棉花数量性状基因定位研究进展

棉花的许多重要性状,包括产量、纤维品质、株型、抗病抗逆性、生理生化等都是数量性状,受遗传和环境因子的共同作用。近年来,随着分子生物学技术的进步,棉花基因组研究得到迅速发展,为棉花数量性状基因（quantitative trait locus,QTL）定位奠定了坚实的基础。概述了近十几年来棉花QTL定位研究及分子标记辅助选择的进展,结合研究实践指出了棉花QTL定位及标记辅助选择存在的问题,并对其发展方向做出了初步探讨。     

The X chromosome in quantitative trait locus mapping

The X chromosome requires special treatment in the mapping of quantitative trait loci (QTL). However, most QTL mapping methods, and most computer programs for QTL mapping, have focused exclusively on autosomal loci. We describe a method for appropriate treatment of the X chromosome for QTL mapping in experimental crosses. We address the important issue of formulating the null hypothesis of no linkage appropriately. If the X chromosome is treated like an autosome, a sex difference in the phenotype can lead to spurious linkage on the X chromosome. Further, the number of degrees of freedom for the linkage test may be different for the X chromosome than for autosomes, and so an X chromosome-specific significance threshold is required. To address this issue, we propose a general procedure to obtain chromosome-specific significance thresholds that controls the genomewide false positive rate at the desired level. We apply our methods to data on gut length in a large intercross of mice carrying the Sox10Dom mutation, a model of Hirschsprung disease. We identified QTL contributing to variation in gut length on chromosomes 5 and 18. We found suggestive evidence of linkage to the X chromosome, which would be viewed as strong evidence of linkage if the X chromosome was treated as an autosome. Our methods have been implemented in the package R/qtl.     

Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Power of quantitative trait locus mapping for polygenic binary traits using generalized and regression interval mapping in multi-family half-sib designs

A generalized interval mapping (GIM) method to map quantitative trait loci (QTL) for binary polygenic traits in a multi-family half-sib design is developed based on threshold theory and implemented using a Newton-Raphson algorithm. Statistical power and bias of QTL mapping for binary traits by GIM is compared with linear regression interval mapping (RIM) using simulation. Data on 20 paternal half-sib families were simulated with two genetic markers that bracketed an additive QTL. Data simulated and analysed were: (1) data on the underlying normally distributed liability (NDL) scale, (2) binary data created by truncating NDL data based on three thresholds yielding data sets with three different incidences, and (3) NDL data with polygenic and QTL effects reduced by a proportion equal to the ratio of the heritabilities on the binary versus NDL scale (reduced-NDL). Binary data were simulated with and without systematic environmental (herd) effects in an unbalanced design. GIM and RIM gave similar power to detect the QTL and similar estimates of QTL location, effects and variances. Presence of fixed effects caused differences in bias between RIM and GIM, where GIM showed smaller bias which was affected less by incidence. The original NDL data had higher power and lower bias in QTL parameter estimates than binary and reduced-NDL data. RIM for reduced-NDL and binary data gave similar power and estimates of QTL parameters, indicating that the impact of the binary nature of data on QTL analysis is equivalent to its impact on heritability.     

Rank-based statistical methodologies for quantitative trait locus mapping

This article addresses the identification of genetic loci (QTL and elsewhere) that influence nonnormal quantitative traits with focus on experimental crosses. QTL mapping is typically based on the assumption that the traits follow normal distributions, which may not be true in practice. Model-free tests have been proposed. However, nonparametric estimation of genetic effects has not been studied. We propose an estimation procedure based on the linear rank test statistics. The properties of the new procedure are compared with those of traditional likelihood-based interval mapping and regression interval mapping via simulations and a real data example. The results indicate that the nonparametric method is a competitive alternative to the existing parametric methodologies.     

Parallel computing in interval mapping of quantitative trait loci.

Linear regression analysis is considered the least computationally demanding method for mapping quantitative trait loci (QTL). However, simultaneous search for multiple QTL, the use of permutations to obtain empirical significance thresholds, and larger experimental studies significantly increase the computational demand. This report describes an easily implemented parallel algorithm, which significantly reduces the computing time in both QTL mapping and permutation testing. In the example provided, the analysis time was decreased to less than 15% of a single processor system by the use of 18 processors. We indicate how the efficiency of the analysis could be improved by distributing the computations more evenly to the processors and how other ways of distributing the data facilitate the use of more processors. The use of parallel computing in QTL mapping makes it possible to routinely use permutations to obtain empirical significance thresholds for multiple traits and multiple QTL models. It could also be of use to improve the computational efficiency of the more computationally demanding QTL analysis methods.     

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.     

