A unified DNA sequence and non‐DNA sequence mapping model of complex traits

Increasing evidence shows that quantitative inheritance is based on both DNA sequence and non‐DNA sequence variants. However, how to simultaneously detect these variants from a mapping study has been unexplored, hampering our effort to illustrate the detailed genetic architecture of complex traits. We address this issue by developing a unified model of quantitative trait locus (QTL) mapping based on an open‐pollinated design composed of randomly sampling maternal plants from a natural population and their half‐sib seeds. This design forms a two‐level hierarchical platform for a joint linkage‐linkage disequilibrium analysis of population structure. The EM algorithm was implemented to estimate and test DNA sequence‐based effects and non‐DNA sequence‐based effects of QTLs. We applied this model to analyze genetic mapping data from the OP design of a gymnosperm coniferous species, Torreya grandis, identifying 25 significant DNA sequence and non‐DNA sequence QTLs for seedling height and diameter growth in different years. Results from computer simulation show that the unified model has good statistical properties and is powerful for QTL detection. Our model enables the tests of how a complex trait is affected differently by DNA‐based effects and non‐DNA sequence‐based transgenerational effects, thus allowing a more comprehensive picture of genetic architecture to be charted and quantified.     

A general model for detecting genetic determinants underlying longitudinal traits with unequally spaced measurements and nonstationary covariance structure

A mixture model for determining quantitative trait loci (QTL) affecting growth trajectories has been proposed in the literature. In this article, we extend this model to a more general situation in which longitudinal traits for each subject are measured at unequally spaced time intervals, different subjects have different measurement patterns, and the residual correlation within subjects is nonstationary. We derive an EM-simplex hybrid algorithm to estimate the allele frequencies, Hardy-Weinberg disequilibrium, and linkage disequilibrium between QTL in the original population and parameters contained in the growth equation and in the covariance structure. A worked example of head circumference growth in 145 children is used to validate our extended model. A simulation study is performed to examine the statistical properties of the parameter estimation obtained from this example. Finally, we discuss the implications and extensions of our model for detecting QTL that affect growth trajectories.     

关联分析及其在植物遗传学研究中的应用

植物的很多重要经济性状均属于复杂性状。基于连锁分析的QTL作图是研究复杂性状的有效手段,但其尚存在一定的局限性。随着现代生物学的发展,一种基于连锁不平衡的新剖分复杂性状方法——关联分析法,开始应用于植物遗传学研究。与QTL作图法相比,应用关联分析法具有不需要构建特殊的群体,可同时对多个等位基因进行分析,定位QTL精度可达到单基因水平等优势。该文介绍了关联分析方法学的基础和特性,简述了其在植物遗传学研究中的进展情况,并对其未来发展和在植物遗传学研究中的应用进行了展望。     

Deciphering the genomic architecture of the stickleback brain with a novel multilocus gene‐mapping approach

Quantitative traits important to organismal function and fitness, such as brain size, are presumably controlled by many small‐effect loci. Deciphering the genetic architecture of such traits with traditional quantitative trait locus (QTL) mapping methods is challenging. Here, we investigated the genetic architecture of brain size (and the size of five different brain parts) in nine‐spined sticklebacks (Pungitius pungitius) with the aid of novel multilocus QTL‐mapping approaches based on a de‐biased LASSO method. Apart from having more statistical power to detect QTL and reduced rate of false positives than conventional QTL‐mapping approaches, the developed methods can handle large marker panels and provide estimates of genomic heritability. Single‐locus analyses of an F₂ interpopulation cross with 239 individuals and 15 198, fully informative single nucleotide polymorphisms (SNPs) uncovered 79 QTL associated with variation in stickleback brain size traits. Many of these loci were in strong linkage disequilibrium (LD) with each other, and consequently, a multilocus mapping of individual SNPs, accounting for LD structure in the data, recovered only four significant QTL. However, a multilocus mapping of SNPs grouped by linkage group (LG) identified 14 LGs (1–6 depending on the trait) that influence variation in brain traits. For instance, 17.6% of the variation in relative brain size was explainable by cumulative effects of SNPs distributed over six LGs, whereas 42% of the variation was accounted for by all 21 LGs. Hence, the results suggest that variation in stickleback brain traits is influenced by many small‐effect loci. Apart from suggesting moderately heritable (h² ≈ 0.15–0.42) multifactorial genetic architecture of brain traits, the results highlight the challenges in identifying the loci contributing to variation in quantitative traits. Nevertheless, the results demonstrate that the novel QTL‐mapping approach developed here has distinctive advantages over the traditional QTL‐mapping methods in analyses of dense marker panels.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

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     

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.     

