Modeling and inferring quantitative trait loci using linkage disequilibrium in natural populations.

WANG, TAO. MODELING AND INFERRING QUANTITATIVE TRAIT LOCI USING LINKAGE DISEQUILIBRIUM IN NATURAL POPULATIONS. (Under the direction of Dr. Zhao-Bang Zeng and Bruce Weir.) Quantitative trait loci (QTL) are those chromosome regions that contribute to variation of quantitative traits. Analysis of QTL is helpful for further study of molecular basis of the quantitative genetic variation. The discovery of highly abundant and dense polymorphic markers (e.g., single nucleotide polynorphisms, or SNPs) covering a whole genome provides an opportunity to localize QTL in a variety of populations. While classical linkage studies have a relatively limited resolution in QTL localization, the association mapping or linkage disequilibrium (LD) mapping approach can offer an alternative way for fine mapping of genes. Currently there are few LD methods available for QTL mapping in natural populations. Development of more efficient methods is still a challenging problem. In this thesis, we first review the LD approach for fine mapping of QTL in Chapter 1. Some basic issues in LD analysis and recent developments in LD methodology are discussed. Particular attention is paid to limitations and potential problems of these methods. This provides the motivation for the research in this thesis. Next, we explore Cockerham’s genetic model (Cockerham, 1954) for quantitative traits in Chapter 2. A revised form of the Cockerham model is presented using some coding variables. The relationship between Cockerham model and some specific genetic models for designed experimental populations, such as backcross or F2, is then established. We study extensively the properties of QTL effects and partitions of various genetic variance components for these reduced models under both linkage equilibrium and linkage disequilibrium situations. A general multi-locus-two-allele model is also proposed that may serve as a basis for mapping QTL in natural populations. The main research of the thesis is on development of an exact multipoint likelihood approach to infer QTL in natural populations. In Chapter 3, we first generalize the formulation of the likelihood analysis for a polymorphic marker locus and a trait locus in a general natural population. From this generalization, we derive a closed form solution of an efficient EM algorithm for the likelihood analysis. This is a major achievement of the research. The importance of this generalization is that it can be readily and systematically extended to multiple markers and multiple QTL. Based on this formulation, a multipoint likelihood analysis with the EM algorithm is developed that can take into account higher-order linkage disequilibria between QTL and markers without making approximation to the likelihood function. This analysis can offer a simultaneous estimation of the linkage disequilibrium structure between a QTL and multiple markers. From this estimation, we find that the linkage disequilibrium between one or a subset of markers and a QTL conditional on other markers can offer as a more accurate measure for fine mapping of QTL. In Chapter 4, we further extend the analysis to multiple QTL and propose a general framework for likelihood analysis of multiple QTL and markers. With this approach, the joint gametic frequencies of QTL and markers (thus various measures of linkage disequilibria between QTL and markers) as well as various genetic effects of QTL (including epistasis) can be estimated simultaneously. This general approach has a lot of potential for a complete analysis of genetic architecture of quantitative traits in natural populations. Although the foundation of this general framework has been laid down, more studies are still needed on a number of issues, such as efficiency and reliability of the optimization algorithm, statistical tests for QTL identification, model selection of complex QTL, and more efficient approaches to analyze large data sets. In the last chapter (Chapter 5), we draw some general conclusions from the research. We discuss the advantages as well as limitations of the approach developed in this thesis and problems for further research. To my parents, wife and son