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1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
2<HTML>
3<HEAD>
4<TITLE>clique</TITLE>
5<META NAME="description" CONTENT="clique">
6<META NAME="keywords" CONTENT="clique">
7<META NAME="resource-type" CONTENT="document">
8<META NAME="distribution" CONTENT="global">
9<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
10</HEAD>
11<BODY BGCOLOR="#ccffff">
12<DIV ALIGN=RIGHT>
13version 3.6
14</DIV>
15<P>
16<DIV ALIGN=CENTER>
17<H1>CLIQUE -- Compatibility Program</H1>
18</DIV>
19<P>
20&#169; Copyright 1986-2002 by the University of
21Washington.  Written by Joseph Felsenstein.  Permission is granted to copy
22this document provided that no fee is charged for it and that this copyright
23notice is not removed.
24<P>
25<TABLE><TR><TD BGCOLOR=white>
26<EM><B>Note:</B> Clique is an Old Style program.  This means that it takes
27some of its options information, notably the
28Weights, Ancestral states and Factors
29options from the input file rather than from separate files of their own
30as the New Style programs in this version of PHYLIP do.
31</EM>
32</TD></TR></TABLE>
33<P>
34This program uses the compatibility method for unrooted two-state
35characters to obtain the largest cliques of characters and the trees
36which they suggest.  This approach originated in the work of Le Quesne
37(1969), though the algorithms were not precisely specified until the
38later work of Estabrook, Johnson, and McMorris (1976a, 1976b).   These
39authors proved the theorem that a group of two-state characters which
40were pairwise compatible would be jointly compatible.  This program uses
41an algorithm inspired by the Kent Fiala - George Estabrook program
42CLINCH, though closer in detail to the algorithm of Bron and Kerbosch
43(1973).   I am indebted to Kent Fiala for pointing out that paper to me,
44and to David Penny for decribing to me his branch-and-bound approach to
45finding largest cliques, from which I have also borrowed.   I am
46particularly grateful to Kent Fiala for catching a bug in versions 2.0
47and 2.1  which resulted in those versions failing to find all of the
48cliques which they should.  The program computes a compatibility matrix
49for the characters, then uses a recursive procedure to examine all
50possible cliques of characters.
51<P>
52After one pass through all possible cliques, the program knows the
53size of the largest clique, and during a second pass it prints out the
54cliques of the right size.  It also, along with each clique, prints out a
55the tree suggested by that clique.
56<P>
57<H2>INPUT, OUTPUT, AND OPTIONS</H2>
58<P>
59Input to the algorithm is
60standard, but the "?", "P", and "B" states are not allowed.  This is a
61serious limitation of this program.  If you want to find large cliques in
62data that has "?" states, I recommend that you use MIX instead with the T
63(Threshold) option and the value of the threshold set to 2.0.  The theory
64underlying this is given in my paper on character weighting (Felsenstein,
651981b).
66<P>
67The options are chosen from a menu, which looks like this:
68<P>
69<TABLE><TR><TD BGCOLOR=white>
70<PRE>
71
72Largest clique program, version 3.6a3
73
74Settings for this run:
75  A   Use ancestral states in input file?  No
76  C          Specify minimum clique size?  No
77  O                        Outgroup root?  No, use as outgroup species  1
78  M           Analyze multiple data sets?  No
79  0   Terminal type (IBM PC, ANSI, none)?  none
80  1    Print out the data at start of run  No
81  2  Print indications of progress of run  Yes
82  3        Print out compatibility matrix  No
83  4                        Print out tree  Yes
84  5       Write out trees onto tree file?  Yes
85
86  Y to accept these or type the letter for one to change
87
88</PRE>
89</TD></TR></TABLE>
90<P>
91The A (Ancestors), O (Outgroup) and M (Multiple Data Sets)
92options are the usual ones, described in the main
93documentation file.  However, Clique being an Old Style program,
94the options information for the Ancestors, Factors, and Weights
95options must be specified, not in separate files, but in the input
96data file.  This is done by putting the letters A, F, or W on
97the first line of the input file, separated by blanks from the
98number of characters.  The options information then follows, with the
99first line of each option's information starting with its letter,
100followed by at least 9 spaces or other characters to fill out to
101the length of a species name before the options information occurs:
102You can continue to a new line within the options information at
103any time.  Here is a simple example:
104<P>
105<TABLE><TR><TD BGCOLOR=white>
106<PRE>
107     5    6 FAW
108WEIGHTS   111101
109ANCESTORS 001111
110FACTORS   112234
111Alpha     110110
112Beta      110000
113Gamma     100110
114Delta     001001
115Epsilon   001110
116</PRE>
117</TD></TR></TABLE>
118<P>
119If you use option A (Ancestors) you should also choose it in the menu.
