Probabilities on Phylogenetic Trees

[John Trueman]

James wrote:

>>        Explicitly, the degree of
>>        corrorboration afforded to the sets of congruent hypotheses
>>        is lower than it could be because previously screened
>>        hypotheses of homology have a a HIGH, not a LOW,
>>        probability, as so the presence of congruence has a HIGH, not
>>        a LOW logical probability, so boldness is low.

And Tom responded:

>Here is a hint as to why your logic is faulty. In Poppers view (and
>you are using his concepts so I imagine you are making reference to
>him), a hypothesis of low boldness is indeed one with high
>probability. It is also a hypothesis which departs minimally from
>"adhocness". An ad hoc hypothesis is one which explains the details
>of particular phenomena, with minimal recourse to general notions. It
>is highly probable because it it says almost nothing beyond
>describing the immediate phenomenon, and so it has low boldness. In a
>parsimony analysis, the *least* parsimonious tree would be one which
>maximizes ad hoc statements. Those 4000 instances of hair are not
>one, they are 4000 separate instances. Describe each one
>separately,,,no generalization, no boldness, very hgh probability.
>Now think hard about what the opposite situation (*most* parsimonious
>tree) would be,,,,,

I'm with Tom almost all the way.  Except one thing:  Is the *least*
parsimonious tree really the least bold, or is it almost as bold as the
*most* parsimonious tree?  I'd have thought a tree somewhere in the middle,
where the distribution of hair across taxa if there were no hierarchy of
hairy-taxa to discover, so that hairyness occurred merely by chance, would
be the least bold of all tree-like hypotheses?

John

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John Trueman
Bioinformatics Unit
Research School of Biological Sciences
Australian National University        -------------------------------
Canberra, ACT 0200,  AUSTRALIA       | Progress is made when a timid |
                                     | hypothesis is rejected or a   |
                                     | bold one is not.              |
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