MICROSATELLITE GENETIC DISTANCES WITH RANGE CONSTRAINTS - ANALYTIC DESCRIPTION AND PROBLEMS OF ESTIMATION

Statistical properties of the symmetric stepwise-mutation model for mi crosatellite evolution are studied under the assumption that the numbe r of repeats is strictly bounded above and below. An exact analytic ex pression is found for the expected products of the frequencies of alle les separated by k repeats. This permits characterization of the asymp totic behavior of our distances D-1 and (delta mu)(2) under range cons traints. Based on this characterization we develop transformations tha t partially restore linearity when allele size is restricted. We show that the appropriate transformation cannot be applied in the case of v arying mutation rates (beta) and range constraints (R) because of stat istical difficulties. In the special case of no variation in beta and R across loci, however, the transformation simplifies to a usable form and results in a distance much more linear with time than distances d eveloped for an infinite range. Although analytically incorrect in the case of variation in beta and R, the simpler transformation is surpri singly insensitive to variation in these parameters, suggesting that i t may have considerable utility in phylogenetic studies.