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Stochastic Models for Genetic Evolution (BM)


The goal of this course is to present a series of elementary stochastic models from population dynamics capable of describing rudimentary aspects of DNA-sequence evolution. Most of the course focuses on the Wright-Fisher model and its variations. In this model, alleles are represented by individuals living in colonies and changing type over the course of time. A large part of the course deals with populations living in a single colony subject to resampling, mutation and/or selection. Towards the end of the course populations living in many colonies subject to migration are described. A key notion is that of the Kingman coalescent, which arises when the genealogy of the population is traced backwards in time. This notion is the key to building up a coherent theory. No prior knowledge of genetics is required. Basic knowledge of probability theory is needed, in particular, properties of Markov chains and the Poisson process. The course provides basic knowledge of mathematical population theory. Literature: R. Durrett, Probability Models for DNA Sequence Evolution (2nd edition), Springer, New York, 2008. F. den Hollander, Stochastic Models for Genetic Evolution, June 2012. This is a “collegediktaat” that will be made available at the beginning of the course.