Molecular biology makes extensive use of methods that can accurately estimate the evolutionary relationships between species, particularly when the evolutionary history can be represented on an `evolutionary tree'. However, attention is increasingly turning towards approaches that can be applied when the history might not be adequately represented by a tree.
This thesis presents computational methods that work towards the goal of inferring a `evolutionary network' directly from sequence data. The particular focus was on computational methods that are `fit agnostic' which refers to the idea that any method for evaluating how well a structure matches provided data could be used in place of the one used here. Given the underlying mechanisms used the evaluation methods that do well will be those that preserve the relationship that if a particular tree gives a good fit to the data then restricting the tree and data to a subset of taxa will also give a good fit. The final goal of achieving a network was not reached as there remain some problems and no obvious way yet to solve them. As a temporary placeholder in order to ascertain if the methods \emph{could} be applied to networks sets of evolutionary trees were used whereby the sets of evolutionary trees are to be interpreted as existing in some network which a future algorithm may work on directly. The methods and theory in this paper have thus been formulated so that there should be an analogue from these that are developed for sets of evolutionary trees to ones that can be applied to evolutionary networks.
The first chapters and bulk of the thesis concentrates on developing methods that can infer the history on this simpler structure and the last chapter is initial work on a method that is intended to allow extension of the previous methods to networks, although the new structure described turns up results that are interesting in their own right.
