Multiple-interval mapping for quantitative trait loci controlling endosperm traits

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

胚乳性状数量基因的定位方法

将三倍体胚乳性状的数量遗传模型和二倍体性状数量基因（QTL）图构建方法相结合,导出双侧标记基因型下有关胚乳性状QTL的遗传组成、平均数和遗传方差分量,据之提出以某一区间双侧标记基因型胚乳性状的平均值为依变数,以该区间内任一点假定存在的QTL的加性效应d、显性效应h1和／或h2的系数为自变数,进行有重复观察值的多元线性回归分析,根据多元线性回归的显著性测验该点是否存在QTL,并估计出QTL的遗传效应。给定区间内任一点,皆可以此进行分析,从而可在整条染色体上作图,并以之确定QTL的数目和最可能位置,同时,在检测某一区间时,利用多元线性回归方法将该区间外可能存在的QTL的干扰进行统计控制,以提高QTL检测的精度。此外,还讨论了如何将之推广应用于其他类型的DNA不对应资料以及具复杂遗传模型的胚乳性状资料。     

A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples

Endosperm traits are of triploid inheritance and have become a focus of breeding effort for their close relations with the grain quality. Current methods for mapping quantitative trait loci (QTL) underlying endosperm traits are restricted to the use of the phenotypes of single grain samples as input data set, which are often not available in practice due to the small size of the cereal seeds. This paper proposed a statistical model for one specially tailored mapping strategy, where the marker genotypes are obtained from the maternal plants in the segregation population and the phenotypic responses are replaced by the trait means of composite endosperm samples pooled from each plant. It should therefore be more practical and have wide applicability in mapping endosperm traits. The method was implemented by fitting the phenotypic means of endosperms into a Gaussian mixture model. Both the exact and approximate Expectation-Maximization algorithms were proposed to estimate the model parameters. The presence of the QTL was determined by likelihood ratio test statistics. Statistical power and other properties of the new method were investigated and compared to the current single-seed method under a variety of scenarios through simulation studies. The simulations suggest a reasonable sample size should be used to ensure reliable results. The proposed method was also applied to a simulated genome data for further evaluation. As an illustration, a real data of maize was analyzed to find the loci responsible for the popping expansion volume.     

Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design

Triploid endosperm is of great economic importance owing to its nutritious quality. Mapping endosperm trait loci (ETL) can provide an efficient way to genetically improve grain quality. However, most triploid ETL mapping methods do not produce unbiased estimates of the two dominant effects of ETL. A random hybridization design is an alternative method that may be used to overcome this problem. However, epistasis has an important role in the dissection of genetic architecture for complex traits. In this study, therefore, an attempt was made to map epistatic ETL (eETL) under a triploid genetic model of endosperm traits in a random hybridization design. The endosperm trait means of random hybrid lines, together with known marker genotype information from their corresponding parental F(2) plants, were used to estimate, efficiently and without bias, the positions and all of the effects of eETL using a penalized maximum likelihood method. The method proposed in this article was verified by a series of Monte Carlo simulation experiments. Results from the simulated studies show that the proposed method provides accurate estimates of eETL parameters with a low false-positive rate and a relatively short running time. This new method enables us to map triploid eETL in the same way as diploid quantitative traits.     

Experimental designs and statistical methods for mapping quantitative trait loci underlying triploid endosperm traits without maternal genetic variation

Many endosperm traits are related to grain quality in cereal crops. Endosperm traits are mainly controlled by the endosperm genome but may be affected by the maternal genome. Studies have shown that maternal genotypic variation could greatly influence the estimation of the direct effects of quantitative trait loci (QTLs) underlying endosperm traits. In this paper, we propose methods of interval mapping of endosperm QTLs using seeds of F2 or BC1 (an equal mixture of F1 x P1 and F1 x P2 with F1 as the female parent) derived from a cross between 2 pure lines (P1 x P2). The most significant advantage of our experimental designs is that the maternal effects do not contribute to the genetic variation of endosperm traits and therefore the direct effects of endosperm QTLs can be estimated without the influence of maternal effects. In addition, the experimental designs can greatly reduce environmental variation because a few F1 plants grown in a small block of field will produce sufficient F2 or BC1 seeds for endosperm QTL analysis. Simulation studies show that the methods can efficiently detect endosperm QTLs and unbiasedly estimate their positions and effects. The BC1 design is better than the F2 design.     

Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model

The endosperm, a result of double fertilization in flowering plants, is a triploid tissue whose genetic composition is more complex than diploid tissue. We present a new maximum-likelihood-based statistical method for mapping quantitative trait loci (QTL) underlying endosperm traits in an autogamous plant. Genetic mapping of quantitative endosperm traits is qualitatively different from traits for other plant organs because the endosperm displays complicated trisomic inheritance and represents a younger generation than its mother plant. Our endosperm mapping method is based on two different experimental designs: (1) a one-stage design in which marker information is derived from the maternal genome and (2) a two-stage hierarchical design in which marker information is derived from both the maternal and offspring genomes (embryos). Under the one-stage design, the position and additive effect of a putative QTL can be well estimated, but the estimates of the dominant and epistatic effects are upward biased and imprecise. The two-stage hierarchical design, which extracts more genetic information from the material, typically improves the accuracy and precision of the dominant and epistatic effects for an endosperm trait. We discuss the effects on the estimation of QTL parameters of different sampling strategies under the two-stage hierarchical design. Our method will be broadly useful in mapping endosperm traits for many agriculturally important crop plants and also make it possible to study the genetic significance of double fertilization in the evolution of higher plants.     

