Estimating divergence times

A statistical method of estimating population splitting times is developed in this paper. We consider three populations, with an assumed known tree topology for their phylogenetic tree. From simulation studies, we find that the method of moments performs very well, in particular for both large number of loci and divergence times, in estimating genetic divergence times. The bias decreases as the number of loci increases. The maximum likelihood method proves to be a good method for constructing an unknown phylogenetic tree, in particular for large divergence times.     

The genetic divergence of three populations

This paper considers the effect of the genetic divergence on the genetic composition of three samples drawn from three populations at some time after the populations had split. It generalizes the two-sample case studied earlier by Watterson (1985a). Under the assumptions that (i) mating is at random, (ii) the genes at a locus can be any of infinitely many alleles and all mutants are assumed to be new alleles, and (iii) no selective differences exist, we find the probability distribution of the sample gene configurations. From this distribution the single-sample allelic distribution after one-step and two-step bottlenecks and the allelic distribution in the two-sample case can be obtained as marginal distributions. Some numerical results on the number of alleles in common in the three samples are compared with those obtained by Watterson's simulation method; the agreement is excellent. Also, the probability that the three samples are monomorphic for the same allele is found, and numerical examples are given.