version 3.6

# PARS - Discrete character parsimony

© Copyright 1986-2004 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.

PARS is a general parsimony program which carries out the Wagner parsimony method with multiple states. Wagner parsimony allows changes among all states. The criterion is to find the tree which requires the minimum number of changes. The Wagner method was originated by Eck and Dayhoff (1966) and by Kluge and Farris (1969). Here are its assumptions:

1. Ancestral states are unknown unknown.
2. Different characters evolve independently.
3. Different lineages evolve independently.
4. Changes to all other states are equally probable (Wagner).
5. These changes are a priori improbable over the evolutionary time spans involved in the differentiation of the group in question.
6. Other kinds of evolutionary event such as retention of polymorphism are far less probable than these state changes.
7. Rates of evolution in different lineages are sufficiently low that two changes in a long segment of the tree are far less probable than one change in a short segment.

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), but also read the exchange between Felsenstein and Sober (1986).

## INPUT FORMAT

The input for PARS is the standard input for discrete characters programs, described above in the documentation file for the discrete-characters programs, except that multiple states (up to 9 of them) are allowed. Any characters other than "?" are allowed as states, up to a maximum of 9 states. In fact, one can use different symbols in different columns of the data matrix, although it is rather unlikely that you would want to do that. The symbols you can use are:

- The digits `0-9`,
- The letters `A-Z` and `a-z`,
- The symbols `"!\"#$%&'()*+,-./:;<=>?@\[\\]^_`\{|}~`
  (of these, probably only + and - will be of interest to most users).

But note that these do not include blank (" "). Blanks in the input data are simply skipped by the program, so that they can be used to make characters into groups for ease of viewing. The "?" (question mark) symbol has special meaning. It is allowed in the input but is not available as the symbol of a state. Rather, it means that the state is unknown.

PARS 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 programs such as MIX.

The options are selected using a menu:

    Discrete character 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?  100
      J     Randomize input order of species?  No. Use input order
      O                        Outgroup root?  No, use as outgroup species 1
      T              Use Threshold parsimony?  No, use ordinary parsimony
      W                       Sites weighted?  No
      M           Analyze multiple data sets?  No
      I            Input species 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 character 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 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, and M are the usual Jumble, Outgroup, Threshold parsimony, and Multiple Data Sets options, described either in the main documentation file or in the Discrete Characters Programs documentation file.

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 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 FORMAT

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 D appears which gives you the opportunity to turn off dot-differencing so that complete ancestral sequences are shown. If the inferred state is a "?", there will be multiple equally-parsimonious assignments of states; the user must work these out for themselves by hand. 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 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. It is important to understand that the test assumes that all the discrete characters are evolving independently, which is unlikely to be true for

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 characters 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 characters, 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.

### TEST DATA SET

         5    6
    Alpha     110110
    Beta      110000
    Gamma     100110
    Delta     001001
    Epsilon   001110

### TEST SET OUTPUT (with all numerical options on)

    Discrete character parsimony algorithm, version 3.6

     5 species,   6  sites

    Name         Sequences
    ----         ---------

    Alpha        110110
    Beta         ...00.
    Gamma        .0....
    Delta        001001
    Epsilon      001...

    One most parsimonious tree found:

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

    requires a total of      8.000

      between      and       length
      -------      ---       ------
         1           2         1.00
         2           3         2.00
         3      Epsilon        0.00
         3      Delta          3.00
         2      Gamma          0.00
         1      Beta           2.00
         1      Alpha          0.00

    steps in each site:
             0   1   2   3   4   5   6   7   8   9
         *-----------------------------------------
        0|       1   1   1   2   2   1

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

              1                110110
       1      2         yes    .0....
       2      3         yes    0.1...
       3   Epsilon      no     ......
       3   Delta        yes    ...001
       2   Gamma        no     ......
       1   Beta         yes    ...00.
       1   Alpha        no     ......