Phylogenetic networks are a generalization of phylogenetic trees that allow for reticulation. Reconstruction of phylogenetic trees from distances is well studied, but for networks, there are relatively few results. Recent results have focused on restricting the space of phylogenetic networks to speci c subclasses with desirable properties, in particular, normal, tree-child and orchard networks. In this thesis, we explore new methods of reconstructing phylogenetic networks, as well as extend existing reconstruction results beyond these classes.

Orchard and temporal networks play a signi cant role in phylogenetic results, as they provide enough restrictions to exclude undesirable structures, whilst still having enough complexity to maintain mathematical interest. However, little is known about the structure of these networks. In particular, there are few structural characterisations for these networks. The rst part of the thesis outlines forbidden structures characterisations for orchard and temporal networks.

The second part of the thesis explores reconstruction of phylogenetic networks using distance. We extend the results of Bordewich et al., and show that equidistant semibinary normal networks can be reconstructed using their minimum distances. We also show that equidistant orchard networks can be reconstructed using distances, up to an equivalence class known as sinks.

Finally, the last part of the thesis considers reconstructing phylogenetic networks from the relative unexplored information type of ancestral pro les. We show that like distances, stack-free phylogenetic networks can be reconstructured using ancestral pro les, with the exception of some special structures.