Barking up the wrong tree : some obstacles to phylogenetic reconstruction

Phylogenetics is the study of evolutionary relationships between entities, usually biological in nature. The primary aim of such study is to elucidate the structure of these evolutionary histories. Unfortunately, such study can run into a variety of obstacles, both practical and theoretical. In this thesis we explore theoretical obstacles to phylogenetic reconstruction, by examining several scenarios in which distinguishing between similar structures can become quite difficult. In Chapter 2, we consider when metrics on trees and metrics on networks can become indistinguishable, and present several novel results in this area, showing that it is possible for any tree metric to be represented on a non-trivial network, and provide early results on the possible structures of these networks. In Chapter 3, we consider tree-based networks - a phenomenon in which networks have a strong tree-like signal. We present the first findings on these networks in the context of unrooted non-binary networks. We characterise the circumstances under which such networks can become `saturated' by these signals, and provide some graph theoretical results in this area as well. In Chapter 4 we consider the scenario in which two trees can appear similar due to their hierarchical structure. We present a new metric to quantify this similarity, and use simulations to show several promising properties of the metric and the relative accuracy of a function that gives an upper bound to the metric