Séminaire de Probabilités

The infinite-parent SLFV - Definition and growth properties

by Apolline Louvet

Amphi L. Schwartz

Amphi L. Schwartz


The infinite-parent spatial Lambda-Fleming Viot process, or infinite-parent SLFV, is a measure-valued population genetics process for expanding populations in a spatial continuum whose dynamics is reminiscent of the Eden growth model. As for other SLFV processes, its main feature is that the reproduction dynamics can be seen as "event-based" rather than "individual-based": the process is associated to a Poisson point process which indicates in which areas reproduction occurs at each instant. In this talk, I will first introduce three possible definitions of the process, each valid under more or less restrictive conditions on the underlying Poisson point process: as a set-valued process, as the unique solution to a martingale problem, or as the limit of coupled SLFVs. I will then present what is currently known of the growth properties of the process. I will focus in particular on the growth of the front, which can be investigated using a (self) duality relation satisfied by the process. These results are important as a first step towards studying genetic diversity at the front edge. 
Based on a joint work with Amandine Véber (MAP5, Univ. Paris Cité) and an ongoing work with Matt Roberts (Univ. Bath) and Jan Lukas Igelbrink (GU Frankfurt and JGU Mainz).