Weights

Tom DiBenedetto tdib at UMICH.EDU
Tue Mar 4 10:41:14 CST 1997


I dont know if it would be relevant to the main line of the
discussion for me to finish this series of repsonses with the extra
stuff I have left out of this one an dthe preivious one, for much of
it takes up a bit far afield,,,,I'll see....
Apologies to all those who have emailed me in the past few
days,,,,its hard for me to find the time to respond to each of you
personally.

 James Francis Lyons-Weiler wrote:
Tom:
>>....proto-hypothesis [on homology] has passed all of our initial testing,
>>analyzing, poking and kicking, and has survived as a tenable hypothesis,
>>or it has not. If it fails, it gets tossed.

James:
>       On the surface, this appears to be a Popperian approach. A
>careful reading of Popper tells us that he considered how a hypothesis
>was CONSTRUCTED to be trivial, and that all that matters was how one TESTS
>the hypothesis.

So, what is the relevance of this comment? Sure, it doesnt matter how
the
hypothesis was formed. The point is the testing,,,fine. In my snippet
above I speak of the testing we apply to homology hypotheses before
the final test.

>Second, Popper took time to reject the Popperian interpretation of parsimonious phylogenetic inference.

reference please. I know Popper was uncomfortable with his notions
being applied in biology, but AFAIK he never addressed specific
methodologies.

Third, Popperian
>tests require making (A) explicit the background knowledge one puts into
>an hypothesis, (B) some critical test statement upon which that hypothesis
>that may be rejected, and (C) some evidence upon which the test statement
>is supported or refuted.  "Unweighted" parsimony hides ignores the fact
>that the background knowledge includes different levels of corroboration
>for the various hypotheses of homology, and simply squashed them to be
>equivalent.

Background knowledge does not refer to the testing-history of the
hypothesis, but merely refers to the assumption context in which the
hypothesis is formulated and tested. Homology hypotheses go through
several tests from the moment they are first conceived, through the
final test (in a particualr research cycle); the test of congruence
with other homology hypotheses.

  I reject the parsimony criterion as a critical test.  A
>Popperian hypothesis is "bold"; it is not expected to survived the
>critical test, and it aquires support because it has in fact survived the
>test. The test is critical only is it does not rely upon ANY of
>the background knowledge; to do otherwise would be INDUCTIVE , not
>hypothetico-deductive, and circular.

I think you are wrong in how you interpret cladistic parsimony in a
Popperian framework. The background knowledge does not in any way
structure the choice of tree. I'll expand on this below when we get
into specifics. If you cannot see the parsimony criterion as a
critical test, perhaps it is because you are not seeing that the
parsimony criterion merely implements a test of congruence; that is
the critical test. Homologous character-state distributions (grouping
hypotheses in the phylogenetic context) are expected to be congruent;
a bold expectation to be sure.

>       The fact that the degree of corroboration can fluctuate as one
>examines and re-examines the evidence for homology tells me that an
>implicit probabilistic interpretation is present, and that these
>probabilities fluctuate between 1 and 0, and if they could be made
>explicit (i.e., statistical), then the process  would be better justified.

I dont knopw what you mean "fluctuate". If a homology hypothesis is
refuted at some point in the analyses which lead up to the congruence
test, it will not make it into the matrix. We are applying a series
of tests to a hypothesis; you can see them as filters. Pass the test
and proceed,,fail the test and be abandonded. The congruence test is
merely the last in the series. Probabilism is not a part of this
approach.

>       If one has hypotheses of homology (HH) as background knowledge,

Excusez moi? How can you imagine that HH is background knowledge?
Homology hypotheses are the hypotheses we are testing. Each
hypothesis of character homology is also a phylogenetic hypothesis,
for shared homologies are the evidence of phylogenetic relationship.
The set of congruent homologies which survive throught the congruence
test revel the phylogeny best supported by character evidence.

>and then uses character congruence (CC) on an MP tree as a test,

yes, congruence on the MP tree is the test; it is the test of the
homology hypotheses,,and it leads us to reject some and to accept
others..

>the fact that the test statement (the tree) is directed entirely by HH makes the
>exercise circular.  To then say that the tree is a phylogeny requires an
>inductive step.

