Determination of Mutation Rates with Two Symmetric and Asymmetric Mutation Types

Abstract

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator μ^n for an unknown mutation rate μ of microorganisms. Previously, we proved that the associated sequence of estimators μ^n converges to μ almost surely pointwise on a nonextinct set Ω0. Here, we show that this sequence converges also in the mean square with respect to conditional probability measure P0·=P·∩Ω0/PΩ0 and that, with respect to P0, the estimator is asymptotically unbiased. We further assume that a microorganism can mutate or turn to a different variant of one of the two types. In particular, it can mean that bacteria under attack by a virus or chemical agent are either perishing or surviving, turning them to stronger variant. We propose estimators for their respective types and show that they are a.s. pointwise and L2-consistent and asymptotically unbiased with respect to measure P0.