# Probabilities of trees

Richard Zander bryo at COMMTECH.NET
Thu Sep 25 08:34:52 CDT 1997

```Okay, one last time. After the latest flurry of go-rounds from the

Maximum likelihood techniques, if you allow all the assumptions,
introduce a probability model (if you allow that) which allows
calculation of posterior probabilities (chance that a given tree is the
correct tree). With a small data set, you can get a probability greater
than .5 for a particular tree, and so you have a phylogenetic
hypothesis. With large data sets, however, the tree with greatest
probability is generally less than .5, lots less. Only some parts of
that tree may be the same in all trees of the .5 "credible region."
There is a pool of trees, therefore, that probably include the true
tree, but the true tree is improbably the same as the tree of maximum
probability.

Maximum parsimony techniques are parsimonious in eliminating trees
that are grossly unreasonable by the theory of common descent with
modification. At the (vague) point that the method begins to eliminate
trees that are not unreasonable phylogenetic hypotheses, it is
to eliminate all but the tree that assumes that ALL covariance that can
possibly be ascribed to common ancestry must be so. We get then the tree
of maximum synapomorphy, or alternatively of minimum convergence. This
is only very doubtfully the true tree. There is no probability involved
since the assumption that all covariance possible with a particular
polarization must be treated as ancestrally shared is false, because at
least at the species level, characters are usually simple and commonly
often separately evolved (judging at least from cladistic homoplasy) if
not in the group studied then in related groups (the larger the group,
the smaller the consistency index, which is expected of course).

The tree of maximum synapomorphy is valuable as a basis for a
classification emphasizing theoretically possible ancestral
relationships, but it must be recognized as overly interpreted, and
hardly a "reconstruction through a discovery process." It can also be
used as a tree of minimum convergence: overlaid on a phenetic ordination
it can identify theoretical convergence of taxa.

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Richard H. Zander, Buffalo Museum of Science
1020 Humboldt Pkwy, Buffalo, NY 14211 USA bryo at commtech.net
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