This book is part science, part technical, and all about the computational analysis of heritable traits: things like genes, languages, behaviours and morphology. This book is centred around the description of the theory and practice of a particular open source software package called BEAST (Bayesian evolutionary analysis by sampling trees). The BEAST software package started life as a small science project in New Zealand but it has since grown tremendously through the contributions of many scientists from around the world, chief among them the research groups of Alexei Drummond, Andrew Rambaut and Marc Suchard. A full list of contributors to the BEAST software package can be found on the BEAST GitHub page or printed to the screen when running the software.

Very few things challenge the imagination as much as does evolution. Every living thing is the result of the unfolding of this patient process. While the basic concepts of Darwinian evolution and natural selection are second nature to many of us, it is the detail of life's tapestry which still inspires an awe of the natural world. The scientific community has spent a couple of centuries trying to understand the intricacies of the evolutionary process, producing thousands of scientific articles on the subject. Despite this Herculean effort, it is tempting to say that we have only just scratched the surface.

As with many other fields of science, the study of biology has rapidly become dominated by the use of computers in recent years. Computers are the only way that biologists can effectively organise and analyse the vast amounts of genomic data that are now being collected by modern sequencing technologies. Although this revolution of data has really only just begun, it has already resulted in a flourishing industry of computer modelling of molecular evolution.

This book has the modest aim of describing this still new computational science of evolution, at least from the corner we are sitting in. In writing this book we have not aimed for it to be comprehensive and gladly admit that we mostly focus on the models that the BEAST software currently supports. Dealing, as we do, with computer models of evolution, there is a healthy dose of mathematics and statistics. However, we have made a great effort to describe in plain language, as clearly as we can, the essential concepts behind each of the models described in this book.