Quantitative Trait Locus Mapping Reveals Regions of the Maize Genome Controlling Root System Architecture

The quest to determine the genetic basis of root system architecture (RSA) has been greatly facilitated by recent developments in root phenotyping techniques. Methods that are accurate, high throughput, and control for environmental factors are especially attractive for quantitative trait locus mapping. Here, we describe the adaptation of a nondestructive in vivo gel-based root imaging platform for use in maize (Zea mays). We identify a large number of contrasting RSA traits among 25 founder lines of the maize nested association mapping population and locate 102 quantitative trait loci using the B73 (compact RSA) × Ki3 (exploratory RSA) mapping population. Our results suggest that a phenotypic tradeoff exists between small, compact RSA and large, exploratory RSA.Maize (Zea mays) serves a key role in food, feedstock, and biofuel production throughout the world. To date, maize improvement through breeding has kept pace with the increasing demand for this crop (faostat3.fao.org). This feat has been accomplished through the utilization of the tremendous genetic diversity in maize (Flint-Garcia et al., 2005; Jiao et al., 2012), but increasing environmental pressures and a growing global population will require unprecedented gains in yield in the coming years. In the last decade, researchers have begun to explore the possibility of yield improvements through the manipulation of root systems, for example through breeding for roots better able to cope with drought (Uga et al., 2013) and flooding (Jackson and Armstrong, 1999), the use of plant growth-promoting rhizobacteria (Silby et al., 2009), or increasing nutrient use efficiency (Garnett et al., 2009). The potential of belowground solutions to enhanced plant productivity has driven the development of numerous methodologies for phenotyping root system architecture (RSA), which is the spatial organization of the plant’s root system.Several methods ranging from techniques adapted from medical imaging, such as x-ray tomography (Hargreaves et al., 2008) and combined positron emission tomography-magnetic resonance imaging (Jahnke et al., 2009), to refined versions of classical methods, such as field excavations (Trachsel et al., 2010) and pouch systems (Le Marié et al., 2014), have been used in attempts to understand the phenotypic consequences of genetic and environmental variation on root traits. Each root-phenotyping method has its advantages and disadvantages. Although the medical imaging-based techniques can produce highly detailed representations of roots, they are also very time consuming and require specialized equipment. Excavations, although more easily scaled to higher throughput and not requiring special equipment, are destructive and offer only coarse measurements of RSA. An alternative method for root phenotyping based on an optically clear gel substrate strikes an effective balance between throughput and detail, using a simple digital camera while maintaining precise control over environmental conditions. This platform has been used to quantify and classify distinctive root architectures from 12 rice (Oryza sativa) genotypes (Iyer-Pascuzzi et al., 2010), conduct a quantitative trait locus (QTL) mapping study of rice root traits in three dimensions (Topp et al., 2013), study interspecific and intraspecific rice root interactions (Fang et al., 2013), and quantify contributions of different root types to overall RSA (Clark et al., 2011).Here, we describe the adaptation of this gel imaging platform for use with the large maize root system. We used the platform to quantify the phenotypic diversity of RSA among 25 of the 26 nested association mapping (NAM) founder lines, which encompass a wide spectrum of maize genetic diversity (Yu et al., 2008; McMullen et al., 2009). We found that these lines exhibit diverse RSAs, ranging from small and compact to large and exploratory, suggesting tradeoffs between different types of architectures. In order to identify genetic loci that control maize RSA traits, we characterized a subpopulation that best represented the contrast between the compact and exploratory RSAs. We phenotyped the B73 (compact) × Ki3 (exploratory) recombinant inbred line (RIL) NAM subpopulation for 19 RSA traits at three time points (Topp et al., 2013). These data were used to map 102 QTLs that localized to nine genomic clusters. We found high heritability and large-effect QTLs for most traits, in contrast to maize flowering time QTLs (Buckler et al., 2009). Additionally, several of our QTL clusters overlapped with meta-QTLs for yield traits (Tuberosa et al., 2003; Semagn et al., 2013) as well as novel and previously unreported loci, suggesting that this system can provide a time- and cost-effective means to identify genes controlling root architecture in maize.     

