Statistical approaches to phylogenetic networks, recombination and testing of incongruence

Abstract

Phylogenetics is the study of relationships between species using Deoxyribose Nucleic Acid (DNA). This thesis takes a statistical approach to two phenomenon which violate the assumption that evolution is treelike, and examines ways of visualising non-treelike signal. We use networks to display phylogenetic signal as they are robust and capable of displaying uncertainty. Phylogenetic network inference involves estimating discrete (topology) and continuous (branch length) parameters. One particular class of phylogenetic networks, split networks, can be viewed as points in Euclidean space of high dimension. In theory, then, phylogenetic analysis become a problem of inferring simple real valued parameters. In this thesis we report on our experiences turning this theory into practice. We use the Least Absolute Shrinkage and Selection Operator (LASSO) approach to regression in the first instance and then extend the LASSO to a partial LASSO. Within genes, phenomena like recombination (combining genetic material from more than one source) leads to non-treelike evolutionary histories. We introduce two methods for estimating the location of a recombination event. The first method is based on detecting a regime shift in the presence of recombination and the second method models the signal in each pair of DNA sites. Even if each gene has a treelike evolutionary history, the histories may not be shared. Therefore, we developed an approach to constructing a confidence set of topologies for a set of genes. If this set is empty then the genes do not share an evolutionary history. We conclude that the new statistical approaches to these phenomena, developed here, can give further insight into an evolutionary history