  We consider a fixed size population that undergoes an evolutionary adaptation
in the weak mutuation rate limit, which we model as a biased Langevin process
in the genotype space. We show analytically and numerically that, if the
fitness landscape has a small highly epistatic (rough) and time-varying
component, then the population genotype exhibits a high effective diffusion in
the genotype space and is able to escape local fitness minima with a large
probability. We argue that our principal finding that even very small
time-dependent fluctuations of fitness can substantially speed up evolution is
valid for a wide class of models.
