The estimation, and testing for the presence, of a selective advantage of one allele over another is considered. It is assumed that a population's allele frequencies are known from some initial time until fixation of one or other allele occurs. The statistics needed to perform the estimation and testing are the heterozygosity of the population summed over all generations, and the observation of which allele fixes. It is shown that certain asymptotic probability distributions arise which are similar to those proved by Brown and Hewitt for statistical inference from diffusion processes, but their results assumed that the diffusion had a stationary density which is not the case for alleles which fix.
The genetic diffusion may be transformed to Brownian motion with constant drift, and the inference questions concerning selection can be transformed to questions about the first exit of a Brownian motion from an interval. It is thus possible to construct significance tests, and to calculate the power of those tests, for detecting selection.
