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.     

Spurious linkage between markers in QTL mapping

Selective genotyping of extreme progeny is a powerful method to increase the information content per individual when looking for quantitative trait loci (QTLs) using molecular markers for which a map is known. However, if marker information from the selected individuals is used to construct the map of the markers, this can lead to distorted segregation of the markers that in turn can lead to the estimation of a spurious linkage between independently inherited markers. The mistaken estimation of linkage between independently inherited markers will occur when there are two (or more) independently inherited QTLs linked to two (or more) markers and the same individuals are used to estimate the map of the markers and to do the QTL estimation. The incorrect linkage occurs because in selecting individuals from the tails of the phenotypic distribution we will also be selecting certain combinations of the markers instead of obtaining a random sample of the true distribution of the marker genotypes. Analytical results are outlined and the analyses of a simulated data set illustrate the problems that could arise when data from individuals chosen by selective genotyping are incorrectly employed to construct a marker map. A strategy is proposed to remedy this problem.     

Advances in Statistical Methods to Map Quantitative Trait Loci in Outbred Populations

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.     

FunMap: functional mapping of complex traits

SUMMARY: FunMap is a Web-based user interface designed to map quantitative trait loci (QTL) affecting function-valued traits or infinite-dimensional traits in well-structured pedigrees or natural populations. User input includes three files: longitudinal trait data, marker genotypes and/or a linkage map. This software allows for a systematic genome-wide scan and significance test of QTL throughout the map. The dynamic change of QTL effects during the time course of growth is automatically drawn, from which specific biological hypotheses regarding the genetic control mechanisms of growth and development can be tested. AVAILABILITY: http://web.biostat.ufl.edu/~cma/genetics/software.html     

豌豆遗传图谱构建及QTL定位研究进展

豌豆的许多性状是多基因控制的数量性状,QTL定位就是以分子标记技术为工具、以遗传连锁图谱为基础、利用分子标记与QTL之间的连锁关系确定控制数量性状的基因在基因组中的位置.本文对QTL定位原理、方法进行了简单介绍;对豌豆遗传图谱构建及主要性状,如产量、品质、抗病性等QTL定位、遗传效应分析等方面的研究进行综述;对目前基于QTL豌豆分子标记育种存在的问题、应用前景进行了探讨.     

作物数量性状基因座定位及分析研究进展

近年来,分子数量遗传学的快速发展,使作物复杂数量性状尤其是经济性状的QTL研究取得了巨大进展,大大促进了复杂数量性状的遗传改良和分子操纵。本文从分子标记连锁图谱的构建、QTL定位力方法及效应分析、精细定位和QTL验证及应用等方面综述了二十多年来作物QTL的研究进展,讨论当前QTL研究中存在的问题,并展望了作物QTL研究的发展前景。     

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F(5) maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.     

Time-related mapping of quantitative trait loci underlying tiller number in rice.

Using time-related phenotypic data, methods of composite interval mapping and multiple-trait composite interval mapping based on least squares were applied to map quantitative trait loci (QTL) underlying the development of tiller number in rice. A recombinant inbred population and a corresponding saturated molecular marker linkage map were constructed for the study. Tiller number was recorded every 4 or 5 days for a total of seven times starting at 20 days after sowing. Five QTL were detected on chromosomes 1, 3, and 5. These QTL explained more than half of the genetic variance at the final observation. All the QTL displayed an S-shaped expression curve. Three QTL reached their highest expression rates during active tillering stage, while the other two QTL achieved this either before or after the active tillering stage.     

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.     

数量性状基因座位及其在家禽中的定位

近年来随着现代分子生物学的发展 ,一些高效的分子遗传标记将各种畜禽的遗传图谱研究推向深入。为高密度、覆盖面广的连锁图谱的构建及QTL的定位奠定了基础。有关QTL的基本理论、QTL定位的步骤、QTL的检测方法以及家禽中定位的QTL已经展开了深入的研究 ,但目前QTL定位中存在诸多问题的问题     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

Mapping quantitative trait loci in complex pedigrees: a two-step variance component approach

There is a growing need for the development of statistical techniques capable of mapping quantitative trait loci (QTL) in general outbred animal populations. Presently used variance component methods, which correctly account for the complex relationships that may exist between individuals, are challenged by the difficulties incurred through unknown marker genotypes, inbred individuals, partially or unknown marker phases, and multigenerational data. In this article, a two-step variance component approach that enables practitioners to routinely map QTL in populations with the aforementioned difficulties is explored. The performance of the QTL mapping methodology is assessed via its application to simulated data. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Combined genetic and physiological analysis of a locus contributing to quantitative variation

The natural variation of many traits is controlled by multiple genes, individually referred to as quantitative trait loci (QTL), that interact with the environment to determine the ultimate phenotype of any individual. A QTL has yet to be described molecularly, in part because strategies to systematically identify them are underdeveloped and because the subtle nature of QTLs prevents the application of standard methods of gene identification. Therefore, it will be necessary to develop a systematic approach(es) for the identification of QTLs based upon the numerous positional data now being accumulated through molecular marker analyses. We have characterized a QTL by the following three-step approach: (1) identification of a QTL in complex populations, (2) isolation and genetic mapping of this QTL in near-isogenic lines, and (3) identification of a candidate gene using map position and physiological criteria. Using this approach we have characterized a plant height QTL in maize that maps to chromosome 9 near the centromere. Both map position and physiological criteria suggest the gibberillin biosynthesis gene dwarf3 as a candidate gene for this QTL.     

A Bayesian Approach to Detect Quantitative Trait Loci Using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) techniques are applied to simultaneously identify multiple quantitative trait loci (QTL) and the magnitude of their effects. Using a Bayesian approach a multi-locus model is fit to quantitative trait and molecular marker data, instead of fitting one locus at a time. The phenotypic trait is modeled as a linear function of the additive and dominance effects of the unknown QTL genotypes. Inference summaries for the locations of the QTL and their effects are derived from the corresponding marginal posterior densities obtained by integrating the likelihood, rather than by optimizing the joint likelihood surface. This is done using MCMC by treating the unknown QTL genotypes, and any missing marker genotypes, as augmented data and then by including these unknowns in the Markov chain cycle along with the unknown parameters. Parameter estimates are obtained as means of the corresponding marginal posterior densities. High posterior density regions of the marginal densities are obtained as confidence regions. We examine flowering time data from double haploid progeny of Brassica napus to illustrate the proposed method.     

A statistical framework for quantitative trait mapping

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.     

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。     

Variation in feed quality traits for beef cattle in Steptoe?×?Morex barley population

Barley is a major feed source for livestock in the western regions of North America. Feed quality of beef cattle has been neglected as a selection criterion because of lack of understanding of the feed characteristics that could be responsive to selection and would improve feedlot performance. A Steptoe × Morex population was planted in irrigated and rain-fed environments, and collected data were used to evaluate the genetic variation in dry matter and starch digestibilities, acid detergent fiber, protein and starch contents, and to map quantitative trait loci controlling the variation in these traits. Transgressive genotypes indicate the wide genetic variation of these traits. High heritability estimates for these traits suggest that early selection for these traits during breeding would be achievable. A total of 32 main effect QTL and five epistatic QTL were identified which conditioned feed traits on different barley chromosomes. QTL for acid detergent fiber and starch contents overlapped on chromosome 6H at the Nar7 locus. Tight negative correlation between the two traits suggest the usability of Nar7 as anchor marker in marker-assisted selection programs to develop barley with low acid detergent fiber and high starch content.     

Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.