Statistical Inference For Recombination Fraction In Linkage Analysis

Recombination fraction plays a very important role in genetic linkage analysis. Especially, in the linkage map constructing and gene mapping, the statistical inference for recombination fraction is an necessary step. Genetic linkage analysis refers to determining the chromosomal location of the gene(s) for a trait of interest such as a common disease by the analysis of gene data. With the fulfillment of human genome sequencing, people have found many marker loci that can be used to detect genes of interest. So far, scientists have mapped many loci of single-gene disease, and obtained new discoveries every year. A basic problem in gene mapping is to determine how far is the trait locus from the marker locus by statistical methods, given a concrete marker location. From statistical aspect, it needs to estimate recombination fraction, so that the distance between the two loci can be determined, and the distance can be transformed by recombination fraction using map function; Or it can be answered by testing hypotheses whether the trait locus is farther from the marker locus. However, in almost all of the existing studies of linkage analysis and gene mapping some natural and necessary restrictions on parameters have not been considered sufficiently. Neglecting these restrictions must affect the statistical inference in genetics, so that illegimate results often appear. This dissertation aims to emphasize the natural restrictions on recombination fractions, and proposes the statistical inference methods for recombination fractions under the restrictions; In addition, we also consider the problem of quantitative trait loci (QTL) mapping, and linkage analysis in outcrossing population.In this dissertation, we first discuss the three-locus linkage analysis of phase-unknown triple backcross, and present an inference method for recombination fraction under restrictions. For two-offspring families, we develop a restricted expectation maximization (EM) algorithm, called REM. Whereas more offspring in each family will provide more information in linkage analysis, we extend the REM algorithm to cases of multiple offspring (sibship) in each family, give a method for offspring phenotype classification of multiple offspring family, and present a explicit formula of the number of the offspring phenotype classification; We also consider the case of unequal prior probabilities of linkage phases, results showing that the REM algorithm can be taken as a unified method. Secondly, linkage analysis in outcrossing population is also mentioned. Finally, we perform some research on the more popular QTL mapping, considering the interval mapping for QTL when crossover interference is present. We carry out simulations to evaluate all the proposed methods and to compare them with other methods, and we also apply our methods to real data successfully. Both theoretical and numerical studies show that our proposed methods work well in practice and can improve the precision of inference of recombination fractions.