Bayesian Quantitative Trait Locus Mapping Using Inferred Haplotypes

We describe a fast hierarchical Bayesian method for mapping quantitative trait loci by haplotype-based association, applicable when haplotypes are not observed directly but are inferred from multiple marker genotypes. The method avoids the use of a Monte Carlo Markov chain by employing priors for which the likelihood factorizes completely. It is parameterized by a single hyperparameter, the fraction of variance explained by the quantitative trait locus, compared to the frequentist fixed-effects model, which requires a parameter for the phenotypic effect of each combination of haplotypes; nevertheless it still provides estimates of haplotype effects. We use simulation to show that the method matches the power of the frequentist regression model and, when the haplotypes are inferred, exceeds it for small QTL effect sizes. The Bayesian estimates of the haplotype effects are more accurate than the frequentist estimates, for both known and inferred haplotypes, which indicates that this advantage is independent of the effect of uncertainty in haplotype inference and will hold in comparison with frequentist methods in general. We apply the method to data from a panel of recombinant inbred lines of Arabidopsis thaliana, descended from 19 inbred founders.AS the power of haplotypic association has become better appreciated, studies using inferred multiallelic loci (i.e., haplotypes or pairs of haplotypes) are becoming more common. This is because single-nucleotide polymorphisms (SNPs), which are the most commonly used type of marker, are very susceptible to a loss of power to detect QTL, due to a mismatch in allele frequencies between the SNP and the causative variant. While multiallelic markers contain more information and have greater power than SNPs for QTL mapping, they are more costly and cumbersome. Consequently a major analytical advance has been the combination of multiple SNP marker information, either to infer haplotypes as in many human association studies or to infer the mosaic of ancestral founder haplotypes in synthetic populations descended from multiple founder strains. The latter scenario includes crosses between inbred strains of mice or rats or inbred accessions of plants.However, there are two potential difficulties with haplotypic association. First, in a fixed-effects framework, a parameter is estimated for each haplotype, which is undesirable when the number of haplotypes is large. In a synthetic population descended from N inbred strains, up to N haplotypes may segregate; for the mouse collaborative cross (Threadgill et al. 2002) N = 8 and for the Arabidopsis thaliana multiparent advanced generation intercross (MAGIC) population of recombinant inbred lines, N = 19 (Kover et al. 2009). For complex traits, where many QTL are expected to segregate, multiple QTL mapping only exacerbates problems with the numbers of parameters.Second, one must account for uncertainty in the inference of haplotypes, which depends on the marker density and how well one can distinguish between all founders at a locus. At some loci the founders'' haplotypes may be identical, for example, in crosses descended from inbred strains of mice.These problems are well known in haplotype association mapping involving human populations, where in general fixed-effects regression modeling is used. Consequently methods have been developed to reduce the number of haplotype groups at a marker locus, using hierarchical clustering and Bayesian partitioning algorithms (Molitor et al. 2003; Durrant et al. 2004; Bardel et al. 2006; Morris 2006; Tzeng et al. 2006; Waldron et al. 2006; Igo et al. 2007; Liu et al. 2007; Tachmazidou et al. 2007; Knight et al. 2008).Bayesian methods are increasingly the approach of choice for QTL mapping, particularly for multiple QTL mapping and the modeling of interactions (Yi and Shriner 2008). The hierarchical Bayesian framework can accommodate more complicated models with more parameters, even when there are many more parameters than observations (Meuwissen et al. 2001; Xu 2003). The Bayesian approach has an additional advantage when the inferred haplotypes are not all identifiable. Reliable estimates of haplotype effects can be determined because the shrinkage effect of the prior distribution restricts the posterior. However, these methods must be fast if these complex analyses are to be practical.In a hierarchical model the key problem is how to model the distribution of the variance attributable to a QTL and its prior. Meuwissen et al. (2001) consider a hierarchical Bayesian random-effects model (HBREM) for observed multiallelic marker loci. They choose normal priors centered at zero for the individual genotype effects, with different variances for each locus. The prior distributions for the variance parameters are scaled inverse chi square, with parameters chosen to give the mean and variance preestimated from the data. However, this prior has a tiny probability of a QTL effect being equal to zero, whereas that is clearly very likely in a genome scan. Hence they also showed an alternative prior, a mixture of a point mass at zero and a scaled inverse chi-square distribution, which gave better results.Xu (2003) considers a noninformative Jeffrey''s prior on the locus variance. The model fits all markers simultaneously and can detect large-effect QTL with little noise at other markers, despite the negligible probability of zero locus variance. However, the model is limited to markers with two or three possible genotypes. Wang et al. (2005) extend this approach to inferred genotypes, but still with only two or three possible genotypes per locus and the method is very computationally intensive.Yi and Xu (2008) argue that the noninformative Jeffrey''s prior on the locus variance induces constant shrinkage on the haplotype effects and that it would be preferable to vary shrinkage according to the data. They compare exponential and scaled inverse chi-square priors on the locus variance, using hyperparameters with vague hyperpriors. They also consider a second prior on the haplotype effects (first proposed by Park and Casella 2008), of a normal distribution with variance proportional to the residual error variance. The four models performed equally when tested on populations with only two genotypes segregating at a locus.There are several frequentist approaches to dealing with haplotype uncertainty in QTL mapping. One is to perform a fixed-effects multiple linear regression or generalized linear regression of the phenotype, treating the haplotype probabilities at the locus as the design matrix (Haley and Knott 1992; Mott et al. 2000). Another is to use multiple imputation to draw samples of haplotypes from the haplotype probabilities (Sen and Churchill 2001). A third is to use the EM algorithm to estimate the haplotypes (Excoffier and Slatkin 1995; Hawley and Kidd 1995; Long et al. 1995; Qin et al. 2002; Lin et al. 2005, 2008; Lin and Zeng 2006; Zeng et al. 2006). An alternative is data expansion, where instead of multiple imputation, the data set is expanded by drawing 10–20 replicate haplotype pairs for every individual from their inferred probability distribution, assigning the same value of the response variable to each, and analyzing the expanded data set. However, this may alter the characteristics of the data, such as the haplotype frequencies.In a Bayesian setting, haplotype uncertainty can be accommodated either by including the predictor variables as unknowns in the updating procedure or by multiple imputation. In a fully Bayesian treatment, the unknown haplotype pair assignments are assigned priors and estimated along with the model parameters. However, Markov chain Monte Carlo (MCMC) is then needed to fit the model, updating the parameters on the basis of the haplotype pairs and then updating the haplotype pairs on the basis of the parameters. Updating the haplotype assignments by MCMC is slow and suffers from the label-switching problem among others (Jasra et al. 2005), so an alternative approach would be preferable.In this article, we present a new HBREM for QTL mapping applicable to observed or inferred haplotypes. It does not require costly MCMC techniques, since the joint posterior distribution factorizes. It parameterizes the variance terms in the model, focusing on the proportion of the variance due to the QTL. We compare its performance with that of the frequentist fixed-effects model for both observed and inferred multiallelic loci. We show first that the posterior mode of the proportion of variance due to a locus is a better outcome measure than two standard Bayesian test statistics and second that the Bayesian estimates of the individual haplotype effects are much more accurate than the corresponding frequentist estimates. Finally we analyze real data from A. thaliana recombinant inbred lines descended from 19 parental lines.     

