version 3.66

# Dnapars -- DNA Parsimony Program

© Copyright 1986-2006 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 carries out unrooted parsimony (analogous to Wagner trees) (Eck and Dayhoff, 1966; Kluge and Farris, 1969) on DNA sequences. The method of Fitch (1971) is used to count the number of changes of base needed on a given tree. The assumptions of this method are analogous to those of MIX:

1. Each site evolves independently.
2. Different lineages evolve independently.
3. The probability of a base substitution at a given site is small over the lengths of time involved in a branch of the phylogeny.
4. The expected amounts of change in different branches of the phylogeny do not vary by so much that two changes in a high-rate branch are more probable than one change in a low-rate branch.
5. The expected amounts of change do not vary enough among sites that two changes in one site are more probable than one change in another.

That these are the assumptions of parsimony methods has been documented in a series of papers of mine: (1973a, 1978b, 1979, 1981b, 1983b, 1988b). 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, 1988), but also read the exchange between Felsenstein and Sober (1986).

Change from an occupied site to a deletion is counted as one change. Reversion from a deletion to an occupied site is allowed and is also counted as one change. Note that this in effect assumes that a deletion N bases long is N separate events.

Dnapars can handle both bifurcating and multifurcating trees. In doing its search for most parsimonious trees, it adds species not only by creating new forks in the middle of existing branches, but it also tries putting them at the end of new branches which are added to existing forks. Thus it searches among both bifurcating and multifurcating trees. If a branch in a tree does not have any characters which might change in that branch in the most parsimonious tree, it does not save that tree. Thus in any tree that results, a branch exists only if some character has a most parsimonious reconstruction that would involve change in that branch.

It also saves a number of trees tied for best (you can alter the number it saves using the V option in the menu). When rearranging trees, it tries rearrangements of all of the saved trees. This makes the algorithm slower than earlier versions of Dnapars.

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 parsimony algorithm, version 3.6

    Setting for this run:
      U                 Search for best tree?  Yes
      S                        Search option?  More thorough search
      V              Number of trees to save?  10000
      J   Randomize input order of sequences?  No. Use input order
      O                        Outgroup root?  No, use as outgroup species  1
      T              Use Threshold parsimony?  No, use ordinary parsimony
      N           Use Transversion parsimony?  No, count all steps
      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 out steps in each site  No
      5  Print sequences at all nodes of tree  No
      6       Write out trees onto tree file?  Yes

      Y to accept these or type 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 S (search) option controls how, and how much, rearrangement is done on the tied trees that are saved by the program. If the "More thorough search" option (the default) is chosen, the program will save multiple tied trees, without collapsing internal branches that have no evidence of change on them. It will subsequently rearrange on all parts of each of those trees. If the "Less thorough search" option is chosen, before saving, the program will collapse all branches that have no evidence that there is any change on that branch. This leads to less attempted rearrangement. If the "Rearrange on one best tree" option is chosen, only the first of the tied trees is used for rearrangement. This is faster but less thorough. If your trees are likely to have large multifurcations, do not use the default "More thorough search" option as it could result in too large a number of trees being saved.

The N option allows you to choose transversion parsimony, which counts only transversions (changes between one of the purines A or G and one of the pyrimidines C or T). This setting is turned off by default.

The Weights (W) option takes the weights from a file whose default name is "weights". The weights follow the format described in the main documentation file, with integer weights from 0 to 35 allowed by using the characters 0, 1, 2, ..., 9 and A, B, ... Z.

The User tree (option U) is read from a file whose default name is `intree`. The trees can be multifurcating. They must be preceded in the file by a line giving the number of trees in the file.

The options J, O, T, 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 M (multiple data sets option) will ask you whether you want to use multiple sets of weights (from the weights file) or multiple data sets. The ability to use a single data set with multiple weights means that much less disk space will be used for this input data. The bootstrapping and jackknifing tool Seqboot has the ability to create a weights file with multiple weights.

The O (outgroup) option will have no effect if the U (user-defined tree) option is in effect. The T (threshold) option allows a continuum of methods between parsimony and compatibility. Thresholds less than or equal to 1.0 do not have any meaning and should not be used: they will result in a tree dependent only on the input order of species and not at all on the data!

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. Each tree has branch lengths. These are computed using an algorithm published by Hochbaum and Pathria (1997) which I first heard of from Wayne Maddison who invented it independently of them. This algorithm averages the number of reconstructed changes of state over all sites a over all possible most parsimonious placements of the changes of state among branches. Note that it does not correct in any way for multiple changes that overlay each other.

If option 2 is toggled on a table of the number of changes of state required in each character is also printed. 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. This is a reconstruction of the ancestral sequences in the tree. If you choose option 5, a menu item "." appears which gives you the opportunity to turn off dot-differencing so that complete ancestral sequences are shown. 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 deletion 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 step 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 steps for each tree, the differences of each from the best one, the variance of that quantity as determined by the step differences at individual sites, and a conclusion as to whether that tree is or is not significantly worse than the best one. If the U (User Tree) option is used and more than one tree is supplied, and the program is not told to assume autocorrelation between the rates at different sites, the program also performs a statistical test of each of these trees against the one with highest likelihood. If there are two user trees, this 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) It uses the mean and variance of the differences in the number of steps between trees, taken across sites. If the two trees' means 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 sums of steps across 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 number of steps, numbers of steps 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 lowest number of steps 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 number of steps for each tree, the differences of each from the lowest one, the variance of that quantity as determined by the differences of the numbers of steps at individual sites, and a conclusion as to whether that tree is or is not significantly worse than the best one.

Option 6 in the menu controls whether the tree estimated by the program is written onto a tree file. The default name of this output tree file is "outtree". If the U option is in effect, all the user-defined trees are written to the output tree file. 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.

The program is a straightforward relative of MIX and runs reasonably quickly, especially with many sites and few species.

### TEST DATA SET

       5   13
    Alpha     AACGUGGCCAAAU
    Beta      AAGGUCGCCAAAC
    Gamma     CAUUUCGUCACAA
    Delta     GGUAUUUCGGCCU
    Epsilon   GGGAUCUCGGCCC

### CONTENTS OF OUTPUT FILE (if all numerical options are on)

    DNA parsimony algorithm, version 3.66

     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
                   +----------------------------3
      +------------2                            +-------Delta
      |            |
      |            +----------------Gamma
      |
      1----Beta
      |
      +---------Alpha

    requires a total of     19.000

      between      and       length
      -------      ---       ------
         1           2       0.217949
         2           3       0.487179
         3      Epsilon      0.096154
         3      Delta        0.134615
         2      Gamma        0.275641
         1      Beta         0.076923
         1      Alpha        0.173077

    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

    From    To     Any Steps?    State at upper node
                                 ( . means same as in the node below it on tree)

              1                AABGTCGCCA AAY
       1      2         yes    V.KD...... C..
       2      3         yes    GG.A..T.GG .C.
       3   Epsilon     maybe   ..G....... ..C
       3   Delta        yes    ..T..T.... ..T
       2   Gamma        yes    C.TT...T.. ..A
       1   Beta        maybe   ..G....... ..C
       1   Alpha        yes    ..C..G.... ..T