The population genetics of parthenogenetic strains of Drosophila mercatorum - I. One locus model and statistics

A one locus model has been developed to describe parthenogenetic populations restoring diploidy by central fusion, terminal fusion and gamete duplication. It was found that in the absence of selection all populations become homozygous. With selection, however, it is possible to maintain heterozygotes and homozygotes. The conditions required to yield such an equilibrium are a function of (1) the proportions of the various diploid restoring mechanisms (2) linkage to the kinetochore and (3) the intensity of selection. The model was then used to derive one-generation likelihood functions. These likelihoods were used in deriving estimation procedures for the frequency of gamete duplication which is important in forming isogenic lines and for the probability of a heterozygous female giving rise to a heterozygous zygoid. Next, n-generation likelihood functions with and without selection were calculated. These were used to estimate the selection coefficient and to derive two tests of the hypothesis of no selection versus the hypothesis of selection. The first test is a locally best test in the vicinity of no selection, and the second an "odds" for the hypotheses using a prior distribution on the selection coefficient.