Expression Quantitative Trait Locus Mapping across Water Availability Environments Reveals Contrasting Associations with Genomic Features in Arabidopsis

The regulation of gene expression is crucial for an organism’s development and response to stress, and an understanding of the evolution of gene expression is of fundamental importance to basic and applied biology. To improve this understanding, we conducted expression quantitative trait locus (eQTL) mapping in the Tsu-1 (Tsushima, Japan) × Kas-1 (Kashmir, India) recombinant inbred line population of Arabidopsis thaliana across soil drying treatments. We then used genome resequencing data to evaluate whether genomic features (promoter polymorphism, recombination rate, gene length, and gene density) are associated with genes responding to the environment (E) or with genes with genetic variation (G) in gene expression in the form of eQTLs. We identified thousands of genes that responded to soil drying and hundreds of main-effect eQTLs. However, we identified very few statistically significant eQTLs that interacted with the soil drying treatment (GxE eQTL). Analysis of genome resequencing data revealed associations of several genomic features with G and E genes. In general, E genes had lower promoter diversity and local recombination rates. By contrast, genes with eQTLs (G) had significantly greater promoter diversity and were located in genomic regions with higher recombination. These results suggest that genomic architecture may play an important a role in the evolution of gene expression.     

Genetic Analysis and Major Quantitative Trait Locus Mapping of Leaf Widths at Different Positions in Multiple Populations

Background

Leaf width is an important agricultural trait in maize. Leaf development is dependent on cell proliferation and expansion, and these processes exhibit polarity with respect to the longitudinal and transverse axes of the leaf. However, the molecular mechanism of the genetic control of seed vigor remains unknown in maize, and a better understanding of this mechanism is required.

Methodology/Principal Findings

To reveal the genetic architecture of leaf width, a comprehensive evaluation using four RIL populations was performed, followed by a meta-analysis. Forty-six QTLs associated with the widths of leaves at different positions above the uppermost ear were detected in the four RIL populations in three environments. The individual effects of the QTLs ranged from 4.33% to 18.01% of the observed phenotypic variation, with 14 QTLs showing effects of over 10%. We identified three common QTLs associated with leaf width at all of the examined positions, in addition to one common QTL associated with leaf width at three of the positions and six common QTLs associated with leaf width at two of the positions. The results indicate that leaf width at different leaf positions may be affected by one QTL or several of the same QTLs. Such traits may also be regulated by many different QTLs. Thirty-one of the forty-six initial QTLs were integrated into eight mQTLs through a meta-analysis, and 10 of the 14 initial QTLs presenting an R2>10% were integrated into six mQTLs.

