The limit distribution of the number of rare mutants

Abstract

We study the number of mutants in a mutation process in which reverse mutation is allowed and in which both normal and mutant organisms reproduce at the same rate. Under a mild side condition on the rate of forward mutation we find necessary and sufficient conditions for the number of mutants to converge in distribution. We find the probability generating function of the limit distribution, when it exists. We present an example which shows that the mild side condition cannot be relaxed.