In the process of best inferring the most likely tree, not just any tree, given final haplotypes,, one must involve inferences of the node haplotypes --- that I am sure about --- unless one is willing to accept some loss of inference quality. Actually, the tree structure inference must yield a distribution of trees having different probabilities. This distribution may have a most likely tree, i.e. peak or peak(s) in the distribution. How much that improves the process I don't know. But if we are just interested in inferring the distribution of total time depth of the tree, or total time depth of tree and time for its nodes, some averaging over the different unseen haplotypes at those nodes can be done explicitly or implicitly through methods which don't invoke them in the first place. There must be some cost in quality of tree inference it would seem, however. From: Terry Sent: Sunday, March 25, 2012 9:09 PM To: y-dna-haplogroup-i@rootsweb.com Subject: Re: [yDNAhgI] PhyloTrees and Time Ken, Are you talking about an algorithm for how to construct a tree, like the ones I do, from a large set of haplotypes? Or are you talking about how to infer a haplotype of some past person, from just the set of haplotypes of known descendants living today? Terry On Mon, Mar 26, 2012 at 1:17 PM, Kenneth Nordtvedt <knordtvedt@bresnan.net>wrote: > I have never invested in trying to set up the software to try this, but I > suspect the best tree inference algorithm must be something like this. > > ... > ------------------------------- To unsubscribe from the list, please send an email to Y-DNA-HAPLOGROUP-I-request@rootsweb.com with the word 'unsubscribe' without the quotes in the subject and the body of the message