Conclusions/Significance

mQTL1-2, mQTL3-1, mQTL7, and mQTL8 were composed of the initial QTLs showing an R2>10% and included four to six of the initial QTLs that were associated with two to four positions in a single population. Therefore, these four chromosome regions may be hot spots for important QTLs for these traits. Thus, they warrant further studies and may be useful for marker-assisted breeding.     

水稻粒长QTL定位与主效基因的遗传分析

该研究利用短粒普通野生稻矮杆突变体和长粒栽培稻品种KJ01组配杂交组合F_1,构建分离群体F_2;并对该群体粒长进行性状遗传分析,利用平均分布于水稻的12条染色体上的132对多态分子标记对该群体进行QTL定位及主效QTLs遗传分析,为进一步克隆新的主效粒长基因奠定基础,并为水稻粒形育种提供理论依据。结果表明:(1)所构建的水稻杂交组合分离群体F_2的粒长性状为多基因控制的数量性状。(2)对543株F_2分离群体进行QTL连锁分析,构建了控制水稻粒长的连锁遗传图谱,总长为1 713.94 cM,共检测出24个QTLs,只有3个表现为加性遗传效应,其余位点均表现为遗传负效应。(3)检测到的3个主效QTLs分别位于3号染色体的分子标记PSM379～RID24455、RID24455～RM15689和RM571～RM16238之间,且三者对表型的贡献率分别为54.85%、31.02%和7.62%。(4)在标记PSM379～RID24455之间已克隆到的粒长基因为该研究新发现的主效QTL位点。     

R/qtlcharts: Interactive Graphics for Quantitative Trait Locus Mapping

Every data visualization can be improved with some level of interactivity. Interactive graphics hold particular promise for the exploration of high-dimensional data. R/qtlcharts is an R package to create interactive graphics for experiments to map quantitative trait loci (QTL) (genetic loci that influence quantitative traits). R/qtlcharts serves as a companion to the R/qtl package, providing interactive versions of R/qtl’s static graphs, as well as additional interactive graphs for the exploration of high-dimensional genotype and phenotype data.     

Quantitative Trait Locus Mapping and Candidate Gene Analysis for Plant Architecture Traits Using Whole Genome Re-Sequencing in Rice

Plant breeders have focused on improving plant architecture as an effective means to increase crop yield. Here, we identify the main-effect quantitative trait loci (QTLs) for plant shape-related traits in rice (Oryza sativa) and find candidate genes by applying whole genome re-sequencing of two parental cultivars using next-generation sequencing. To identify QTLs influencing plant shape, we analyzed six traits: plant height, tiller number, panicle diameter, panicle length, flag leaf length, and flag leaf width. We performed QTL analysis with 178 F₇ recombinant in-bred lines (RILs) from a cross of japonica rice line ‘SNUSG1’ and indica rice line ‘Milyang23’. Using 131 molecular markers, including 28 insertion/deletion markers, we identified 11 main- and 16 minor-effect QTLs for the six traits with a threshold LOD value > 2.8. Our sequence analysis identified fifty-four candidate genes for the main-effect QTLs. By further comparison of coding sequences and meta-expression profiles between japonica and indica rice varieties, we finally chose 15 strong candidate genes for the 11 main-effect QTLs. Our study shows that the whole-genome sequence data substantially enhanced the efficiency of polymorphic marker development for QTL fine-mapping and the identification of possible candidate genes. This yields useful genetic resources for breeding high-yielding rice cultivars with improved plant architecture.     

Unraveling the Complex Trait of Crop Yield With Quantitative Trait Loci Mapping in Brassica napus