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.     

A model for quantitative trait loci mapping,linkage phase,and segregation pattern estimation for a full-sib progeny

Quantitative trait loci (QTL) mapping is an important approach for the study of the genetic architecture of quantitative traits. For perennial species, inbred lines cannot be obtained due to inbreed depression and a long juvenile period. Instead, linkage mapping can be performed by using a full-sib progeny. This creates a complex scenario because both markers and QTL alleles can have different segregation patterns as well as different linkage phases between them. We present a two-step method for QTL mapping using full-sib progeny based on composite interval mapping (i.e., interval mapping with cofactors), considering an integrated genetic map with markers with different segregation patterns and conditional probabilities obtained by a multipoint approach. The model is based on three orthogonal contrasts to estimate the additive effect (one in each parent) and dominance effect. These estimatives are obtained using the EM algorithm. In the first step, the genome is scanned to detect QTL. After, segregation pattern and linkage phases between QTL and markers are estimated. A simulated example is presented to validate the methodology. In general, the new model is more effective than existing approaches, because it can reveal QTL present in a full-sib progeny that segregates in any pattern present and can also identify dominance effects. Also, the inclusion of cofactors provided more statistical power for QTL mapping.     

Bayesian functional mapping of dynamic quantitative traits

Without consideration of other linked QTLs responsible for dynamic trait, original functional mapping based on a single QTL model is not optimal for analyzing multiple dynamic trait loci. Despite that composite functional mapping incorporates the effects of genetic background outside the tested QTL in mapping model, the arbitrary choice of background markers also impact on the power of QTL detection. In this study, we proposed Bayesian functional mapping strategy that can simultaneously identify multiple QTL controlling developmental patterns of dynamic traits over the genome. Our proposed method fits the change of each QTL effect with the time by Legendre polynomial and takes the residual covariance structure into account using the first autoregressive equation. Also, Bayesian shrinkage estimation was employed to estimate the model parameters. Especially, we specify the gamma distribution as the prior for the first-order auto-regressive coefficient, which will guarantee the convergence of Bayesian sampling. Simulations showed that the proposed method could accurately estimate the QTL parameters and had a greater statistical power of QTL detection than the composite functional mapping. A real data analysis of leaf age growth in rice is used for the demonstration of our method. It shows that our Bayesian functional mapping can detect more QTLs as compared to composite functional mapping.     

Time‐specific and pleiotropic quantitative trait loci coordinately modulate stem growth in Populus

In perennial woody plants, the coordinated increase of stem height and diameter during juvenile growth improves competitiveness (i.e. access to light); however, the factors underlying variation in stem growth remain unknown in trees. Here, we used linkage‐linkage disequilibrium (linkage‐LD) mapping to decipher the genetic architecture underlying three growth traits during juvenile stem growth. We used two Populus populations: a linkage mapping population comprising a full‐sib family of 1,200 progeny and an association mapping panel comprising 435 unrelated individuals from nearly the entire natural range of Populus tomentosa. We mapped 311 quantitative trait loci (QTL) for three growth traits at 12 timepoints to 42 regions in 17 linkage groups. Of these, 28 regions encompassing 233 QTL were annotated as 27 segmental homology regions (SHRs). Using SNPs identified by whole‐genome re‐sequencing of the 435‐member association mapping panel, we identified significant SNPs (P ≤ 9.4 × 10^?7) within 27 SHRs that affect stem growth at nine timepoints with diverse additive and dominance patterns, and these SNPs exhibited complex allelic epistasis over the juvenile growth period. Nineteen genes linked to potential causative alleles that have time‐specific or pleiotropic effects, and mostly overlapped with significant signatures of selection within SHRs between climatic regions represented by the association mapping panel. Five genes with potential time‐specific effects showed species‐specific temporal expression profiles during the juvenile stages of stem growth in five representative Populus species. Our observations revealed the importance of considering temporal genetic basis of complex traits, which will facilitate the molecular design of tree ideotypes.     

