Compatibility methods originated with Le Quesne's (1969) suggestion that one ought to look for trees supported by the largest number of perfectly fitting (compatible) characters. Fitch (1975) showed by counterexample that one could not use the pairwise compatibility methods used in CLIQUE to discover the largest clique of jointly compatible characters.
The assumptions of this method are similar to those of CLIQUE. In a paper in the Biological Journal of the Linnean Society (1981b) I discuss this matter extensively. In effect, the assumptions are that:
There is, however, some reason to believe that the present criterion is not the proper way to correct for the presence of some sites with high rates of change in nucleotide sequence data. It can be argued that sites showing more than two nucleotide states, even if those are compatible with the other sites, are also candidates for sites with high rates of change. It might then be more proper to use DNAPARS with the Threshold option with a threshold value of 2.
Change from an occupied site to a gap is counted as one change. Reversion from a gap to an occupied site is allowed and is also counted as one change. Note that this in effect assumes that a gap N bases long is N separate events. This may be an overcorrection. When we have nonoverlapping gaps, we could instead code a gap as a single event by changing all but the first "-" in the gap into "?" characters. In this way only the first base of the gap causes the program to infer a change.
The input data is standard. The first line of the input file contains the number of species and the number of sites. If the Weights option is being used, there must also be a W in this first line to signal its presence. There are only two options requiring information to be present in the input file, W (Weights) and U (User tree). All options other than W are invoked using the menu.
Next come the species data. Each sequence starts on a new line, has a ten-character species name that must be blank-filled to be of that length, followed immediately by the species data in the one-letter code. The sequences must either be in the "interleaved" or "sequential" formats described in the Molecular Sequence Programs documentation. The I option selects between them. The sequences can have internal blanks in the sequence but there must be no extra blanks at the end of the terminated line. Note that a blank is not a valid symbol for a deletion.
The options are selected using an interactive menu. The menu looks like this:
DNA compatibility algorithm, version 3.5c Settings for this run: U Search for best tree? Yes J Randomize input order of sequences? No. Use input order O Outgroup root? No, use as outgroup species 1 M Analyze multiple data sets? No I Input sequences interleaved? Yes 0 Terminal type (IBM PC, VT52, ANSI)? ANSI 1 Print out the data at start of run No 2 Print indications of progress of run Yes 3 Print out tree Yes 4 Print steps & compatibility at sites No 5 Print sequences at all nodes of tree No 6 Write out trees onto tree file? Yes Are these settings correct? (type Y or the letter for one to change)The user either types "Y" (followed, of course, by a carriage-return) if the settings shown are to be accepted, or the letter or digit corresponding to an option that is to be changed.
The options U, J, O, M, and 0 are the usual ones. They are described in the main documentation file of this package. Option I is the same as in other molecular sequence programs and is described in the molecular sequence programs documentation file.
The O (outgroup) option has no effect if the U (user-defined tree) option is in effect. The user-defined trees (option U) fed in must be strictly bifurcating, with a two-way split at their base.
The interpretation of weights (option W) in the case of a compatibility method is that they count how many times the character (in this case the site) is counted in the analysis. Thus a character can be dropped from the analysis by assigning it zero weight. On the other hand, giving it a weight of 5 means that in any clique it is in, it is counted as 5 characters when the size of the clique is evaluated.
Output is standard: if option 1 is toggled on, the data is printed out, with the convention that "." means "the same as in the first species". Then comes a list of equally parsimonious trees, and (if option 2 is toggled on) a table of the number of changes of state required in each character. If option 5 is toggled on, a table is printed out after each tree, showing for each branch whether there are known to be changes in the branch, and what the states are inferred to have been at the top end of the branch. If the inferred state is a "?" or one of the IUB ambiguity symbols, there will be multiple equally- parsimonious assignments of states; the user must work these out for themselves by hand. A "?" in the reconstructed states means that in addition to one or more bases, a gap may or may not be present. If option 6 is left in its default state the trees found will be written to a tree file, so that they are available to be used in other programs.
If the U (User Tree) option is used and more than one tree is supplied, the program also performs a statistical test of each of these trees against the best tree. This test, which is a version of the test proposed by Alan Templeton (1983) and evaluated in a test case by me (1985a). It is closely parallel to a test using log likelihood differences due to Kishino and Hasegawa (1989), and uses the mean and variance of weighted compatibility differences between trees, taken across sites. If the mean is more than 1.96 standard deviations different then the trees are declared significantly different. The program prints out a table of the compatibilities for each tree, the differences of each from the highest one, the variance of that quantity as determined by the compatibility differences at individual sites, and a conclusion as to whether that tree is or is not significantly worse than the best one.
The algorithm is a straightforward modification of DNAPARS, but with some extra machinery added to calculate, as each species is added, how many base changes are the minimum which could be required at that site. The program runs fairly quickly.
The constants which can be changed at the beginning of the program are: the name length "nmlngth", "maxtrees", the maximum number of trees which the program will store for output, and "maxuser", the maximum number of user trees that can be used in the paired sites test.
TEST DATA SET
Contents of output file (if all numerical options are turned on)
DNA compatibility algorithm, version 3.5c
Alpha AACGUGGCCA AAU
Beta ..G..C.... ..C
Gamma C.UU.C.U.. C.A
Delta GGUA.UU.GG CC.
Epsilon GGGA.CU.GG CCC
One most parsimonious tree found:
remember: this is an unrooted tree!
total number of compatible sites is 11.0
steps in each site:
0 1 2 3 4 5 6 7 8 9
0! 2 1 3 2 0 2 1 1 1
10! 1 1 1 3
compatibility (Y or N) of each site with this tree:
0 ! YYNYYYYYY
From To Any Steps? State at upper node
( . means same as in the node below it on tree)
1 AABGTSGCCA AAY
1 2 maybe .....C.... ...
2 3 yes V.KD...... C..
3 4 yes GG.A..T.GG .C.
4 Epsilon maybe ..G....... ..C
4 Delta yes ..T..T.... ..T
3 Gamma yes C.TT...T.. ..A
2 Beta maybe ..G....... ..C
1 Alpha maybe ..C..G.... ..T
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