Yield is the most important and complex trait for the genetic improvement of crops. Although much research into the genetic basis of yield and yield-associated traits has been reported, in each such experiment the genetic architecture and determinants of yield have remained ambiguous. One of the most intractable problems is the interaction between genes and the environment. We identified 85 quantitative trait loci (QTL) for seed yield along with 785 QTL for eight yield-associated traits, from 10 natural environments and two related populations of rapeseed. A trait-by-trait meta-analysis revealed 401 consensus QTL, of which 82.5% were clustered and integrated into 111 pleiotropic unique QTL by meta-analysis, 47 of which were relevant for seed yield. The complexity of the genetic architecture of yield was demonstrated, illustrating the pleiotropy, synthesis, variability, and plasticity of yield QTL. The idea of estimating indicator QTL for yield QTL and identifying potential candidate genes for yield provides an advance in methodology for complex traits.YIELD is the most important and complex trait in crops. It reflects the interaction of the environment with all growth and development processes that occur throughout the life cycle (Quarrie et al. 2006). Crop yield is directly and multiply determined by yield-component traits (such as seed weight and seed number). Yield-related traits (such as biomass, harvest index, plant architecture, adaptation, resistance to biotic and abiotic constraints) may also indirectly affect yield by affecting the yield-component traits or by other, unknown mechanisms. Increasing evidence suggests that “fine-mapped” quantitative trait loci (QTL) or genes identified as affecting crop yield involve diverse pathways, such as seed number (Ashikari et al. 2005; Tian et al. 2006b; Burstin et al. 2007; Xie et al. 2008; Xing et al. 2008; Xue et al. 2008), seed weight (Ishimaru 2003; Song et al. 2005; Shomura et al. 2008; Wang et al. 2008; Xie et al. 2006, 2008; Xing et al. 2008; Xue et al. 2008), flowering time (Cockram et al. 2007; Song et al. 2007; Xie et al. 2008; Xue et al. 2008), plant height (Salamini 2003; Ashikari et al. 2005; Xie et al. 2008; Xue et al. 2008), branching (Clark et al. 2006; Burstin et al. 2007; Xing et al. 2008), biomass yield (Quarrie et al. 2006; Burstin et al. 2007), resistance and tolerance to biotic and abiotic stresses (Khush 2001; Brown 2002; Yuan et al. 2002; Waller et al. 2005; Zhang 2007; Warrington et al. 2008), and root architecture (Hochholdinger et al. 2008).Many experiments have explored the genetic basis of yield and yield-associated traits (yield components and yield-related traits) in crops. Summaries of identified QTL have been published for wheat (MacCaferri et al. 2008), barley (Von Korff et al. 2008), rice, and maize (http://www.gramene.org/). The results show several common patterns. First, QTL for yield and yield-associated traits tend to be clustered in the genome, which suggests that the QTL of the yield-associated traits have pleiotropic effects on yield. Second, this kind of pleiotropy has not been well analyzed genetically. The QTL for yield (complicated factor), therefore, have not been associated with any yield-associated traits (relatively simple factors, such as plant height). Therefore, they are unlikely to predict accurately potential candidate genes for yield. Third, only a few loci (rarely >10) have been found for each of these traits. Thus, the genetic architecture of yield has remained ambiguous. Fourth, trials were carried out in a few environments and how the mode of expression of QTL for these complex traits might respond in different environments is unclear.In this study, the genetic architecture of crop yield was analyzed through the QTL mapping of seed yield and eight yield-associated traits in two related populations of rapeseed (Brassica napus) that were grown in 10 natural environments. The complexity of the genetic architecture of seed yield was demonstrated by QTL meta-analysis. The idea of estimating indicator QTL (QTL of yield-associated traits, which are defined as the potential genetic determinants of the colocalized QTL for yield) for yield QTL in conjunction with the identification of candidate genes is described.     

Selecting Informative Traits for Multivariate Quantitative Trait Locus Mapping Helps to Gain Optimal Power

A major consideration in multitrait analysis is which traits should be jointly analyzed. As a common strategy, multitrait analysis is performed either on pairs of traits or on all of traits. To fully exploit the power of multitrait analysis, we propose variable selection to choose a subset of informative traits for multitrait quantitative trait locus (QTL) mapping. The proposed method is very useful for achieving optimal statistical power for QTL identification and for disclosing the most relevant traits. It is also a practical strategy to effectively take advantage of multitrait analysis when the number of traits under consideration is too large, making the usual multivariate analysis of all traits challenging. We study the impact of selection bias and the usage of permutation tests in the context of variable selection and develop a powerful implementation procedure of variable selection for genome scanning. We demonstrate the proposed method and selection procedure in a backcross population, using both simulated and real data. The extension to other experimental mapping populations is straightforward.     

Quantitative Trait Locus Mapping for Yield-Associated Agronomic Traits in a BC2F6 Population of Japonica Hybrid Rice Liaoyou 5218

Journal of Plant Growth Regulation - RAD-seq method is a recently developed, cost-effective, and high-throughput approach for detecting genetic variability based on single-nucleotide polymorphisms...     

