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Convergence and Coding Characters

Message text written by INTERNET:znc14@TTACS.TTU.EDU
>       My morphometrics teacher likes to say that "any discrete
is a continuous character in disguise." Not sure I agree, but there it

        Well, to some extent this is true; although we must temper this by
stating that although evolutionary changes don't proceed on infinitesimal
minisculae, they generally _do_ proceed at such a pace that the odds of
finding _every_ intermediate step between any two points is vanishingly
small.  (Then again, there's always the Bob Martin perspective, in which
any series of fossil organisms found at differing horizons within a
continuous depositional sequence ought to be regarded as a single
species, regardless of how much change has occurred!)

>There are many, many cases I've found (mostly in my own
piddling around) where multistate characters are not only the right thing
do, but, as the saying goes, a tasty way to do it, in that they allow you
better organize discrete character data and reduce the overall number of

        Hear, hear!  I tried hard to do that in my _Acrocanthosaurus_
paper, for better or for worse.

>One of my biggest problems is with the like of the following
characters (based on an actual paper):
        1       "Tail:          0 full length, 1 with pygostyle"
        2       "Pygostyle:     0 with <5 vertebrae, 1 with >= 5

        So, how do you code _Velociraptor_? Most people seem to want to
it "00". But, how do you *know* which state the pygostyle exhibits is it

        As I did in my _Acrocanthosaurus_ paper, I held out a special code
("9" in my paper, although certainly any number can be used if 9 or more
differing states come up in a multi-state character) which I labeled as
"not applicable."  I'm not quite sure how this affected the analysis --
possibly the program examined and maybe even combined taxa based on how
many "9's" they shared, but I don't think I used so many that that was a
risk (an intuitive feeling, not anything based on sound statistics).  I'm
unaware if PAUP or MacClade has the capacity to ignore a character for a
given taxon...  8-S  I'm sure Tom or Chris or someone will set us
straight on this!

>Sure, of course, most people will say, "the animal never had
one, so it should be the primitive state." Well, how do you know it never
had one?<

        Based on specimens of _Velociraptor_ we have, _Velociraptor_ does
not have a pygostyle.  If we ever found a specimen that was identical to
_Velociraptor_ in all respects except that it had a pygostyle instead of
a longer tail, would we still call it _Velociraptor_?  ...at any rate, I
see what you're trying to say:  we don't know if, historically, the
immediate _ancestors_ of _Velociraptor_ had a pygostyle or a long
tail...but then again, by including a large number of other taxa, both
with and without pygostyles, we can try to get a handle on the
probability that pygostyles evolved lower down in the lineage leading to
_Velociraptor_, and that _Velociraptor_'s long tail is a reversal, or if
it evolved later, which strongly indicates (but doesn't prove) that it's
long tail is a retained primitive condition.

 >The better solution, in my mind, is this:
        1       "Tail: 0 full length, 1 with pygostyle<5 verts, 2 >=5
                This is an ordered character<

        Exactly; I agree wholeheartedly.  The additional benefit to this
system is that, when you look at an individual character in the data
matrix, you can easily eyeball some "trends" in the evolution of a
character (that is, you can visually scan down the line and see where 0's
turn into 1's, 1's to 2's, etc.)  It's harder to do this when everything
is restricted to 0's and 1's and all additional possibilities are, as you
outlined above, coded as entirely separate characters.

        >Now you shouldn't be able to ralph it up. Some might suggest
chaging 2 to:
        "Pygostyle:     0 absent, 1 with <5 vertebrae, 2 with >= 5

        Will work. My problem is that, then, a reversal to lack of
requires 2 steps (character 1 1->0, character 2 1or2->0). You are
overwieghting the reversal.<

        Again, I agree...but hopefully the coding cladist would be astute
enough to realize that characters 1 and 2 are really rather redundant...

>Now, lemme get this straight, you're getting on my back because I
posted a gut-simple cladistics exercise on a completely different topic
you feel you have to nitpick the details?
        Very me-ish. I wholeheartedly approve! :) <

        Lest anyone think I was taunting my thoughtful colleague with a
poor imitation:  such never entered my mind!  I merely sought to add some
of my own thoughts on the issue (having been through it all) for the
benefit of others on the list!  (Of course, imitation being the sincerest
form of flattery, I'm sure Pete'll take it as a compliment anyway!  ;-D

>>0 = unfused
>>1 = fused only proximally
>>2 = fusion proceeds from proximal to distal end through ontogeny
>>3 = fusion only distally
>>4 = fusion proceeds from distal to proximal end through ontogeny
       > Assuming, of course, that this is unordered. "Y"-shaped other
such advanced character transformation trees would be potentially useful

        I think it may be useful if, in instances such as this where
multi-state characters are present, both unordered and ordered analyses
be performed, just to compare the results.

