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.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behavior of a system, differential equations have proven to be powerful for modeling and unraveling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge-Kutta fourth order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

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 statistical model for the identification of genes governing the incidence of cancer with age

The cancer incidence increases with age. This epidemiological pattern of cancer incidence can be attributed to molecular and cellular processes of individual subjects. Also, the incidence of cancer with ages can be controlled by genes. Here we present a dynamic statistical model for explaining the epidemiological pattern of cancer incidence based on individual genes that regulate cancer formation and progression. We incorporate the mathematical equations of age-specific cancer incidence into a framework for functional mapping aimed at identifying quantitative trait loci (QTLs) for dynamic changes of a complex trait. The mathematical parameters that specify differences in the curve of cancer incidence among QTL genotypes are estimated within the context of maximum likelihood. The model provides testable quantitative hypotheses about the initiation and duration of genetic expression for QTLs involved in cancer progression. Computer simulation was used to examine the statistical behavior of the model. The model can be used as a tool for explaining the epidemiological pattern of cancer incidence.     

A differential equation model for functional mapping of a virus-cell dynamic system

The dynamic pattern of viral load in a patient’s body critically depends on the host’s genes. For this reason, the identification of those genes responsible for virus dynamics, although difficult, is of fundamental importance to design an optimal drug therapy based on patients’ genetic makeup. Here, we present a differential equation (DE) model for characterizing specific genes or quantitative trait loci (QTLs) that affect viral load trajectories within the framework of a dynamic system. The model is formulated with the principle of functional mapping, originally derived to map dynamic QTLs, and implemented with a Markov chain process. The DE-integrated model enhances the mathematical robustness of functional mapping, its quantitative prediction about the temporal pattern of genetic expression, and therefore its practical utilization and effectiveness for gene discovery in clinical settings. The model was used to analyze simulated data for viral dynamics, aimed to investigate its statistical properties and validate its usefulness. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the molecular genetic mechanism of virus dynamics and disease progression.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

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.     

QTL editing confers opposing yield performance in different rice varieties

Grain yield is one of the most important and complex trait for genetic improvement in crops; it is known to be controlled by a number of genes known as quantitative trait loci(QTLs). In the past decade, many yield-contributing QTLs have been identified in crops.However, it remains unclear whether those QTLs confer the same yield performance in different genetic backgrounds. Here, we performed CRISPR/Cas_9-mediated QTL editing in five widely-cultivated rice varieties and revealed that the same QTL can have diverse, even opposing, effects on grain yield in different genetic backgrounds.     

Deciphering genetic basis of developmental and agronomic traits by integrating high-throughput optical phenotyping and genome-wide association studies in wheat

Dissecting the genetic basis of complex traits such as dynamic growth and yield potential is a major challenge in crops. Monitoring the growth throughout growing season in a large wheat population to uncover the temporal genetic controls for plant growth and yield-related traits has so far not been explored. In this study, a diverse wheat panel composed of 288 lines was monitored by a non-invasive and high-throughput phenotyping platform to collect growth traits from seedling to grain filling stage and their relationship with yield-related traits was further explored. Whole genome re-sequencing of the panel provided 12.64 million markers for a high-resolution genome-wide association analysis using 190 image-based traits and 17 agronomic traits. A total of 8327 marker-trait associations were detected and clustered into 1605 quantitative trait loci (QTLs) including a number of known genes or QTLs. We identified 277 pleiotropic QTLs controlling multiple traits at different growth stages which revealed temporal dynamics of QTLs action on plant development and yield production in wheat. A candidate gene related to plant growth that was detected by image traits was further validated. Particularly, our study demonstrated that the yield-related traits are largely predictable using models developed based on i-traits and provide possibility for high-throughput early selection, thus to accelerate breeding process. Our study explored the genetic architecture of growth and yield-related traits by combining high-throughput phenotyping and genotyping, which further unravelled the complex and stage-specific contributions of genetic loci to optimize growth and yield in wheat.     

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.     

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     

The genetic architecture of quantitative traits: lessons from Drosophila

Understanding the genetic architecture of quantitative traits begins with identifying the genes regulating these traits, mapping the subset of genetically varying quantitative trait loci (QTLs) in natural populations, and pinpointing the molecular polymorphisms defining QTL alleles. Studies in Drosophila have revealed large numbers of pleiotropic genes that interact epistatically to regulate quantitative traits, and large numbers of QTLs with sex-, environment- and genotype-specific effects. Multiple molecular polymorphisms in regulatory regions of candidate genes are often associated with variation for complex traits. These observations offer valuable lessons for understanding the genetic basis of variation for complex traits in other organisms, including humans.     

Quantitative trait nucleotide analysis using Bayesian model selection

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.     

Functional mapping of reaction norms to multiple environmental signals

Whether there are different genes involved in response to different environmental signals and how these genes interact to determine the final expression of the trait are of fundamental importance in agricultural and biological research. We present a statistical framework for mapping environment-induced genes (or quantitative trait loci, QTLs) of major effects on the expression of a trait that respond to changing environments. This framework is constructed with a maximum-likelihood-based mixture model, in which the mean and covariance structure of environment-induced responses is modelled. The means for responses to continuous environmental states, referred to as reaction norms, are approximated for different QTL genotypes by mathematical equations that were derived from fundamental biological principles or based on statistical goodness-of-fit to observational data. The residual covariance between different environmental states was modelled by autoregressive processes. Such an approach to studying the genetic control of reaction norms can be expected to be advantageous over traditional mapping approaches in which no biological principles and statistical structures are considered. We demonstrate the analytical procedure and power of this approach by modelling the photosynthetic rate process as a function of temperature and light irradiance. Our approach allows for testing how a QTL affects the reaction norm of photosynthetic rate to a specific environment and whether there exist different QTLs to mediate photosynthetic responses to temperature and light irradiance, respectively.     

