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.     

Bayesian shrinkage analysis of quantitative trait Loci for dynamic traits

Many quantitative traits are measured repeatedly during the life of an organism. Such traits are called dynamic traits. The pattern of the changes of a dynamic trait is called the growth trajectory. Studying the growth trajectory may enhance our understanding of the genetic architecture of the growth trajectory. Recently, we developed an interval-mapping procedure to map QTL for dynamic traits under the maximum-likelihood framework. We fit the growth trajectory by Legendre polynomials. The method intended to map one QTL at a time and the entire QTL analysis involved scanning the entire genome by fitting multiple single-QTL models. In this study, we propose a Bayesian shrinkage analysis for estimating and mapping multiple QTL in a single model. The method is a combination between the shrinkage mapping for individual quantitative traits and the Legendre polynomial analysis for dynamic traits. The multiple-QTL model is implemented in two ways: (1) a fixed-interval approach where a QTL is placed in each marker interval and (2) a moving-interval approach where the position of a QTL can be searched in a range that covers many marker intervals. Simulation study shows that the Bayesian shrinkage method generates much better signals for QTL than the interval-mapping approach. We propose several alternative methods to present the results of the Bayesian shrinkage analysis. In particular, we found that the Wald test-statistic profile can serve as a mechanism to test the significance of a putative QTL.     

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     

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.     

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.     

3FunMap: full-sib family functional mapping of dynamic traits

MOTIVATION: Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation. AVAILABILITY: http://statgen.psu.edu/software.     

植物QTL分析的理论研究进展

数量性状的表型是由数量性状基因座 ( Quantitative trait locus,QTL)和环境效应共同作用的结果。传统的数量遗传学采用统计学的方法由一级统计量和二级统计量描述处理 QTL的复合作用 ,估计各种遗传参数 (例如遗传力、遗传相关、遗传进度、有效因子数等 ) ,用于指导遗传育种实践。然而 ,在传统的数量遗传学分析中 ,往往假设数量性状受微效多基因控制 ,这些基因具有相同的并且是较微小的效应 ,所估计的遗传参数反映的是数量性状多基因系统的整体特征 ,其理论方法不能用于追踪研究和描述单个数量性状基因的作用。近年来 ,由于分子生物学技…     

Bayesian inference for genomic imprinting underlying developmental characteristics

The identification of imprinted genes is becoming a standard procedure in searching for quantitative trait loci (QTL) underlying complex traits. When a developmental characteristic such as growth or drug response is observed at multiple time points, understanding the dynamics of gene function governing the underlying feature should provide more biological information regarding the genetic control of an organism. Recognizing that differential imprinting can be development-specific, mapping imprinted genes considering the dynamic imprinting effect can provide additional biological insights into the epigenetic control of a complex trait. In this study, we proposed a Bayesian imprinted QTL (iQTL) mapping framework considering the dynamics of imprinting effects and model multiple iQTLs with an efficient Bayesian model selection procedure. The method overcomes the limitation of likelihood-based mapping procedure, and can simultaneously identify multiple iQTLs with different gene action modes across the whole genome with high computational efficiency. An inference procedure using Bayes factors to distinguish different imprinting patterns of iQTL was proposed. Monte Carlo simulations were conducted to evaluate the performance of the method. The utility of the approach was illustrated through an analysis of a body weight growth data set in an F(2) family derived from LG/J and SM/J mouse stains. The proposed Bayesian mapping method provides an efficient and computationally feasible framework for genome-wide multiple iQTL inference with complex developmental traits.     

Efficiency of selective genotyping for genetic analysis of complex traits and potential applications in crop improvement

