Title: Using the Wright-Fisher diffusion for statistical inference of evolution
Abstract: Evolution is a change in allele frequencies over time. How should we model this? If random genetic drift, which can introduce stochastic variation on short timescales, plays a role then it is appropriate to use a diffusion process. This idea was introduced and studied by Wright, Fisher, and Kimura, among others. In this talk I will give an overview of the Wright-Fisher diffusion which can be used for modelling genetic drift jointly with other evolutionary processes including mutation and selection. I will describe some recent work relevant to the problem of statistical inference from allele frequency time series data: if I observe the path of an allele frequency over time, is there anything I can say with certainty about the underlying parameters? Mathematically the question is closely related to whether one diffusion path measure is absolutely continuous with respect to another. It turns out that this question is determined by whether or not you observe an allele go to fixation or extinction.
About the speaker: https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/jenkins/
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Video of the talk: https://youtu.be/lKLWpk_FzEs