>On the other hand, that would involve at least some a-priori assumtion
of evolutionary processes (e.g. that you don't get proximo-distal fusion
without first having just proximal fusion). <

        Well, conceivably, the proximal and distal ends could fuse at the
same time and fusion then grows towards the middle from both ends; even
if that character doesn't really exist (or isn't recognized in any
taxon), the possibility might warrant the separation of the states, if
only in the mind of the scientist trying to make sense of it all!  ;-D

>Just please be very careful that your character selection and coding
are not accidentally implying, refuting, or overwieghting homologies a
priori of the analysis. Trying to figure out whether they are or not can
you in knots, but it is worth it, IMHO.<

        Well, I don't know that trying to account for all the
possibilities would overweight anything (as long as you really _did_
account for them all!), although yes, I agree it's possible to be _too_
careful and _too_ anal about it all!  ;-D

>>      Similarly, one can easily further divide the presence or absence
>>streptostyly by coupling the actual functional movement (that defines
>>streptostyly) with other anatomical traits (osteological, myological,
>>that accompany the capacity to attain streptostylic movement.
        >As long as you do not legislate the possibility that the
movement is
homologous out of the picture. The more detailed you get into this, I am
afraid you run more quickly into the problem that, lacking "transitional"
forms of the character "complex", you will lead to a situation in which
is impossible to demonstrate the homology of the function within the

        While it's true that one can be _too_ careful in trying to account
for all possibilities (this could also be perceived as being "too anal"
;-D  ), I think that the best one could hope for in a scheme of coding
and designating useful characters would be to attain a matrix and
resultant cladogram that is accurate down to the level of differences
between species, or possibly sub-species...after all, you can't code for
taxonomic "ranks" that don't exist!  If the cladogram did ultimately just
indicate splits between species, then at best it would be proposing
hypothetical common ancestors where they don't exist (that is, given that
one taxon must spring from another, the common ancestor would _be_ one of
the taxa, so no hypothetical taxon is called for).  I'm not an expert in
statistics, so I can't speak to the statistical functions utilized by
cladistic analysis programs, but I suspect that even if minute
differences were coded for, ultimately we'd only see species-level

>>If we
>>code only for the presence or absence of streptostyly, we increase the
>>that the analysis will find that it is present in the common ancestor
>>both squamates and birds
       > I don't see this at all. Unless you do not code for the
state "streptostyly" itself, it pretty much has an equal chance of
transforming at that node whether or not you add more detail through
potential transformations. It goes without saying that I am very willing
be proven wrong on this point, but I think I'm right.<

        Well, let's take another (!) hypothetical example:  let's pretend
that we have one streptostylic organism, A, in which the quadrate is
mobile and hinged as a joint with the squamosal; organism B is also
streptostylic, but the while the quadrate is mobile, it is fused with the
quadratojugal and the whole assembly forms a joint with the paroccipital.
If we just code for the presence or absence of streptostyly, the analysis
might conclude that A and B were close sister taxa, indicating that
streptostyly arose only once, in the common ancestor of A and B.
However, if we also code for the status of the quadrate in relation to
the quadratojugal, and the nature of the joint, then the analysis would
probably put the relationship of A and B further apart (theoretically
we'd have more intermediate taxa in the analysis and they'd appear
between A and B); we'd have to conclude that streptostyly arose twice,
once in the lineage leading to A and once to B.

        To address your specific point, concerning the likelihood of
streptostyly arising at the Squamata+Aves (Avialae) node, if you're just
looking at those two groups, then yes, it has an equivocal chance of
arising at that particular node.  So I guess we both hope that no one
will perform an analysis on just two taxa!  ;-D

>Again, what concerns me is only that you might actually eliminate
the possibility that it is homologous.<

        I'm still not positive that this is possible, particularly if lots
of intermediate taxa are included in the analysis.

>What is important is the level of similarity (expressed in number
of characters) SHARED by both taxa, and how this relates to the
they share with other ingroup OTUs.<


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                     Jerry D. Harris
                 Fossil Preparation Lab
          New Mexico Museum of Natural History
                   1801 Mountain Rd NW
               Albuquerque  NM  87104-1375
                 Phone:  (505) 899-2809
                  Fax: ; (505) 841-2866