Selective genotyping of individuals from the two tails of the phenotypic distribution of a population provides a cost efficient alternative to analysis of the entire population for genetic mapping. Past applications of this approach have been confounded by the small size of entire and tail populations, and insufficient marker density, which result in a high probability of false positives in the detection of quantitative trait loci (QTL). We studied the effect of these factors on the power of QTL detection by simulation of mapping experiments using population sizes of up to 3,000 individuals and tail population sizes of various proportions, and marker densities up to one marker per centiMorgan using complex genetic models including QTL linkage and epistasis. The results indicate that QTL mapping based on selective genotyping is more powerful than simple interval mapping but less powerful than inclusive composite interval mapping. Selective genotyping can be used, along with pooled DNA analysis, to replace genotyping the entire population, for mapping QTL with relatively small effects, as well as linked and interacting QTL. Using diverse germplasm including all available genetics and breeding materials, it is theoretically possible to develop an “all-in-one plate” approach where one 384-well plate could be designed to map almost all agronomic traits of importance in a crop species. Selective genotyping can also be used for genomewide association mapping where it can be integrated with selective phenotyping approaches. We also propose a breeding-to-genetics approach, which starts with identification of extreme phenotypes from segregating populations generated from multiple parental lines and is followed by rapid discovery of individual genes and combinations of gene effects together with simultaneous manipulation in breeding programs.     

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

In biology, many quantitative traits are dynamic in nature. They can often be described by some smooth functions or curves. A joint analysis of all the repeated measurements of the dynamic traits by functional quantitative trait loci (QTL) mapping methods has the benefits to (1) understand the genetic control of the whole dynamic process of the quantitative traits and (2) improve the statistical power to detect QTL. One crucial issue in functional QTL mapping is how to correctly describe the smoothness of trajectories of functional valued traits. We develop an efficient Bayesian nonparametric multiple-loci procedure for mapping dynamic traits. The method uses the Bayesian P-splines with (nonparametric) B-spline bases to specify the functional form of a QTL trajectory and a random walk prior to automatically determine its degree of smoothness. An efficient deterministic variational Bayes algorithm is used to implement both (1) the search of an optimal subset of QTL among large marker panels and (2) estimation of the genetic effects of the selected QTL changing over time. Our method can be fast even on some large-scale data sets. The advantages of our method are illustrated on both simulated and real data sets.     

Characterization of variation and quantitative trait loci related to terpenoid indole alkaloid yield in a recombinant inbred line mapping population of <Emphasis Type="Italic">Catharanthus roseus</Emphasis>

Improved Catharanthus roseus cultivars are required for high yields of vinblastine, vindoline and catharanthine and/or serpentine and ajmalicine, the pharmaceutical terpenoid indole alkaloids. An approach to derive them is to map QTL for terpenoid indole alkaloids yields, identify DNA markers tightly linked to the QTL and apply marker assisted selection. Towards the end, 197 recombinant inbred lines from a cross were grown over two seasons to characterize variability for seven biomass and 23 terpenoid indole alkaloids content-traits and yield-traits. The recombinant inbred lines were genotyped for 178 DNA markers which formed a framework genetic map of eight linkage groups (LG), spanning 1786.5 cM, with 10.0 cM average intermarker distance. Estimates of correlations between traits allowed selection of seven relatively more important traits for terpenoid indole alkaloids yields. QTL analysis was performed on them using single marker (regression) analysis, simple interval mapping and composite interval mapping procedures. A total of 20 QTL were detected on five of eight LG, 10 for five traits on LG1, five for four traits on LG2, three for one trait on LG3 and one each for different traits on LG three and four. QTL for the same or different traits were found clustered on three LG. Co-location of two QTL for biomass traits was in accord of correlation between them. The QTL were validated for use in marker assisted selection by the recombinant inbred line which transgressively expressed 16 traits contributory to the yield vinblastine, vindoline and catharanthine from leaves and roots that possessed favourable alleles of 13 relevant QTL.     

Mapping QTL for grain yield and other agronomic traits in post-rainy sorghum [Sorghum bicolor (L.) Moench]

Sorghum, a cereal of economic importance ensures food and fodder security for millions of rural families in the semi-arid tropics. The objective of the present study was to identify and validate quantitative trait loci (QTL) for grain yield and other agronomic traits using replicated phenotypic data sets from three post-rainy dry sorghum crop seasons involving a mapping population with 245 F₉ recombinant inbred lines derived from a cross of M35-1 × B35. A genetic linkage map was constructed with 237 markers consisting of 174 genomic, 60 genic and 3 morphological markers. The QTL analysis for 11 traits following composite interval mapping identified 91 QTL with 5–12 QTL for each trait. QTL detected in the population individually explained phenotypic variation between 2.5 and 30.3 % for a given trait and six major genomic regions with QTL effect on multiple traits were identified. Stable QTL across seasons were identified. Of the 60 genic markers mapped, 21 were found at QTL peak or tightly linked with QTL. A gene-based marker XnhsbSFCILP67 (Sb03g028240) on SBI-03, encoding indole-3-acetic acid-amido synthetase GH3.5, was found to be involved in QTL for seven traits. The QTL-linked markers identified for 11 agronomic traits may assist in fine mapping, map-based gene isolation and also for improving post-rainy sorghum through marker-assisted breeding.     

