  We study a mutation-selection model with a fluctuating environment. More
precisely, individuals in a large population are assumed to have a modifier
locus determining the mutation rate $u \in [0,\vartheta]$ at a second locus
with types $v \in [0,1]$. In addition, the environment fluctuates, meaning that
individual types change their fitness at some high rate. Fitness only depends
on the type of the second locus. We obtain general limit results for the
evolution of the allele frequency distribution for rapidly fluctuating
environments. As an application, we make use of the resulting Fleming-Viot
process and compute the fixation probabilities for higher mutation rates in the
special case of two bi-allelic loci in the limit of small fitness differences
at the second locus.

Probability