  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
local peaks with a characteristic width that undergo drift, even in the
infinite population limit. We analytically calculate the mean peak width and
the effective random walk step size, and obtain the distribution of the peak
width which has a power law tail. We find that independent local mutations act
as a diffusion of interacting particles with increased stepsize.
