# [Fwd: Re: Probabilities on Phylogenetic Trees]

Tom DiBenedetto tdib at UMICH.EDU
Tue Sep 16 11:28:28 CDT 1997

``` Richard Zander wrote:

>, suppose the results of phylogenetic analysis were probabilistic,
>had some statistical basis (just suppose...maybe there is no such
>basis). Then suppose a 12-sided regular die, with sides numbered 1
>through 12. It is a totally unbiased and fairly cast die. Suppose you
>painted three sides red. The chance of rolling a red side is four times
>greater than that of rolling any one other side. Maximum likelihood is
>that the red side is the best explanation for any resultant number after
>a roll; *but* the chance of being right is low. I think a cladogram is
>similar. You bet your science on a result of low probability (the least
>wrong answer).

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

> In other sciences this is okay since you can test least
>wrong answers right away, but we can't do that.

Why not? Search out more evidence. (Focus on a different
charcter-system,,,now there is an idea!)

>A series of cladograms, each depending on the one previous to establish a correct >outgroup, is a house of cards.

Whatever the problem might be that you are trying to point out, it
would seem to be addressed only by a method which could objectivly
root the tree of life, and then establish relationships for all of
life  at one pass. Do you have such a method?

>  But then, if there is no probabilistic, statistical basis, are we then
>dealing with a second way of using cladistic analysis, as a clustering
>method that interprets data on the basis of theory, where nothing is
>discovered, and the taxa are grouped according to a distance measure
>from a presumed hypothetical ancestor.

huh??? i havent a clue as to what you mean by this...

> I kind of like this second way of
>using cladistics, since it is an advance over phenetics and over
>"omnispection" guesswork since it uses computers to project (simple)
>theory into the relationships of all taxa.

Doesnt sound anything like cladistics to me, so once again......?????

>Question: How much Bremer support does it take to give the subclade a
>probability >.5 that is matches the same in the true tree?

Bremer support does not attempt to answer such a question.

> Does
>Bremer support of 4 as opposed to Bremer support of 3 mean anything?

Yes, it means that the clade is somewhat better supported by
character evidence.

>> Are you basing that [this talk of the probability of the true tree] on some belief >>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.

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

```

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