Estimating the genetic architecture of quantitative traits

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.     

Multiple-interval mapping for ordinal traits

Many statistical methods have been developed to map multiple quantitative trait loci (QTL) in experimental cross populations. Among these methods, multiple-interval mapping (MIM) can map QTL with epistasis simultaneously. However, the previous implementation of MIM is for continuously distributed traits. In this study we extend MIM to ordinal traits on the basis of a threshold model. The method inherits the properties and advantages of MIM and can fit a model of multiple QTL effects and epistasis on the underlying liability score. We study a number of statistical issues associated with the method, such as the efficiency and stability of maximization and model selection. We also use computer simulation to study the performance of the method and compare it to other alternative approaches. The method has been implemented in QTL Cartographer to facilitate its general usage for QTL mapping data analysis on binary and ordinal traits.     

Use of randomization testing to detect multiple epistatic QTLs

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.     

胡萝卜(Daucus carota L.)中主要胡萝卜素和番茄红素含量的QTL分析

以高胡萝卜素自交系P50006和HCM A.C.为亲本构建的F2群体为作图群体,对胡萝卜中α-胡萝卜素、α-胡萝卜素、总胡萝卜素和番茄红素含量进行QTL定位及遗传分析。结果表明,α、β-胡萝卜素、总胡萝卜素和番茄红素含量的广义遗传力分别为0.75、0.50、0.31和0.93。遗传图谱包含91个SRAP(Sequence-related amplified polymorphism)标记,分布于9个连锁群,总长度502.9cM,标记间平均距离5.5cM。除α-胡萝卜素含量外,α-胡萝卜素、总胡萝卜素和番茄红素含量分别检测到1个主效QTL,均为加性遗传效应,分别解释表型变异为12.79%、12.87%和14.61%。此外,α-胡萝卜素和番茄红素含量还分别检测到1对上位性QTL,最大遗传效应分别为显性×加性互作和显性×显性互作,分别解释表型变异为15.1%和6.5%。文章中与QTL连锁的分子标记可用于高胡萝卜素、番茄红素的种质筛选和聚合育种。     

Detection of multiple quantitative trait loci and their pleiotropic effects in outbred pig populations

Background

Simultaneous detection of multiple QTLs (quantitative trait loci) may allow more accurate estimation of genetic effects. We have analyzed outbred commercial pig populations with different single and multiple models to clarify their genetic properties and in addition, we have investigated pleiotropy among growth and obesity traits based on allelic correlation within a gamete.

Methods

Three closed populations, (A) 427 individuals from a Yorkshire and Large White synthetic breed, (B) 547 Large White individuals and (C) 531 Large White individuals, were analyzed using a variance component method with one-QTL and two-QTL models. Six markers on chromosome 4 and five to seven markers on chromosome 7 were used.

Results

Population A displayed a high test statistic for the fat trait when applying the two-QTL model with two positions on two chromosomes. The estimated heritabilities for polygenic effects and for the first and second QTL were 19%, 17% and 21%, respectively. The high correlation of the estimated allelic effect on the same gamete and QTL test statistics suggested that the two separate QTL which were detected on different chromosomes both have pleiotropic effects on the two fat traits. Analysis of population B using the one-QTL model for three fat traits found a similar peak position on chromosome 7. Allelic effects of three fat traits from the same gamete were highly correlated suggesting the presence of a pleiotropic QTL. In population C, three growth traits also displayed similar peak positions on chromosome 7 and allelic effects from the same gamete were correlated.

Conclusion

Detection of the second QTL in a model reduced the polygenic heritability and should improve accuracy of estimated heritabilities for both QTLs.     

Multiple-interval mapping for quantitative trait loci controlling endosperm traits

Endosperm traits are trisomic inheritant and are of great economic importance because they are usually directly related to grain quality. Mapping for quantitative trait loci (QTL) underlying endosperm traits can provide an efficient way to genetically improve grain quality. As the traditional QTL mapping methods (diploid methods) are usually designed for traits under diploid control, they are not the ideal approaches to map endosperm traits because they ignore the triploid nature of endosperm. In this article, a statistical method considering the triploid nature of endosperm (triploid method) is developed on the basis of multiple-interval mapping (MIM) to map for the underlying QTL. The proposed triploid MIM method is derived to broadly use the marker information either from only the maternal plants or from both the maternal plants and their embryos in the backcross and F2 populations for mapping endosperm traits. Due to the use of multiple intervals simultaneously to take multiple QTL into account, the triploid MIM method can provide better detection power and estimation precision, and as shown in this article it is capable of analyzing and searching for epistatic QTL directly as compared to the traditional diploid methods and current triploid methods using only one (or two) interval(s). Several important issues in endosperm trait mapping, such as the relation and differences between the diploid and triploid methods, variance components of genetic variation, and the problems if effects are present and ignored, are also addressed. Simulations are performed to further explore these issues, to investigate the relative efficiency of different experimental designs, and to evaluate the performance of the proposed and current methods in mapping endosperm traits. The MIM-based triploid method can provide a powerful tool to estimate the genetic architecture of endosperm traits and to assist the marker-assisted selection for the improvement of grain quality in crop science. The triploid MIM FORTRAN program for mapping endosperm traits is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations

