Mapping genome-genome epistasis: a high-dimensional model

MOTIVATION: The proper development of any organ or tissue requires the coordinated expression of its underlying genes that can be located on different genomes present in an organism. For instance, each step in the development of seed for a higher plant is the consequence of gene interactions from the maternal, embryo and endosperm genomes. RESULTS: We present a multivariate statistical model for mapping quantitative trait loci (QTL) by incorporating two important aspects of seed development in plants-QTL interactions derived from different genomes, the maternal, embryo and endosperm, and genetic correlations among phenotypic traits expressed in different genome-specific tissues. This model, which has a high dimensionality, is constructed within the maximum-likelihood context based on a finite mixture model. The implementation of the expectation-maximization algorithm allows for the efficient estimation of QTL positions, their action and interaction effects and pleiotropic effects. The application of this high-dimensional model to a real rice dataset has validated its usefulness.Conclusions: Our model was derived for self-pollinated plants, but it can be extended to cross-pollinated plants and to animals. With the burgeoning of genetic and genomic data, this high-dimensional model will have many implications for agricultural and evolutionary genetic research. AVAILABILITY: A package of software will be provided from the corresponding author upon request.     

A statistical model for estimating maternal-zygotic interactions and parent-of-origin effects of QTLs for seed development

Proper development of a seed requires coordinated exchanges of signals among the three components that develop side by side in the seed. One of these is the maternal integument that encloses the other two zygotic components, i.e., the diploid embryo and its nurturing annex, the triploid endosperm. Although the formation of the embryo and endosperm contains the contributions of both maternal and paternal parents, maternally and paternally derived alleles may be expressed differently, leading to a so-called parent-of-origin or imprinting effect. Currently, the nature of how genes from the maternal and zygotic genomes interact to affect seed development remains largely unknown. Here, we present a novel statistical model for estimating the main and interaction effects of quantitative trait loci (QTLs) that are derived from different genomes and further testing the imprinting effects of these QTLs on seed development. The experimental design used is based on reciprocal backcrosses toward both parents, so that the inheritance of parent-specific alleles could be traced. The computing model and algorithm were implemented with the maximum likelihood approach. The new strategy presented was applied to study the mode of inheritance for QTLs that control endoreduplication traits in maize endosperm. Monte Carlo simulation studies were performed to investigate the statistical properties of the new model with the data simulated under different imprinting degrees. The false positive rate of imprinting QTL discovery by the model was examined by analyzing the simulated data that contain no imprinting QTL. The reciprocal design and a series of analytical and testing strategies proposed provide a standard procedure for genomic mapping of QTLs involved in the genetic control of complex seed development traits in flowering plants.     

Dissecting Genetic Architecture Underlying Seed Traits in Multiple Environments

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

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.     

Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.     

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.     

Mapping of quantitative trait loci for oil content in cottonseed kernel

Oil content in cottonseed is a major quality trait which when improved through breeding could enhance the competitiveness of cottonseed oil among other vegetable oils. Cottonseed oil content is a quantitative trait controlled by genes in the tetraploid embryo and tetraploid maternal plant genomes, and the knowledge of quantitative trait loci (QTLs) and the genetic effects related to oil content in both genomes could facilitate the improvement in its quality and quantity. However, till date, QTL mapping and genetic analysis related to this trait in cotton have only been conducted in the tetraploid embryo genome. In the current experiment, an IF₂ population of cottonseed kernels from the random crossing of 188 intraspecific recombinant inbred lines which were derived from the hybrid of two parents, HS46 and MARCABUCAG8US-1-88, were used to simultaneously locate QTLs for oil content in the embryo and maternal plant genomes. The four QTLs found to be associated with oil content in cottonseed were: qOC-18-1 on chromosome 18; qOC-LG-11 on linkage group 11; qOC-18-2 on chromosome 18; and qOC-22 on chromosome 22. At a high selection threshold of 0.05, there was strong evidence linking the QTLs above the oil content in cottonseed. Embryo additive and dominant effects from the tetraploid embryo genome, as well as maternal additive effects from the tetraploid maternal plant genome were found to be significant contributors to genetic variation in cottonseed oil content.     

