Parametric proportional hazards model for mapping genomic imprinting of survival traits

A number of imprinted genes have been observed in plants, animals and humans. They not only control growth and developmental traits, but may also be responsible for survival traits. Based on the Cox proportional hazards (PH) model, we constructed a general parametric model for dissecting genomic imprinting, in which a baseline hazard function is selectable for fitting the effects of imprinted quantitative trait loci (iQTL) genotypes on the survival curve. The expectation–maximisation (EM) algorithm is derived for solving the maximum likelihood estimates of iQTL parameters. The imprinting patterns of the detected iQTL are statistically tested under a series of null hypotheses. The Bayesian information criterion (BIC) model selection criterion is employed to choose an optimal baseline hazard function with maximum likelihood and parsimonious parameterisation. We applied the proposed approach to analyse the published data in an F₂ population of mice and concluded that, among five commonly used survival distributions, the log-logistic distribution is the optimal baseline hazard function for the survival time of hyperoxic acute lung injury (HALI). Under this optimal model, five QTL were detected, among which four are imprinted in different imprinting patterns.     

A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

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.     

Statistical optimization of parametric accelerated failure time model for mapping survival trait loci

Most existing statistical methods for mapping quantitative trait loci (QTL) are not suitable for analyzing survival traits with a skewed distribution and censoring mechanism. As a result, researchers incorporate parametric and semi-parametric models of survival analysis into the framework of the interval mapping for QTL controlling survival traits. In survival analysis, accelerated failure time (AFT) model is considered as a de facto standard and fundamental model for data analysis. Based on AFT model, we propose a parametric approach for mapping survival traits using the EM algorithm to obtain the maximum likelihood estimates of the parameters. Also, with Bayesian information criterion (BIC) as a model selection criterion, an optimal mapping model is constructed by choosing specific error distributions with maximum likelihood and parsimonious parameters. Two real datasets were analyzed by our proposed method for illustration. The results show that among the five commonly used survival distributions, Weibull distribution is the optimal survival function for mapping of heading time in rice, while Log-logistic distribution is the optimal one for hyperoxic acute lung injury.     

A random model for mapping imprinted quantitative trait loci in a structured pedigree: an implication for mapping canine hip dysplasia

Genetic imprinting may have played a more notable role in shaping embryonic development of plants, animals, and humans than previously appreciated. Quantitative trait loci that are imprinted (iQTL) exert monoallelic effects, depending on the parent of origin, which is an exception to the laws of Mendelian genetics. In this article, we present a modified random effect-based mapping model to use in a genome-wide scan for the distribution of iQTL that contribute to genetic variance for a complex trait in a structured pedigree. This model, implemented with the maximum likelihood method, capitalizes on a network of relatedness for maternally and paternally derived alleles through identical-by-descent sharing, thus allowing for the discrimination of the genetic variances due to alleles derived from maternal and paternal parents. The model was employed to map iQTL responsible for canine hip dysplasia in a multihierarchical canine pedigree, founded with seven greyhounds and six Labrador retrievers. Of eight significant QTL detected, three, located on CFA1, CFA8, and CF28, were found to trigger significant parent-of-origin effects on the age of femoral capital ossification measured at the left and right hips of a canine. The detected iQTL provide important candidate regions for fine-mapping of imprinted genes and for studying their structure and function in the control of complex traits.     

A statistical model for dissecting genomic imprinting through genetic mapping

As a result of nonequivalent genetic contribution of maternal and paternal genomes to offsprings, genomic imprinting or called parent-of-origin effect, has been broadly identified in plants, animals and humans. Its role in shaping organism’s development has been unanimously recognized. However, statistical methods for identifying imprinted quantitative trait loci (iQTL) and estimating the imprinted effect have not been well developed. In this article, we propose an efficient statistical procedure for genomewide estimating and testing the effects of significant iQTL underlying the quantitative variation of interested traits. The developed model can be applied to two different genetic cross designs, backcross and F₂ families derived from inbred lines. The proposed procedure is built within the maximum likelihood framework and implemented with the EM algorithm. Extensive simulation studies show that the proposed model is well performed in a variety of situations. To demonstrate the usefulness of the proposed approach, we apply the model to a published data in an F₂ family derived from LG/S and SM/S mouse stains. Two partially maternal imprinting iQTL are identified which regulate the growth of body weight. Our approach provides a testable framework for identifying and estimating iQTL involved in the genetic control of complex traits.     