It has long been recognized that epistasis or interactions between non-allelic genes plays an important role in the genetic control and evolution of quantitative traits. However, the detection of epistasis and estimation of epistatic effects are difficult due to the complexity of epistatic patterns, insufficient sample size of mapping populations and lack of efficient statistical methods. Under the assumption of additivity of QTL effects on the phenotype of a trait in interest, the additive effect of a QTL can be completely absorbed by the flanking marker variables, and the epistatic effect between two QTL can be completely absorbed by the four marker-pair multiplication variables between the two pairs of flanking markers. Based on this property, we proposed an inclusive composite interval mapping (ICIM) by simultaneously considering marker variables and marker-pair multiplications in a linear model. Stepwise regression was applied to identify the most significant markers and marker-pair multiplications. Then a two-dimensional scanning (or interval mapping) was conducted to identify QTL with significant digenic epistasis using adjusted phenotypic values based on the best multiple regression model. The adjusted values retain the information of QTL on the two current mapping intervals but exclude the influence of QTL on other intervals and chromosomes. Epistatic QTL can be identified by ICIM, no matter whether the two interacting QTL have any additive effects. Simulated populations and one barley doubled haploids (DH) population were used to demonstrate the efficiency of ICIM in mapping both additive QTL and digenic interactions.     

Genetic mapping of QTLs for sugar-related traits in a RIL population of Sorghum bicolor L. Moench

The productivity of sorghum is mainly determined by quantitative traits such as grain yield and stem sugar-related characteristics. Substantial crop improvement has been achieved by breeding in the last decades. Today, genetic mapping and characterization of quantitative trait loci (QTLs) is considered a valuable tool for trait enhancement. We have investigated QTL associated with the sugar components (Brix, glucose, sucrose, and total sugar content) and sugar-related agronomic traits (flowering date, plant height, stem diameter, tiller number per plant, fresh panicle weight, and estimated juice weight) in four different environments (two locations) using a population of 188 recombinant inbred lines (RILs) from a cross between grain (M71) and sweet sorghum (SS79). A genetic map with 157 AFLP, SSR, and EST-SSR markers was constructed, and several QTLs were detected using composite interval mapping (CIM). Further, additive × additive interaction and QTL × environmental interaction were estimated. CIM identified more than five additive QTLs in most traits explaining a range of 6.0–26.1% of the phenotypic variation. A total of 24 digenic epistatic locus pairs were identified in seven traits, supporting the hypothesis that QTL analysis without considering epistasis can result in biased estimates. QTLs showing multiple effects were identified, where the major QTL on SBI-06 was significantly associated with most of the traits, i.e., flowering date, plant height, Brix, sucrose, and sugar content. Four out of ten traits studied showed a significant QTL × environmental interaction. Our results are an important step toward marker-assisted selection for sugar-related traits and biofuel yield in sorghum.     

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.）.     

Bayesian analysis for genetic architecture of dynamic traits

The dissection of the genetic architecture of quantitative traits, including the number and locations of quantitative trait loci (QTL) and their main and epistatic effects, has been an important topic in current QTL mapping. We extend the Bayesian model selection framework for mapping multiple epistatic QTL affecting continuous traits to dynamic traits in experimental crosses. The extension inherits the efficiency of Bayesian model selection and the flexibility of the Legendre polynomial model fitting to the change in genetic and environmental effects with time. We illustrate the proposed method by simultaneously detecting the main and epistatic QTLs for the growth of leaf age in a doubled-haploid population of rice. The behavior and performance of the method are also shown by computer simulation experiments. The results show that our method can more quickly identify interacting QTLs for dynamic traits in the models with many numbers of genetic effects, enhancing our understanding of genetic architecture for dynamic traits. Our proposed method can be treated as a general form of mapping QTL for continuous quantitative traits, being easier to extend to multiple traits and to a single trait with repeat records.     

