(c) Copyright 1986-1993 by Joseph Felsenstein and by the University of
Washington. Written by Joseph Felsenstein. Permission is granted to copy this
document provided that no fee is charged for it and that this copyright notice
is not removed.
This program uses the compatibility method for unrooted two-state
characters to obtain the largest cliques of characters and the trees which they
suggest. This approach originated in the work of Le Quesne (1969), though the
algorithms were not precisely specified until the later work of Estabrook,
Johnson, and McMorris (1976a, 1976b). These authors proved the theorem that a
group of two-state characters which were pairwise compatible would be jointly
compatible. This program uses an algorithm inspired by the Kent Fiala - George
Estabrook program CLINCH, though closer in detail to the algorithm of Bron and
Kerbosch (1973). I am indebted to Kent Fiala for pointing out that paper to
me, and to David Penny for decribing to me his branch-and-bound approach to
finding largest cliques, from which I have also borrowed. I am particularly
grateful to Kent Fiala for catching a bug in versions 2.0 and 2.1 which
resulted in those versions failing to find all of the cliques which they
should. The program computes a compatibility matrix for the characters, then
uses a recursive procedure to examine all possible cliques of characters.
After one pass through all possible cliques, the program knows the size of
the largest clique, and during a second pass it prints out the cliques of the
right size. It also, along with each clique, prints out a the tree suggested
by that clique.
INPUT, OUTPUT, AND OPTIONS
Input to the algorithm is standard, but the "?", "P", and "B" states are
not allowed. This is a serious limitation of this program. If you want to
find large cliques in data that has "?" states, I recommend that you use MIX
instead with the T (Threshold) option and the value of the threshold set to
2.0. The theory underlying this is given in my paper on character weighting
(Felsenstein, 1981b).
The options are chosen from a menu, which looks like this:
Largest clique program, version 3.5c
Settings for this run:
A Use ancestral states in input file? No
C Specify minimum clique size? No
O Outgroup root? No, use as outgroup species 1
M Analyze multiple data sets? No
0 Terminal type (IBM PC, VT52, ANSI)? ANSI
1 Print out the data at start of run No
2 Print out compatibility matrix No
3 Print out tree Yes
4 Write out trees onto tree file? Yes
Are these settings correct? (type Y or the letter for one to change)
The A (Ancestors), O (Outgroup) and M (Multiple Data Sets) options are the
usual ones, described in the main documentation file. The compatibility matrix
calculation in effect assumes if the Ancestors option is invoked that there is
in the data another species that has all the ancestral states. This changes
the compatibility patterns in the proper way. The Ancestors option also
requires information on the ancestral states of each character to be in the
input file.
The Outgroup option will take effect only if the tree is not rooted by the
Ancestral States option.
The C (Clique Size) option indicates that you wish to specify a minimum
clique size and print out all cliques (and their associated trees) greater than
or equal to than that size. The program prompts you for the minimum clique
size.
Note that this allows you to list all cliques (each with its tree) by
simply setting the minimum clique size to 1. If you do one run and find that
the largest clique has 23 characters, you can do another run with the minimum
clique size set at 18, thus listing all cliques within 5 characters of the
largest one.
Options that require information in the input file are W, A, and F, the
usual Weights, Ancestral States, and Factors options. They must be declared on
the first line of the input file and other information must be present in the
input file. They are described in the main documentation file. The Weights
are used in counting clique sizes, so that the program finds the clique(s)
whose characters have the largest sum of weights over all characters. Note
that this allows you to analyze a subset of your characters by giving them
weight 1 and the rest of the characters weight zero. The Ancestral States
option also requires you to choose A in the menu.
Output involves a compatibility matrix (using the symbols "." and "1") and
the cliques and trees.
If you have used the F option there will be two lists of characters for
each clique, one the original multistate characters and the other the binary
characters. It is the latter that are shown on the tree. When the F option is
not used the output and the cliques reflect only the binary characters.
The trees produced have it indicated on each branch the points at which
derived character states arise in the characters that define the clique. There
is a legend above the tree showing which binary character is involved. Of
course if the tree is unrooted you can read the changes as going in either
direction.
The program runs very quickly but if the maximum number of characters is
large it will need a good deal of storage, since the compatibility matrix
requires ActualChars x ActualChars boolean variables, where ActualChars is the
number of characters (in the case of the factors option the total number of
true multistate characters.
ASSUMPTIONS
Basically the following assumptions are made:
1. Each character evolves independently.
2. Different lineages evolve independently.
3. The ancestral state is not known.
4. Each character has a small chance of being one which evolves so
rapidly, or is so thoroughly misinterpreted, that it provides no information on
the tree.
5. The probability of a single change in a character (other than in the
high rate characters) is low but not as low as the probability of being one of
these "bad" characters.
6. The probability of two changes in a low-rate character is much less
than the probability that it is a high-rate character.
7. The true tree has segments which are not so unequal in length that two
changes in a long are as easy to envisage as one change in a short segment.
The assumptions of compatibility methods have been treated in several of
my papers (1978b, 1979, 1981b, 1988b), especially the 1981 paper. For an
opposing view arguing that the parsimony methods make no substantive
assumptions such as these, see the papers by Farris (1983) and Sober (1983a,
1983b), but also read the exchange between Felsenstein and Sober (1986).
The constants available for alteration at the beginning of the program are
the name length, "NmLngth" and the form width, "FormWide", which you may want
to change to make it as large as possible consistent with the page width
available on your output device, so as to avoid the output of cliques and of
trees getting wrapped around unnecessarily.
------------------------TEST DATA SET------------------------------------
5 6
Alpha 110110
Beta 110000
Gamma 100110
Delta 001001
Epsilon 001110
-------- TEST SET OUTPUT (with all numerical options on) ----------------
Largest clique program, version 3.5c
Species Character states
------- --------- ------
Alpha 11011 0
Beta 11000 0
Gamma 10011 0
Delta 00100 1
Epsilon 00111 0
Character Compatibility Matrix (1 if compatible)
--------- ------------- ------ -- -- -----------
111..1
111..1
111..1
...111
...111
111111
Largest Cliques
------- -------
Characters: ( 1 2 3 6)
Tree and characters:
2 1 3 6
0 0 1 1
. +1-Delta
. +0--1-+
+--0-+ +--Epsilon
! !
! +--------Gamma
!
+-------------Alpha
!
+-------------Beta
remember: this is an unrooted tree!