Probabilities on phylogenetic trees

Ted Schultz schultz at ONYX.SI.EDU
Mon Sep 8 10:07:23 CDT 1997

I am confused by Richard Zander's recent comments on Taxacom about how
phylogenetic trees have low "posterior probabilities."

Three questions:

1) How do you calculate the posterior probabilities of phylogenetic trees?
Where do you obtain the prior probabilities that are a necessary part of
the calculation of posterior probability?  (As I understand it,
maximum-likelihood values are not such probabilities.)

2) Where in a reading of Farris 1973 do you find a proof that phylogenetic
trees have low posterior probability?

3) If a tree topology is 99% correct and 1% incorrect, does that tree fall
into the category of "incorrect"?  If so, this might explain why any tree
topology has a low probability of being 100% correct, but a high
probability of being, say, 95% correct.  (I can't say for certain, however,
since I don't know where these posterior probabilities are coming from.)

A way of dealing with the fact that any given tree may have a low
probability of being 100% correct (in parsimony or likelihood methods) is
to include in your solution set multiple trees such that, together, you are
confident (at, for instance, the 95% level) that the set includes the
correct tree.  This "error" range on trees has been advocated for some time
now, and is part of the rationale behind putting support values on
branches.  It is often the case that such sets of trees often have many
features in common, e.g., they usually all share the same well-supported
branches.  Obviously, then, the idea that an optimal tree is kind of a
random draw from the set of all possible trees that is suggested by the
"low posterior probability" argument is not borne out by the results of
phylogenetic analyses to date.

Ted Schultz, Research Entomologist
Department of Entomology, MRC 165
National Museum of Natural History
Smithsonian Institution
Washington, DC 20560

schultz at
Phone (voice and fax): 202-357-1311

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