Mapping Environment-Specific Quantitative Trait Loci

Environment-specific quantitative trait loci (QTL) refer to QTL that express differently in different environments, a phenomenon called QTL-by-environment (Q × E) interaction. Q × E interaction is a difficult problem extended from traditional QTL mapping. The mixture model maximum-likelihood method is commonly adopted for interval mapping of QTL, but the method is not optimal in handling QTL interacting with environments. We partitioned QTL effects into main and interaction effects. The main effects are represented by the means of QTL effects in all environments and the interaction effects are represented by the variances of the QTL effects across environments. We used the Markov chain Monte Carlo (MCMC) implemented Bayesian method to estimate both the main and the interaction effects. The residual error covariance matrix was modeled using the factor analytic covariance structure. A simulation study showed that the factor analytic structure is robust and can handle other structures as special cases. The method was also applied to Q × E interaction mapping for the yield trait of barley. Eight markers showed significant main effects and 18 markers showed significant Q × E interaction. The 18 interacting markers were distributed across all seven chromosomes of the entire genome. Only 1 marker had both the main and the Q × E interaction effects. Each of the other markers had either a main effect or a Q × E interaction effect but not both.GENOTYPE-BY-ENVIRONMENT (G × E) interaction is a very important phenomenon in quantitative genetics. With the advanced molecular technology and statistical methods for quantitative trait loci (QTL) mapping (Lander and Botstein 1989; Jansen 1993; Zeng 1994), G × E interaction analysis has shifted to QTL-by-environment (Q × E) interaction. In the early stage of QTL mapping, almost all statistical methods were developed in a single environment (Paterson et al. 1991; Stuber et al. 1992). Data from different environments were analyzed separately and the conclusions were drawn from the separate analyses of QTL across environments. These methods do not consider the correlation of data under different environments and thus may not extract maximum information from the data. Composite interval mapping for multiple traits can be used for Q × E interaction if different traits are treated as the same trait measured in different environments (Jiang and Zeng 1995). This multivariate composite interval mapping approach makes good use of all data simultaneously and increases statistical power of QTL detection and accuracy of the estimated QTL positions. However, the number of parameters of this method increases dramatically as the number of environments increases. Therefore, the method may not be applied when the number of environments is large. Several other models have been proposed to solve the problem of a large number of environments (Jansen et al. 1995; Beavis and Keim 1996; Romagosa et al. 1996). These methods were based on some special situations and assumptions. One typical assumption was independent errors or constant variances across environments. These assumptions are often violated in real QTL mapping experiments.Earlier investigators realized the problem and adopted the mixed-model methodology to solve the problem (Piepho 2000; Boer et al. 2007). Under the mixed-model framework, people can choose which model effects are random and which are fixed. The mixed-model methodology is very flexible, leading to an easy way to model genetic and environmental correlation between environments using a suitable error structure. Piepho (2000) proposed a mixed model to detect QTL main effect across environments. Similar to the composite interval mapping analysis, his model incorporated one putative QTL and a few cofactors. The Q × E effects in the model were assumed to be random, which greatly reduced the number of estimated parameters. However, the fact that only one QTL is included in the model means that Piepho''s (2000) model remains a single-QTL model rather than a multivariate model. Boer et al. (2007) proposed a step-by-step mixed-model approach to detecting QTL main effects, Q × E interaction effects, and QTL responses to specific environmental covariates. In the final step, Boer et al. (2007) rewrote the model to include all QTL in a multiple-QTL model and reestimated their effects.In this study, we extended the Bayesian shrinkage method (Xu 2003) to map Q × E interaction effects of QTL. In the original study (Xu 2003), we treated each marker as a putative QTL and used the shrinkage method to simultaneously estimate marker effects of the entire genome. In the multiple-environment case, we can still use this approach to simultaneously evaluate marker effects under multiple environments but we can further partition the marker effects into main and Q × E interaction effects. For any particular marker, the mean of the marker effects represents the main effect and the variance of the marker effects represents the Q × E interaction effect for that marker. Under the Bayesian framework, we assigned a normal prior with zero mean and an unknown variance to each marker main effect and a multivariate normal prior with zero vector mean and homogeneous diagonal variance–covariance matrix to the Q × E interaction effects of each maker. In multiple environments, the structure of the error terms might be very complicated since we need to consider the correlation of the same genotype under different environments. In our analysis, we used different variance–covariance structures to model the error terms. The simplest case was the homogeneous diagonal matrix, and the most complex choice was an unstructured matrix. We also used a heterogeneous diagonal matrix whose parameters are somewhere between the two models. Finally, we considered several factor analytic models. The reason to use the factor analytic structure is that it can separate genetic effects into common effects and environment-specific effects. In addition, the factor analytic structure is parsimonious and thus can substantially reduce the computational burden of the mixed-model analyses.     

