Tree numbers

[Jan Bosselaers]

Dear Gurcharan Singh,

If I am not mistaken, when n = the number of taxa, the formula is
(2(n+1)-5) times the number of trees for n-1 taxa. So for 2 taxa there
is only one tree, for 3 taxa there are (2.4-5).1 = 3 trees, for 4 taxa
(2.5-5).3 = 15 trees and so on. Please bear in mind that this only goes
true for rooted, fully dichotomously branched trees. If the trees are
unrooted, the number of possible trees is one step lower, i.e. 1 tree
for tree taxa, 3 trees for 4 taxa and so on. If polychotomous branching
is also allowed, the calculation becomes more complicated and is beyond
me. But I know there are 26 rooted polychotomous trees for 4 taxa and
236 for 5 taxa. There is something on this in "Cladistics" by Kitching
et al. (1998) Oxford University Press, page 39 etc.

Best regards,
Jan

>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
>************************************************************************
>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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Dr. Jan Bosselaers
"Dochterland", R. novarumlaan 2
B-2340 Beerse, Belgium               tel / fax 32-14-615896
home: dochterland at pandora.be  /  hortipes at dochterland.org
work: jbossela at janbe.jnj.com
web: http://www.dochterland.org/ or http://wyith.ch/home/dochterland.org/

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