Dissecting genetic networks underlying complex phenotypes: the theoretical framework

Great progress has been made in genetic dissection of quantitative trait variation during the past two decades, but many studies still reveal only a small fraction of quantitative trait loci (QTLs), and epistasis remains elusive. We integrate contemporary knowledge of signal transduction pathways with principles of quantitative and population genetics to characterize genetic networks underlying complex traits, using a model founded upon one-way functional dependency of downstream genes on upstream regulators (the principle of hierarchy) and mutual functional dependency among related genes (functional genetic units, FGU). Both simulated and real data suggest that complementary epistasis contributes greatly to quantitative trait variation, and obscures the phenotypic effects of many 'downstream' loci in pathways. The mathematical relationships between the main effects and epistatic effects of genes acting at different levels of signaling pathways were established using the quantitative and population genetic parameters. Both loss of function and "co-adapted" gene complexes formed by multiple alleles with differentiated functions (effects) are predicted to be frequent types of allelic diversity at loci that contribute to the genetic variation of complex traits in populations. Downstream FGUs appear to be more vulnerable to loss of function than their upstream regulators, but this vulnerability is apparently compensated by different FGUs of similar functions. Other predictions from the model may account for puzzling results regarding responses to selection, genotype by environment interaction, and the genetic basis of heterosis.     

Ranking candidate genes in rat models of type 2 diabetes

Background  

Rat models are frequently used to find genomic regions that contribute to complex diseases, so called quantitative trait loci (QTLs). In general, the genomic regions found to be associated with a quantitative trait are rather large, covering hundreds of genes. To help selecting appropriate candidate genes from QTLs associated with type 2 diabetes models in rat, we have developed a web tool called Candidate Gene Capture (CGC), specifically adopted for this disorder.     

A Multi-Marker Model for Detecting Chromosomal Segments Displaying Qtl Activity

A statistical method is presented for detecting quantitative trait loci (QTLs), based on the linear model. Unlike methods able to detect a few well separated QTLs and to estimate their effects and positions, this method considers the genome as a whole and enables the detection of chromosomal segments involved in the differences between two homozygous lines, and their backcross, doubled haploid, or F(2) progenies, for a quantitative trait. Genetic markers must be codominant, but missing markers are accepted, provided they are missing independently from the experiment. Asymptotic properties, which are of practical use, are developed. This method does not rely on strong genetic hypotheses, and thus does not permit any precise genetic analysis of the trait under study, but it does assess which regions of the genome are involved, whatever the complexity of the genetic determinism (number, effects and interactions among QTLs). Simultaneous use of several methods, including this one, should lead to better efficiency in QTL detection.     

Heritability, correlations and in silico mapping of locomotor behavior and neurochemistry in inbred strains of mice

The midbrain dopamine system mediates normal and pathologic behaviors related to motor activity, attention, motivation/reward and cognition. These are complex, quantitative traits whose variation among individuals is modulated by genetic, epigenetic and environmental factors. Conventional genetic methods have identified several genes important to this system, but the majority of factors contributing to the variation remain unknown. To understand these genetic and environmental factors, we initiated a study measuring 21 behavioral and neurochemical traits in 15 common inbred mouse strains. We report trait data, heritabilities and genetic and non-genetic correlations between pheno-types. In general, the behavioral traits were more heritable than neurochemical traits, and both genetic and non-genetic correlations within these trait sets were high. Surprisingly, there were few significant correlations between the behavioral and the individual neurochemical traits. However, striatal serotonin and one measure of dopamine turnover (DOPAC/DA) were highly correlated with most behavioral measures. The variable accounting for the most variation in behavior was mouse strain and not a specific neurochemical measure, suggesting that additional genetic factors remain to be determined to account for these behavioral differences. We also report the prospective use of the in silico method of quantitative trait loci (QTL) analysis and demonstrate difficulties in the use of this method, which failed to detect significant QTLs for the majority of these traits. These data serve as a framework for further studies of correlations between different midbrain dopamine traits and as a guide for experimental cross designs to identify QTLs and genes that contribute to these traits.     

Mapping quantitative trait loci using binned genotypes

Precise mapping of quantitative trait loci(QTLs)is critical for assessing genetic effects and identifying candidate genes for quantitative traits.Interval and composite interval mappings have been the methods of choice for several decades,which have provided tools for identifying genomic regions harboring causal genes for quantitative traits.Historically,the concept was developed on the basis of sparse marker maps where genotypes of loci within intervals could not be observed.Currently,genomes of many organisms have been saturated with markers due to the new sequencing technologies.Genotyping by sequencing usually generates hundreds of thousands of single nucleotide polymorphisms(SNPs),which often include the causal polymorphisms.The concept of interval no longer exists,prompting the necessity of a norm change in QTL mapping technology to make use of the high-volume genomic data.Here we developed a statistical method and a software package to map QTLs by binning markers into haplotype blocks,called bins.The new method detects associations of bins with quantitative traits.It borrows the mixed model methodology with a polygenic control from genome-wide association studies(GWAS)and can handle all kinds of experimental populations under the linear mixed model(LMM)framework.We tested the method using both simulated data and data from populations of rice.The results showed that this method has higher power than the current methods.An R package named binQTL is available from GitHub.