Generalized linear model for interval mapping of quantitative trait loci

We developed a generalized linear model of QTL mapping for discrete traits in line crossing experiments. Parameter estimation was achieved using two different algorithms, a mixture model-based EM (expectation–maximization) algorithm and a GEE (generalized estimating equation) algorithm under a heterogeneous residual variance model. The methods were developed using ordinal data, binary data, binomial data and Poisson data as examples. Applications of the methods to simulated as well as real data are presented. The two different algorithms were compared in the data analyses. In most situations, the two algorithms were indistinguishable, but when large QTL are located in large marker intervals, the mixture model-based EM algorithm can fail to converge to the correct solutions. Both algorithms were coded in C++ and interfaced with SAS as a user-defined SAS procedure called PROC QTL.     

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses

ABSTRACT: BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.     

Empirical Bayesian elastic net for multiple quantitative trait locus mapping

In multiple quantitative trait locus (QTL) mapping, a high-dimensional sparse regression model is usually employed to account for possible multiple linked QTLs. The QTL model may include closely linked and thus highly correlated genetic markers, especially when high-density marker maps are used in QTL mapping because of the advancement in sequencing technology. Although existing algorithms, such as Lasso, empirical Bayesian Lasso (EBlasso) and elastic net (EN) are available to infer such QTL models, more powerful methods are highly desirable to detect more QTLs in the presence of correlated QTLs. We developed a novel empirical Bayesian EN (EBEN) algorithm for multiple QTL mapping that inherits the efficiency of our previously developed EBlasso algorithm. Simulation results demonstrated that EBEN provided higher power of detection and almost the same false discovery rate compared with EN and EBlasso. Particularly, EBEN can identify correlated QTLs that the other two algorithms may fail to identify. When analyzing a real dataset, EBEN detected more effects than EN and EBlasso. EBEN provides a useful tool for inferring high-dimensional sparse model in multiple QTL mapping and other applications. An R software package ‘EBEN'' implementing the EBEN algorithm is available on the Comprehensive R Archive Network (CRAN).     

A sib-pair approach to interval mapping of quantitative trait loci.

An interval mapping procedure based on the sib-pair method of Haseman and Elston is developed, and simulation studies are carried out to explore its properties. The procedure is analogous to other interval mapping procedures used with experimental material, such as plants and animals, and yields very similar results in terms of the location and effect size of a quantitative trait locus (QTL). The procedure offers an advantage over the conventional Haseman and Elston approach, in terms of power, and provides useful information concerning the location of a QTL. Because of its simplicity, the method readily lends itself to the analysis of selected samples for increased power and the evaluation of multilocus models of complex phenotypes.     

Significance thresholds for quantitative trait locus mapping under selective genotyping

In the case of selective genotyping, the usual permutation test to establish statistical significance for quantitative trait locus (QTL) mapping can give inappropriate significance thresholds, especially when the phenotype distribution is skewed. A stratified permutation test should be used, with phenotypes shuffled separately within the genotyped and ungenotyped individuals.     

Nonparametric confidence interval estimators for heritability and expected selection response

Statistical methods have not been described for comparing estimates of family-mean heritability (H) or expected selection response (R), nor have consistently valid methods been described for estimating R intervals. Nonparametric methods, e.g., delete-one jackknifing, may be used to estimate variances, intervals, and hypothesis test statistics in estimation problems where parametric methods are unsuitable, nonrobust, or undefinable. Our objective was to evaluate normal-approximation jackknife interval estimators for H and R using Monte Carlo simulation. Simulations were done using normally distributed within-family effects and normally, uniformly, and exponentially distributed between-family effects. Realized coverage probabilities for jackknife interval (2) and parametric interval (5) for H were not significantly different from stated probabilities when between-family effects were normally distributed. Coverages for jackknife intervals (3) and (4) for R were not significantly different from stated coverages when between-family effects were normally distributed. Coverages for interval (3) for R were occasionally significantly less than stated when between-family effects were uniformly or exponentially distributed. Coverages for interval (2) for H were occasionally significantly less than stated when between-family effects were exponentially distributed. Thus, intervals (3) and (4) for R and (2) for H were robust. Means of analysis of variance estimates of R were often significantly less than parametric values when the number of families evaluated was 60 or less. Means of analysis of variance estimates of H were consistently significantly less than parametric values. Means of jackknife estimates of H calculated from log transformed point estimates and R calculated from untransformed or log transformed point estimates were not significantly different from parametric values. Thus, jackknife estimators of H and R were unbiased. Delete-one jackknifing is a robust, versatile, and effective statistical method when applied to estimation problems involving variance functions. Jackknifing is especially valuable in hypothesis test estimation problems where the objective is comparing estimates from different populations.     

Computing power of quantitative trait locus association mapping for haploid loci

Background  

Statistical power calculations are a critical part of any study design for gene mapping. Most calculations assume that the locus of interest is biallelic. However, there are common situations in human genetics such as X-linked loci in males where the locus is haploid. The purpose of this work is to mathematically derive the biometric model for haploid loci, and to compute power for QTL mapping when the loci are haploid.     

