Mathematical Sciences Institute, ANU

Consider the family tree of a population in which we ignore all males and consider only female lines of descent. In such a model each individual has only one parent. Now trace the ancestry of this reduced population back in time to its most recent common ancestor. In the human population this ancestor is known as mitochondrial Eve. Mitochondrial Eve was not the only female alive at the time, but she was the only one whose female descendant lines did not become extinct.

Estimating the time since mitochondrial Eve is a typical problem arising in population genetics. In this talk I will address the problem of tracing ancestry to the most recent common ancestor in a population by modelling the population's evolution through time as a Bienaymé-Galton-Watson branching process. In this approach each individual female produces a random number of daughters, and hence the total population size is generated stochastically. This differs from the standard approach known as the Wright-Fisher model, in which the population size as a function fo time is specified externally, and each individual daughter randomly chooses her mother from the previous generation. If time permits, I will also illustrate a calculation of the spread of genetic mutations through a population whose growth is modelled as a Bienaymé-Galton-Watson process.

**Conrad Burden** is an Associate Professor in the Mathematical Sciences Institute at the Australian National University lecturing in bioinformatics. His research interests include mathematical population genetics, aligment-free sequence comparison, the analysis of high-throughput sequencing data, and the physico-chemical modelling of microarrays. Before making the move into bioinformatics in 2003 he spent 20 years as a theoretical physicist. In particular, from 1988 to 1999 he held a research position in the Department of Theoretical Physics, Australian National University, working mainly in quantum field theory and subatomic particle physics.

**Theoretical Physics @ANU** is a new cross-campus seminar series to cover recent important developments in the area.**Convenors:** Vladimir Bazhanov & Anatoli Kheifets (RSPE)**Advisory Board: ** Geoff Bicknell (RSAA), Denis Evans (RSPE), Peter Gill (RSC), Andy Hogg (RSES), Stephen Hyde (RSPE), Cedric Simenel (RSPE), Susan Scott (RSPE), Andrei Sukhorukov (RSPE), Bai-Ling (Brian) Wang (MSI)