A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters

Embryos of crop seeds are one of the major sources of the plant protein and lipid for human nutrition. The genetic expression for embryo-specific characters in crop seeds can be controlled exclusively by the embryo or the maternal genotypes and sometimes by both simultaneously. However, current methods for mapping quantitative trait loci (QTLs) underlying characters of maternal plants have not been effective in dealing with the QTL analysis of embryo characters. On the basis of the expression feature of embryo, a statistical method was proposed for the identification of expression mode and mapping of QTL controlling embryo traits. The maximum likelihood method implemented via the expectation maximization algorithm was used to estimate parameters of a putative embryo-specific QTL. The QTL expression mode was identified by the likelihood ratio test statistic. Statistical power and other properties of the proposed method were investigated under a variety of scenarios through simulation studies. The results showed that the mapping method neglecting the effects of embryo genotype or maternal effects could neither identify the expression mode of QTL nor estimate its genetic effects accurately, whereas the proposed method could effectively map the embryo-specific QTL of various expression modes.     

Correcting for bias in estimation of quantitative trait loci effects

Estimates of quantitative trait loci (QTL) effects derived from complete genome scans are biased, if no assumptions are made about the distribution of QTL effects. Bias should be reduced if estimates are derived by maximum likelihood, with the QTL effects sampled from a known distribution. The parameters of the distributions of QTL effects for nine economic traits in dairy cattle were estimated from a daughter design analysis of the Israeli Holstein population including 490 marker-by-sire contrasts. A separate gamma distribution was derived for each trait. Estimates for both the α and β parameters and their SE decreased as a function of heritability. The maximum likelihood estimates derived for the individual QTL effects using the gamma distributions for each trait were regressed relative to the least squares estimates, but the regression factor decreased as a function of the least squares estimate. On simulated data, the mean of least squares estimates for effects with nominal 1% significance was more than twice the simulated values, while the mean of the maximum likelihood estimates was slightly lower than the mean of the simulated values. The coefficient of determination for the maximum likelihood estimates was five-fold the corresponding value for the least squares estimates.     

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.     

Identification of quantitative trait loci that affect endoreduplication in maize endosperm

Endoreduplication in maize endosperm precedes the onset of starch and storage protein synthesis, and it is generally thought to influence grain filling. We created four backcross populations by reciprocally crossing the F₁ progeny of a cross between Sg18 and Mo17 to the parental inbreds, which differ in endoreduplication by two parameters—mean ploidy and percentage of endoreduplicated nuclei. This four-backcross design allowed us to estimate and test the additive and dominant genetic effects of quantitative trait loci (QTLs) affecting endoreduplication. An analysis of endosperm from the four backcross populations at 16 days after pollination using a modified triploid mapping approach identified three endosperm QTLs influencing mean ploidy and two endosperm QTLs affecting the percentage of endoreduplicated nuclei. Some of these QTLs may manifest their effects on endoreduplication via expression in the embryo. The QTLs detected display strong dominance or over-dominance and interacted epistatically with an embryo-expressed QTL. This helps to explain the genetic basis for transgressive segregation in the backcross progeny. Although the favorable alleles that increase mean ploidy and percentage of endoreduplicated nuclei can be contributed by both parents, the Mo17-derived alleles for endoreduplication were often dominant or over-dominant to the Sg18-derived allele. One QTL on chromosome 7 that may be expressed in both the embryo and endosperm exerted a pleiotropic effect on two different parameters of endoreduplication. The results from this study shed light on the regulation of endoreduplication in maize endosperm and provide a marker-assisted selection strategy for potentially improving grain yield. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. C. M. Coelho and S. Wu contributed equally to this work and should be considered as first authors.     

A genome-wide survey of imprinted genes in rice seeds reveals imprinting primarily occurs in the endosperm

Genomic imprinting causes the expression of an allele depending on its parental origin. In plants, most imprinted genes have been identified in Arabidopsis endosperm, a transient structure consumed by the embryo during seed formation. We identified imprinted genes in rice seed where both the endosperm and embryo are present at seed maturity. RNA was extracted from embryos and endosperm of seeds obtained from reciprocal crosses between two subspecies Nipponbare (Japonica rice) and 93-11 (Indica rice). Sequenced reads from cDNA libraries were aligned to their respective parental genomes using single-nucleotide polymorphisms (SNPs). Reads across SNPs enabled derivation of parental expression bias ratios. A continuum of parental expression bias states was observed. Statistical analyses indicated 262 candidate imprinted loci in the endosperm and three in the embryo (168 genic and 97 non-genic). Fifty-six of the 67 loci investigated were confirmed to be imprinted in the seed. Imprinted loci are not clustered in the rice genome as found in mammals. All of these imprinted loci were expressed in the endosperm, and one of these was also imprinted in the embryo, confirming that in both rice and Arabidopsis imprinted expression is primarily confined to the endosperm. Some rice imprinted genes were also expressed in vegetative tissues, indicating that they have additional roles in plant growth. Comparison of candidate imprinted genes found in rice with imprinted candidate loci obtained from genome-wide surveys of imprinted genes in Arabidopsis to date shows a low degree of conservation, suggesting that imprinting has evolved independently in eudicots and monocots.     