This is wrong. The tree is not determined by background knowledge; it
is merely the combination of the hypotheses in their most logically
supported permutation. The congruence test inherently refers to a
prediction expected of the individual hypotheses within the context
of such a combination.

>  In that sense, no probabilistic support can ever exist
>for hypotheses of phylogeny; .......
>That does not mean that probabilistic support for hypotheses of homology
>are impossible.

Well, since I dont follow you, I guess I cant really dive in and
enjoy the delicious logic of these two sentences.

As far as a Popperian analysis is concerned:
We start formulating our homology hypotheses with the perception of
the similarities and differences in characters in organisms.  By
attempting to define these sims and difs, we arrive eventually at a
coding for a character and its states. We pass this hypothesis
through a series of tests, approapriate for the particulars of the
character type, to assure ourselves it is heritable, diagnostic etc
etc. When we have exhausted all of our tests, we have a
corroborated homology hypothesis. This homology hypothesis is also a
phylogenetic hypothesis, for our conception of homology inevitably
carries with it the notion that the taxa sharing the homology are
related through that homology. The background knowledge here is
whatever biological context the character exists in, and the basic
notion of evolution through descent with modification. Once we have a
set of well corroborated homology hypotheses, we find, inevitably, a
problem. They are almost never completely congruent with each other,
in terms of the phylogenetic groupings they indicate.
Then we apply a final test, one which is also directly deducable from
evolutionary theory. The test is *congruence* (not parsimony - lets
be precise, eh?). A homology hypothesis is expected to be congruent
with all other homologies. This is certainly a bold expectation and a
challenging test (and oft refuted,,witness the trail of homoplasy we
leave in our wake). Since the test imposes an expectation on all
homology hypotheses in relation to each other, they are combined into
a single analysis (here we see the emphasis on "total evidence" which
many of us emphasize). The parsimony criterion is not the test
itself; it merely implements the combination of homology hypotheses
into a best-supported logical hierarchy.
It is then, on this best-supported combination, that we observe the
congruence of individual transformations in the context of all other
proposed transformations, and we see the results of our final
"filtering" test. The logical combination of independantly derived
homology hypotheses into a parsimonious hierarchy is not a procedure
for which differential weighting seems at all to be indicated, IMHO.

>       Congruent evidence is hardly corroborative; Correlation is a form
>of congruence (variable A rises, variable B rises), but mere correlations
>are not accepted as critical tests.

Very faulty logic here. That correlation is a form of congruence and
mere correlation is not accepted  as a critical test does not lead
to the conclusion that congruence cannot be a criitical test. It most
certainly is a critical test. It demands that independant homology
hypotheses
not be contradictory, and clearly many fail.

 The type of congruence that you
>accept as a test is not critical; there are no bold statements; nothing
>about congruence goes beyond the background knowledge used to construct
>the hypotheses of tree and homology;

Huh? The expectation of congruence is certainly a bold expectation. I
think you misundersand what background knowledge refers to in this
situation.

> in fact, there are no test statements.

sorry James, you just dont get what it is all about.

>You get a tree length, and some of your HH appear to be synapomorphies.
>Big deal!  The same occurs with random data. Therefore, there is no
>Popperian corroboration; we don't know whether the degree of congruence
>observed are (to use another Popperian term) "remarkable".

But we are not asking the question "is there hierarchical structure
in this data" we are asking " is this implied transformation
congruent with all these other implied transformations in the context
of a logical combination of all of the hypothesized
transformations?". That is the question for the character homology
hypotheses, and we end up with a set of character homologies for
which the answer is yes. The phylogenetic implications of the
homology hypotheses are simply revealed simultaneously when we arrive
at the parsimonious set of character homologies.

I am not all that concerned with a notion of "degree of congruence"
of a character; the character distribution implies either one or a
set of implied transformations; these are individually congruent with
the parsimonious pattern or not, and are accepted or rejected on that
basis.
The only concern I have for the "degree of congruence" of a  topology
is that it be greater than that for any other topology, for only then
have I combined my homology hypotheses in their most logically
consistent form.

 For tree
>lengths, this is now an exception; Archie's randomization test, which are
>better known as Faith and Cranston's' PTP test (permutation tail
>probability test), can afford one a measured degree of corroboration that
>in fact the length of the set of the shortest trees is remarkable.

