  We consider an infinite asexual population with a mutator allele which can
elevate mutation rates. With probability $f$, a transition from nonmutator to
mutator state occurs but the reverse transition is forbidden. We find that at
$f=0$, the population is in the state with minimum mutation rate and at
$f=f_c$, a phase transition occurs between a mixed phase with both nonmutators
and mutators and a pure mutator phase. We calculate the critical probability
$f_c$ and the total mutator fraction $Q$ in the mixed phase exactly. Our
predictions for $Q$ are in agreement with those seen in microbial populations
in static environments.
