One question, though: Are the number of nodes and the connectivity of the tree determined by the N final haplotypes, or could they in principle vary? If the latter then I suspect the Monte Carlo would be at best a lot harder, maybe too hard. [[I left the connectivity of the tree out to help audience digestibility before we faced that. What was described in previous message would have to be done for all alternative tree connectivities in principle, and the maximum liklihoods for each then compared. N final haplotypes certainly don't specify the tree connectivity. This makes a Monte Carlo method which could run backward in time more promising perhaps? Haplotype pairs close together in the given set of "final" haplotypes will be more likely to converge to same haplotype as time goes backward than haplotypes further apart, so it naturally gives the more likely connectivities added weight (count) in the reversed time Monte Carlo. ]] - Rich Holmes p.s. Maybe you have made a convert of me to a backward in time Monte Carlo approach? Ken p.p.s Now I am really in a tizzy about Monte Carlo running backward in time. Surely the transition or mutation rate for the STR molecules is time reversal invariant. But I see no chance that N different haplotypes will, except in the tiniest fraction of cases, collapse back to a single founding haplotype after some finite number of generations into the past. They will most of the time become more different from each other --- i.e. increase their population variance. So at the moment I find the Monte Carlo running backward in time paradoxical? I guess a flashback to Boltzmann and entropy and time reversal arguments in physics more than a century ago is upon me.