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.     

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。     

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.     

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.     

Multiple-trait quantitative trait locus mapping with incomplete phenotypic data

Background

The goal of linkage analysis is to determine the chromosomal location of the gene(s) for a trait of interest such as a common disease. Three-locus linkage analysis is an important case of multi-locus problems. Solutions can be found analytically for the case of triple backcross mating. However, in the present study of linkage analysis and gene mapping some natural inequality restrictions on parameters have not been considered sufficiently, when the maximum likelihood estimates (MLEs) of the two-locus recombination fractions are calculated.

Results

In this paper, we present a study of estimating the two-locus recombination fractions for the phase-unknown triple backcross with two offspring in each family in the framework of some natural and necessary parameter restrictions. A restricted expectation-maximization (EM) algorithm, called REM is developed. We also consider some extensions in which the proposed REM can be taken as a unified method.

Conclusion

Our simulation work suggests that the REM performs well in the estimation of recombination fractions and outperforms current method. We apply the proposed method to a published data set of mouse backcross families.     

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).     

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.     

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.     

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.     

Biased estimators of quantitative trait locus heritability and location in interval mapping

In many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of parameters. There are two key steps in QTL modeling, each of which biases the estimation of genetic effects. First, test procedures are employed to select the regions of the genome for which there is significant evidence for the presence of QTL. Second, and most important for this demonstration, estimates of the genetic effects are reported only at the locations for which the evidence is maximal. We demonstrate that even when we know there is just one QTL present (ignoring the testing bias), and we use interval mapping to estimate its location and effect, the estimator of the effect will be biased. As evidence, we present results of simulations investigating the relative importance of the two sources of bias and the dependence of bias of heritability estimators on the true QTL heritability, sample size, and the length of the investigated part of the genome. Moreover, we present results of simulations demonstrating the skewness of the distribution of estimators of QTL locations and the resulting bias in estimation of location. We use computer simulations to investigate the dependence of this bias on the true QTL location, heritability, and the sample size.     

Accommodating pathway information in expression quantitative trait locus analysis

The availability of high-throughput genotyping technologies and microarray assays has allowed researchers to consider pursuing investigations whose ultimate goal is the identification of genetic variations that influence levels of gene expression, e.g., "expression quantitative trait locus" or "eQTL" mapping studies. However, the large number of genes whose expression levels can be tested for association with genetic variations in such studies can create both statistical and biological interpretive problems. We consider the integrated analysis of eQTL mapping data that incorporates pathway, function, and disease process information. The goal of this analysis is to determine if compelling patterns emerge from the data that are consistent with the notion that perturbations in the molecular physiologic environment induced by genetic variations implicate the expression patterns of multiple genes via genetic network relationships or feedback mechanisms. We apply available genetic network and pathway analysis software, as well as a novel regression analysis technique, to carry out the proposed studies. We also consider extensions of the proposed strategies and areas of future research.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

A large nested association mapping population for breeding and quantitative trait locus mapping in Ethiopian durum wheat

The Ethiopian plateau hosts thousands of durum wheat (Triticum turgidum subsp. durum) farmer varieties (FV) with high adaptability and breeding potential. To harness their unique allelic diversity, we produced a large nested association mapping (NAM) population intercrossing fifty Ethiopian FVs with an international elite durum wheat variety (Asassa). The Ethiopian NAM population (EtNAM) is composed of fifty interconnected bi‐parental families, totalling 6280 recombinant inbred lines (RILs) that represent both a powerful quantitative trait loci (QTL) mapping tool, and a large pre‐breeding panel. Here, we discuss the molecular and phenotypic diversity of the EtNAM founder lines, then we use an array featuring 13 000 single nucleotide polymorphisms (SNPs) to characterize a subset of 1200 EtNAM RILs from 12 families. Finally, we test the usefulness of the population by mapping phenology traits and plant height using a genome wide association (GWA) approach. EtNAM RILs showed high allelic variation and a genetic makeup combining genetic diversity from Ethiopian FVs with the international durum wheat allele pool. EtNAM SNP data were projected on the fully sequenced AB genome of wild emmer wheat, and were used to estimate pairwise linkage disequilibrium (LD) measures that reported an LD decay distance of 7.4 Mb on average, and balanced founder contributions across EtNAM families. GWA analyses identified 11 genomic loci individually affecting up to 3 days in flowering time and more than 1.6 cm in height. We argue that the EtNAM is a powerful tool to support the production of new durum wheat varieties targeting local and global agriculture.     

Fine mapping of a quantitative trait locus for twinning rate using combined linkage and linkage disequilibrium mapping

A novel and robust method for the fine-scale mapping of genes affecting complex traits, which combines linkage and linkage-disequilibrium information, is proposed. Linkage information refers to recombinations within the marker-genotyped generations and linkage disequilibrium to historical recombinations before genotyping started. The identity-by-descent (IBD) probabilities at the quantitative trait locus (QTL) between first generation haplotypes were obtained from the similarity of the marker alleles surrounding the QTL, whereas IBD probabilities at the QTL between later generation haplotypes were obtained by using the markers to trace the inheritance of the QTL. The variance explained by the QTL is estimated by residual maximum likelihood using the correlation structure defined by the IBD probabilities. Unlinked background genes were accounted for by fitting a polygenic variance component. The method was used to fine map a QTL for twinning rate in cattle, previously mapped on chromosome 5 by linkage analysis. The data consisted of large half-sib families, but the method could also handle more complex pedigrees. The likelihood of the putative QTL was very small along most of the chromosome, except for a sharp likelihood peak in the ninth marker bracket, which positioned the QTL within a region <1 cM in the middle part of bovine chromosome 5. The method was expected to be robust against multiple genes affecting the trait, multiple mutations at the QTL, and relatively low marker density.     

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     

Cytonuclear epistatic quantitative trait locus mapping for plant height and ear height in maize

Plant height (PH) and ear height (EH) are important traits in maize (Zea mays L.) breeding. Previous research has indicated that these traits are influenced by quantitative trait loci (QTL). However, previous studies attempting to identify the genetic bases of PH and EH have ignored the possibility that cytoplasmic effects and cytonuclear interactions may influence these traits. The objectives of this study were to identify the cytonuclear epistatic QTL and to evaluate the contributions of cytoplasm and QTL × cytoplasm interactions to phenotypic variation of PH and EH. A reciprocal mating design was conducted to generate F2 mapping populations comprising 120 F2 plants from the direct cross (JB × Y53) and 120 F2 plants from the reciprocal cross (Y53 × JB). F2:3 mapping populations were further generated with 91 direct F2:3 families and 120 reciprocal F2:3 families (ten plants per family). The PH and EH of the above F2 and F2:3 mapping populations were evaluated in the same field at the same experimental station in 2007 and 2008. A genetic linkage map with 154 microsatellite markers was constructed, which covered 1,735.0 cM of the maize genome with an average marker spacing of 11.3 cM. A joint-analysis method incorporating the cytonuclear interaction mapping approach was proposed and performed to detect cytonuclear interacting QTL affecting PH and EH. We identified six cytonuclear epistatic QTL affecting PH and five affecting EH. The average phenotypic variance explained by the genetic components of the QTL × cytoplasm interaction for each QTL was 18 % for PH and 9 % for EH. In addition, we observed cytoplasmic effects contributing substantially to phenotypic variance, reaching 9 and 40 % of the phenotypic contributions to PH and EH, respectively.