SICSA Summer School ‐ Statistical Inference in Computational Biology INFERENCE OF PHYLOGENIES AND EVOLUTIONARY HISTORIES Michael Stumpf, Imperial College, London In this set of lectures I will cover the basics of phylogenetic inference related. Following a brief outline of present challenges in comparative, evolutionary and systems biology I will review the various probabilistic models of DNA and amino acid sequence evolution and how these can be used in order to infer phylogenetic trees. Particular emphasis will be placed on likelihood and Bayesian approaches and their respective limitations and strengths compared to traditional methods. One of the important problems that has arisen in recent years is how to combine the evolutionary information derived from individual gene or protein sequences in order to understand functional and evolutionary processes at the species (or system) level. As we have more and better resolved sequence data the statistical problems related to their analysis have increased quite considerably and I will discuss these problems and some of the proposed solutions in the context of both prokaryotic and eukaryotic organisms. I will conclude by surveying how phylogenetic methods are now being adapted to study the evolution of biological networks and systems and how we can combine the network with the sequence information.