From Monday January 22, 2007 until Friday February 2, 2007, there will be a two week concentration period on Biomathematics at the Lorentz Center organized by the Thomas Stieltjes Institute for Mathematics and the NWO-cluster Nonlinear Dynamics of Natural Systems (NDNS+).

The first week will be devoted to a Stieltjes Onderwijsweek entitled

**Probability and
Statistics in Population Genetics**

Lorentz Center, 22 January 2007 - 26 January 2007

The second week will be devoted to an international NDNS+ Workshop

**Mathematical Modeling
and Analysis of Biological Networks**

Lorentz Center, 29 January 2007 - 2 February 2007.

A. **The Stieltjes Onderwijsweek **Probability
and Statistics in Population Genetics

This week is directed at 4th and 5th year master students and PhD students in mathematics interested in applications of models from probability and statistics in population

genetics.

The week centers around Kingman’s coalescent process, a Markov process in continuous time, which is used to model the genealogy of a population backwards in time. The idea is that any group of subjects (e.g. people, cancer cells, DNA molecules, species) has a common ancestor, from whom each individual derives through a branching process. Kingman’s coalescent (Kingman, 1970) is a probabilistic model for the structure of this branching process, obtained from the Fisher-Wright model of evolution. The model has very recently gained new interest because of the developments in molecular genetics. Questions that it can help answer are: when did the first human (”Eve”) originate, what is the phylogeny (evolutionary tree) of species, which gene is responsible for a certain disease, when did a tumor start growing and when did metastasis start?

This week will be directed at mathematical theory, but the intention is to end with a clear view how this theory can be applied to answer biological questions of this type.

The theory will be built up from basic probability, and will include introductions to continuous time Markov chains, and Bayesian statistical inference, and a reminder of Poisson processes.

**Lecturers:**

– Richard Gill,

– Mathisca de Gunst,

– Frank den Hollander,

– Ronald Meester,

– Aad van der Vaart.

**Material:**

– Handouts

– St. Flour lectures notes by Simon Tavare.

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