Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection

The process of ‘Evolutionary Diffusion’, i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.