Self-similarity in selection dynamics

In a population where individuals reproduce at different rates (i.e. have different “fitness”), the fraction of high-fitness types naturally increases over time—this is what Darwin coined "natural selection". This process can be represented abstractly as a non-linear yet exactly soluble integro-differential equation. I will show that this equation possesses self-similar solutions and describe their basins of attractions. The presentation will be guided by analogies with extreme value statistics on the one hand and and mean-field coarsening dynamics on the other.