# Circularity & testing.

James Lyons-Weiler weiler at ERS.UNR.EDU
Sun Oct 20 16:02:44 CDT 1996

```On Sun, 20 Oct 1996, Tom DiBenedetto wrote:

> On Sun, 20 Oct 1996 11:39:40 -0700 (PDT), James Lyons-Weiler wrote:
>
> >A cladogram will result from random data, and shortes trees do exist for
> >random data.  Because cladistic parsimony alone cannot provide a
> >distinction between random data and data generated by a phylogenetic
> >process, it cannot possibly be testing anything at all.
>
> ???? Once again again again, it is testing the congruence of the
> elements which are entered into the analysis, under the constraint of
> combining them into a hierarchy. If the units are data arrived at
> randomly, then you might feel inclined to explain why this data set
> exhibits pattern. The algorithm simply displays the pattern that is
> there. The meaning of the pattern is a separate matter, being a
> function of the meaning of the units.
>
You are obfuscating the point that the algorithm will display pattern when
there is no pattern to be displayed.

> >By your argument, homoplasy is the measure of incongruence.  Adding
> >additional taxa alone results in a decrease in congruence (i.e.,
> >homoplasy ratios go up).
>
> ???not necessarily. If the new taxa have sets of characters which are
> fully congruent with the pattern emerging from the original analysis,
> then the homoplasy ratio goes down. If their character sets have a
> similar amount of incongruence as does the original analysis, the
> ratios remain about the same. If they have more incongruence than the
> "average" in the original set then the ratios go up. Ratios are
> pretty simple things. None of this is relevant anyway,,the ratios are
> only used to compare alternative topolgies for the same matrix, they
> are meaningless when compared across two different matrices.
>
Yes, necessarily.  This has been demonstrated by Donoghue and Sanderson..
Homoplasy indices show an across-taxon, among study, very general trend:
when more taxa are added, the congruence goes down.  The ratios are
supposed to summarize congruence.  You have not addressed that.

> > If I recall, the discussion is on whether or not reciprocal
> > illumination
> >provides a reciprocal test, or is simply circular.  Somewhere in there the
> >hypotheses of homology came up, and you're offering congruence as a
> >critical test for homology.  What's the mystery?
>
> Well, then perhaps you should explain exactly what you think
> "reciprocal illumination" means; there being plenty of room for
> misunderstanding underneath our joint use of that term. I admit that
> I have simply been responding to your individual blatent assertions
> on various matters and letting the discussion wander. Reciprocal
> illumination in systematics refers to testing phylogenetic hypotheses
> against independant data-sets drawn from other research programs,
> e.g. consilience with biogeographic or host/parasite patterns.
> Obviously you are using the term in a different context, but I dont
> see your point.
>
The congruence which you call as test is nothing more than reciprocal
illumination, referred to by Wiley (again, p. 139) when referring to "the
idea that truth is approached aymptotically, that is, by testing and
retesting in a system of reciprocal illumination".  A tad out of context,
so I'll remind you that what Wiley was in fact discussing was how to
address the hypothesis of homology.  It is not a specialized term
referring only to patterns found to be common among research programs.

> >Popper demonstrated with elegance that if a test statement for a
> >particular hypopthesis includes the background information used to
> >construct the hypothesis, the test requires inductive, probabilistic
> >support.
>
> So translate this into systematics for me. I assert that the state
> "presence of an amnion" has a generality encompassing all of my taxa;
> the state "fusion of the first two intercentra" is general for the
> turtle, the snake and the bird; the state "presence of hair" is
> general for the platypus, the kangaroo and the bat; and the state
> "presence of wings" is general for the bird and the bat. I will save
> space by imaging a lot of other characters as well, that will be
> congruent. I examine all possible topologies for these taxa and find
> that the currently accepted one requires the least number of
> modifications to my generality statements; I need only reject the
> generality of wings in order for the data to be mapped on that tree.
> All other trees require more modifications. Now, tell me what the
> "test statement" is, the "background information", and where on earth
> one is required to invoke induction or probabilities.
>
Induction is required when you generalize about proponderant patterns.
Probabilities are formalized statements (observed or deduced) of events.
