Weights

Tom DiBenedetto tdib at UMICH.EDU
Fri Feb 28 20:26:21 CST 1997


well folks,,,this is long,,fair warning to those not interested....I
recieved 5 emails encouraging me to keep the discussion public, and
not one thanking me profusely for offering to go private. I know that
its different from the usual topics and style of the group, so if you
object, send those nasty emails, and I will respect the consensus.

James Francis Lyons-Weiler wrote:

>My point is that .....equal weighting presumes equal probabilities and information
>content.

I ask you to let go, just for a moment, from your seemingly firm
belief that phylogenetics should be viewed from the statistical
perspective (as
Felsenstien seems to insist that it must be). I ask this only so that
we dont waste a lot of time talking past each other, for the first
thing you must understand is that I do not see phylogenetics in that
way.
        Your statement above is perfectly logical from your
perspective; It is not from mine. Since probabilities do not even
enter my calculations, and I have a very different concept of
information, the statement is really irrelevant.
        I think we can agree that phylogeny must be inferred, and
that there is no such thing as certain evidence. So we must deal with
the problem of deciding what we will and what we will not accept as
the evidence by which we make our inference, and how we actually go
about making that inference. Right away, I sense a big divergence. It
seems that for you, evidence is comprised of the set of potential
transformations which are indicated by a data-set, with an
accompanying set of probabilites attached, probabilities calculated
in light of trends you may have discerned in transformations of a
similar kind, in other circumstances. For me, evidence consists of
the set of distributions which i have discovered for character-states
determined to
be homologous, to the best of my ability. Perhaps it is this emphasis
on homology which sets off a lot of the subsequent differences. For
me, homology is something which is inferred as well; one proposes
hypotheses of homology, just as one proposes hypotheses of phylogeny.
In fact, there is a parallel between the two inferences; phylogeny
being the inferred relationships of taxa (ultimatly of organisms),
homology the inferred relationship of parts of organisms. We infer
phylogeny as we infer homology. What are the
steps? From the initial perception of similarity, we begin a process
of testing against whatever criterea are relevant to assure that the
character is definable, consistently identifiable, heritable, is
truly diagnostic of a group, and is not artifactual in any way. Once
we have determined this, we can advance a hypothesis of homology
grouping those states. The character then may be seen as evidence to
support a phylogenetic hypothesis grouping the taxa. Thus the
hypothesis must, as all other scientific hypotheses, pass a threshold
test,,,either we conclude that the proto-hypothesis 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. If it
survives, we advance it to the phylogenetic level as a legitimate
"piece of evidence"; a grouping hypothesis for the taxa which share
the homology.
In a sense, we are adopting a far stricter standard than you are, for
a hypothesis (a column of states in a matrix) is only advanced when
we are convinced that it is homologous, rather than assigning weights
to evidence we are, in some sense, not sure of. But of course we
often (always)
confront the fact that different characters, different surviving
homologies, indicate contradictory grouping hypotheses. The solution
is to apply another test, and we have a handy one; one which follows
directly from generally accepted evolutionary principles, and one
which directly addresses the problem of sorting out contradictory
grouping hypotheses. And that is the expectation, based in
evolutionary theory, that true homologies are congruent; given but
one history of life, the history of homologous characters is
congruent with the history of taxa.
        So this is the test, and the demands of the test define what
our evidence must be. The evidence is not a set of judgements as to
the probability of certain events, the evidence is a set of
characters which we conclude are homologous, to the best of our
ability. These characters will again be judged homologous or not; the
test demands that each be congruent with each other. For the purpose
of applying the test (running the parsimony algorithm), the specific
information they refer to is not relevant; the test questions simply
whether they indicate congruent distributions or not. They inherently
stand in equal relation to each other *for the purpose of this test*.
Whether they are probable or not in light of larger trends is not the
issue *in this test*.

And this then is where we differ on the meaning of information.
Information derives meaning from its context. Within the context of a
test of the congruence of homology hypotheses, information content
refers to the degree of order discerned in the data; the level of
congruence. We use the concept "information content" usually to
discriminate between topologies; the most parsimonious topology being
the one with the most information (the topology which can account for
as many of our cherished hypotheses as possible, needing the least
recourse to ad hoc hypotheses). Your concept of "information" seems
to be applied to transformations, or to characters. For me, the only
relvant meaning of an application to a character would be a statement
regarding how well the individual character is congruent with the MP
topology (i.e. something determined a posteriori).

>         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.

Only if you are working in a context of assessing the probability of
events. We are not. Once the two transformations are determined to
both refer to homologous characters, it really doesnt matter how
complex one is relative to the other. The demands of congruence are
not violated by making higher level comparsions. Nor is it relevant
to determine that one or the other is more or less probable given
what you sense has occurred in other, fundamentally independant
situations. We are trying to plunge the depths of determining what
actually happened in this one particular case, and we *need* to be
unconstrained by what we think we have learned has happened
elsewhere.Can you imagine what kind of phylogenies we would be
churning out if (all) systematists had taken such process insights as
the molecular clock seriously?

           (Arguments about whether one should
>       or should not combine such data also hinge on the implicit
>       probabilities of character state changes.

Once again, it is only the probabilists who are swinging on that
hinge. Evidence is evidence; we are comparing independant grouping
hypotheses to determine their congruence.

>       Parsimony is a probability argument; it's just a rather diffuse argument.

Funny, but the only people who find it diffuse are those who insist
on regarding it outside of its proper context. It is not a
probability argument. If you want a remedy for your perception of
diffuseness,
then forget Felsenstien's attempt to have
everyone see it for what it aint,,,try to see it for what it is.

>> 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!!!!!!

You mean a _different_ reputation, dont you? :)
But this leaves me a bit puzzeled. If you agree with me that *all*
weighting regimes are inherently arbitrary in a probabilistic
framework, why insist on adopting a probabilistic framework in the
first place? And how do you justify any of them, or even worse, the
liklihood approaches which take such problems to an extreme?

>       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.

Yes, but your a priori imposition of a measured amount of relevance
to a particular transformation leads to a phylogeny based on what you
think you already know, rather than one which is structured to allow
discovery of new facts.

>> >(Felsenstein (1983); NATO symposium) made the excellent and astute point
>> >that parsimony requires implicit statements about .....

>> In fact, a parsimony-based approach makes no such implicit statements

>       What's an implicit statement?  (I think it's an oxymoron.)

Gee, I guess I meant by that the same that you meant in the statement
to which I was responding....(Do you mean that oxymorons can
be excellent and astute?)!

>> 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.

I dont follow your logic. We do not calculate event probabilities a
priori, thus we do not incorporate them into the tree calculation,
and thus do not suffer from this
circularity.

>         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:...

Sorry, I dont see what you are driving at with your example at all,
so I wont confuse matters more by responding in an inappropriate way.
But to the general point; I intended to emphasize the two extremes of
the probability continuum to make the point that our goal is to
discover whether particular singular events occurred or not; we have
a relativly simple test of this, either they are or are not congruent
with the preponderant pattern in the data; evolutionary theory
demands that they be so if they are to be seen as homologies.
Probability scores are only indicative of tendencies amongst defined
classes of phenomena. As unique historical events, influenced by more
factors than we imagine, the calculated probabilites of
particular events are not to be expected to be anything but a very
weak
test of whether the event actually happened. I find a
homology/congruence test far more compelling.




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