MHC polymorphism and disease resistance to vibrio anguillarum in 8 families of half-smooth tongue sole (Cynoglossus semilaevis)

Background

Most quantitative traits are controlled by multiple quantitative trait loci (QTL). The contribution of each locus may be negligible but the collective contribution of all loci is usually significant. Genome selection that uses markers of the entire genome to predict the genomic values of individual plants or animals can be more efficient than selection on phenotypic values and pedigree information alone for genetic improvement. When a quantitative trait is contributed by epistatic effects, using all markers (main effects) and marker pairs (epistatic effects) to predict the genomic values of plants can achieve the maximum efficiency for genetic improvement.

Results

In this study, we created 126 recombinant inbred lines of soybean and genotyped 80 makers across the genome. We applied the genome selection technique to predict the genomic value of somatic embryo number (a quantitative trait) for each line. Cross validation analysis showed that the squared correlation coefficient between the observed and predicted embryo numbers was 0.33 when only main (additive) effects were used for prediction. When the interaction (epistatic) effects were also included in the model, the squared correlation coefficient reached 0.78.

Conclusions

This study provided an excellent example for the application of genome selection to plant breeding.     

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

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

Mapping genome-wide QTL of ratio traits with Bayesian shrinkage analysis for its component traits

The ratio trait is defined as a ratio of two regular quantitative traits with normal distribution, which is distinguished from regular quantitative traits in the genetic analysis because it does not follow the normal distribution. On the basis of maximum likelihood method that uses a special linear combination of the two component traits, we develop a Bayesian mapping strategy for ratio traits, which firstly analyzes the two component traits by Bayesian shrinkage method, and then generates a new posterior sample of genetic effects for a ratio trait from ones of population means and genetic effects for the two component traits, finally, infers QTL for the ratio trait via post MCMC analysis for the new posterior sample. A simulation study demonstrates that the new method has higher detecting power of the QTL than maximum likelihood method. An application is illustrated to map genome-wide QTL for relative growth rate of height on soybean.     

Statistical model for characterizing epistatic control of triploid endosperm triggered by maternal and offspring QTLs

To study the effects of maternal and endosperm quantitative trait locus (QTL) interaction on endosperm development, we derive a two-stage hierarchical statistical model within the maximum-likelihood context, implemented with an expectation-maximization algorithm. A model incorporating both maternal and offspring marker information can improve the accuracy and precision of genetic mapping. Extensive simulations under different sampling strategies, heritability levels and gene action modes were performed to investigate the statistical properties of the model. The QTL location and parameters are better estimated when two QTLs are located at different intervals than when they are located at the same interval. Also, the additive effect of the offspring QTLs is better estimated than the additive effect of the maternal QTLs. The implications of our model for agricultural and evolutionary genetic research are discussed.     

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。     

Mapping quantitative trait Loci interactions from the maternal and offspring genomes

The expression of most developmental or behavioral traits involves complex interactions between quantitative trait loci (QTL) from the maternal and offspring genomes. The maternal-offspring interactions play a pivotal role in shaping the direction and rate of evolution in terms of their substantial contribution to quantitative genetic (co)variation. To study the genetics and evolution of maternal-offspring interactions, a unifying statistical framework that embraces both the direct and indirect genetic effects of maternal and offspring QTL on any complex trait is developed. This model is derived for a simple backcross design within the maximum-likelihood context, implemented with the EM algorithm. Results from extensive simulations suggest that this model can provide reasonable estimation of additive and dominant effects of the QTL at different generations and their interaction effects derived from the maternal and offspring genomes. Although our model is framed to characterize the actions and interactions of maternal and offspring QTL affecting offspring traits, the idea can be readily extended to decipher the genetic machinery of maternal traits, such as maternal care. Our model provides a powerful means for studying the evolutionary significance of indirect genetic effects in any sexually reproductive organisms.     

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.