| Summary: | The evolutionary history of a set of species is commonly represented by a phylogenetic tree. Often, however, the data contain conflicting signals, which can be better represented by a more general structure, namely a phylogenetic network. Such networks allow the display of several alternative evolutionary scenarios simultaneously but this can come at the price of complex visual representations. Using so-called circular split networks reduces this complexity, because this type of network can always be visualized in the plane without any crossing edges. These circular split networks form the core of this thesis. We construct them, use them as a search space for minimum evolution trees and explore their properties. More specifically, we present a new method, called SuperQ, to construct a circular split network summarising a collection of phylogenetic trees that have overlapping leaf sets. Then, we explore the set of phylogenetic trees associated with a �fixed circular split network, in particular using it as a search space for optimal trees. This set represents just a tiny fraction of the space of all phylogenetic trees, but we still �find trees within it that compare quite favourably with those obtained by a leading heuristic, which uses tree edit operations for searching the whole tree space. In the last part, we advance our understanding of the set of phylogenetic trees associated with a circular split network. Specifically, we investigate the size of the so-called circular tree neighbourhood for the three tree edit operations, tree bisection and reconnection (tbr), subtree prune and regraft (spr) and nearest neighbour interchange (nni).
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