corroboration

[Christopher A. Meacham]

Following up on previous discussion:

>> I seem to recall that compatibility analysis *can* be used to evaulate
>>probabilities; i.e., the probability that these characters support the
>same tree.
>>
>>Meacham wrote several papers on this in the 80's, but I don't have the
>references
>>at hand.
>>
>>Richard Jensen
>>Department of Biology
>>Saint Mary's College
>>Notre Dame, IN  46556
>
>        Compatibility attempts to measure the probability that a character is
>random, viz. given the distribution of a character, with respect to other
>characters, what is the probability that it is composed of random elements
>(each taxon with a particular character state obtained it convergently for
>example)?
>        A low probability of being random infers a high probability of being
>informative...according to proponents. Of course, others suggest that a low
>probability of being random suggests that the probability of the character
>being random is low but nothing more.
>
>
>Dr. Michael J. Sharkey
>http://www.uky.edu/~mjshar0
>
>

Well, since you asked....

Some time ago, I took to heart the criticism that "others suggest that a low
probability of being random suggests that the probability of being random is
low and nothing more" and performed a parsimony analysis using probability
of compatibility to do _nothing more_ than filter out the characters that
have
a _high_ probability of being random in a dataset on primitive angiosperms
compiled by Donoghue and Doyle.  The results are reported in the 1994 paper
listed below.  Basically, I divided the dataset into two halves; a worse half
(designated H2) and a better half (H1).  I then analyzed the two half datasets
separately by maximum parsimony and showed that for the H2 (worse) half,
the maximum parsimony tree had a C.I. of 0.354 and that for the H1 (better)
half, the maximum parsimony tree had a C.I. of 0.522.  Other optimality
measures were similar between the two halves.  So I raised the question
of why we would want to include the characters in the H2 half along with
the H1 (better) characters when we have a technique that seems to be able
to distinguish "better" characters from "worse" characters.

A paragraph from the paper (1994):

"To make this argument more acute, consider the following formulation.
Assume that two systematists, label them 'H1' and 'H2,' working
independently, had developed the H1 and H2 data sets respectively.
The results obtained under maximum parsimony by systematist H1 would be
considered far superior to the results obtained by systematist H2.
The evolutionary relationships of taxa based on the trees obtained by
systematist H2 would be considered suspect and, in view of of the strong
conflict with prevailing opinion, probably generally discounted.  Because
the quality of the H2 data as judged by maximum parsimony is so inferior
to the H1 data, it is unlikely that it would be suggested to systematist
H1 that the H1 tree would be improved by combining the H2 data set with
the H1 data set in order to bring a larger number of characters (thus,
more information) into the analysis.  This argument holds here.  It is
the quality of the character information with respect to phylogenetic
reconstruction that is important.  It does not matter that in this case
the H1 and H2 data sets were created by the same systematists, the results
obtained from the combined data set are not better than the results
obtained from the H1 data set alone."

More complete details are given in the 1994 paper.  (I have reprints if
anyone is interested.)  The probability technique is only one of
several techniques based on compatibility (see the 1985 ARES paper for
older literature).

More recently, Mark Wilkinson of the University of Bristol has been
publishing on theory and applications of compatibility analysis.  His URL:

http://www.bio.bris.ac.uk/research/markwilk/mw.htm

Cheers,

Christopher Meacham
Research Associate
Jepson Herbarium
U. C. Berkeley

1998.  Meacham, C. A. and H. Hartman.  Comparison of
  animal and plant cytochrome c sequences by probability
  analysis of character compatibility.  Pp. 454-461 in
  M. Syvanen and C. I. Kado (eds.), Horizontal Gene
  Transfer.  Chapman and Hall, London.
1994.  Meacham, C. A.  Phylogenetic relationships at the
  basal radiation of angiosperms: Further study by
  probability of character compatibility.  Systematic
  Botany 19:506-522.
1985.  Meacham, C. A. and G. F. Estabrook.  Compatibility
  methods in systematics.  Annual Review of Ecology and
  Systematics 16:431-446.
1984a.  Meacham, C. A.  Evaluating characters by character
  compatibility analysis.  Pp. 152-165 in T. Duncan and
  T. F. Stuessy (eds.), Cladistics: Perspectives on the
  Estimation of Evolutionary History.  Columbia Univ.
  Press, New York.
1984b.  Meacham, C. A.  The role of hypothesized direction
  of characters in the estimation of evolutionary history.
  Taxon 33:26-38.
1981a.  Meacham, C. A.  A probability measure for character
  compatibility.  Mathematical Biosciences 57:1-18.
1981b.  Meacham, C. A.  A manual method for character
  compatibility analysis.  Taxon 30:591-600.
1980.  Meacham, C. A.  Phylogeny of the Berberidaceae with
  an evaluation of classifications.  Systematic Botany
  5:149-172.