The genetic architecture of Drosophila sensory bristle number

We have mapped quantitative trait loci (QTL) for Drosophila mechanosensory bristle number in six recombinant isogenic line (RIL) mapping populations, each of which was derived from an isogenic chromosome extracted from a line selected for high or low, sternopleural or abdominal bristle number and an isogenic wild-type chromosome. All RILs were evaluated as male and female F(1) progeny of crosses to both the selected and the wild-type parental chromosomes at three developmental temperatures (18 degrees, 25 degrees, and 28 degrees ). QTL for bristle number were mapped separately for each chromosome, trait, and environment by linkage to roo transposable element marker loci, using composite interval mapping. A total of 53 QTL were detected, of which 33 affected sternopleural bristle number, 31 affected abdominal bristle number, and 11 affected both traits. The effects of most QTL were conditional on sex (27%), temperature (14%), or both sex and temperature (30%). Epistatic interactions between QTL were also common. While many QTL mapped to the same location as candidate bristle development loci, several QTL regions did not encompass obvious candidate genes. These features are germane to evolutionary models for the maintenance of genetic variation for quantitative traits, but complicate efforts to understand the molecular genetic basis of variation for complex traits.     

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.     

QTL analyses of seed weight during the development of soybean (Glycine max L. Merr.)

At harvest traits such as seed weight are the sum of development and responses to stresses over the growing season and particularly during the reproductive phase of growth. The aim here was to measure quantitative trait loci (QTL) underlying the seed weight from early development to drying post harvest. One hundred forty-three F(5) derived recombinant inbred lines (RILs) developed from the cross of soybean cultivars 'Charleston' and 'Dongnong 594' were used for the analysis of QTL underlying mean 100-seed weight at six different developmental stages. QTL x Environment interactions (QE) were analyzed by a mixed genetic mode based on 3 years' data. At an experiment-wise threshold of a=0.05 and by single-point analysis 94 QTL unaffected by QE underlay the mean seed weight at different developmental stages. Sixty-eight QTL affected by QE that also underlay mean seed weight were identified. From the 162 QTL 42 could be located on 12 linkage groups by composite interval mapping (LOD>2.0). The numbers, locations and types of the QTL and the genetic effects were different at each developmental stage. On linkage group C2 the distantly linked QTL swC2-1, swC2-2 and swC2-3 each affected mean seed weight throughout the different developmental stages. The DNA markers linked to the QTL possessed potential for use in marker-assisted selection for soybean seed size. The identification of QTL with genetic main effects and QE interaction effects suggested that such interactions might significantly alter seed weight during seed development.     

Do large effect QTL fractionate? A case study at the maize domestication QTL teosinte branched1

Quantitative trait loci (QTL) mapping is a valuable tool for studying the genetic architecture of trait variation. Despite the large number of QTL studies reported in the literature, the identified QTL are rarely mapped to the underlying genes and it is usually unclear whether a QTL corresponds to one or multiple linked genes. Similarly, when QTL for several traits colocalize, it is usually unclear whether this is due to the pleiotropic action of a single gene or multiple linked genes, each affecting one trait. The domestication gene teosinte branched1 (tb1) was previously identified as a major domestication QTL with large effects on the differences in plant and ear architecture between maize and teosinte. Here we present the results of two experiments that were performed to determine whether the single gene tb1 explains all trait variation for its genomic region or whether the domestication QTL at tb1 fractionates into multiple linked QTL. For traits measuring plant architecture, we detected only one QTL per trait and these QTL all mapped to tb1. These results indicate that tb1 is the sole gene for plant architecture traits that segregates in our QTL mapping populations. For most traits related to ear morphology, we detected multiple QTL per trait in the tb1 genomic region, including a large effect QTL at tb1 itself plus one or two additional linked QTL. tb1 is epistatic to two of these additional QTL for ear traits. Overall, these results provide examples for both a major QTL that maps to a single gene, as well as a case in which a QTL fractionates into multiple linked QTL.     

