pierre deleporte pierre.deleporte at UNIV-RENNES1.FR
Fri Sep 6 19:33:00 CDT 2002

```A 11:17 05/08/2002 +0200, Zdenek Skala wrote :
>to summarize a bit:
>
> >My class theory accepts any kind of "equivalent
> >properties of individals" for classifying into classes of equivalence (by
> >difference with similarity clustering). A "character of an object" may thus
> >be historically defined (why not ?).
>
>Yes, why not. The problem is still the same; in the case of matrix:
>
>   1 2 3 4 5
>A - + + + +
>B + + + + +
>C + + + - -
>D + - - - -
>(((AB)C)D)
>
>... you simple have no "equivalent property" shared by all individuals.
>You can recode the homoplasy (-1) in (A) into something like (-1)' arguing
>that the (-1) in "A" is different from the (-1) in the outgroup. Even in
>this case you have no property shared by all individuals; you have only
>one new character state (-1)' which is, of course, also different from
>(+1). Arguing that this (-1)' "is a plain historical avatar of (+1)"
>(pierre d.) does not make any sense - sorry. In the same manner you can
>say that +2 or +5 is a historical avatar of -2 or -5 and thus deny all the
>structure of character matrix and the resulting cladogram.
>Hence: clades are not classes but similarity-based objects like in the
>cluster analysis.
>Best regards!
>Zdenek

I think I see your point.
For monophyletic taxa to be classes of equivalence, the matrix above should
be recoded :

1   1'        2   3   4   5
A   +   -        +   +   +   +
B   +   -        +   +   +   +
C   +   -        +   +    -    -
D   +   -         -    -    -    -

The recopding of columns 1 and 1'  makes sense only because the
1'  character state is considered a derived avatar of 1. The formal
recoding above highlights the class nature of clades.
My point is that such a recoding is just what we do, implicitly, when we
accept the cladogram and all its consequences, including identifying
homoplasies (I suppose you finally agree that we don't overlook homoplasy),
and including interpreting the absence of 1 in taxon A as a reversal, a
"secondary loss of 1", that is the historical inherinytance of "presence of
1" turned into the state "disappeared" (could also be : transformed in
another, derived, character state "1'').
The status of classes of monophyletic groups can be aknowledged neither if
one sticks to the initial data matrix coding despite the discovery of the
best cladogram, nor if one does not accept a "historically continuous"
definition of homology between different states of a same character.

Symptomatically, if you drop this notion of homology by descent and recode
your data matrix in terms of mere presence of character states taken
individually (ignoring which of them belong to the same character), you
obtain... a phenetic clustering. This is exactly what happened to a version
of "three taxon analysis" to which I referred in previous posts.
I stop here, for fear of developing the argument again.

So I must disagree : clades are classes. Viewed this way, for a cladist
using cladistic concepts of homology, of course.

Maybe this would give a handle for accepting some notion of "natural
classification" after all:
features interpreted as nested synapomorphies define classes... to the
difference of phenetic clustering based overall and "face value"
similarity, which would constitute a set of "natural similarity-based
objects", not natural classes.

best,
Pierre

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