Apolline Louvet

Spatial Λ-Fleming Viot processes, or SLFVs, are a family of models describing the evolution of genetic diversity for populations living in a spatial continuum. Their main characteristic is their "event-based" reproduction dynamics, which makes it possible to control local reproduction rates. Therefore, they are particularly suited to the study of populations living in unbounded regions. 

In this talk, I will show how the SLFV modelling framework can be extended to spatially expanding populations, giving rise to two family of processes: ∞-parent SLFV processes, which are a measure-valued analog of continuous first-passage percolation, and k-parent SLFV processes, in which local extinctions due to low local population densities are possible. I will show that when k → +∞, the k-parent SLFV converges in distribution towards the ∞-parent SLFV. I will then present what is currently known of the growth properties of these processes. 

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).