[Fwd: Re: Probabilities on Phylogenetic Trees]

James Francis Lyons-Weiler weiler at ERS.UNR.EDU
Wed Sep 17 15:20:23 CDT 1997

On Wed, 17 Sep 1997, Tom DiBenedetto wrote:

> On Tue, 16 Sep 1997 12:53:42 -0700, James Francis Lyons-Weiler wrote:
> >      So
> >        you really rely on the covariance of the evidence,
> I rely on the congruence of evidence. If this is a foreign concept to
> you, then perhaps you are approaching systematics from the wrong
> conceptual framework.

        You determine, however, whether the evidence is congruent
        or not one a parsimony tree.  Hence statements of congruence
        are inferences, not observations. This congruence is measured
        by the degree to which (inferred) character state TRANSFORMATIONS
        covary on the same branch.  The hypotheses of transformation
        imply process (you don't aquire vertebrae without process,
        do you Tom?).  Cladistics as a formal processes of inference
        does not make it incompatible with probabilistic thinking.

> >In fact, for the shortest tree,
> >> it is maximized, relative to the evidence.
> >
> >        Huh, again?  The probability of a tree is maximized
> >        relative to evidence if it is the shortest tree?
> >        What does that mean? What are you saying?
>>>>I said explicitly that it has a high probability *given the
In plain english that means that if "piece of evidence A" indicates
grouping 1, and "piece of evidence B" indicates grouping 2 (which is
an internested subset of grouping 1) and "piece of evidence C"
indicates grouping 3 (which is an internested subset of grouping 2)
then overall pattern T is a highly probable general pattern for this
evidence if T contains grouping 3 nested within 2 nested within 1. If
pattern X has a somewhat different set of internested groupings it is
a less probable general result for this evidence.

        RIGHT.  Like I said, covariance.
> The probability that a given tree is a reconstruction of the
> phylogenetic
> pattern is maximized for the tree which orders homologies
> parsimoniously; i.e. with the minimal number of steps. Is
> this really that complicated?

        This is merely an assertion; a hope.  It has been
        known for a VERY long time (sorry, Joe) since 1978
        that conditions exist that have perfectly mundane,
        realistic predicates that will cause the mp tree to
        have a low probability of being a reconstruction.

        Long branch attraction can occur simply because of
        sparse taxon sampling.  If enough time has passed
        between two nodes in the true tree without speciation,
        mutations and character evolution can erase the
        phylogenetically informative aquisitions.  It is
        a fact that if you don't sample a taxon, it might
        as well be extinct (for the purposes of your analysis),
        so long branch attraction can occur because we don't
        have sufficient funds to sample some extant taxa,
        to spend time on character analysis of some taxa we
        have got, etc.  (I've a paper coming out soon that
        describes how to find long branch taxa... and yes,
        they mislead morphological data, too).
> >      That
> >        given the shortest tree, the shortest tree becomes
> >        a highly probable event?
> No James, that given the set of homologies, it is highly probable
> that the shortest tree reflects the pattern of taxic divergence.

        Again, this is not universal.  The probability that the
        parsimony tree will be correct is a complex function of
        the (1) shape of the true tree, (2) the evolutionary
        distance (= rates of evolution, or taxon sampling) among
        the taxa sampled, AND (3) the number of characters one has.

        This is largely because the set of homologies is influenced
        and what makes it into your set is also influenced by
        the three factors I listed because they all influence
        the amount and distribution of convergence
> Well, I must admit that I am quite surprised by some of the results
> of statistical phylogenetics. However I tend to feel that the results
> gain corroboration from the amount of empirical evidence which
> supports them, rather than from some quantification of my surprise at
> the findings.

        Then you mean to CONFIRM, not to test.  Philosophers
        distinguish markedly between corrboration and confirmation;
        in fact, they are antithetical.  A long string of confirming
        instances leads to ZERO probabilistic support for the next
        such instance (I've seen lots of grass, but my bet is on
        the fact that it's NOT all green).  Measuring the degree of
        covariation beyond that which one expects by chance alone
        is a good way out of the confirming instances straightjacket.

> But I sense that you are embarking once again on your old mission to
> find
> some Popperian principle to turn against the cladists. But you are
> mired, as ever, in a perspective which simply cannot see the
> conceptual level at which systematics is practiced. Your sense of
> what the "hypothesis" in systematics is, is firmly tied to the tree
> itself. As I have tried to explain several times, systematics is
> about the study of characters, and the formulation of hypotheses of
> *homology* for those characters. The "bold hypotheses", the
> 'improbable results" which Popper alludes to, are found in
> systematics in such statements as "all of these 4000 instances of
> ectodermal outpocketings are really the same thing, and we will find
> other characters which will display distribution patterns which are
> congruent with this".

