Weights

Tom DiBenedetto tdib at UMICH.EDU
Fri Mar 7 08:43:25 CST 1997


Guy Hoelzer wrote:

Tom sez:
>>As to the question of simply using such an apriori factor or not,,I
>>choose not to. My justification makes no reference to process
>>considerations, because my approach does not attempt to include
>>presumptive knowledge of these factors to begin with.
>
>I beg to differ here.  By weighting equally you are asserting presumptive
>knowledge.

Well I guess its brick wall time for the two of us,,,,I dont know how
to put this any differently,,,whatever "presumptive" knowledge I am
asserting has nothing to do with the probabilities which fascinate
you,,my method is not structured around such concerns,,,my equal
weighting is based on a perception that there are no inherent
inequalities in homologies, and I am merely trying to combine a set
of corroborated homologies and thus subjecting them to a logical
test. Were I to observe perfect congruence in my set of homologies, I
would publish it as is; I would have a nice, clean reconstruction of
phylogeny based on character evidence.  My perception of incongruence
leads me to apply a final test, using a parsimony critereon, to find
the pattern supported by the preponderance of the evidence. You are
doing something different,,in your method, any value
assigned to the weighting factor refers to probabiltites...I dont
really understand why you refuse to accept that yours is not the only
appraoch to phylogeny,,

>>I am dealing with a set of homology hypotheses which are being combined in the
>>parsimony algorithm into a logical hierarchy.
>
>You are also doing this.

well thank you very much. I take this as great progress.

>But you explicitly recognize inherent equality in the frequency with which
>different characters will contain homoplasy.

I recognize in general that this will be so for different specific
characters. I *do not* make generalized presumptions on this issue a
priori.

>You seem to recognize that
>homoplasy can pass through your filters, even though you do your best to include
>only homologous characters.  The homoplasy will probably not be distributed
>evenly among the characters, so asserting equality among characters is likely to
>be wrong and might mislead your tree.  You have imposed a variable which can
>structure the outcome.

Obviously homoplasy can pass thru my filters; if that were not the
case, I would only need to filter a few characters, and they would
all be congruent, and I woulnt need a congruence test. But given that
I arrive at a matrix with a set of characters which have passed
through all the tests I am willing and able to apply, I have no
inkling of how the homoplasy might be distributed. That is
*precisely* one of the things I wish to *discover*. I do not presume
to know that in advance, and I do not think that the probabilities
you propose do anything but bend the outcome toward your
preconceptions.

>>Were I to operate in your concpetual framework; were
>>I to be trying to discover a tree which is probable given a
>>consideration of process generalizations, then yes, equal weighting
>>would represent an assertion on that score. But that is not what I am
>>doing at all. I am using the algorithm to logically combine a set of
>>grouping hypotheses, each of which has an inherently equal standing
>>as a corroborated homology. Thats all.
>
>This is the justification argument I was looking for.  I can see two ways to
>interpret your statement.  1) Even though your characters probably contain
>different levels of homoplasy, you feel that you have no way to judge these
>differences before you build your tree; hence, you start from a point of
>equality.

yes, in a sense,,,I'l flesh this out a bit below.

> Or 2) you are saying that independent data on the degree of homoplasy
>in each character has already shown that it is quantitatively equal for each of
>your characters.  I suspect that you mean #1, which is basically what I have
>assumed all along.  I believe that you take your corroboration of the homology
>hypothesis from your tree, so are you saying that each character has an
>inherently equal standing as a corroborated homology before tree building
>because they are all uncorroborated at that point?

They are all corroborated by previous tests. There are as many tests
as there are dimensions to the notion of homology.

> If that is correct, I accept
>it as a justification; however, I still do not find that justification any more
>compelling than justifications for unequal weighting, such as a
>transition/transversion weighting scheme.

But tr/tv ratios are derived from the behavior of classes of
characters. Classes are composed of transformations which have
occurred in  very different independant situations. Perhaps if you
were to append an assumption that these transformations are functions
of nothing more than pure chemical reactions, and that the specific
situations in which these reactions took place were fundamentally
similar, perhaps I could see a justification for the notion that
there is an underlying regularity at work. Even then, as mutations,
the reactions would be predictable only on average; why should the
expectation of average behavior be imposed on specific cases?

