The non-local variant of the celebrated Fisher-KPP equation describes the growth and spread of population in which individuals diffuse, reproduce and – crucially – interact through a non-local competition mechanism. This type of equation is intrinsically harder to study than the classical Fisher-KPP equation because we lose such powerful tools as the comparison principle and the maximum principle. In this talk, I will show how this equation arises as the hydrodynamic limit of a particle system -the branching Brownian motion with decay of mass, and use this to study front propagation behaviours.

This is based on joint work with Louigi Addario-Berry and Sarah Penington.