远交群体动态性状基因定位的似然分析Ⅰ.理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发 ,将关于时间 (测定日期 )的Legendre多项式镶嵌在遗传模型的每个遗传效应中 ,以刻画QTL对动态性状变化过程的作用 ,从而建立起动态性状基因定位的数学模型。利用远交设计群体 ,阐述了动态性状基因定位的似然分析原理 ,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展 ,还提出了有关动态性状基因定位进一步研究的设想     

Quantitative trait loci mapping and the genetic basis of heterosis in maize and rice

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive × additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.     

Generalized linear mixed models for mapping multiple quantitative trait loci

Many biological traits are discretely distributed in phenotype but continuously distributed in genetics because they are controlled by multiple genes and environmental variants. Due to the quantitative nature of the genetic background, these multiple genes are called quantitative trait loci (QTL). When the QTL effects are treated as random, they can be estimated in a single generalized linear mixed model (GLMM), even if the number of QTL may be larger than the sample size. The GLMM in its original form cannot be applied to QTL mapping for discrete traits if there are missing genotypes. We examined two alternative missing genotype-handling methods: the expectation method and the overdispersion method. Simulation studies show that the two methods are efficient for multiple QTL mapping (MQM) under the GLMM framework. The overdispersion method showed slight advantages over the expectation method in terms of smaller mean-squared errors of the estimated QTL effects. The two methods of GLMM were applied to MQM for the female fertility trait of wheat. Multiple QTL were detected to control the variation of the number of seeded spikelets.     

Genome-wide evaluation for quantitative trait loci under the variance component model

The identity-by-descent (IBD) based variance component analysis is an important method for mapping quantitative trait loci (QTL) in outbred populations. The interval-mapping approach and various modified versions of it may have limited use in evaluating the genetic variances of the entire genome because they require evaluation of multiple models and model selection. In this study, we developed a multiple variance component model for genome-wide evaluation using both the maximum likelihood (ML) method and the MCMC implemented Bayesian method. We placed one QTL in every few cM on the entire genome and estimated the QTL variances and positions simultaneously in a single model. Genomic regions that have no QTL usually showed no evidence of QTL while regions with large QTL always showed strong evidence of QTL. While the Bayesian method produced the optimal result, the ML method is computationally more efficient than the Bayesian method. Simulation experiments were conducted to demonstrate the efficacy of the new methods.     

Genetic Mapping of Quantitative Trait Loci Controlling Growth and Wood Quality Traits in Eucalyptus Grandis Using a Maternal Half-Sib Family and Rapd Markers

Quantitative trait loci (QTL) mapping of forest productivity traits was performed using an open pollinated half-sib family of Eucalyptus grandis. For volume growth, a sequential QTL mapping approach was applied using bulk segregant analysis (BSA), selective genotyping (SG) and cosegregation analysis (CSA). Despite the low heritability of this trait and the heterogeneous genetic background employed for mapping. BSA detected one putative QTL and SG two out of the three later found by CSA. The three putative QTL for volume growth were found to control 13.7% of the phenotypic variation, corresponding to an estimated 43.7% of the genetic variation. For wood specific gravity five QTL were identified controlling 24.7% of the phenotypic variation corresponding to 49% of the genetic variation. Overlapping QTL for CBH, WSG and percentage dry weight of bark were observed. A significant case of digenic epistasis was found, involving unlinked QTL for volume. Our results demonstrate the applicability of the within half-sib design for QTL mapping in forest trees and indicate the existence of major genes involved in the expression of economically important traits related to forest productivity in Eucalyptus grandis. These findings have important implications for marker-assisted tree breeding.     

Genetic architecture of a selection response in Arabidopsis thaliana

Quantitative trait locus (QTL) mapping has become an established and effective method for studying the genetic architecture of complex traits. In this report, we use a QTL mapping approach in combination with data from a large selection experiment in Arabidopsis thaliana to explore a response to selection of experimental populations with differentiated genetic backgrounds. Experimental populations with genetic backgrounds derived from ecotypes Landsberg and Niederzenz were exposed to multiple generations of fertility and viability selection. This selection resulted in phenotypic shifts in a number of life-history and fitness-related characters including early development time, flowering time, dry biomass, longevity, and fruit production. Quantitative trait loci were mapped for these traits and their positions were compared to previously characterized allele frequency changes in the experimental populations (Ungerer et al. 2003). Quantitative trait locus positions largely colocalized with genomic regions under strong and consistent selection in populations with differentiated genetic backgrounds, suggesting that alleles for these traits were selected similarly in differentiated genetic backgrounds. However, one QTL region exhibited a more variable response; being positively selected on one genetic background but apparently neutral in another. This study demonstrates how QTL mapping approaches can be combined with map-based population genetic data to study how selection acts on standing genetic variation in populations.     

