Abstract: Mathematical population genetics has been an incredible culture broth for the recent developments of the modern theory of stochastic duality. Duality in genetics clarifies the intrinsic link between forward-in-time dynamics of a population’s allele frequencies evolution and backward-in-time dynamics of  the same population’s ancestry. I will show that a duality with very much the same genetic ancestral structure can be established for an infinite-dimensional diffusion – the Two-parameter Poisson-Dirichlet diffusion – helping significantly the tractability of such processes for simulation and inference.

Webpage: https://economiaefinanza.luiss.it/research-seminar/dualities-and-intertwinings-in-the-two-parameter-poisson-dirichlet-diffusion