This is missing from the ancient art of phylogenetic argumentation.  The
fact remains that the preponderant assessment of homology (loose
definition) may be erroneous, and yet result in a preponderant pattern.

> >> As I explained twice now, the real test is made in reference to
the
> >> assumption that true homologies must be congruent. Thus when you
> >> combine character A (with its set of state-generalities) and
> >> character B (with its set of state-generalities), both of which are
> >> considered truly homologous, to the best of our knoweldge, you have
> >> an expectation that they will be congruent. If they are not, then you
> >> have decisive reason to believe that they cannot both be truly
> >> homologous, despite your best knowledge. The cladogram is simply the
> >> grouping scheme which presents the arrangement of homologies which
> >> minimizes the need for abandoning character generality statements;
> >> statements which we have no other reason to abandon.
> >>
> >As I have responded twice now, that's not much of a test, expecially when
> >the reason why you might end up abandoning correct character generality
> >statement is because other character generality statements are erroneous.
>
> Well, perhaps we are making progress; "not much of a test" is better
> than "no test at all"! All that you are now demanding is some test
> which will prevent us from ever being wrong! Hah!
>
I'll make my own arguments, thank you very much.  I'm not demanding
anything; I'm simply pointing out "here is a limitation, and here is a
statistical solution".

> >>I think you are confusing this approach with a statsitical estimation
> >> analysis. Despite the assertions of some statisticians, the two
> >> approaches are fundamentally different.
> >>
> >Yes; one is inductive. (Max lik is inductive, too, by the way).
>
> Hmmm, "yes" they are fundamnetally different...one is
> inductive,,,,and so is the other. I think I understand.......
>
I presumed that you knew that maximum likelihood was not the only form of
statistical inference; my fault.  Let me make this more explicit for you:
you have inferential statistics, where the focus is on hypothesis testing
via comparisons to null hypotheses, and maximum likelihood, where the
result is a likelihood estimate through modelling.  Maximum parsimony and
maximum likelihood are inductive; INFERENTIAL statistics are not.

The argument revolves around what one considers to be a
> >> >critical test; I simply reject that whatever you mean by congruence
> >> >provides anything resembling a critical test.
> >>
> >> Well, that is your problem.
> >
> >I don't think so; it would be my problem if I continued to use
> >phylogenetic argumentation despite its very obvious flaws and limitations.
>
> It would also be your problem if what seems obvious to you now were
> really not so obvious, and you never bothered to discover that.
>
> >An analogy would be to continue to use parametric statistics when you know
> >the distribution of the population or sample is not normal.
>
> Well then since you use statistics, I am sure you have a cogent and
> well delimited sense of what are and are not statsitical questions.
> (?)

> > > The rest of the biological
> >> >sciences see the danger of circular reasoning, and Hull (in 1967!) warned
> >> >us about the limitations of the same within
> >> >systematics.
> >>
> >> and yet for the past thirty years this approach has become nearly
> >> paradigmatic in systematics. Now either thousands of practicing
> >> systematists are too dumb to notice a fundamental flaw in their
> >> logic, or perhaps you have not yet arrived at the point of fully
> >> understanding what the approach is all about.
> >
> >You're commiting the fallacy of consensus gentium, and relying on the
> >beliefs and behaviors of a majority to make you point.  This holds no
> >water.
>
> nah, it was just a semi-polite way of suggesting that you might
> consider holding off on the grand assertions until you fully
> understood the approach. It would save us from having to conduct the
> discussion on different levels at the same time.
>
> >>> If the homology is "dead on", I guess you mean that it is really
> >> really true. Could you please tell me how you can combine a set of
> >> really really true hypotheses of homology and get a really reallly
> >> false tree?
> >
> >Homoplasies can be entirely homologous.
>
> ??? I am at a total loss to understand this assertion. First of all
> you discussed a set of "dead on" homologies. A cladogram of such a
> set would exhibit no homoplasy, by definition. Furthermore, if all
> the homologies were true, the tree would have to be true, contra your
> original assertion. Now we have homoplasies? On that tree? and they
> are entirely homologous? What do you mean?
>
>
> ---------------------------------------------
> Tom DiBenedetto
> Fish Division
> Museum of Zoology
> University of Michigan
>

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