Dynamic Quantitative Trait Locus Analysis of Seed Vigor at Three Maturity Stages in Rice

Seed vigor is an important characteristic of seed quality. In this study, one rice population of recombinant inbred lines (RILs) was used to determine the genetic characteristics of seed vigor, including the germination potential, germination rate, germination index and time for 50% of germination, at 4 (early), 5 (middle) and 6 weeks (late) after heading in two years. A total of 24 additive and 9 epistatic quantitative trait loci (QTL) for seed vigor were identified using QTL Cartographer and QTLNetwork program respectively in 2012; while 32 simple sequence repeat (SSR) markers associated with seed vigor were detected using bulked segregant analysis (BSA) in 2013. The additive, epistatic and QTL × development interaction effects regulated the dry maturity developmental process to improve seed vigor in rice. The phenotypic variation explained by each additive, epistatic QTL and QTL × development interaction ranged from 5.86 to 40.67%, 4.64 to 11.28% and 0.01 to 1.17%, respectively. The QTLs were rarely co-localized among the different maturity stages; more QTLs were expressed at the early maturity stage followed by the late and middle stages. Twenty additive QTLs were stably expressed in two years which might play important roles in establishment of seed vigor in different environments. By comparing chromosomal positions of these stably expressed additive QTLs with those previously identified, the regions of QTL for seed vigor are likely to coincide with QTL for grain size, low temperature germinability and seed dormancy; while 5 additive QTL might represent novel genes. Using four selected RILs, three cross combinations of seed vigor for the development of RIL populations were predicted; 19 elite alleles could be pyramided by each combination.     

Fine Mapping and Candidate Gene Prediction of a Pleiotropic Quantitative Trait Locus for Yield-Related Trait in Zea mays

The yield of maize grain is a highly complex quantitative trait that is controlled by multiple quantitative trait loci (QTLs) with small effects, and is frequently influenced by multiple genetic and environmental factors. Thus, it is challenging to clone a QTL for grain yield in the maize genome. Previously, we identified a major QTL, qKNPR6, for kernel number per row (KNPR) across multiple environments, and developed two nearly isogenic lines, SL57-6 and Ye478, which differ only in the allelic constitution at the short segment harboring the QTL. Recently, qKNPR6 was re-evaluated in segregating populations derived from SL57-6×Ye478, and was narrowed down to a 2.8 cM interval, which explained 56.3% of the phenotypic variance of KNPR in 201 F_2∶3 families. The QTL simultaneously affected ear length, kernel weight and grain yield. Furthermore, a large F₂ population with more than 12,800 plants, 191 recombinant chromosomes and 10 overlapping recombinant lines placed qKNPR6 into a 0.91 cM interval corresponding to 198Kb of the B73 reference genome. In this region, six genes with expressed sequence tag (EST) evidence were annotated. The expression pattern and DNA diversity of the six genes were assayed in Ye478 and SL57-6. The possible candidate gene and the pathway involved in inflorescence development were discussed.     

Precision Mapping of Quantitative Trait Loci

Adequate separation of effects of possible multiple linked quantitative trait loci (QTLs) on mapping QTLs is the key to increasing the precision of QTL mapping. A new method of QTL mapping is proposed and analyzed in this paper by combining interval mapping with multiple regression. The basis of the proposed method is an interval test in which the test statistic on a marker interval is made to be unaffected by QTLs located outside a defined interval. This is achieved by fitting other genetic markers in the statistical model as a control when performing interval mapping. Compared with the current QTL mapping method (i.e., the interval mapping method which uses a pair or two pairs of markers for mapping QTLs), this method has several advantages. (1) By confining the test to one region at a time, it reduces a multiple dimensional search problem (for multiple QTLs) to a one dimensional search problem. (2) By conditioning linked markers in the test, the sensitivity of the test statistic to the position of individual QTLs is increased, and the precision of QTL mapping can be improved. (3) By selectively and simultaneously using other markers in the analysis, the efficiency of QTL mapping can be also improved. The behavior of the test statistic under the null hypothesis and appropriate critical value of the test statistic for an overall test in a genome are discussed and analyzed. A simulation study of QTL mapping is also presented which illustrates the utility, properties, advantages and disadvantages of the method.     

