[Fwd: Re: Probabilities on Phylogenetic Trees]

Richard Zander bryo at COMMTECH.NET
Mon Sep 15 14:15:10 CDT 1997


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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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Message-ID: <341D71EE.7F15 at commtech.net>
Date: Mon, 15 Sep 1997 10:35:42 -0700
From: Richard Zander <bryo at commtech.net>
Reply-To: bryo at commtech.net
Organization: Buffalo Museum of Science
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To: Tom DiBenedetto <tdib at umich.edu>
Subject: Re: Probabilities on Phylogenetic Trees
References: <199709150201.WAA22853 at mothra.rs.itd.umich.edu>
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Tom DiBenedetto wrote:
>
> On Thu, 11 Sep 1997 07:40:13 -0700, Richard Zander wrote:
>
> >Simply put, I'd like a
> >measure of when my shortest tree has more evidence for than against.
>
> I dont understand. Given that there are a finite number of trees, the
> "evidence
> against" must refer to evidence for an alternative. The shortest tree
> has more
> evidence supporting it than does any of the alternatives, By

Yes, more evidence supporting it than any ONE of the other trees. But
the sum of the probabilities (total evidence AGAINST) of all other trees
is larger than that for the shortest tree.

> defintion. If you
> want to know whether your shortest tree has more evidence supporting
> it than
> there is evidence for all alternatives combined, then I wonder,,,why?
> What is
> the significance, or even the meaning of that?

Well, 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). In other sciences this is okay since you can test least
wrong answers right away, but we can't do that. A series of cladograms,
each depending on the one previous to establish a correct outgroup, is a
house of cards.
  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. 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.

>
> >  Also, if my shortest tree isn't well-supported, I'd like to identify
> >portions of the cladogram that have more evidence for than against.
>
> once again, why would the branch be present in the shortest tree if
> there wasnt more evidence for it than against it?

See above.

>
> > (I
> >think this is what people mean by "we don't think our cladograms are
> >necessarily exactly right, but they are probably mostly right." Surely
> >one can provide a measure of how right various subclades are other than
> >the open ended ones of Bremer support, etc.)
>
> What is your problem with Bremer support, and why do you need an
> alternative?

Question: How much Bremer support does it take to give the subclade a
probability >.5 that is matches the same in the true tree?
(Mathematically, I mean, assuming all the assumptions were okay.) Does
Bremer support of 4 as opposed to Bremer support of 3 mean anything?

>
> >  I think that if you have poor support (evaluated as the probablility
> >of being the true tree is < .5),
>
> Sorry I havent been following the thread carefully (been out of the
> country), but how can such a thing be calculated without knowledge of
> the true tree? Are you basing
> that 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? What do
you need to do this? I don't know how. Does anybody? Maximum likelihood
people seem to know how, and use estimates for evolutionary rates and
other regularity assumptions. See
http://www.stat.wisc.edu/~newton/papers/abstracts/tr961a.html
Can we do this with max parsimony? How? What assumptions must be spelled
out?

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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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