A philosophical question

Joe Felsenstein joe at evolution.genetics.washington.edu
Sat May 13 01:50:03 EST 1995

In article <m.a.charleston-0505951831410001 at youbastard.zo.utexas.edu>,
Michael A. Charleston <m.a.charleston at mail.utexas.edu> wrote:
>I'm new to this, so forgive me for any clangers I may make.

Don't believe him -- he already writes good papers on the subject.

>You have a phylogeny problem on n taxa,
[and a space of possible trees]
>The objective function on this space is something like the parsimony
>length or the log-likeligood.
>So you can imagine "hills" and "troughs" in this graph, where the "height"
>is proportional to the goodness - to be maximised - of the trees.
>Anyway - the situation is this: you have a great many trees in one big
>Somewhere far removed from this
>broad hill is a single spike, so there are many fewer starting trees (and
>climbs) that would lead you to the top of this spike, but the objective
>function value is higher at the top of this spike than it is at the top of
>the broad hill.
>My question is this: which tree - or trees - do you consider as "better"?

The spike, no contest.

>My view is that there should (ideally) be some commonality between the
>trees at the top of the hill and at the top of the spike, which is being
>obscured by out choice of tree perturbation (and therefore tree
>adjacency), and that by choosing more appropriate criteria for "closeness"
>of two trees we may figure out what's going on.  This may be very naive of
>me: I would appreciate the views of those reading this.
>Knowing some properties of the "slopes" of this kind of graph would
>clearly be useful in determining when this situation will arise, if ever,
>but that's not the question.  If it *does* arise, what do you do?

If the hill and spike are close in height then any interval estimate of the
tree (confidence interval, for example) should include the tops of both.
If they are not close in height then the hill tree are worse.

I think it's a challenge to find all these trees, but not to deside what to
prefer once you have found them.

Joe Felsenstein         joe at genetics.washington.edu     (IP No.
 Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360

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