SIMULTANEOUS ESTIMATION OF ALL THE PARAMETERS OF A STEPWISE MUTATION MODEL

Minisatellite and microsatellite are short tandemly repetitive sequenc es dispersed in eukaryotic genomes, many of which are highly polymorph ic due to copy number variation of the repeats. Because mutation chang es copy numbers of the repeat sequences in a generalized stepwise fash ion, stepwise mutation models are widely used for studying the dynamic s of these loci. We propose a minimum chi-square (MCS) method for simu ltaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator require s knowing the mean number of alleles of a certain size in a sample, wh ich can be estimated using Monte Carlo samples generated by a coalesce nt algorithm. The method is applied to samples of seven (CA), repeat l oci from eight human populations and one chimpanzee population. The es timated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutatio n has a slight tendency to cause size increase and (2) the mean size i ncrease is larger than the mean size decrease for a mutation. Our esti mates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majorit y of the estimated ancestral allelic types are reasonably accurate. Im plications of our analysis and potential extensions of the method are discussed.