On an unbiased and consistent estimator for mutation rates

Spontaneous mutations are stochastic events. The mutation rate, defined as mutations per genome per replication, is generally very low, and it is widely accepted that spontaneous mutations occur at defined, but different, rates in bacteriophage and in bacterial, insect, and mammalian cells. The calculation of mutation rates has proved to be a significant problem. Mutation rates can be calculated by following mutant accumulation during growth or from the distribution of mutants obtained in parallel cultures. As Luria and Delbrück described in 1943, the number of mutants in parallel populations of bacterial cells varies widely depending on when a spontaneous mutation occurs during growth of the culture. Since 1943, many mathematical refinements to estimating rates, called estimators, have been described to facilitate determination of the mutation rate from the distribution or frequency of mutants detected following growth of parallel cultures. We present a rigorous mathematical solution to the mutation rate problem using an unbiased and consistent estimator. Using this estimator we demonstrate experimentally that mutation rates can be easily calculated by determining mutant accumulation, that is, from the number of mutants measured in two successive generations. Moreover, to verify the consistency of our estimator we conduct a series of simulation trials that show a surprisingly rapid convergence to the targeted mutation rate (reached between 25th and 30th generations).