© Copyright 1986-2008 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 implements the compatibility method for DNA sequence data. For a four-state character without a character-state tree, as in DNA sequences, the usual clique theorems cannot be applied. The approach taken in this program is to directly evaluate each tree topology by counting how many substitutions are needed in each site, comparing this to the minimum number that might be needed (one less than the number of bases observed at that site), and then evaluating the number of sites which achieve the minimum number. This is the evaluation of the tree (the number of compatible sites), and the topology is chosen so as to maximize that number.
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:
That these are the assumptions of compatibility methods has been documented in a series of papers of mine: (1973a, 1978b, 1979, 1981b, 1983b, 1988b). For an opposing view arguing that arguments such as mine are invalid and that parsimony (and perhaps compatibility) methods make no substantive assumptions such as these, see the papers by Farris (1983) and Sober (1983a, 1983b, 1988), but also read the exchange between Felsenstein and Sober (1986).
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.
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 document. 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 3.69 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 W Sites weighted? No M Analyze multiple data sets? No I Input sequences interleaved? Yes 0 Terminal type (IBM PC, ANSI, none)? 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, W, 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 documentation file for the sequence programs.
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. Generally, weights other than 0 or 1 do not have much meaning when dealing with DNA sequences.
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 program finds multiple trees tied for best, all of these are written out onto the output tree file. Each is followed by a numerical weight in square brackets (such as [0.25000]). This is needed when we use the trees to make a consensus tree of the results of bootstrapping or jackknifing, to avoid overrepresenting replicates that find many tied trees.
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 one with highest likelihood. If there are two user trees, the test done is one which is due to Kishino and Hasegawa (1989), a version of a test originally introduced by Templeton (1983). In this implementation it uses the mean and variance of weighted compatibility differences between trees, taken across sites. If the two trees' compatibilities are more than 1.96 standard deviations different then the trees are declared significantly different.
If there are more than two trees, the test done is an extension of the KHT test, due to Shimodaira and Hasegawa (1999). They pointed out that a correction for the number of trees was necessary, and they introduced a resampling method to make this correction. In the version used here the variances and covariances of the sum of weighted compatibilities of sites are computed for all pairs of trees. To test whether the difference between each tree and the best one is larger than could have been expected if they all had the same expected compatibility, compatibilities for all trees are sampled with these covariances and equal means (Shimodaira and Hasegawa's "least favorable hypothesis"), and a P value is computed from the fraction of times the difference between the tree's value and the highest compatibility exceeds that actually observed. Note that this sampling needs random numbers, and so the program will prompt the user for a random number seed if one has not already been supplied. With the two-tree KHT test no random numbers are used.
In either the KHT or the SH test the program prints out a table of the compatibility of 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.
5 13 Alpha AACGUGGCCAAAU Beta AAGGUCGCCAAAC Gamma CAUUUCGUCACAA Delta GGUAUUUCGGCCU Epsilon GGGAUCUCGGCCC
DNA compatibility algorithm, version 3.69 5 species, 13 sites Name Sequences ---- --------- 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: +--Epsilon +--4 +--3 +--Delta ! ! +--2 +-----Gamma ! ! 1 +--------Beta ! +-----------Alpha 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: 0123456789 *---------- 0 ! YYNYYYYYY 10 !YYYN 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