Doktorandseminarium: An application of Poisson random measures in population genetics


In my talk I will discuss the theory and some properties of random measures, and present an application thereof in population genetics. In population genetics one studies the genetic variation in a population which is mainly driven by mutations. These mutations arrive randomly on a site of an individual’s genome and the mutated site may be passed to the next generation. By chance it segregates through the population.

I will derive a mathematical representation of the collection of segregating sites in a population and show that it can be represented as a stochastic integral with respect to a Poisson random measure.