        Yes, but the relevant question not answered by (gulp)
        cladists is how much corroboration should be attributed to
        hypotheses when they pass the test?  For Popper,
        c = 1/b, where b is the boldness of the hypothesis...
        so the question becomes, how bold is your hypothesis?
        That question can be directly answered by addressing the
        question, "Well, how often do I expect this level of
        (congruence, covariation) by chance alone?", which is
        a statistical question applied to a cladistic problem.

        Ecology is also a formalized field, yet ecologists
        far and wide would guffaw at the intimation that
        because they sat and watched a population or community,
        and made lots of notes, and checked and counter-checked
        among various hypotheses, that the theory they then
        developed has been tested by the mystical properties of
        the methods of Ecology!  Yet you insist that that's all
        it takes to do cladistics.  Look around, Tom.  Biologists
        all over the place are doing statistics.  On all sorts
        of things (like morphology, for instance).  They
        have learned to be careful about the assertions they make
        about their systems.  They report remarkable events after
        they have been determined to be robust.  Your cladistic
        protocol has all the pieces, all the potential, all the
        good intentions of every other field... but it's STUCK.
        Try disproving your hypotheses with a test that has some
        teeth.  You'll be surprise at the increase in your
        subjective confidence, which (contra Popper) is all we
        really have anyway.

. Every homology hypothesis is also a grouping
> hypothesis. This homology defines a monophyletic group. A parsimony
> criterion is the implimentation of a *test* of these hypotheses (ever
> hear of the "test of congruence"?). In good Popperian fashion we are
> subjecting our hypotheses to a severe test (and the advocates of
> "total evidence" are merely asserting that no hiding is allowed). The
> parsimony criterion orders these individual grouping/homology
> hypotheses into a hierarchy which reveals what congruence is present.
> At this
> step we are not trying to formulate bold, low probability hypotheses,
> we are testing a set of hypotheses under a criterion which demands of
> them that they be congruent.  The most parsimonious solution is the
> set of homology hypotheses which survive this test, and since the
> homology hypotheses are also grouping hypotheses, the groups which
> emerge are accepted as those which are most consistent with what we
> have discovered about characters,

        THIS is a great example of where the process of
        formulating a hypothesis and actually testing it
        is entirely conflated.  OF COURSE your data will
        be congruent, because you formulate a set of
        hypotheses under a criterion that demands that
        they be congruent... and then the set of hypotheses
        that survives the test of congruence is preferred.

        Here's an analogy.  I am studying a community of
        organisms for evidence of competition.  I formulate
        hypotheses of competition under a criterion that
        demands that they indicate competition.  Then I
        examine my sets of hypotheses for competition...
        BINGO!  competition!

        No test.

> >      You can't discuss the
> >        objective application of probability theory if
> >        one never bothers to measure the probability of an
> >        event.  A roll a die.  It lands on six.  What was the
> >        P(6)?  I look at the evidence.  P(6) = 1.0?  No.
> >        P(Tom will get an F on a probability exam) = ????
> But James, I dont give a damn what the probability of 6 WAS, I care
> about what the result IS. It is either 6 or it is not 6. You are
> trying to get me to pretend that it is not 6 because 6 might be
> highly improbable.

        Nope.  I'm trying to get you to pretend that the
        probability of it being a six is 1/6.

>. You are telling
> me that the "C" at this site in
> taxon A is not homologous to the "C" at that site in taxon B because
> you think you know enough about how nucleotides change that you can
> calculate that it is somewhat less probable they are homologous than
> not.
        I don't think I am saying anything about dna. Again, there
        is more to statistical inference than maximum likelihood.
        If you bothered you examine the tests I do advocate
        you'd see that they can be used on sets of morphological
        hypotheses as well.

>. And I say that you dont know how nucleotides change in these
> taxa, and you wont begin to make coherent
> statements about how they do until AFTER you have a phylogeny in
> hand.

