Re: Convergence Test for Cladistic Analysis

[chris brochu <cbrochu@fmppr.fmnh.org>]

>Ladies and Gentlemen:
>
>I've been following with great interest and small understanding the
>thread(s) on cladistics.  I believe I generally understand the principle
>behind cladistic analysis, in that the grouping of characters from most
>common to least common (with some [subjective? non-subjective?]) weighting
>of the characters) will produce nested sets of species.  I think I am
>beginning to understand the importance of the identification of convergent
>characters, in that their inclusion in a cladistic analysis will lead to
>errors in the result.

The problem, though, is that a convergence is, by definition, a feature
that has been inherited independently from a similar structure in a
different lineage.  The identity of convergences therefore requires prior
knowledge of evolutionary relationships - otherwise, how would we know they
were not derived from the same common ancestor?  But the only way we have
to determine evolutionary relationships is phylogenetic analysis.  Prior
exclusion of convergences is thus circular reasoning.

In practice, we can make some a priori determinations that two outwardly
similar structures are convergent - but, when we've done that, we would
score them as different characters, assuming we can discern them as such.




>
>My idea of the process all of you are going through is that you are
>developing cladistic analyses, and comparing them to discover which one is
>correct.


Sort of.  More correctly, we're sampling an ever-broader chunk of nature
for the most comprehensive hypothesis of relationships.  For dinosaur
workers, this means including newer fossils, accessing parts of the
skeleton not studied before, and (for the living dinosaurs) including
molecular as well as morphological features.


>
>In mathematics the study of the convergence of a series involves a test for
>convergence.  (That is, "Is the answer I just got better or worse than the
>previous answer?")
>
>If I understand what you all have been saying, parsimony cannot be the
>test.  Parsimony is one of the tie-breaker rules by which results are
>obtained.  Use of parsimony as the test for convergence would be circular
>reasoning.

Parsimony is one of three tests.  Here they all are:

1.  Test of similarity.  This is one of the a priori tests I mentioned
above - if the developmental and structural details between two features
are different enough, we might declare them nonhomologous.  But, one has to
be very careful about this:  developmentally, the tetrapod dorsal hollow
nerve cord forms from an infolding of the neurectoderm, whereas it becomes
hollow from spontaneous cavitation in teleost fishes.  Is the hollow nerve
cord thus not homologous across all vertebrates?  Or can early
developmental stages also evolve?

2.  Test of conjunction.  We think human arms and bird wings are homologous
as forelimbs.  What if we discovered a flying dragon, or an angel?  Can
forelimbs and wings be homologous if they both appear in the same animal?

3.  Test of congruence.  This is the parsimony test - if the character
cannot be optimized as a synapomorphy, it isn't homologous for all
organisms involved.  The issue of independence can be met by simply
excluding that character or characters from the parsimony analysis and
mapping it onto the tree later.

Please bear in mind, "congruence" does not mean the same thing in
phylogenetics that it means in mathematics.  In the natural sciences, one
cannot ever prove things - only try to falsify.



>
>So, here're the questions:
>1.  What formulation is used to test the divergence of a cladistic analysis
>from the ideal cladistic analysis?

Not sure what you mean (see question 2), but there are lots of tests out
there to assess the degree of support a particular data set lends to a
tree.  Some are based on randomization procedures (e.g., bootstrapping or
jackknifing; for broader analyses, permutation tests), and others are more
complicated (likelihood ratio tests, which are of minimal value for
parsimony analsyses sensu stricto)




>2.  What is the ideal cladistic analysis?


Not sure such a thing exists.


chris


-=--=--=--=--=--=--=--=--=--=
Christopher Brochu, Ph.D.

Postdoctoral Research Scientist
Department of Geology
Field Museum of Natural History
Lake Shore Drive at Roosevelt Road
Chicago, IL  60605  USA

phone:  312-922-9410, ext. 469
fax:  312-922-9566

cbrochu@fmppr.fmnh.org