelic transmission probabilities. An example data set with pedigree and linked markers was used to demonstrate the methods developed. Although this study dealt with two QTLs coupled with linked markers, the same principle can be readily extended to the situation of multiple QTL. The treatment of missing marker information and unknown linkage phase between markers for calculating the covariance between relatives was discussed.     

Genome-wide detection of genetic loci triggering uneven descending of gametes from a natural hybrid pine

Marker transmission ratio distortion (TRD) revealed in genetic mapping studies on distant crosses can be used to infer the genetic basis relating to reproductive barriers between species. Unlike measuring the degree of TRD by the overall number of segregation distorted markers in the affected genome regions, mapping the segregation distorting loci (SDL) provides reliable statistic parameters that help to confine the target genomic regions for further characterization at molecular level. Using the linkage map constructed for a natural hybrid of Pinus hwangshanensis and Pinus massoniana, we perform SDL analyses and align the established map to the loblolly pine consensus map. Altogether, six SDLs with relatively strong LOD supports are detected on four linkage groups of the established map. Since gametes inheriting different alternate chromatid blocks from the SDL affecting genome regions have uneven chance to descend to the offspring, the corresponding genome regions are supposed to play more significant roles in rendering the reproductive isolations between P. hwangshanensis and P. massoniana. This paper presents a case study on a crucial step for uncovering the hidden genetic factors that trigger the uneven descending of gametes in a natural hybrid pine.     

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.     

A likelihood approach for mapping growth trajectories using dominant markers in a phase-unknown full-sib family

Dominant markers have been commonly used in mapping quantitative trait loci (QTLs) in outcrossing species, in which not much prior genome information is available. But the dominant nature of these markers may lead to reduced QTL mapping precision and power. A new statistical method is proposed to incorporate growth laws into a QTL mapping framework, under which the use of the efficiency of dominant markers can be increased. This new method can be used to identify specific QTLs affecting differentiation in growth trajectories, and further estimate the timing of a QTL to turn on, or turn off, affecting growth during the entire ontogeny of a species. Using this method based on dominant markers we have successfully mapped a QTL for stem height growth trajectories to a linkage group in a forest tree. The implications of this method for the understanding of the genetic architecture of growth using dominant markers are discussed.Communicated by F. Salamini     

Linear models for joint association and linkage QTL mapping

Background

Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.

Results

We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders'' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.

Conclusion

The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.     

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     

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.     

Genetic Map Construction and Detection of Genetic Loci Underlying Segregation Distortion in an Intraspecific Cross of Populus deltoides

Based on a two-way pseudo-testcross strategy, high density and complete coverage linkage maps were constructed for the maternal and paternal parents of an intraspecific F2 pedigree of Populus deltoides. A total of 1,107 testcross markers were obtained, and the mapping population consisted of 376 progeny. Among these markers, 597 were from the mother, and were assigned into 19 linkage groups, spanning a total genetic distance of 1,940.3 cM. The remaining 519 markers were from the father, and were also were mapped into 19 linkage groups, covering 2,496.3 cM. The genome coverage of both maps was estimated as greater than 99.9% at 20 cM per marker, and the numbers of linkage groups of both maps were in accordance with the 19 haploid chromosomes in Populus. Marker segregation distortion was observed in large contiguous blocks on some of the linkage groups. Subsequently, we mapped the segregation distortion loci in this mapping pedigree. Altogether, eight segregation distortion loci with significant logarithm of odds supports were detected. Segregation distortion indicated the uneven transmission of the alternate alleles from the mapping parents. The corresponding genome regions might contain deleterious genes or be associated with hybridization incompatibility. In addition to the detection of segregation distortion loci, the established genetic maps will serve as a basic resource for mapping genetic loci controlling traits of interest in future studies.     

The genetic variance for multiple linked quantitative trait loci conditional on marker information in a crossed population

In the prediction of genetic values and quantitative trait loci (QTLs) mapping via the mixed model method incorporating marker information in animal populations, it is important to model the genetic variance for individuals with an arbitrary pedigree structure. In this study, for a crossed population originated from different genetic groups such as breeds or outbred strains, the variance of additive genetic values for multiple linked QTLs that are contained in a chromosome segment, especially the segregation variance, is investigated assuming the use of marker data. The variance for a finite number of QTLs in one chromosomal segment is first examined for the crossed population with the general pedigree. Then, applying the concept of the expectation of identity-by-descent proportion, an approximation to the mean of the conditional probabilities for the linked QTLs over all loci is obtained, and using it an expression for the variance in the case of an infinite number of linked QTLs marked by flanking markers is derived. It appears that the approach presented can be useful in the segment mapping using, and in the genetic evaluation of, crosses with general pedigrees in the population of concern. The calculation of the segregation variance through the current approach is illustrated numerically, using a small data-set.     

The Statistical Power of Inclusive Composite Interval Mapping in Detecting Digenic Epistasis Showing Common F2 Segregation Ratios

Epistasis is a commonly observed genetic phenomenon and an important source of variation of complex traits,which could maintain additive variance and therefore assure the long-term genetic gain in breeding.Inclusive composite interval mapping（ICIM） is able to identify epistatic quantitative trait loci（QTLs） no matter whether the two interacting QTLs have any additive effects.In this article,we conducted a simulation study to evaluate detection power and false discovery rate（FDR） of ICIM epistatic mapping,by considering F₂ and doubled haploid（DH） populations,different F₂ segregation ratios and population sizes.Results indicated that estimations of QTL locations and effects were unbiased,and the detection power of epistatic mapping was largely affected by population size,heritability of epistasis,and the amount and distribution of genetic effects.When the same likelihood of odd（LOD） threshold was used,detection power of QTL was higher in F₂ population than power in DH population;meanwhile FDR in F₂ was also higher than that in DH.The increase of marker density from 10 cM to 5 cM led to similar detection power but higher FDR.In simulated populations,ICIM achieved better mapping results than multiple interval mapping（MIM） in estimation of QTL positions and effect.At the end,we gave epistatic mapping results of ICIM in one actual population in rice（Oryza sativa L.）.     

Conditional QTL mapping of protein content in wheat with respect to grain yield and its components

Grain protein content in wheat (Triticum aestivum L.) is generally considered a highly heritable character that is negatively correlated with grain yield and yield-related traits. Quantitative trait loci (QTL) for protein content was mapped using data on protein content and protein content conditioned on the putatively interrelated traits to evaluate possible genetic interrelationships between protein content and yield, as well as yield-related traits. Phenotypic data were evaluated in a recombinant inbred line population with 302 lines derived from a cross between the Chinese cultivar Weimai 8 and Luohan 2. Inclusive composite interval mapping using IciMapping 3.0 was employed for mapping unconditional and conditional QTL with additives. A strong genetic relationship was found between protein content and grain yield, and yield-related traits. Unconditional QTL mapping analysis detected seven additive QTL for protein content, with additive effects ranging in absolute size from 0.1898% to 0.3407% protein content, jointly accounting for 43.45% of the trait variance. Conditional QTL mapping analysis indicated two QTL independent from yield, which can be used in marker-assisted selection for increasing yield without affecting grain protein content. Three additional QTL with minor effects were identified in the conditional mapping. Of the three QTLs, two were identified when protein content was conditioned on yield, which had pleiotropic effects on those two traits. Conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the individual QTL level for closely correlated traits. Further, conditional QTL mapping can reveal additional QTL with minor effects that are undetectable in unconditional mapping.