Bayesian mapping of genome-wide epistatic imprinted loci for quantitative traits

Genomic imprinting, an epigenetic phenomenon of parent-of-origin-specific gene expression, has been widely observed in plants, animals, and humans. To detect imprinting genes influencing quantitative traits, the least squares and maximum likelihood approaches for fitting a single quantitative trait locus (QTL) and Bayesian methods for simultaneously modeling multiple QTL have been adopted, respectively, in various studies. However, most of these studies have only estimated imprinting main effects and thus ignored imprinting epistatic effects. In the presence of extremely complex genomic imprinting architectures, we introduce a Bayesian model selection method to analyze the multiple interacting imprinted QTL (iQTL) model. This approach will greatly enhance the computational efficiency through setting the upper bound of the number of QTLs and performing selective sampling for QTL parameters. The imprinting types of detected main-effect QTLs can be estimated from the Bayes factor statistic formulated by the posterior probabilities for the genetic effects being compared. The performance of the proposed method is demonstrated by several simulation experiments. Moreover, this method is applied to dissect the imprinting genetic architecture for body weight in mouse and fruit weight in tomato. Matlab code for implementing this approach will be available from the authors upon request.     

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.     

Model for mapping imprinted quantitative trait loci in an inbred F2 design

The role of imprinting in shaping development has been ubiquitously observed in plants, animals, and humans. However, a statistical method that can detect and estimate the effects of imprinted quantitative trait loci (iQTL) over the genome has not been extensively developed. In this article, we propose a maximum likelihood approach for testing and estimating the imprinted effects of iQTL that contribute to variation in a quantitative trait. This approach, implemented with the EM algorithm, allows for a genome-wide scan for the existence of iQTL. This approach was used to reanalyze published data in an F(2) family derived from the LG/S and SM/S mouse strains. Several iQTL that regulate the growth of body weight by expressing paternally inherited alleles were identified. Our approach provides a standard procedure for testing the statistical significance of iQTL involved in the genetic control of complex traits.     

A Model for Transgenerational Imprinting Variation in Complex Traits

Despite the fact that genetic imprinting, i.e., differential expression of the same allele due to its different parental origins, plays a pivotal role in controlling complex traits or diseases, the origin, action and transmission mode of imprinted genes have still remained largely unexplored. We present a new strategy for studying these properties of genetic imprinting with a two-stage reciprocal F mating design, initiated with two contrasting inbred lines. This strategy maps quantitative trait loci that are imprinted (i.e., iQTLs) based on their segregation and transmission across different generations. By incorporating the allelic configuration of an iQTL genotype into a mixture model framework, this strategy provides a path to trace the parental origin of alleles from previous generations. The imprinting effects of iQTLs and their interactions with other traditionally defined genetic effects, expressed in different generations, are estimated and tested by implementing the EM algorithm. The strategy was used to map iQTLs responsible for survival time with four reciprocal F populations and test whether and how the detected iQTLs inherit their imprinting effects into the next generation. The new strategy will provide a tool for quantifying the role of imprinting effects in the creation and maintenance of phenotypic diversity and elucidating a comprehensive picture of the genetic architecture of complex traits and diseases.     

家畜抗性等级性状的QTL定位方法

在广义线性模型的框架内模拟研究了家畜抗性等级性状的QTL定位方法,QTL参数的估计采用最大似然方法,比较了阈模型方法与一般线性方法的QTL定位效率,并对影响等级性状QTL定位效率的主要因素（QTL效应、性状的遗传力）进行了模拟研究,实验设计为多个家系的女儿设计,资源群体大小为500头。研究结果表明：在QTL位置参数估计及检验功效方面,阈模型方法具有一定的优势,对抗性等级性状QTL定位的功效也高于线性方法。另外,性状遗传力和QTL效应的大小对QTL定位的准确度也有直接的影响,随着性状遗传力QTL效应的     

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.     

A note on QTL detecting for censored traits

Most existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and that it is fully observed. However, some phenotypes have skewed distributions and may be censored. This note proposes a simple and efficient approach to QTL detecting for censored traits with the Cox PH model without estimating the baseline hazard function which is "nuisance".     

Genomic imprinting and genetic effects on muscle traits in mice

ABSTRACT: BACKGROUND: Genomic imprinting refers to parent-of-origin dependent gene expression caused by differential DNA methylation of the paternally and maternally derived alleles. Imprinting is increasingly recognized as an important source of variation in complex traits, however, its role in explaining variation in muscle and physiological traits, especially those of commercial value, is largely unknown compared with genetic effects. RESULTS: We investigated both genetic and genomic imprinting effects on key muscle traits in mice from the Berlin Muscle Mouse population, a key model system to study muscle traits. Using a genome scan, we first identified loci with either imprinting or genetic effects on phenotypic variation. Next, we established the proportion of phenotypic variation explained by additive, dominance and imprinted QTL and characterized the patterns of effects. In total, we identified nine QTL, two of which show large imprinting effects on glycogen content and potential, and body weight. Surprisingly, all imprinting patterns were of the bipolar type, in which the two heterozygotes are different from each other but the homozygotes are not. Most QTL had pleiotropic effects and explained up to 40% of phenotypic variance, with individual imprinted loci accounting for 4-5% of variation alone. CONCLUSION: Surprisingly, variation in glycogen content and potential was only modulated by imprinting effects. Further, in contrast to general assumptions, our results show that genomic imprinting can impact physiological traits measured at adult stages and that the expression does not have to follow the patterns of paternal or maternal expression commonly ascribed to imprinting effects.     

Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model

Interval mapping using normal mixture models has been an important tool for analyzing quantitative traits in experimental organisms. When the primary phenotype is time-to-event, it is natural to use survival models such as Cox's proportional hazards model instead of normal mixtures to model the phenotype distribution. An extra challenge for modeling time-to-event data is that the underlying population may consist of susceptible and nonsusceptible subjects. In this article, we propose a semiparametric proportional hazards mixture cure model which allows missing covariates. We discuss applications to quantitative trait loci (QTL) mapping when the primary trait is time-to-event from a population of mixed susceptibility. This model can be used to characterize QTL effects on both susceptibility and time-to-event distribution, and to estimate QTL location. The model can naturally incorporate covariate effects of other risk factors. Maximum likelihood estimates for the parameters in the model as well as their corresponding variance estimates can be obtained numerically using an EM-type algorithm. The proposed methods are assessed by simulations under practical settings and illustrated using a real data set containing survival times of mice after infection with Listeria monocytogenes. An extension to multiple intervals is also discussed.     

Genome-wide analysis reveals a complex pattern of genomic imprinting in mice

Parent-of-origin–dependent gene expression resulting from genomic imprinting plays an important role in modulating complex traits ranging from developmental processes to cognitive abilities and associated disorders. However, while gene-targeting techniques have allowed for the identification of imprinted loci, very little is known about the contribution of imprinting to quantitative variation in complex traits. Most studies, furthermore, assume a simple pattern of imprinting, resulting in either paternal or maternal gene expression; yet, more complex patterns of effects also exist. As a result, the distribution and number of different imprinting patterns across the genome remain largely unexplored. We address these unresolved issues using a genome-wide scan for imprinted quantitative trait loci (iQTL) affecting body weight and growth in mice using a novel three-generation design. We identified ten iQTL that display much more complex and diverse effect patterns than previously assumed, including four loci with effects similar to the callipyge mutation found in sheep. Three loci display a new phenotypic pattern that we refer to as bipolar dominance, where the two heterozygotes are different from each other while the two homozygotes are identical to each other. Our study furthermore detected a paternally expressed iQTL on Chromosome 7 in a region containing a known imprinting cluster with many paternally expressed genes. Surprisingly, the effects of the iQTL were mostly restricted to traits expressed after weaning. Our results imply that the quantitative effects of an imprinted allele at a locus depend both on its parent of origin and the allele it is paired with. Our findings also show that the imprinting pattern of a locus can be variable over ontogenetic time and, in contrast to current views, may often be stronger at later stages in life.     

Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Maternal effects as the cause of parent-of-origin effects that mimic genomic imprinting

Epigenetic effects are increasingly recognized as an important source of variation in complex traits and have emerged as the focus of a rapidly expanding area of research. Principle among these effects is genomic imprinting, which has generally been examined in analyses of complex traits by testing for parent-of-origin-dependent effects of alleles. However, in most of these analyses maternal effects are confounded with genomic imprinting because they can produce the same patterns of phenotypic variation expected for various forms of imprinting. Distinguishing between the two is critical for genetic and evolutionary studies because they have entirely different patterns of gene expression and evolutionary dynamics. Using a simple single-locus model, we show that maternal genetic effects can result in patterns that mimic those expected under genomic imprinting. We further demonstrate how maternal effects and imprinting effects can be distinguished using genomic data from parents and offspring. The model results are applied to a genome scan for quantitative trait loci (QTL) affecting growth- and weight-related traits in mice to illustrate how maternal effects can mimic imprinting. This genome scan revealed five separate maternal-effect loci that caused a diversity of patterns mimicking those expected under various modes of genomic imprinting. These results demonstrate that the appearance of parent-of-origin-dependent effects (POEs) of alleles at a locus cannot be taken as direct evidence that the locus is imprinted. Moreover, they show that, in gene mapping studies, genetic data from both parents and offspring are required to successfully differentiate between imprinting and maternal effects as the cause of apparent parent-of-origin effects of alleles.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.     

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.