[Taxacom] Molecular statistics

[Richard Zander]

Anent the recent and continuing discussion of molecules versus
morphology, there is an assumption that morphology cannot be
statisticized. (If that is not a word, I here propose it.)

Scenario 1. Two morphological taxa that do converge, by Dollo's Rule,
cannot converge completely. There are always some telling traits from a
previous separate lineage that are dragged along during convergence.
Identification of such traits is then decisive probabilistically because
they occur only in that one taxon and also extensively in another
phylogenetically distant taxon, and very rarely elsewhere. That rarity
of occurring elsewhere is the measure of probability, and this can be
measured as a proportion of all taxa that conceivably tolerate
developmentally those dragged along traits. This probability is small.

Scenario 2. Assume molecules say ((A,B)C).... at 95% credibility for
(A,B), but morphology says ((A,C)B).... Can we compare statistics mole
versus morph?

Suppose there are three binary morphological traits that C has in common
with A that would have required convergence of A and C to get a
molecular tree ((A,B)C ... What is the chance of that? Well, B would
have to change 3 traits, also, so we have six traits involved. If each
morphological trait change is 50% probability, then the chance of those
six traits having converged is 0.50^6, or 0.02. The complement, 1 minus
0.02, is 98% or the chance that the morphological cladogram is correct. 

Comparing the two via the Bayesian formula where a bit of morphological
support is made to support, as a prior, molecular cladogram, versus when
a bit of molecule support are made to support, as a prior, morphology:

Molecular posterior of 0.95 with prior of 0.02 for morphological support
for ((A,B)C) = 0.28.

Morphological posterior 0.98 with prior of 0.05 for molecular support
for ((A,C)B = 0.72.

Thus we generate exact, rocket science statistics demonstrating, in this
simulation, that morphological cladograms can be better than molecular
cladograms by a significant factor. Try it yourself. (See my spreadsheet
for simple Bayesian calculations):
http://www.mobot.org/plantscience/ResBot/phyl/silkpursespreadsheet.htm
or http://tinyurl.com/43sgc83 

(The probability discussion of morphological traits is of course
nonsense, or perhaps an ideal, since many morphological traits are
doubtless adaptive, and any clear indication of correlation with
environment greatly increases the chance that the morphological
cladogram is correct. This is because we must then accept the idea that
adaptation cannot be an explanation for clear-cut correlations of
morphological traits with environment. Who would do that?)
 
* * * * * * * * * * * * 
Richard H. Zander 
Missouri Botanical Garden, PO Box 299, St. Louis, MO 63166-0299 USA 
Web sites: http://www.mobot.org/plantscience/resbot/ and
http://www.mobot.org/plantscience/bfna/bfnamenu.htm
Modern Evolutionary Systematics Web site:
http://www.mobot.org/plantscience/resbot/21EvSy.htm