基于F3种子的胚乳性状QTL区间定位

文章提出了包括胚乳效应和母体效应的胚乳性状QTL定位的统计方法,该方法的实验设计是分子标记基因型信息来自F2母体植株和F3种子胚(或植株),胚乳性状表型值来自F3单粒种子胚乳,称之为两步等级设计。同时,用计算机全面模拟以验证该模型的可行性,模拟结果表明,只要群体足够大,该模型能较有效地进行胚乳性状QTL定位并精确地估计出胚乳QTL的各种遗传效应和母体效应。     

More about quantitative trait locus mapping with diallel designs

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.     

Molecular mapping in tropical maize (Zea mays L.) using microsatellite markers. 2. Quantitative trait loci (QTL) for grain yield, plant height, ear height and grain moisture

A previous genetic map containing 117 microsatellite loci and 400 F(2) plants was used for quantitative trait loci (QTL) mapping in tropical maize. QTL were characterized in a population of 400 F(2:3) lines, derived from selfing the F(2) plants, and were evaluated with two replications in five environments. QTL determinations were made from the mean of these five environments. Grain yield (GY), plant height (PH), ear height (EH) and grain moisture (GM) were measured. Variance components for genotypes (G), environments (E) and GxE interaction were highly significant for all traits. Heritability was 0.69 for GY, 0.66 for PH, 0.67 for EH and 0.23 for GM. Using composite interval mapping (CIM), a total of 13 distinct QTLs were identified: four for GY, four for PH and five for EH. No QTL was detected for GM. The QTL explained 32.73 % of the phenotypic variance of GY, 24.76 % of PH and 20.91 % of EH. The 13 QTLs displayed mostly partial dominance or overdominance gene action and mapped to chromosomes 1, 2, 7, 8 and 9. Most QTL alleles conferring high values for the traits came from line L-14-4B. Mapping analysis identified genomic regions associated with two or more traits in a manner that was consistent with correlation among traits, supporting either pleiotropy or tight linkage among QTL. The low number of QTLs found, can be due to the great variation that exists among tropical environments.     

On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.     

Inheritance of the number and thickness of cell layers in barley aleurone tissue (<Emphasis Type="Italic">Hordeum vulgare </Emphasis>L.): an approach using F2–F3 progeny

The aleurone tissue of cereal grains, nutritionally rich in minerals and vitamins, is an important target for the improvement of cereals. Inheritance of the thickness and the number of cell layers in barley aleurone was studied on the F2–F3 progeny of an Erhard Frederichen × Criolla Negra cross in which the parental lines have three or two aleurone layers, respectively. F3 grain was sampled from each F2 plant and 96.8% of the entire F3 grain population was classified as being either the 2- or 3-layer type. Using microsatellite, single nucleotide polymorphism (SNP) and morphological markers on 190 F2 plants, a linkage map was built. Three quantitative trait loci (QTLs) affecting aleurone traits were revealed on chromosome 5H (max. LOD = 5.83) and chromosome 7H (max. LOD = 4.45) by interval mapping, and on chromosome 2H by marker analysis with an unmapped marker. These QTLs were consistent with genetic sub-models involving either 2-cell type dominance for 7H and 2H, or putative partial dominance for 5H where 2-cell-layer dominance and additivity gave similar LODs. The number of aleurone cell layers and aleurone thickness were strongly correlated and QTL results for these traits were alike. An SNP marker of sal1, an orthologue of the maize multilayer aleurone gene was mapped to the 7HL chromosome arm. However, the 7H QTL did not co-locate with the barley sal1 SNP, suggesting that an additional gene is involved in determining aleurone traits. These new mapping data allow comparisons to be made with related studies.     

基于BC_1F_（1：2）种子的胚乳QTL区间定位

提出了基于分子标记基因型信息来自BC_1F_1母体植株,胚乳性状表型值来自BC_1F_（1：2）单粒种子胚乳的试验设计的胚乳QTL定位的区间作图方法.同时,用计算机全面模拟以验证该模型的可行性,模拟结果表明,只要群体足够大,该模型能有效地进行胚乳性状QTL定位并能估计出胚乳QTL的各种遗传效应和母体效应.     

