Seminario de Probabilidad y Procesos Estocásticos

Resumen: 

We consider a branching Brownian motion model of a population evolving under selective pressure. The rate at which a particle branches is determined by the particle’s position relative to the average of the population. Individuals that are more fit than average split in two, while individuals that are less fit than average die. Our main result describes the behavior of the particle system in the large-population limit by connecting the process to the solution of a nonlocal reaction-diffusion equation. Through this PDE connection, we show that the population’s fitness distribution approximates a Gaussian traveling wave. This talk is based on joint work with Sarah Penington.