Abstract: It is widely appreciated that population waves have played a crucial role in the evolutionary history of many species. In parallel with Fokker-Planck descriptions of stochastic processes in physics, population geneticists have developed methods for understanding mutations, genetic drift and selective advantage in such situations. Provided number fluctuations at the frontier are taken into account, neutral genetic markers can be used to infer information about growth, ancestral population size and colonization pathways. Neutral mutations optimally positioned at the front of a growing population wave can increase their abundance via a "surfing" phenomenon. Experimental and theoretical studies of this effect will be presented, as well as recent attempts to extend statistical dynamics ideas to microorganisms cooperating and competing in the turbulent environment of the ocean.