Pooled analysis of data from multiple quantitative trait locus mapping populations

Quantitative trait locus (QTL) analysis on pooled data from multiple populations (pooled analysis) provides a means for evaluating, as a whole, evidence for existence of a QTL from different studies and examining differences in gene effect of a QTL among different populations. Objectives of this study were to: (1) develop a method for pooled analysis and (2) conduct pooled analysis on data from two soybean mapping populations. Least square interval mapping was extended for pooled analysis by inclusion of populations and cofactor markers as indicator variables and covariate variables separately in the multiple linear models. The general linear test approach was applied for detecting a QTL. Single population-based and pooled analyses were conducted on data from two F_2:3 mapping populations, Hamilton (susceptible) × PI 90763 (resistant) and Magellan (susceptible) × PI 404198A (resistant), for resistance to soybean cyst nematode (SCN) in soybean. It was demonstrated that where a QTL was shared among populations, pooled analysis showed increased LOD values on the QTL candidate region over single population analyses. Where a QTL was not shared among populations, however, the pooled analysis showed decreased LOD values on the QTL candidate region over single population analyses. Pooled analysis on data from genetically similar populations may have higher power of QTL detection than single population-based analyses. QTLs were identified by pooled analysis on linkage groups (LGs) G, B1 and J for resistance to SCN race 2 whereas QTLs on LGs G, B1 and E for resistance to SCN race 5 in soybean PI 90763 and PI 404198A. QTLs on LG G and B1 were identified in both PI 90763 and PI 404198A whereas QTLs on LG E and J were identified in PI 90763 only. QTLs on LGs G and B1 for resistance to race 2 may be the same or closely linked with QTLs on LG G and B1 for resistance to race 5, respectively. It was further demonstrated that QTLs on G and B1 carried by PI 90763 were not significantly different in gene effect from QTLs on LGs G and B1 in PI 404198A, respectively.     

Fine mapping dissects pleiotropic growth quantitative trait locus into linked loci

A recurring issue in studies of quantitative trait loci (QTLs) is whether QTLs that appear to have pleiotropic effects are indeed caused by pleiotropy at single loci or by linked QTLs. Previous work identified a QTL that affected tail length in mice and the lengths of various bones, including the humerus, ulna, femur, tibia, and mandible. The effect of this QTL on tail length has since been found to be due to multiple linked QTLs and so its apparently pleiotropic effects may have been due to linked QTLs with distinct effects. In the present study we examined a line of mice segregating only for a 0.94-Mb chromosomal region known to contain a subset of the QTLs influencing tail length. We measured a number of skeletal dimensions, including the lengths of the skull, mandible, humerus, ulna, femur, tibia, calcaneus, metatarsus, and a tail bone. The QTL region was found to have effects on the size of the mandible and length of the tail bone, with little or no effect on the other traits. Using a randomization approach, we rejected the null hypothesis that the QTL affected all traits equally, thereby demonstrating that the pleiotropic effects reported earlier were due to linked loci with distinct effects. This result underlines the possibility that seemingly pleiotropic effects of QTLs may frequently be due to linked loci and that high-resolution mapping will often be required to distinguish between pleiotropy and linkage.     

Multipoint interval mapping of quantitative trait loci, using sib pairs.

The sib-pair interval-mapping procedure of Fulker and Cardon is extended to take account of all available marker information on a chromosome simultaneously. The method provides a computationally fast multipoint analysis of sib-pair data, using a modified Haseman-Elston approach. It gives results very similar to those of the earlier interval-mapping procedure when marker information is relatively uniform and a coarse map is used. However, there is a substantial improvement over the original method when markers differ in information content and/or when a dense map is employed. The method is illustrated by using simulated sib-pair data.     

Generation-means analysis and quantitative trait locus mapping of anthracnose stalk rot genes in maize

A generation-means analysis was performed on two maize populations, each segregating for genes conferring resistance to anthracnose stalk rot (ASR). The populations were derived from a cross of DE811ASR x DE811 and of DE811ASR x LH132. The resistant parent, DE811ASR, was obtained through introgression with MP305 as the donor and DE811 as the recurrent parent. The analysis revealed significant additive effects in both populations and a significant additive x dominant effect in the DES11ASR x DES11 population. Quantitative trait locus (QTL) mapping, using restriction fragment length polymorphism (RFLP)-based molecular markers, indicated a significant QTL on linkage group 4 in both populations. The QTL analysis confirmed additive inheritance in both populations. This work demonstrates a close correspondence between generation-means analysis and discrete observations using molecular markers. Linkage of a genetic marker to genes conferring resistance to ASR will be useful for the introgression of resistance into elite germplasm.This research was part of a thesis submitted by the first author in partial fulfillment of the requirements for a MS degree. Published as Miscellaneous Paper number 1491 of the Delaware Agricultural Experiment Station