Nonparametric functional mapping of quantitative trait loci underlying programmed cell death

The development of an organism represents a complex dynamic process, which is controlled by a network of genes and multiple environmental factors. Programmed cell death (PCD), a physiological cell suicide process, occurs during the development of most organisms and is, typically, a complex dynamic trait. Understanding how genes control this complex developmental process has been a long-standing topic in PCD studies. In this article, we propose a nonparametric model, based on orthogonal Legendre polynomials, to map genes or quantitative trait loci (QTLs) that govern the dynamic features of the PCD process. The model is built under the maximum likelihood-based functional mapping framework and is implemented with the EM algorithm. A general information criterion is proposed for selecting the optimal Legendre order that best fits the dynamic pattern of the PCD process. The consistency of the order selection criterion is established. A nonstationary structured antedependence model (SAD) is applied to model the covariance structure among the phenotypes measured at different time points. The developed model generates a number of hypothesis tests regarding the genetic control mechanism of the PCD process. Extensive simulation studies are conducted to investigate the statistical behavior of the model. Finally, we apply the model to a rice tiller number data set in which several QTLs are identified. The developed model provides a quantitative and testable framework for assessing the interplay between genes and the developmental PCD process, and will have great implications for elucidating the genetic architecture of the PCD process.     

Functional mapping - how to map and study the genetic architecture of dynamic complex traits

The development of any organism is a complex dynamic process that is controlled by a network of genes as well as by environmental factors. Traditional mapping approaches for analysing phenotypic data measured at a single time point are too simple to reveal the genetic control of developmental processes. A general statistical mapping framework, called functional mapping, has been proposed to characterize, in a single step, the quantitative trait loci (QTLs) or nucleotides (QTNs) that underlie a complex dynamic trait. Functional mapping estimates mathematical parameters that describe the developmental mechanisms of trait formation and expression for each QTL or QTN. The approach provides a useful quantitative and testable framework for assessing the interplay between gene actions or interactions and developmental changes.     

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Functional mapping has emerged as a next-generation statistical tool for mapping quantitative trait loci (QTL) that affect complex dynamic traits. In this article, we incorporated the idea of nonlinear mixed-effect (NLME) models into the mixture-based framework of functional mapping, aimed to generalize the spectrum of applications for functional mapping. NLME-based functional mapping, implemented with the linearization algorithm based on the first-order Taylor expansion, can provide reasonable estimates of QTL genotypic-specific curve parameters (fixed effect) and the between-individual variation of these parameters (random effect). Results from simulation studies suggest that the NLME-based model is more general than traditional functional mapping. The new model can be useful for the identification of the ontogenetic patterns of QTL genetic effects during time course.     

Functional mapping imprinted quantitative trait loci underlying developmental characteristics

Background

Genomic imprinting, a phenomenon referring to nonequivalent expression of alleles depending on their parental origins, has been widely observed in nature. It has been shown recently that the epigenetic modification of an imprinted gene can be detected through a genetic mapping approach. Such an approach is developed based on traditional quantitative trait loci (QTL) mapping focusing on single trait analysis. Recent studies have shown that most imprinted genes in mammals play an important role in controlling embryonic growth and post-natal development. For a developmental character such as growth, current approach is less efficient in dissecting the dynamic genetic effect of imprinted genes during individual ontology.

Results

Functional mapping has been emerging as a powerful framework for mapping quantitative trait loci underlying complex traits showing developmental characteristics. To understand the genetic architecture of dynamic imprinted traits, we propose a mapping strategy by integrating the functional mapping approach with genomic imprinting. We demonstrate the approach through mapping imprinted QTL controlling growth trajectories in an inbred F₂ population. The statistical behavior of the approach is shown through simulation studies, in which the parameters can be estimated with reasonable precision under different simulation scenarios. The utility of the approach is illustrated through real data analysis in an F₂ family derived from LG/J and SM/J mouse stains. Three maternally imprinted QTLs are identified as regulating the growth trajectory of mouse body weight.

Conclusion

The functional iQTL mapping approach developed here provides a quantitative and testable framework for assessing the interplay between imprinted genes and a developmental process, and will have important implications for elucidating the genetic architecture of imprinted traits.