        BOSH and poppycock.  I know enough about the processes
        of evolution to say that sometimes it leaves behind decent
        evidence of shared geneaology, and sometimes it leaves behind
        baloney. If I examined the data on a tree FIRST, and the tree is
        based on baloney, I'll make coherent statements, but they will
        be lunchmeat.  Sandwiches, anyone?
> The valid way to assess the homology of these "C"s is to test an
> assertion of their homology against the expectations of the theory of
> homology; i.e. that if these "C"s are homologous, their distribution
> will be congruent with all other homologies described from all areas
> of the organism. This is the test that the parsimony criterion
> implements.

        i'll grant you that parismony allows us to present
        hypotheses... and it provides a criterion for choosing
        among hypotheses... but so does throwing a dart, or
        musing to myself in the mountains about my organism,
        and so on... what you keep overlooking is that the
        validity of parsimony as a tool for constructing
        hypotheses fluctuates as a function of the effects of
        processes of all sorts (knowable and unknowable) on
        the patterns in hypotheses of homology.  It's not
        all that complicated, really.
> >        (For the uninitiated, Tom is immune to real criticism,
> >        so my flames are not ever really felt by him).
> luv ya too James,,,(and this is the guy who wrote yesterday "gee, why
> cant we all get along?)???

        I had indigestion or something (Urp!)

> >        Again, most statisticians would disagree.  We use
> >        parsimony to estimate the population mean; in fact,
> >        the sample mean is the value with minimum error around
> >        it, and is the maximum likelihood estimate of the sample
> >        mean when the proper assumptions apply. The fact that
> >        we try to be precise in our measurements is a given.
> Well that is nice, I am always happy to learn what statisticians do.
> Now the day that you become interested in what systematists do, we
> might begin to find some common ground..

        My entire motivation is to improve the trees and
        hypotheses of homology and character transformation
        series estimated because I'm mostly interested in
        the biology.  Is that so wrong?

> If you fear that your sequences have been randomized, you could test
> them against a null model, or, even better, you could test them
> against evidence from other character systems,,in fact you could
> throw in all character systems which have ever been studied in the
> group, or even go out and study new ones.

        I agree with all of this.  I'm not going to sleep tonite,
        but I agree nevertheless... wait... No, I disagree with
        the bit about "better yet".  Whew!
> >        , cladistics in vitro was process-
> >        oriented... evidence of shared geneaological descent
> >        invokes a multitude of processes, among them inheritance,
> >        geneaology, birth, death...
> ahem,,,the fact that cladistics is about living things, all of which
> participate in various and sundry processes, does not make cladistics
> process-oriented.

        The hypotheses of homology you're fond of are there
        by virtue of common descent, right?  WRONG!  They
        may not be.  So the common descent assumption is
        a process assumption.  Convergence is an alternative
        process that can confuse practitioners of such assumptions....
> >     and the evidence is
> >        taken directly from the pattern of character state changes
> >        on a parsimony tree (or so they thought).  So what that the
> >        pattern is really not an observation, but rather is an
> >        inference, a guess?
> inference=guess? Is it a guess that some animals have vertebrae,

        It is a guess that they share these features by common

, and
> that some vertebrates have lungs, and some osteichthyans have four
> limbs, and some tetrapods have hair, and some hairy things do
> statistics,,,is this a guess? or an inference? or an observation?
> I'll go with the statement that we infer the pattern from
> observations within an assumption of hierarchical order,,,but not a
> guess.

        Dressing up guesses in fancy clothes like "hypothesis",
        and "inference" is good for while, but then it gets
        tiresome.  Let's admit at least that they are
        informed guesses?.
> >     So what if the degree to which we
> >        might expect character state distributions to be hierarchically
> >        distributed appears to require knowledge we can't ever have?
> gee, James, the notions of homology and lineage branching are rather
> basic in evolutionary biology.

        Yes, but so is the difference between homology and
        analogy, and so is the distinction between divergent
        and convergent evolution, and (I'll admit a tad more
        sophisticated) are the notions of introgression,
        hybridization, reticulation, horizontal gene transfer,
        mutational saturation, adaptive convergence, random
        convergence, and so on.  The question is can we
        detect with any method of reasoned inference they
        differences between patterns caused by descent with
        modification and lineage branching and these other,
        equally real, potential causes?  Not if the
        method of inference is mislead by such patterns,
        and parsimony is.  Granted, there has been some
        progress on trying to find out what the observable
        consequences of such sources of noise are, but in the
        end, you still get a tree, not a test.
> >        Your process position is a straw man.  The degree to which
> >        we might expect to see something is FAR different that the
> >        degree to which we do in fact see something.  the question
> >        is, are we observing something (an amount of pattern, a
> >        short tree) that deserves a PHYLOGENETIC explanation, or
> >        is it a result that could have happened by chance alone?
> Or maybe god planted it all here on Oct.12 4004 BC,,how do we test
> that? Sorry, but just for the fun of it, I have decided to confine my
> activities to that domain which is bounded by the notions of descent
> with modification as the explanation for regularites in organismal
> character distribution.

