  Within the framework of population genetics we consider the evolution of an
asexual haploid population under the effect of a rapidly varying natural
selection (microevolution). We focus on the case in which the environment
exerting selection changes stochastically. We derive the effective genotype and
fitness dynamics on the slower time-scales at which the relevant genetic
modifications take place. We find that, despite the fast environmental
switches, the population manages to adapt on the fast time-scales yielding a
finite positive contribution to the fitness. However, such contribution is
balanced by the continuous loss in fitness due to the varying selection so that
the statistics of the global fitness can be described neglecting the details of
the fast environmental process. The occurrence of adaptation on fast
time-scales would be undetectable if one were to consider only the effective
genotype and fitness dynamics on the slow time-scales. We therefore propose an
experimental observable to detect it.
