Robust Methods for Analysing Quantitative Trait Loci

The advent of new technology for extracting genetic information from tissue samples has increased the availability of suitable data for finding genes controlling complex traits in plants, animals and humans. Quantitative trait locus (QTL) analysis relies on statistical methods to interpret genetic data in the presence of phenotype data and possibly other factors such as environmental factors. The goal is to both detect the presence of QTL with significant effects on trait value as well as to estimate their locations on the genome relative to those of known markers. This thesis reviews commonly used statistical techniques for QTL mapping in experimental populations. Regression and likelihood methods are discussed. The mixture-modelling approach to QTL mapping is explored in some detail. This thesis presents new matrix formulas for exact and convenient calculation of both the Observed and Fisher information matrices in the context of Multinomial mixtures of Univariate Normal distributions. An extension to Composite Interval mapping is proposed, together with a hypothesis testing strategy which is robust enough to de- tect existing QTL in the presence of slight deviations from model assumptions while reducing false detections.