Epistatic interaction is an important genetic basis of grain yield and its components in maize

A population of 294 recombinant inbred lines (RIL) derived from Yuyu22, an elite maize hybrid extending broadly in China, has been constructed to investigate the genetic basis of grain yield, and associated yield components in maize. The main-effect quantitative trait loci (QTL), digenic epistatic interactions, and their interactions with the environment for grain yield and its three components were identified by using the mixed linear model approach. Thirty-two main-effect QTL and forty-four pairs of digenic epistatic interactions were detected for the four measured traits in four environments. Our results suggest that both additive effects and epistasis (additive × additive) effects are important genetic bases of grain yield and its components in the RIL population. Only 30.4% of main-effect QTL for ear length were involved in epistatic interactions. This implies that many loci in epistatic interactions may not have significant effects for traits alone but may affect trait expression by epistatic interaction with the other loci.     

Capturing pair-wise epistatic effects associated with three agronomic traits in barley

Genetic association mapping has been widely applied to determine genetic markers favorably associated with a trait of interest and provide information for marker-assisted selection. Many association mapping studies commonly focus on main effects due to intolerable computing intensity. This study aims to select several sets of DNA markers with potential epistasis to maximize genetic variations of some key agronomic traits in barley. By doing so, we integrated a MDR (multifactor dimensionality reduction) method with a forward variable selection approach. This integrated approach was used to determine single nucleotide polymorphism pairs with epistasis effects associated with three agronomic traits: heading date, plant height, and grain yield in barley from the barley Coordinated Agricultural Project. Our results showed that four, seven, and five SNP pairs accounted for 51.06, 45.66 and 40.42% for heading date, plant height, and grain yield, respectively with epistasis being considered, while corresponding contributions to these three traits were 45.32, 31.39, 31.31%, respectively without epistasis being included. The results suggested that epistasis model was more effective than non-epistasis model in this study and can be more preferred for other applications.     

Dissecting Genetic Architecture Underlying Seed Traits in Multiple Environments

The seeds of flowering plants develop from double fertilization and play a vital role in reproduction and supplying human and animal food. The genetic variation of seed traits is influenced by multiple genetic systems, e.g., maternal, embryo, and/or endosperm genomes. Understanding the genetic architecture of seed traits is a major challenge because of this complex mechanism of multiple genetic systems, especially the epistasis within or between different genomes and their interactions with the environment. In this study, a statistical model was proposed for mapping QTL with epistasis and QTL-by-environment (QE) interactions underlying endosperm and embryo traits. Our model integrates the maternal and the offspring genomes into one mapping framework and can accurately analyze maternal additive and dominant effects, endosperm/embryo additive and dominant effects, and epistatic effects of two loci in the same or two different genomes, as well as interaction effects of each genetic component of QTL with environment. Intensive simulations under different sampling strategies, heritabilities, and model parameters were performed to investigate the statistical properties of the model. A set of real cottonseed data was analyzed to demonstrate our methods. A software package, QTLNetwork-Seed-1.0.exe, was developed for QTL analysis of seed traits.     

Polygenic mutation in Drosophila melanogaster: Mapping spontaneous mutations affecting sensory bristle number

Our ability to predict long-term responses to artificial and natural selection, and understand the mechanisms by which naturally occurring variation for quantitative traits is maintained, depends on detailed knowledge of the properties of spontaneous polygenic mutations, including the quantitative trait loci (QTL) at which mutations occur, mutation rates, and mutational effects. These parameters can be estimated by mapping QTL that cause divergence between mutation-accumulation lines that have been established from an inbred base population and selected for high and low trait values. Here, we have utilized quantitative complementation to deficiencies to map QTL at which spontaneous mutations affecting Drosophila abdominal and sternopleural bristle number have occurred in 11 replicate lines during 206 generations of divergent selection. Estimates of the numbers of mutations were consistent with diploid per-character mutation rates for bristle traits of 0.03. The ratio of the per-character mutation rate to total mutation rate (0.023) implies that >2% of the genome could affect just one bristle trait and that there must be extensive pleiotropy for quantitative phenotypes. The estimated mutational effects were not, however, additive and exhibited dependency on genetic background consistent with diminishing epistasis. However, these inferences must be tempered by the potential for epistatic interactions between spontaneous mutations and QTL affecting bristle number on the deficiency-bearing chromosomes, which could lead to overestimates in numbers of QTL and inaccurate inference of gene action.