# Probabilities of trees

Tom DiBenedetto tdib at UMICH.EDU
Thu Sep 25 10:19:37 CDT 1997

```Richard Zander wrote:

Richard, I think your comparative analysis of the two approaches is
very thoughtful and thought provoking, but rests on a couple of
points with which I have fundamental disagreements.
1. re. max like:  you say:

>  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).

I think that this is certainly the claim of some proponents, but is
fundamentally a fantasy. The probabilities which one calculates are
probabilities *given the model and its parameters* and *cannot* break
through that to acheive the status of a statement of probabilities of
being the TRUE tree. On a gross conceptual level, in order to speak
to the issue of ultimate truth, you would need to include a factor
which addressed the probability that the model is TRUE, and I dont
think that is even possible, much less implemented. The max-like
phylogeny is simply a statement of what topology maximizes the
liklihood of the data given the model and that is all it can ever be.
The procedure has, in my opinion, the ability to be a very useful
tool in terms of doing just that,,,i.e. drawing out the phylogenetic
implications of a particular model, as it is applied to a dataset,
but that is a very different project than addressing the question of
whether a topology is TRUE.

2. re. parsimony,,you say:

>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.

First off, I am trying to hold onto a sense of your underlying point,
but I think this is a very confusing formulation. Parsimony does not
become antiparsimonious as it closes in on the mpt, and it does not
take up ad hoc assumptions. The criterea are consistent
throughout,,you may wish to claim that it is not appropriate to use a
parsimony criterion "all the way" to the mpt because of your belief
that by so doing one would subsume some number of true convergences
under a descent explanation (I think that is your point), but that
does not represent being "unparsimonious" or using ad hocs. Rather
your charge seems to be that we are being parsimonious when it is not
called for, or are refusing to use ad hocs when it is appropriate to
do so. (If we knew when it is appropriate to use ad hocs, we would
use that knowledge at the level of character coding).

> We get then the tree
>of maximum synapomorphy, or alternatively of minimum convergence. This
>is only very doubtfully the true tree.

By what criterion is this statement made? What is the special insight
you have  which allows you to assess the level of doubt we should
feel relative to the truth?

> 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)

This strikes me as somewhat circular. You criticize parsimony for
underestimating convergences based on your beliefs as to the
commonness of convergence,,this belief stemming from observations of
the amount of homoplasy found in parsimony analyses. If the amount of
homoplasy which one can see in the results of cladistic anayses is a
good basis for judging the prevelance of convergence, then you are
using your confidence in parsimony as an argument against parsimony.

>  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."

Reconstruction refers to a procedure of piecing back together an
"edifice" from the
scattered remnants which have survived. I think it is a very
appropriate metaphor for the approach followed by those who see
corroborated homologies as evidence in the structure of organisms, of
specific taxic relationship. A careful analysis of characters and
their distribution leads to (often unexpected) proposals that two
taxa are in fact more closely related than previously thought, This
is certainly an example of 'discovery". Even when new character
evidence is supportive of existing concepts of relationship, the new
apomorphies are "discovered". Perhaps your complaint is better
characterized by saying that you feel that parsimony is an
inefficient discovery process leading to inaccurate reconstructions,
but that is another matter.
I dont think that parsimony leads necessarily to over-interpretation.
It might do so, when convergences completely "mimic' homologies, but
this limitation is often not fatal to our efforts. For instance, in
the case of 'parallelism",
where sister species independantly evolve the same structure, and we
are unable to distinguish the two, and so propose them as a
homology,,,we may end up asserting one explanation while the other is
true, but if the two species really are sisters, we will not be led
to the wrong phylogenetic hypothesis,,it will merely seem to be
better supported by character evidence than it really is.
Parsimony procedures, like max-like,  do not directly
approach the question of ulitmate truth. We have a difficult task in
our attempts to reconstruct a pattern which is forever out of the
range of direct observation or experimental manipulation. An
examination of the procedures at the level of the details of the
algorithms merely address the question of whether the procedures
accurately deduce the phylogeny implied by the assumptions of the
approach. Max-like algorithms are probably quite excellent at
deducing the most likely tree for the model, just as parsimony
algorithms are excellent at extracting the best supported overall
pattern implied by a set of putative homologies. To address the
question of which prodecure is more likely to yield a correct tree
entails making a judgement as to which assumption set is more likely
to be legit; the model (for max-like) or the assumptions that
homologies are discernable from convergences through the study of
characters and the application of a congruence test over a set of
characters drawn from many different character systems (cladistic
parsimony).
We may argue as to whether there is legitimate reason to have
confidence in the models used by max-like when they are applied to
the questions of high-level phylogeny, but I certainly feel that the
assumptions of the homology/parsimony approach are valid, and must be
dealt with by anyone who adresses phylogenetic questions; either
using it as the primary discovery method, or being willing to deal
with the "homology implications" of relationships proposed through
other approaches.

Tom DiBenedetto                 http://www-personal.umich.edu/~tdib/
Fish Division                                   tdib at umich.edu
University of Michigan Museum of Zoology

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