Leo Tyrpak

Fluctuations of spatial population models with non-local interactions.

We analyse a class of spatial population models where the branching rate of particles depend non-locally on the whole empirircal measure of particles. Scaling limits of this model have previously been shown to include the non-local Fisher-KPP equation and the porous medium equation. In this talk we will discuss the fluctuations of the process around these deterministic limits. We will show how an  understanding of these can be applied to quantify the impact on geographical distance on genetic distance in the spirit of the classical Wright-Malecot formula.