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Probability and Statistics in Population Genetics |
From Monday January
22, 2007 until Friday February 2, 2007, there will be a two week concentration
period on Biomathematics at the The first week will be
devoted to a Stieltjes Onderwijsweek
entitled Probability and
Statistics in Population Genetics The second week will
be devoted to an international NDNS+ Workshop Mathematical Modeling
and Analysis of Biological Networks 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. See http://www-hto.usc.edu/papers/abstracts/saintflour.html [Back] |