Fine Mapping of qRC10-2, a Quantitative Trait Locus for Cold Tolerance of Rice Roots at Seedling and Mature Stages

Cold stress causes various injuries to rice seedlings in low-temperature and high-altitude areas and is therefore an important factor affecting rice production in such areas. In this study, root conductivity (RC) was used as an indicator to map quantitative trait loci (QTLs) of cold tolerance in Oryza rufipogon Griff., Dongxiang wild rice (DX), at its two-leaf stage. The correlation coefficients between RC and the plant survival rate (PSR) at the seedling and maturity stages were –0.85 and –0.9 (P = 0.01), respectively, indicating that RC is a reliable index for evaluating cold tolerance of rice. A preliminary mapping group was constructed from 151 BC₂F₁ plants using DX as a cold-tolerant donor and the indica variety Nanjing 11 (NJ) as a recurrent parent. A total of 113 codominant simple-sequence repeat (SSR) markers were developed, with a parental polymorphism of 17.3%. Two cold-tolerant QTLs, named qRC10-1 and qRC10-2 were detected on chromosome 10 by composite interval mapping. qRC10-1 (LOD = 3.1, RM171-RM1108) was mapped at 148.3 cM, and qRC10-2 (LOD = 6.1, RM25570-RM304) was mapped at 163.3 cM, which accounted for 9.4% and 32.1% of phenotypic variances, respectively. To fine map the major locus qRC10-2, NJ was crossed with a BC₄F₂ plant (L188-3), which only carried the QTL qRC10-2, to construct a large BC₅F₂ fine-mapping population with 13,324 progenies. Forty-five molecular markers were designed to evenly cover qRC10-2, and 10 markers showed polymorphisms between DX and NJ. As a result, qRC10-2 was delimited to a 48.5-kb region between markers qc45 and qc48. In this region, Os10g0489500 and Os10g0490100 exhibited different expression patterns between DX and NJ. Our results provide a basis for identifying the gene(s) underlying qRC10-2, and the markers developed here may be used to improve low-temperature tolerance of rice seedling and maturity stages via marker-assisted selection (MAS).

Key Message

With root electrical conductivity used as a cold-tolerance index, the quantitative trait locus qRC10-2 was fine mapped to a 48.5-kb candidate region, and Os10g0489500 and Os10g0490100 were identified as differently expressed genes for qRC10-2.     

Composite Interval Mapping Based on Lattice Design for Error Control May Increase Power of Quantitative Trait Locus Detection

Experimental error control is very important in quantitative trait locus (QTL) mapping. Although numerous statistical methods have been developed for QTL mapping, a QTL detection model based on an appropriate experimental design that emphasizes error control has not been developed. Lattice design is very suitable for experiments with large sample sizes, which is usually required for accurate mapping of quantitative traits. However, the lack of a QTL mapping method based on lattice design dictates that the arithmetic mean or adjusted mean of each line of observations in the lattice design had to be used as a response variable, resulting in low QTL detection power. As an improvement, we developed a QTL mapping method termed composite interval mapping based on lattice design (CIMLD). In the lattice design, experimental errors are decomposed into random errors and block-within-replication errors. Four levels of block-within-replication errors were simulated to show the power of QTL detection under different error controls. The simulation results showed that the arithmetic mean method, which is equivalent to a method under random complete block design (RCBD), was very sensitive to the size of the block variance and with the increase of block variance, the power of QTL detection decreased from 51.3% to 9.4%. In contrast to the RCBD method, the power of CIMLD and the adjusted mean method did not change for different block variances. The CIMLD method showed 1.2- to 7.6-fold higher power of QTL detection than the arithmetic or adjusted mean methods. Our proposed method was applied to real soybean (Glycine max) data as an example and 10 QTLs for biomass were identified that explained 65.87% of the phenotypic variation, while only three and two QTLs were identified by arithmetic and adjusted mean methods, respectively.     

Multiple Trait Analysis of Genetic Mapping for Quantitative Trait Loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.     

Mapping of a Quantitative Trait Locus for Beef Marbling on Bovine Chromosome 9 in Purebred Japanese Black Cattle

The goal of this study is to detect quantitative trait loci (QTL) for carcass traits applicable for a DNA-based breeding system in a Japanese Black cattle population. A purebred paternal half-sib family from a commercial line composed of 65 steers was initially analyzed using 188 informative microsatellites giving a 16-cM average interval covering 29 autosomes. A significant QTL for marbling was detected in the centromeric portion of bovine chromosome (BTA) 9. After additional marker genotyping across a larger sample size composed of 169 individuals, this locus was refined to a 20-cM confidence interval between microsatellites BM1227 (24 cM) and DIK2741 (50 cM) at a 1% chromosome-wise threshold. The allele substitution effect between Q and q for a beef marbling standard score (1 to 12 range) on BTA9 was 1.0 (5.7% of total phenotypic variance in QTL contribution in this family). This result provides a primary platform for a marker-assisted selection system of the beef marbling trait within the Japanese Black (Wagyu) cattle population.