Development of spherical data analysis techniques for phylogenomics

Three bacteria species are chosen to be analyzed in this thesis. Taking the principle of neutral evolution that evolutionary rate is proportional of time as a null hypothesis, two methods are developed to detect cases consistent with the alternative hypothesis that either horizontal gene transfer or functional divergence has occurred. In order to standardize the estimated branch lengths, I first project each triplet of branch lengths onto the sphere. The model-based clustering method is then developed for the spherical data. Another method based on the Kent distribution is developed to detect outliers on a sphere, which may correspond to HGT or functional divergence. The results of the Listeria dataset show that these two methods are reasonable.