Probabilities on Phylogenetic Trees

Stuart G. Poss sgposs at WHALE.ST.USM.EDU
Tue Sep 9 17:16:48 CDT 1997

I think that there are a number of substantive issues with regard to the
probabilities of evolutionary events we can agree to talk about without
casting aspersions on a colleage who may have a different, if not
entirely clear view of what he means.

Perhaps some other genetic algorithm might like to make this thread even
more improbable by continuing it further.  I did (or was that a foregone

On a more serious note, would it not be that while all such "events" are
rare, the probabilities (improbabilities) we seek are those that provide
the strongest evidence that a given evolutionary event had actually
occurred over a given portion a particular evolutionary tree and having
taken place with an observed consequence relative to another, perhaps
better known event?  If one might be so presumptuous to suppose a
Baysian rather than non-Baysian probability model, we would then only
need to discuss the comparability of potentially unique evolutionary
events.  This would certainly seem easier, for base-pair substitutions,
than for morphological changes (excluding the potential for error
resulting from misalignment, reporting error, or the degree to which one
substitution might be influenced by change at either a "neihboring" or
otherwise linked sites, or the presence of outside selection for
particular base-pair combinations at given sites that might lead to the
non-independence of sites).

If I understand him correctly, I believe Richard Zander goes astray in
focusing on the independent probability of a number changes of state,
some potentially independent of others, in a single lineage.  While a
single evolutionary linneage can be modeled as a Markovian process,
knowledge of probabilities that a particular state change has occurred
within a linneage alone can not lead us to an understanding of the tree
topology that characterizes potentially multiple independent linneages,
unless we have prior knowledge of the distribution of nearly unique
"states" of a variety of characters.  Rather it would appear that such
probabilities are dependent on tree topology and may be conditional in
nature and not necessarily entirely independent from one time of
observation to the next (over the history of the tree).  Consequently,
if one wants to study the probability distributions of "evolutionarily
significant events" (character state changes) across a variety of
potential tree topologies, it might be more useful speak of cladistic
characters in a very formal sense (after Estabrook Felsenstein, and
others) or through detailed empirical study characters of particular
taxonomic groups and not using terms whose definition is vague in the
general case.  In any case, one must be particularly circumspect in
identifying what probabilities are to be calculated.

Fortunately, the probability of compatibility of two cladistic
characters over a given tree topology, while small, is finite.
Consequently, it can be shown to be either greater, lesser, or the same
as that for other pairs of cladistic characters.  Unfortunately, for
many differences, this may not always be enough to produce a consistent
statistical signal large enough to generate enlightened conclusions, at
least for some data sets.  However, only a few such models have been
proposed and for the relatively few studies done to date, their results
remain either highly controversial, thoroughly misunderstood, or right
on target depending on your algorithmic perspective.

Stuart Poss

Neal Evenhuis wrote:
> Well, it had to be done ... and I did it.
> I have employed the all-powerful Bayesian phylogenetic inference via
> Markov chain Monte Carlo Methods and, given the tremendous amount of state
> chages in Richard Zander during his evolution as a human being, I have
> determined that he has a REALLY REALLY low probability of existence. It
> may well be that throughout this thread on this list, we may have been
> merely reading an incredibly complex autoresponse algorithm...from a
> machine....
> ;-)
> Neal
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Stuart G. Poss                       E-mail: sgposs at
Senior Ichthyologist & Curator       Tel: (601)872-4238
Gulf Coast Research Laboratory       FAX: (601)872-4204
P.O. Box 7000
Ocean Springs, MS  39566-7000

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