On three methods for estimating mutation rates indirectly.

Methods for estimating a mutation rate mu has been proposed by Kimura and Ohta; Nei; and Rothman and Adams. It is shown here that all three methods are best applied to rare alleles and that they are all based upon the assumption that all alleles ultimately become extinct. If there is a neutral allele in a growing population, there is conditioning on ultimate extinction, which implies that the underlying stochastic process can be approximated by a branching process for which the mean number of offspring is less than 1. The low numerical values of t0, the mean time to extinction of a line descended from a single mutant, found in two simulation studies, can be attributed to two features. First, the data on which these studies were based came from a fairly rapidly growing population. In such a population, we would expect that extinction, if it does occur, takes place quickly. A second factor is that the effective population size is somewhat lower than the actual number of adults. Population subdivision and migration does not seem to play a significant role. Conservative high and low estimates of mutation rates are computed, and an estimate is obtained for the standard deviation of the estimate of mu. These allow a rough estimate of a 95% confidence interval, which contains estimates of mu found by Neel and Rothman.