关联分析及其在植物遗传学研究中的应用

植物的很多重要经济性状均属于复杂性状。基于连锁分析的QTL作图是研究复杂性状的有效手段, 但其尚存在一定的局限性。随着现代生物学的发展, 一种基于连锁不平衡的新剖分复杂性状方法--关联分析法, 开始应用于植物遗传学研究。与QTL作图法相比, 应用关联分析法具有不需要构建特殊的群体, 可同时对多个等位基因进行分析, 定位QTL精度可达到单基因水平等优势。该文介绍了关联分析方法学的基础和特性, 简述了其在植物遗传学研究中的进展情况, 并对其未来发展和在植物遗传学研究中的应用进行了展望。     

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

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

From plant genomics to breeding practice

New alleles are constantly accumulated during intentional crop selection. The molecular understanding of these alleles has stimulated new genomic approaches to mapping quantitative trait loci (QTL) and haplotype multiplicity of the genes concerned. A limited number of quantitative trait nucleotides responsible for QTL variation have been described, but an acceleration in their rate of discovery is expected with the adoption of linkage disequilibrium and candidate gene strategies for QTL fine mapping and cloning. Additional layers of regulatory variation have been studied that could also contribute to the molecular basis of quantitative genetics of crop traits. Despite this progress, the role of marker-assisted selection in plant breeding will ultimately depend on the genetic model underlying quantitative variation.     

Genome-wide association mapping of Fusarium head blight resistance in contemporary barley breeding germplasm

Utilization of quantitative trait loci (QTL) identified in bi-parental mapping populations has had limited success for improving complex quantitative traits with low to moderate heritability. Association mapping in contemporary breeding germplasm may lead to more effective marker strategies for crop improvement. To test this approach, we conducted association mapping of two complex traits with moderate heritability; Fusarium head blight (FHB) severity and the grain concentration of mycotoxin associated with disease, deoxynivalenol (DON). To map FHB resistance in barley, 768 breeding lines were evaluated in 2006 and 2007 in four locations. All lines were genotyped with 1,536 SNP markers and QTL were mapped using a mixed model that accounts for relatedness among lines. Average linkage disequilibrium within the breeding germplasm extended beyond 4 cM. Four QTL were identified for FHB severity and eight QTL were identified for the DON concentration in two independent sets of breeding lines. The QTL effects were small, explaining 1–3% of the phenotypic variation, as might be expected for complex polygenic traits. We show that using breeding germplasm to map QTL can complement bi-parental mapping studies by providing independent validation, mapping QTL with more precision, resolving questions of linkage and pleiotropy, and identifying genetic markers that can be applied immediately in crop improvement.     

人类复杂遗传疾病QTL分析方法的理论探讨

利用连锁不平衡理论,人类遗传学家已能把影响人类疾病的质量基因定位在小至1cM区域内,有些基因已被克隆出来。罗泽伟等进一步发展统计分析方法检测及估算分子标记与QTL之间的连锁不平衡系数,从而提出了人类复杂遗传病高解析度基因定位的理论策略。以此为基础,进一步探讨了供试群体在双亲基因频率存在差异时检测QTL和检测QTL互作的方法,给出了有关的理论结果。     

A general framework for analyzing the genetic architecture of developmental characteristics

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive x additive epistatic effects on stem height growth trajectories in a forest tree.     

QTL analyses of drought tolerance and growth for a Salix dasyclados × Salix viminalis hybrid in contrasting water regimes

Quantitative trait loci (QTL) for growth traits and water-use efficiency have been identified in two water regimes (normal and drought-treated) and for a treatment index. A tetraploid hybrid F₂ population originating from a cross between a Salix dasyclados clone (SW901290) and a Salix viminalis clone (Jorunn) was used in the study. The growth response of each individual including both above and below ground dry-matter production (i.e. shoot length, shoot diameter, aboveground and root dry weight, internode length, root dry weight/total dry weight, relative growth rate and leaf nitrogen content) was analysed in a replicated block experiment with two water treatments. A composite interval mapping approach was used to estimate number of QTL, the magnitude of the QTL and their position on genetic linkage maps. QTL specific for each treatment and for the treatment index were found, but QTL common across the treatments and the treatment index were also detected. Each QTL explained from 8% to 29% of the phenotypic variation, depending on trait and treatment. Clusters of QTL for different traits were mapped close to each other at several linkage groups, indicating either a common genetic base or tightly linked QTL. Common QTL identified between treatments and treatment index in the complex trait dry weight can be useful tools in the breeding and selection for drought stress tolerance in Salix.