A Unified Semiparametric Framework for Quantitative Trait Loci Analyses, With Application to Spike Phenotypes

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

Finding Quantitative Trait Loci Genes with Collaborative Targeted Maximum Likelihood Learning

Quantitative trait loci mapping is focused on identifying the positions and effect of genes underlying an an observed trait. We present a collaborative targeted maximum likelihood estimator in a semi-parametric model using a newly proposed 2-part super learning algorithm to find quantitative trait loci genes in listeria data. Results are compared to the parametric composite interval mapping approach.

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.

Functional mapping of genotype-environment interactions for soybean growth by a semiparametric approach

BACKGROUND

Functional mapping is a powerful approach for mapping quantitative trait loci (QTLs) that control biological processes. Functional mapping incorporates mathematical aspects of growth and development into a general QTL mapping framework and has been recently integrated with composite interval mapping to build up a so-called composite functional mapping model, aimed to separate multiple linked QTLs on the same chromosomal region.

RESULTS

This article reports the principle of using composite functional mapping to estimate the effects of QTL-environment interactions on growth trajectories by parametrically modeling the tested QTL in a marker interval and nonparametrically modeling the markers outside the interval as co-factors. With this new model, we can characterize the dynamic patterns of the genetic effects of QTLs governing growth trajectories, estimate the global effects of the underlying QTLs during the course of growth and development, and test the differentiation in the shapes of QTL genotype-specific growth curves between different environments. By analyzing a real example from a soybean genome project, our model detects several QTLs that cause significant genotype-environment interactions for plant height growth processes.

CONCLUSIONS

The model provides a basis for deciphering the genetic architecture of trait expression adjusted to different biotic and abiotic environments for any organism.

Composite interval mapping to identify quantitative trait loci for point-mass mixture phenotypes

Increasingly researchers are conducting quantitative trait locus (QTL) mapping in metabolomics and proteomics studies. These data often are distributed as a point-mass mixture, consisting of a spike at zero in combination with continuous non-negative measurements. Composite interval mapping (CIM) is a common method used to map QTL that has been developed only for normally distributed or binary data. Here we propose a two-part CIM method for identifying QTLs when the phenotype is distributed as a point-mass mixture. We compare our new method with existing normal and binary CIM methods through an analysis of metabolomics data from Arabidopsis thaliana. We then conduct a simulation study to further understand the power and error rate of our two-part CIM method relative to normal and binary CIM methods. Our results show that the two-part CIM has greater power and a lower false positive rate than the other methods when a continuous phenotype is measured with many zero observations.

QTL mapping in intercross and backcross populations

In the past two decades, various statistical approaches have been developed to identify quantitative trait locus with experimental organisms. In this chapter, we introduce several commonly used QTL mapping methods for intercross and backcross populations. Important issues related to QTL mapping, such as threshold and confidence interval calculations are also discussed. We list and describe five public domain QTL software packages commonly used by biologists.

Hierarchical generalized linear models for multiple quantitative trait locus mapping

We develop hierarchical generalized linear models and computationally efficient algorithms for genomewide analysis of quantitative trait loci (QTL) for various types of phenotypes in experimental crosses. The proposed models can fit a large number of effects, including covariates, main effects of numerous loci, and gene-gene (epistasis) and gene-environment (G x E) interactions. The key to the approach is the use of continuous prior distribution on coefficients that favors sparseness in the fitted model and facilitates computation. We develop a fast expectation-maximization (EM) algorithm to fit models by estimating posterior modes of coefficients. We incorporate our algorithm into the iteratively weighted least squares for classical generalized linear models as implemented in the package R. We propose a model search strategy to build a parsimonious model. Our method takes advantage of the special correlation structure in QTL data. Simulation studies demonstrate reasonable power to detect true effects, while controlling the rate of false positives. We illustrate with three real data sets and compare our method to existing methods for multiple-QTL mapping. Our method has been implemented in our freely available package R/qtlbim (www.qtlbim.org), providing a valuable addition to our previous Markov chain Monte Carlo (MCMC) approach.

Mapping quantitative trait loci from a single-tail sample of the phenotype distribution including survival data

A new effective Bayesian quantitative trait locus (QTL) mapping approach for the analysis of single-tail selected samples of the phenotype distribution is presented. The approach extends the affected-only tests to single-tail sampling with quantitative traits such as the log-normal survival time or censored/selected traits. A great benefit of the approach is that it enables the utilization of multiple-QTL models, is easy to incorporate into different data designs (experimental and outbred populations), and can potentially be extended to epistatic models. In inbred lines, the method exploits the fact that the parental mating type and the linkage phases (haplotypes) are known by definition. In outbred populations, two-generation data are needed, for example, selected offspring and one of the parents (the sires) in breeding material. The idea is to statistically (computationally) generate a fully complementary, maximally dissimilar, observation for each offspring in the sample. Bayesian data augmentation is then used to sample the space of possible trait values for the pseudoobservations. The benefits of the approach are illustrated using simulated data sets and a real data set on the survival of F(2) mice following infection with Listeria monocytogenes.

A conceptual framework for mapping quantitative trait Loci regulating ontogenetic allometry

Although ontogenetic changes in body shape and its associated allometry has been studied for over a century, essentially nothing is known about their underlying genetic and developmental mechanisms. One of the reasons for this ignorance is the unavailability of a conceptual framework to formulate the experimental design for data collection and statistical models for data analyses. We developed a framework model for unraveling the genetic machinery for ontogenetic changes of allometry. The model incorporates the mathematical aspects of ontogenetic growth and allometry into a maximum likelihood framework for quantitative trait locus (QTL) mapping. As a quantitative platform, the model allows for the testing of a number of biologically meaningful hypotheses to explore the pleiotropic basis of the QTL that regulate ontogeny and allometry. Simulation studies and real data analysis of a live example in soybean have been performed to investigate the statistical behavior of the model and validate its practical utilization. The statistical model proposed will help to study the genetic architecture of complex phenotypes and, therefore, gain better insights into the mechanistic regulation for developmental patterns and processes in organisms.

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.