120The compatibility matrix calculation in effect
121assumes if the Ancestors option is invoked that there is in the data
122another species that has all the ancestral states.  This changes the
123compatibility patterns in the proper way.  The Ancestors option also
124requires information on the ancestral states of each character to be in
125the input file.
126<P>
127The Outgroup option will take effect only if the tree is not rooted by the
128Ancestral States option.
129<P>
130The C (Clique Size) option indicates that
131you wish to specify a minimum clique size and print out all cliques (and their
132associated trees) greater than or equal to than that size.  The program
133prompts you for the minimum clique size.
134<P>
135Note that this allows you to list all cliques (each with its tree) by
136simply setting the minimum clique size to 1.  If you do one run and find
137that the largest clique has 23 characters, you can do another run with
138the minimum clique size set at 18, thus listing all cliques within 5
139characters of the largest one.
140<P>
141Output involves a compatibility matrix (using the symbols "." and "1")
142and the cliques and trees.
143<P>
144If you have used the F option there will be two lists of characters
145for each clique, one the original multistate characters and the other the
146binary characters.  It is the latter that are shown on the tree.  When the
147F option is not used the output and the cliques reflect only the binary
148characters.
149<P>
150The trees produced have it
151indicated on each branch the points at which derived character states
152arise in the characters that define the clique.  There is a legend
153above the tree showing which binary character is involved.  Of course
154if the tree is unrooted you can read the changes as going in either
155direction.
156<P>
157The program runs very quickly but if the
158maximum number of characters is large it will need a good deal of
159storage, since the compatibility matrix requires ActualChars x ActualChars
160boolean variables, where ActualChars is the number of characters (in the
161case of the factors option the total number of true multistate characters.
162<P>
163<H2>ASSUMPTIONS</H2>
164<P>
165Basically the following assumptions are made:
166<OL>
167<LI>Each character evolves independently.
168<LI>Different lineages evolve independently.
169<LI>The ancestral state is not known.
170<LI>Each character has a small chance of being one which evolves
171so rapidly, or is so thoroughly misinterpreted, that it
172provides no information on the tree.
173<LI>The probability of a single change in a character (other than
174in the high rate characters) is low but not as low as the
175probability of being one of these "bad" characters.
176<LI>The probability of two changes in a low-rate character is much
177less than the probability that it is a high-rate character.
178<LI>The true tree has segments which are not so unequal in length
179that two changes in a long are as easy to envisage as one
180change in a short segment.
181</OL>
182<P>
183The assumptions of compatibility methods have been treated in
184several of my papers (1978b, 1979, 1981b, 1988b), especially the 1981
185paper.  For an opposing view arguing that the parsimony methods
186make no substantive
187assumptions such as these, see the papers by Farris (1983) and Sober (1983a,
1881983b), but also read the exchange between Felsenstein and Sober (1986). 
189<P>
190A constant available for alteration at the beginning of the
191program is the form width, "FormWide",
192which you may want to change to make it as large as possible
193consistent with the page width available on your output device,
194so as to avoid the output of cliques and of trees getting wrapped
195around unnecessarily.
196<P>
197<HR>
198<P>
199<H3>TEST DATA SET</H3>
200<P>
201<TABLE><TR><TD BGCOLOR=white>
202<PRE>
203     5    6
204Alpha     110110
205Beta      110000
206Gamma     100110
207Delta     001001
208Epsilon   001110
209</PRE>
210</TD></TR></TABLE>
211<P>
212<HR>
213<P>
214<H3>TEST SET OUTPUT (with all numerical options on)</H3>
215<P>
216<TABLE><TR><TD BGCOLOR=white>
217<PRE>
218
219Largest clique program, version 3.6a3
220
221
222Character Compatibility Matrix (1 if compatible)
223--------- ------------- ------ -- -- -----------
224
225                     111..1
226                     111..1
227                     111..1
228                     ...111
229                     ...111
230                     111111
231
232
233Largest Cliques
234------- -------
235
236
237Characters: (  1  2  3  6)
238
239
240  Tree and characters:
241
242     2  1  3  6
243     0  0  1  1
244
245             +1-Delta     
246       +0--1-+
247  +--0-+     +--Epsilon   
248  !    !
249  !    +--------Gamma     
250  !
251  +-------------Alpha     
252  !
253  +-------------Beta     
254
255remember: this is an unrooted tree!
256
257
258</PRE>
259</TD></TR></TABLE>
260</BODY>
261</HTML>
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