In the pre-genomic era, the relationships among species and their evolutionary histories were often determined by examining the fossil records. In the genomic era, these relationships are identified by analysing the genetic data, which also enables us to take a close-up view of the differences between the individual samples. Nevertheless, these relationships are often described by a tree-like structure or a network. In this thesis, we investigate some of the models that are used to describe these relationships.

This thesis can be divided into two main parts. The first part focuses on investigating the theoretical properties of several neutral tree models that are often considered in phylogenetics and population genetics studies, such as the Yule–Harding model, the proportional to distinguishable arrangements and the Kingman coalescent models.

In comparison to the first part, the other half of the thesis is more computationally oriented: we focus on developing and implementing methods of calculating gene tree probabilities of given species networks, and simulating genealogies within species networks.