> I also still believe that your
>justification, which clearly does not take into account process assertions, does
>not mean that equal weighting carries no such assertions.  Equal weighting
>includes process assertions whether or not they are apparent from your
>justification.  For example, if I said that I will weigh all characters equally
>because I believe that they each actually contain equal amounts of homoplasy, I
>would surely be making process assertions.

Instead of beating heads together, I will try to make reference to
your perspective to illustrate our differences. As a background, I
would re-emphasize a point I tried to make in one of my responses to
James. If you consider truth and falsity to be represented by a 1 and
a 0, then all of us, no matter our approach, share this concept of 1
and 0 so long as we admit to uncertainty. A probabilistic approach
attempts to quantify the middle ground, with reference to some chosen
set of presumed knowledge. Other approaches do not do so, attempting
instead to devise logical tests deduceable from applicable theory, by
which to choose between the two. Merely because you remain cognizant
of the end-points of your probability range, and everyone else also
refers to 1s and 0s, does not mean that a probabilistic
quantification of the middle ground is implicit in everyone elses
approach.
        Now you are claiming that by weighting equally I am making
presumptions about the probability of homoplasy in my characters;
essentially that it is equally probable for all. I claim I am making
no probability statements at all, given my explanation of probability
above. But I will grant you this, In a sense I AM claiming that my
characters stand in an equal position to each other in reference to
the issue of homoplasy. That is, I am claiming that NONE of them are
homoplastic AT ALL. That is, after all, what a hypothesis of homology
means. I have passed my characters through all of the filters I sense
are relevant, and I see no reason to doubt that they are homologous.
This is why the congruence test is a real test; it challanges this
set of bold assertions and demonstrates how, given my assumption that
true homologies form a congruent hierarchy, some of my hypotheses
just cannot be fit into this expectation. They are thus falsified,
and I have learned something.
        I ask you to reflect however, that by making an assertion
that my characters stand in an equal relation to each other in light
of possible homoplasy - specifically that none of them are
homoplastic, that I am merely advancing my homology hypotheses
(provisionally asserting that they are a 1), and allowing the implied
transformations to be falsified (some transformations will be shown
to be spurious). This is an approach which is attempting to choose
between 1 and 0, it is not quantifiying probabilities, nor is such an
attempt a hidden part of the agenda.

>The assertions are inherent in the method.  You can't escape them by using a different sort of justification that does not refer to process.

THE method? You mean YOUR method. I use a different sort of
justification because I have a different method.

>>And it would help if we could stretch our minds to concieve of
>>different approaches which do not necessarily revolve around the
>>process concerns that you have. It shouldnt be too hard; this is how
>>non-molecular systematics has been done for quite some time.
>
>I think (hope) you are mischaracterizing my position.  I like to think of myself
>as openminded to alternative views, but that does not mean that I blindly accept
>any view promoted by another.  I try to critically evaluate each potential
>alternative.  In this case, I think that the way non-molecular systematics has
>been done for some time now suffers from some logical inconsistencies that
>render results from the traditional approach unreliable.

I dont know why you consider them to be logical inconsistencies. I
dont see anything inconsistent in the logic; you seem to be stating
rather, that there is something missing. What is missing is the
quantification of probabilites. If you see this as logical
inconsistency, then you must presume that the calculation of
probabiites is inherent in the type of analysis we are conducting. I
dont see that at all; quite the contrary. I will accept a Popperian
interpretation of our method; we are making bold conjectures about
the relationships of organisms; advancing sets of percieved
similarities as examples of an inherent regularity in nature, and
allowing these conjectures (the homology hypotheses) to live or die
at the hands of logical tests which are defined by our underlying
expectation of regularity. Your attempts at influencing the outcome
of this test by the addition of a factor reflecting your expectations
undermines the power of the test, and introduces an element of
verificationism into a refutationist paradigm.
        But not only are you corrupting the testing of homology
hypotheses by weighting some of the ones you expect to be true, but
you are also undermining your own attempts to establish regularities
in process theory. Leaving aside for a moment the phylogenetic
effort,, let us consider your attempts to define regularities in the
behavior of certain classes of evolutioanry events. These hypotheses
are certainly valid scientific hypotheses, and as such, they need to
be subjected to rigorous testing in light of empirical evidence. They
must be tested in contexts defined by a set of well-corroborated
phylogenies; by introducing weighting factors into the tree-building
procedure, you are undermining these tests. I know that you
acknowledge that to some extent,,,but why then do you insist on doing
it?
I dont think that it is we who are suffering from any logical
inconsistency here.




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