Algorithms for the Calculation and Visualisation of Phylogenetic Networks

Evolution describes the development of species as a steady adaption to the environment. In the classical model, a species develops by mutation and speciation events, which can be modelled using phylogenetic trees. However, if the evolutionary model is generalized by integrating events such as recombination, a tree can no longer describe the process. Phylogenetic networks are a class of graphs that have been developed to describe these more complex processes. These networks can be divided into two groups: those networks that model evolutionary events explicitly and those networks that do so implicitly. In this thesis, we focus on the development of new algorithms for the reconstruction and visualization of explicit phylogenetic networks. A reconstruction is called optimal if it minimizes the evolutionary costs. The large number of possible graphs from which one can choose an optimal solution presents one of the hardest problems in the reconstruction, since no possibility exists to choose the right one efficiently. One possible way to reduce the number of graphs one has to choose from, is to break down the problem into smaller independent sub-problems. By carefully reducing the class of phylogenetic networks under consideration, we were able to show that indeed the main problem can be broken up into smaller parts. Furthermore, we developed an efficient algorithm for calculating all optimal solutions for each independent sub-problem. In addition, we developed an algorithm that is capable of drawing explicit phylogenetic networks. The algorithm was designed in such a way that the algorithms available for drawing phylogenetic trees can be generalized to draw explicit phylogenetic networks. To do so, we modified the explicit phylogenetic network and extended the tree drawing algorithm by adding an optimization step, which minimizes the number of crossing edges. Furthermore, we present two software projects which aim at extending the availability of new phylogenetic methods within SplitsTree and increasing the useablility of large phylogenetic graphs. In the first project, we implemented a management system for plugins, which allows the application to dynamically integrate new methods that are stored on a database in the Internet. In the second project, we developed software that allows for the annotation of phylogenetic graphs within SplitsTree.