Combinatorial properties of phylogenetic networks

Abstract

This thesis is concerned with combinatorial properties of some subclasses of rooted and unrooted phylogenetic networks. We consider several phylogenetic networks and provide enumeration formulas (exact and asymptotic) for them with a given number of leaves and also analyze some of their characterizing parameters. We extend the work of Semple and Steel to rooted and unrooted level 2 networks and can show with generating functions that the studied parameters are asymptotically normally distributed. Furthermore, tree-child and normal networks are treated. Asymptotic and exact formulas are derived, which solves some open problems listed in the literature. Finally, we extend the investigation to general networks.