version 3.5c

                        CLIQUE -- Compatibility Program


(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!