# [Fwd: Re: Probabilities on Phylogenetic Trees]

James Francis Lyons-Weiler weiler at ERS.UNR.EDU
Tue Sep 16 12:53:42 CDT 1997

```On Tue, 16 Sep 1997, Tom DiBenedetto wrote:

In response to Richard Zander

> Wow,,,this is a strange perspective. If you find the bloody knife in
> the butler's locker, and it has his fingerprints on it, and the
> victim was known to be blackkmailing him, and he has no alibi for the
> time of death, perhaps you may bet your career on his guilt. But
> given that there are 6 billion potential murderers in this world, at
> some scale you could consider that to be a low-probability result.
> But of course, you go out to collect evidence precisely for the
> purpose of narrowing the scale of your possibilities. Instead of 6
> billion, you narrow the scope down to those who had no alibi, those
> who were being blackmailed, ultimately, to those whose fingerprints
> match those on the knife.

How can you narrow the scope down to those that have no
alibi, those that were being blackmailed, etc. unless
you have checked all 6 billion?  You can't really.  So
you really rely on the covariance of the evidence, and
the implicit (hidden; read as the opposite of explicit)
probabilistic measure of "surprise" that we actually
found one individual that fits the improbabilistic bill.

Statistics merely formalizes the process you describe.
Our guesses include that the victim was not a rampant
blackmailer, for example (a Bayesian prior, whether

> In systematics, we go out to collect
> evidence. A matrix is the result of our investigations. The
> probability of a result may be low in the face of no evidence, but is
> high in the context of the evidence.

Huh?  The probability of the evidence is high in the
context of the evidence?  No kidding...

It takes a healthly dose of positivism to say that the
tree we get from the evidence we collect then has a
high probability... You've lost the game of science from
the get-go unless you concern yourself with a critical
test of the (apparent) informativeness of the evidence
you have collected.  Dick's point is entirely salient
functions of the data, the algorithm, and the tree(s).
Just because he's posing a complex question doesn't
mean that it's not worth asking.

In fact, for the shortest tree,
> it is maximized, relative to the evidence.

Huh, again?  The probability of a tree is maximized
relative to evidence if it is the shortest tree?
What does that mean? What are you saying?  That
given the shortest tree, the shortest tree becomes
a highly probable event?

Others rampantly disagree.  The LESS probable a result
is, the more surprised we are, and the greater the
corrorborated the result is.  You can't discuss the
objective application of probability theory if
one never bothers to measure the probability of an
event.  A roll a die.  It lands on six.  What was the
P(6)?  I look at the evidence.  P(6) = 1.0?  No.
P(Tom will get an F on a probability exam) = ????

(For the uninitiated, Tom is immune to real criticism,
so my flames are not ever really felt by him).
.
> Ultimate probabilites for unique historical events (did they really
> happen?) are either 0 or 1. Intermediate probabilites can only be
> calculated relative to a base of evidence, and are reflective of our
> sense of the reliability of the evidence. Character matches are
> statements of homology which are conclusions based on the sum of our
> biological knowledge. A shortest tree has the
> highest probability *given the evidence* of everything we think we
> have learned about the biology of the character system. within of
> course, the
> underlying assumptions. I cant imagine that you can do better than
> that.

Again, most statisticians would disagree.  We use
parsimony to estimate the population mean; in fact,
the sample mean is the value with minimum error around
it, and is the maximum likelihood estimate of the sample
mean when the proper assumptions apply. The fact that
we try to be precise in our measurements is a given.

The degree of confidence in a tree or group should be
a function of the low probability of that group given
an appropriate null.  Why?  Because the probability
that one or more shortest trees exist for any matrix
with variable character states is ca. 1.0, and the probability'
that those trees will denote groups can be very high, regardless
of the process that generated the matrix.

>
> >> Are you basing that [this talk of the probability of the true tree] on some b
> elief >>that a particular model is an accurate mirror of evolutionary process?
>
> >Exactly. Assuming that the particular model and particular regularity
> >assumptions you are using are indeed true,*mathematically* can you
> >evaluate the probability that you have retrieved the true tree?
>
> If your process model is TRUE, then why wouldnt your tree be TRUE?
> The whole problem arises from the fact that we KNOW that our process
> models are not true,,and the only way to make them approach the truth
> is to formulate them with reference to well-corroborated observable
> regularities (patterns). We learn about processes through the
> procedure of devising explanations for patterns, not the other way
> around.

Sounds like a justification for maximum likelihood parameter
estimation to me.  Also, cladistics in vitro was process-
oriented... evidence of shared geneaological descent
invokes a multitude of processes, among them inheritance,
geneaology, birth, death... and the evidence is
taken directly from the pattern of character state changes
on a parsimony tree (or so they thought).  So what that the
pattern is really not an observation, but rather is an
inference, a guess?  So what if the degree to which we
might expect character state distributions to be hierarchically
distributed appears to require knowledge we can't ever have?

Your process position is a straw man.  The degree to which
we might expect to see something is FAR different that the
degree to which we do in fact see something.  the question
is, are we observing something (an amount of pattern, a
short tree) that deserves a PHYLOGENETIC explanation, or
is it a result that could have happened by chance alone?
If the result (the degree of covariation in the implied
'       hierarchy found in a matrix) can be easily dismissed as
a chance event, it (in total) doesn't require a geneaological
explanation.  Sure, genealogy and inheritance may have been
ongoing, but those processes and the processes of character
evolution may have interacted in ways that DESTROY or
mask the evidence of geneaology you expect to find on the
mpt. To say otherwise is to claim sufficient knowledge of
evolutionary processes.

J. L-W.

```