Weights
James Francis Lyons-Weiler
weiler at ERS.UNR.EDU
Thu Feb 27 13:28:01 CST 1997
On Thu, 27 Feb 1997, Tom DiBenedetto wrote:
> On Thu, 27 Feb 1997 06:37:40 -0800, James Francis Lyons-Weiler wrote:
>
> >Consider the fact that when one decides to not weight morphological (or
> >molecular) characters, one has decided that a transformation among states
> >in character i has the same information (and therefore relative
> >probability) as a transformation among states in character j.
>
> One does not *necessarily* do that. Only if you are approaching the
> question from the perspective of presuming to be able to make
> judgements as to the "information content" of a particular character
> based on what has happened elsewhere within a similar class of
> character.
My point is that one has no choice but to make such a judgement;
equal weighting presumes equal probabilities and information
content. Take for instance a nucleotide change (A->T) and a
loss of a vertebra; not weighting one over the other implies
(hence the implicit assumption) that both have been and are
equally probable events. (Arguments about whether one should
or should not combine such data also hinge on the implicit
probabilities of character state changes. Character state
DIFFERENCES necessarily translate into CHANGES in the context
of a parsimony tree. One may not by default weight differences,
but once a change is implied (polarity aside), implicit
probability estimate manifest themselves. The assumption that
homoplasy is relatively rare is itself lets in the role
and influences of probability. Parsimony is a probability
argument; it's just a rather diffuse argument.
> >That is, a decision to use equaly weight is arbitrary, and requires
> as much
> >justification as any weight weighting scheme.
>
> Unfortunatly, the decision to use any weight, equal or not, is
> arbitrary in the probabilistic approach, because it must be based on
> some sampling of presumed knowledge, often inferred from different
> (hence irrelevant) systems or based on estimates drawn from
> generalized understandings of process.
>
Are you agreeing with me... AGAIN? If so, please stop;
I'll get a reputation!!!!!!
> This is a problem with the probabilistic approach. In a parsimony
> approach, one does not assign probabilities to presumed
> transformations; one attempts to group taxa in such a way that one
> extracts the best-supported hierarchy of congruent transformations
> amongst presumed homologies. This is supported by the basic
> evolutionary insight that true homologies will be congruent. From
> such a perspective, each transformation is a putative homology, a
> hypothesized evolutionary event. As such, all have equal evidentiary
> weight.
I think you're confusing characters and character states with
their transformation. Maybe you mean something different;
certainly the differences among characters carry the evidentiary
weight, but how much information the _implied_ (parsimonious)
transformations among the states have always been made with
an implicit assumption of the probability of such events.
Differences carry the evidentary weight that they are different,
an nothing else. It's within the context of the relative
probabilities of transformations that weighting has the most
impact. Weighting characters or states can't make them
identical, it can only make their differences or similarities
more or less relevant.
>
> >(Felsenstein (1983); NATO symposium) made the excellent and astute point
> >that parsimony requires implicit statements about the probability of
> >character evolution; these probability statements are merely made explicit
> >under generalized parsimony.
>
> I find Felsenstein's point to be a rhetorical gambit to shore up
> support for a probabilistic approach to phylogeny reconstruction. In
> fact, a parsimony-based approach makes no such implicit statements
What's an implicit statement? (I think it's an oxymoron.)
I obviously disagree. Parsimony doesn't require EXplicit
probabilistic assumptions (excluding, of course, the obvious
point of the (relative) probability of homoplasy). I would
also add that parsimony requires implicit assumptions
about the distribution of homoplasy...
> for it does not operate in a probabilistic framework. And he
> certainly knows that.
I wonder...
> Probabilism seems to run into at least two
> fundamental limitations. First of all, one can only calculate the
> probabilities of historical events from the perspective of a
> sophisticated understanding of the course of history, This makes the
> use of probabilism in the effort to lay out that understanding of
> history rather problematical ("circular" works well here too).
Parsimony is therefore circular.
> Secondly, even if one were to arrive at an "accurate" estimate of the
> probability of an historical event, that would only be useful on a
> general level. The need, in phylogeny reconstruction, is to pass some
> sort of judgement on unique, singular events, and these either
> occurred or did not. Their "probability" is 1 or 0. Their calculated
> probability in the context of presumed knowledge of general processes
> is really irrelevant to the question of whether one particular
> instance occurred or did not.
The "judgement" is the where the implicit assumptions
of probability reside. You are arguing again that
parsimony does in fact require probability statements,
and you have gone so far as to enumerate what YOU think
they are. My point is that P(E) = 1 and P(Not E) = 0
are points on a continuum, and they are used to mask the
fact that the transformation
A -> B -> C -> D -> A -> C -> D -> A -> Z
can look like
A -> Z
on a parsimony tree, and the probability of the latter would
have been (in that transformation series) 1/8, but
an equal weighting that conflates an observaed difference
with a singular would use a default weight of 1.
James Lyons-Weiler wrote:
>Consider the fact that when one decides to not weight morphological (or
>molecular) characters, one has decided that a transformation among states
>is character i has then same information (and therefore relative
>probability) as a transformation among states in character j. That is, a
>decision to use equaly weight is arbitrary, and requires as much
>justification as any weight weighting scheme... .
Alan Harvey wrote:
>>So how's this? "I have no a priori evidence, or other reason to suspect,
>>that any (much less which) of my characters are more informative than
>>others?" Granting that "unweighted" characters do in fact have a weight
>>of one, I'd still say that a prima facie case exists for "oneweighting"
>>characters as your default condition.
That's one strategy. Why not use a sensitivity
analysis, and try out various weighting schemes on either
side of 1:1?. If you have no reason to suspect that
any of your characters are more informative than others,
than you have no reason to suspect that they are equally
informative, eitther. 1:1 is an arbitrary point on
a continuum of arbitrary points, and I'd better quit
before I make an arbitrary point myself!
James Lyons-Weiler
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