Tree numbers

[Richard Zander]

I'd like to point out that the number of possible trees for a particular
number of taxa is a mathematical problem, not a taxonomic one. A tree with
any claim to "real" existence is actually a particular nested data set, one
that convinces someone that there is enough relative support for a
particular set of shared advanced character states to imply shared ancestry
rather than convergence. These "real" trees I suppose are common for
relationships that are already intuitively self-evident, but for problematic
groups or Bold Conjectures, they are few and far between.

Given that a data set of random numbers will almost always generate a fully
resolved tree through max parsimony, telling a "real" tree from one
generated by convergence is a problem. There may not be one "real" tree for
any particular set of taxa if the data is insufficient to treat such a tree
as reliable enough to act on (generate a theory on which further work can be
based).

Thus, the number of trees "possible" for a given number of taxa may be zero
if the data are indistinguishable from random at some level of confidence
(some level of reliability at which you can do good science).


______________________
Richard H. Zander
Bryology Group
Missouri Botanical Garden
PO Box 299
St. Louis, MO 63166-0299
richard.zander at mobot.org <mailto:richard.zander at mobot.org>
Voice: 314-577-5180
Websites:
http://ridgwaydb.mobot.org/bfna/bfnamenu.htm
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-----Original Message-----
From: Gurcharan Singh [mailto:singhg at SATYAM.NET.IN]
Sent: Friday, May 30, 2003 12:58 AM
To: TAXACOM at USOBI.ORG
Subject: [TAXACOM] Tree numbers


Dear members
The number of phologenetic trees possible increases geometrically when the
number of taxa increases: 3 trees for 3 taxa, 15 trees for 4 taxa, 105 trees
for 5 taxa, and so. Can any colleague give me the formula to calculate the
number of trees possible for a cetain number of taxa.
Gurcharan Singh
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Dr. Gurcharan Singh
Department of Botany                  Res. 932 Anand Kunj
S. G. T. B. Khalsa College                    Vikas Puri
University of Delhi                                 New Nelhi-110018
Delhi-110007, INDIA                            INDIA
Phone: 27666469                                Phone: 25531534, 9810359089
                       mail: singhg at satyam.net.in
                               chani at sify.com
                               singhg45 at yahoo.co.uk
                               singhg at khalsacollegedu.com
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