Mathematical Sciences: Stochastic Processes in Genetics and Statistics

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The principal investigator's research consists of two main parts, both of which are in the field of theoretical population genetics. This field is interested in understanding the process of evolution through mathematical modeling. First, Ethier will exploit his recent ideas of including an allele's age and genealogy via diffusion theory. He is working towards unifying the subject by showing that the more conventional approaches to ages and genealogies, such as coalescent processes, can be derived from an appropriate stationary diffusion model, which is often regarded as the basic stochastic model in population genetics. Second, he will continue working on two-locus diffusions models, with emphasis on theoretical aspects of such processes, especially the effect of recombination.