Junior Analysis Seminar – Jacob Mercer (Oxford)

Branching selection particle systems are models for populations with fixed population size, N, and in which we have births and ‘survival of the fittest’. In this talk we will discuss two specific branching selection particle systems. Notably, in the limit as N goes to infinity, the distribution of particles in these systems converges to the solution of free boundary problems with Neumann type boundary conditions. We will discuss some elements of the proof of this result and think about how survival of the fittest results in ‘fitness’ increasing over time with a calculable asymptotic speed.