What difference would that make? No matter how remarkable or not a
tree might be (by your standards of remarkable), it remains as the
best supported hypothesis (if it is the MP tree) for the available
data. In any case,
people will still continue to study the critters and improve the
matrix.

>       At best, parsimony provides a summary of whatever congruence
>happens to exist among the characters in a given matrix, but it does not
>tells us anything more about that congruence.

Because there is no need to. My goal is to find the tree which
represents the parsimonious combination of my homology hypotheses.

>In fact, parsimony will result in resolved trees given random data, a result that is >apparently surprising to some practicioner.

Well lets be precise here. A parsimony criterion may reveal a
best-supported
pattern in data which was generated under conditions which were
designed to be random. If there is a pattern which emerges from the
sea of randomness, then what is one to say? What are you saying? Does
the parsimony algorithm reveal a truly spurious best-supported
pattern when no such thing really exists (how would it do that?) or
is it that small "random" datsets or datasets resulting from "faulty'
randomness generators actually have best-supported patterns within
them?

>  If tree length is your test, probability
>can assist in the process of making that test critical and allow one to
>hold the character state data to a higher standard.

I dont see how it would do anything of the kind. You are not talking
about overturning the MP tree are you?,,,if so, how could you justify
doing that?,,,if not, then whats the point of all this,,,,we arent
going to
carve anything in stone anyway,,,,,
and we cant really do anything about it until we get more characters
anyway...
I dont know what you consider tree length to be test of; as far as I
see it merely is a score-keeping value by which we can track whether
we are combining our homology hypotheses in the most efficient manner
possible.

>       It is elementary that a tree length of L implies L events
>(inferred transformations), and it follows that if each is taken as
>providing an equivalent degree of support, they are given equal weights,
>which is arbitrary  and really doesn't reflect how well each
>proto-hypothesis of homology passed your initial screening test.

Why on Earth should that be a concern? Your notion that these initial
screening tests give the character its "weight" is pretty off the
wall as far as I can see.
They provide equal support because they are statements about equal
phenomena; evolutioanry events,,,,or they are mistaken and "should"
be weighted zero.

>Certainly each proto-hypothesis didn't pass the same screen, for the
>evidence weighed in favor and against each is different, and some to the
>test must have been more critical than others. At the very least, a
>practicioner will afford more corroboration (in a diffuse sense) to a
>proto-hypothesis of homology that has passed 100 evaluations  than those
>that have passed fewer. Your favored methods of inference appear to me to
>be steeped in probabilistic thinking, and yet you dismiss it.

Well, I'll repeat that I see no relavance to what you discuss here,
and that last sentence in not only absurdly wrong, i dont see how it
follows at all from what precedes it.
The pre-matrix tests are just that,,,tests against certain standards.
They are not meant to contribute to some summation of probabilities.

>>Whether they are probable or not in light of larger trends is not the
>issue *in this test*.
>
>       That's just not how it is generally understood.

By you perhaps. Now thats a problem.....

>Generalized parsimony allows one to incorporate varying degrees of corrorboration >one might think they have into the parsimony procedure, and make (hopefully)
>better use of the results of the outcome of the initial testing (if that's
>how one decides puts a data matrix together).

And if one thinks this is irrelevant and a meaningless?

>Hennig's auxiliary assumption was an ad-hoc procedural necessity that is
>no longer necessary, and was never sufficient.

I dont think you understand the point of it. It merely refers to the
fact that a perception of similarity, in a cross taxa analysis, is
inherently a hypothesis of homology if the similarity is to be
advanced as having any relevance to historical relationship. Defining
a character for systematic purposes means you have made such a
hypothesis, and should proceed to test it in all the ways that are
relevant to what we expect of true homologies.

> Its antithesis, to first assume non-homology and try to reject this null hypothesis, > is more in keeping with Popper's approach to hypothesis testing, because critical
>tests now exist to reject this null without relying on how characters
>interact on a tree,

Well, I dont really see how the very act of coding a character and
its states can be consistent with an assumption that they are
non-homologous. That seems a fundamental contradiction. Nor do I see
how a null-rejecting exercise can be applied to each hypothesized
transformation to result in a tree. But perhaps this is not what you
mean,,,am I correct in assuming that you are referring here to some
other procedure,,,Perhaps you might want to briefly explain the
concepts which go into your apporach so that all can be on an equal
footing with regard to what you are referring to.




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