        Like looking for your keys in the light?

> . Not to be overly facetious, I think that if
> you demonstrate that a particular result is within the range of
> expectations from a random process, you must then demonstrate to me
> that this process has some biological reality,,, that there really is
> some process by which characters can be distributed randomly amongst
> taxa (and yes, once again I will try to drag you out of your
> exclusively ACTG world).

        See thelitany of processes listed above.  I have more, if
        you like...

> Failing that, you do not have a legitimate
> explanation for the pattern. If you suceed, then I would admit
> that my pattern might have a shaky foundation,,,but what would I do
> then? It is the best pattern I have,,,,maybe I would have to accept
> it for now and look for more evidence!
> (Horrors)

        I think it would be reasonable to present hypotheses of
        hybridization, for instance, if one could detect such
        things... I know of some folks who have, but I can't
        for the life of me recall any cladists doing such things.
        You know how shy I am about forwarding my own research,
        but you may want to examine a paper of mine out this year.

> >        If the result (the degree of covariation in the implied
> >'       hierarchy found in a matrix) can be easily dismissed as
> >        a chance event, it (in total) doesn't require a geneaological
> >        explanation.  Sure, genealogy and inheritance may have been
> >        ongoing, but those processes and the processes of character
> >        evolution may have interacted in ways that DESTROY or
> >        mask the evidence of geneaology you expect to find on the
> >        mpt. To say otherwise is to claim sufficient knowledge of
> >        evolutionary processes.
> Ah, but I dont. I just say that although that (randomness) might have
> been demonstrated to be possible, it couldnt cause me to choose
> another pattern, it merely might undermine some of the conviction
> with which I assert my result. Given that investigatons are never
> complete anyway, that lack of conviction would simply be a matter of
> degree,,,I will go looking for more characters in any case, and hope
> to make progress.

        I'll grant you that there has been a dearth of tests
        designed for specific alternatives.  Send me YOUR
        list of alternative, biological explanations for noise
        in character state distributions (anyone!), and I'll
        try to eventually devise a reasonable test for it.
        I'm good about giving credit, too.

> We all know about information destruction, James. That is why I
> marvel at your adherence to a class of evidence in which this problem
> is endemic; where because of the limited number of possible states,
> evidence is destroyed at nearly every step.

        There is ALWAYS a limited number of states, and to inform
        you, I've no preference for morphological or molecular data
        in general... it's what the data say in specific instances
        that matters.

> . If the amount of
> variation is sufficiently low across taxa for a particular sequence,
> then I dont suppose any method will have many problems in finding
> good results, and they probably will hold up well to all manner of
> statsitsical testing. At the other extreme, when much of the
> information has been overwritten, then no method has a prayer of
> uncovering useful evidence. All the disputes center on the areas in
> between, when a sufficient amount of evidence has been destroyed such
> that the pattern is either hard to retrieve or spurious. At this
> point, it seems that the statisticians, bound as they are by the
> blinders of their genophilia, are committed to devising ever more
> arcane ways in which to decide which evidence has and which hasnt
> been destroyed, rather than looking to other character systems,
> systems in which the problem (although certainly present) is present
> to a far lesser degree. Is the goal to find the phylogenetic
> relationships of the group? Or is the goal to develop the models of
> genetic evolution? If the former, then seek out the evidence wherever
> it exists. If the latter (wonderful and legitimate research program -
> but not systematics), then accept that that is your field.
> I dont know how much this applies to you personally, but since you
> defend the statisticians, I'll send it your way.

        I don't see the two alternatives as mutually exclusive.
        Of course we should find out where information has been
        obliterated or muddled, AND we should look at various
        different genes, AND various different character systems.
        Understanding genomic evolution is a worthwhile task, and
        so is understanding the evolution of dentition in the Equus
        lineages.  As I've said before, these artificial classes of
        morphology and molecule, character transformation and
        models of genetic evolution, are SO harmful to the
        shared goal of studying biology from an evolutionary
        standpoint.  No one has anything to lose, for instance, by
        gathering up all the molecular data they can to study
        dentition evolution.  They should just be careful about
        misleading information in the molecules and the morphology.


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