Mapping of epistatic quantitative trait loci in four-way crosses

Four-way crosses (4WC) involving four different inbred lines often appear in plant and animal commercial breeding programs. Direct mapping of quantitative trait loci (QTL) in these commercial populations is both economical and practical. However, the existing statistical methods for mapping QTL in a 4WC population are built on the single-QTL genetic model. This simple genetic model fails to take into account QTL interactions, which play an important role in the genetic architecture of complex traits. In this paper, therefore, we attempted to develop a statistical method to detect epistatic QTL in 4WC population. Conditional probabilities of QTL genotypes, computed by the multi-point single locus method, were used to sample the genotypes of all putative QTL in the entire genome. The sampled genotypes were used to construct the design matrix for QTL effects. All QTL effects, including main and epistatic effects, were simultaneously estimated by the penalized maximum likelihood method. The proposed method was confirmed by a series of Monte Carlo simulation studies and real data analysis of cotton. The new method will provide novel tools for the genetic dissection of complex traits, construction of QTL networks, and analysis of heterosis.     

Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.     

Mixed linear model approach for mapping quantitative trait loci underlying crop seed traits

The crop seed is a complex organ that may be composed of the diploid embryo, the triploid endosperm and the diploid maternal tissues. According to the genetic features of seed characters, two genetic models for mapping quantitative trait loci (QTLs) of crop seed traits are proposed, with inclusion of maternal effects, embryo or endosperm effects of QTL, environmental effects and QTL-by-environment (QE) interactions. The mapping population can be generated either from double back-cross of immortalized F₂ (IF₂) to the two parents, from random-cross of IF₂ or from selfing of IF₂ population. Candidate marker intervals potentially harboring QTLs are first selected through one-dimensional scanning across the whole genome. The selected candidate marker intervals are then included in the model as cofactors to control background genetic effects on the putative QTL(s). Finally, a QTL full model is constructed and model selection is conducted to eliminate false positive QTLs. The genetic main effects of QTLs, QE interaction effects and the corresponding P-values are computed by Markov chain Monte Carlo algorithm for Gaussian mixed linear model via Gibbs sampling. Monte Carlo simulations were performed to investigate the reliability and efficiency of the proposed method. The simulation results showed that the proposed method had higher power to accurately detect simulated QTLs and properly estimated effect of these QTLs. To demonstrate the usefulness, the proposed method was used to identify the QTLs underlying fiber percentage in an upland cotton IF₂ population. A computer software, QTLNetwork-Seed, was developed for QTL analysis of seed traits.     

Modelling epistatic effects of embryo and endosperm QTL on seed quality traits

Coordinated expression of embryo and endosperm tissues is required for proper seed development. The coordination among these two tissues is controlled by the interaction between multiple genes expressed in the embryo and endosperm genomes. In this article, we present a statistical model for testing whether quantitative trait loci (QTL) active in different genomes, diploid embryo and triploid endosperm, epistatically affect a trait expressed on the endosperm tissue. The maximum likelihood approach, implemented with the EM algorithm, was derived to provide the maximum likelihood estimates of the locations of embryo- and endosperm-specific QTL and their main effects and epistatic effects. This model was used in a real example for rice in which two QTL, one from the embryo genome and the other from the endosperm genome, exert a significant interaction effect on gel consistency on the endosperm. Our model has successfully detected Waxy, a candidate gene in the embryo genome known to regulate one of the major steps of amylose biosynthesis in the endosperm. This model will have great implications for agricultural and evolutionary genetic research.     

QTL mapping of complex binary traits in an advanced intercross line

An advanced intercross line (AIL) is an easier and more cost-effective approach compared to recombinant inbred lines for fine mapping of quantitative trait loci (QTL) identified by F(2) designs. In an AIL, a complex binary trait can be mapped through analysis of either continuously distributed proxy traits for the liability of the binary trait or the liability itself, the latter presenting the greater statistical challenge. In another work, we successfully applied both approaches in an AIL to fine map previously identified QTL underlying anatomical parameters of the cardiac inter-atrial septum including patent foramen ovale. Here, we describe the statistical methods that we used to analyse complex binary traits in our AIL design. This is achieved using a likelihood-based method, with the expectation-maximisation algorithm allowing use of standard logistic regression methods for model fitting.     

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.     

Varying coefficient models for mapping quantitative trait loci using recombinant inbred intercrosses

There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F(2) individuals but with up to eight alleles segregating at any one locus. In contrast to F(2) mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.     

QTL mapping and introgression of yield-related traits from <Emphasis Type="Italic">Oryza glumaepatula</Emphasis> to cultivated rice (<Emphasis Type="Italic">Oryza sativa</Emphasis>) using microsatellite markers

Rice ( Oryza sativa) cultivar development currently faces the task of overcoming yield plateaus, which is difficult due to the narrow genetic base of breeding programs. Oryza glumaepatula is a diploid wild relative of cultivated rice, native to Central and South America, and is therefore a potential source of alleles of agronomic importance to rice breeding programs. We studied 11 agronomic traits in BC(2)F(2) families of the interspecific cross Oryza sativa x O. glumaepatula. Transgressive lines which are almost isogenic to the elite recurrent O. sativa parent were identified for most of these traits. Quantitative trait locus (QTL) analysis was performed by single-point and interval mapping using a molecular map based on 157 microsatellite and STS markers. Marker regions accounting for 14.5 to 72.9% of a phenotypic variation trait were identified in 9 of the 12 rice chromosomes. Positive QTL effects from O. glumaepatula were observed in chromosomal regions associated with tillering and panicle-number traits.