| fpars

## Function

Discrete character parsimony

## Description

Multistate discrete-characters parsimony method. Up to 8 states (as well as "?") are allowed. Cannot do Camin-Sokal or Dollo Parsimony. Can cope with multifurcations, reconstruct ancestral states, use character weights, and infer branch lengths.

## Algorithm

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).

## Usage

Here is a sample session with fpars

    % fpars
    Discrete character parsimony
    Input file: pars.dat
    Phylip tree file (optional):
    Phylip pars program output file [pars.fpars]:

    Adding species:
       1. Alpha
       2. Beta
       3. Gamma
       4. Delta
       5. Epsilon

    Doing global rearrangements on the first of the trees tied for best
      !---------!
       .........
       .........

    Collapsing best trees
       .

    Output written to file "pars.fpars"

    Tree also written onto file "pars.treefile"

    Done.

Go to the input files for this example
Go to the output files for this example

## Command line arguments

       Standard (Mandatory) qualifiers:
      [-infile]            discretestates File containing one or more data sets
      [-intreefile]        tree       Phylip tree file (optional)
      [-outfile]           outfile    [*.fpars] Phylip pars program output file

       Additional (Optional) qualifiers (* if not always prompted):
       -weights            properties Weights file
       -method             menu       [Wagner] Choose the parsimony method to use
                                      (Values: w (Wagner); c (Camin-Sokal))
       -maxtrees           integer    [100] Number of trees to save (Integer from
                                      1 to 1000000)
    *  -[no]thorough       toggle     [Y] More thorough search
    *  -[no]rearrange      boolean    [Y] Rearrange on just one best tree
    *  -njumble            integer    [0] Number of times to randomise (Integer 0
                                      or more)
    *  -seed               integer    [1] Random number seed between 1 and 32767
                                      (must be odd) (Integer from 1 to 32767)
       -outgrno            integer    [0] Species number to use as outgroup
                                      (Integer 0 or more)
       -thresh             toggle     [N] Use threshold parsimony
    *  -threshold          float      [1] Threshold value (Number 1.000 or more)
       -[no]trout          toggle     [Y] Write out trees to tree file
    *  -outtreefile        outfile    [*.fpars] Phylip tree output file (optional)
       -printdata          boolean    [N] Print data at start of run
       -[no]progress       boolean    [Y] Print indications of progress of run
       -[no]treeprint      boolean    [Y] Print out tree
       -stepbox            boolean    [N] Print steps at each site
       -ancseq             boolean    [N] Print states at all nodes of tree
    *  -[no]dotdiff        boolean    [Y] Use dot differencing to display results

       Advanced (Unprompted) qualifiers: (none)
       Associated qualifiers:

       "-outfile" associated qualifiers
       -odirectory3        string     Output directory

       "-outtreefile" associated qualifiers
       -odirectory         string     Output directory

       General qualifiers:
       -auto               boolean    Turn off prompts
       -stdout             boolean    Write standard output
       -filter             boolean    Read standard input, write standard output
       -options            boolean    Prompt for standard and additional values
       -debug              boolean    Write debug output to program.dbg
       -verbose            boolean    Report some/full command line options
       -help               boolean    Report command line options. More
                                      information on associated and general
                                      qualifiers can be found with -help -verbose
       -warning            boolean    Report warnings
       -error              boolean    Report errors
       -fatal              boolean    Report fatal errors
       -die                boolean    Report dying program messages

Standard (Mandatory) qualifiers | Allowed values | Default
--- | --- | ---
[-infile] (Parameter 1) | File containing one or more data sets | Discrete states file |
[-intreefile] (Parameter 2) | Phylip tree file (optional) | Phylogenetic tree |
[-outfile] (Parameter 3) | Phylip pars program output file | Output file | <*>.fpars
Additional (Optional) qualifiers | Allowed values | Default
-weights | Weights file | Property value(s) |
-method | Choose the parsimony method to use |
w | (Wagner)
c | (Camin-Sokal)
| Wagner
-maxtrees | Number of trees to save | Integer from 1 to 1000000 | 100
-[no]thorough | More thorough search | Toggle value Yes/No | Yes
-[no]rearrange | Rearrange on just one best tree | Boolean value Yes/No | Yes
-njumble | Number of times to randomise | Integer 0 or more | 0
-seed | Random number seed between 1 and 32767 (must be odd) | Integer from 1 to 32767 | 1
-outgrno | Species number to use as outgroup | Integer 0 or more | 0
-thresh | Use threshold parsimony | Toggle value Yes/No | No
-threshold | Threshold value | Number 1.000 or more | 1
-[no]trout | Write out trees to tree file | Toggle value Yes/No | Yes
-outtreefile | Phylip tree output file (optional) | Output file | <*>.fpars
-printdata | Print data at start of run | Boolean value Yes/No | No
-[no]progress | Print indications of progress of run | Boolean value Yes/No | Yes
-[no]treeprint | Print out tree | Boolean value Yes/No | Yes
-stepbox | Print steps at each site | Boolean value Yes/No | No
-ancseq | Print states at all nodes of tree | Boolean value Yes/No | No
-[no]dotdiff | Use dot differencing to display results | Boolean value Yes/No | Yes
Advanced (Unprompted) qualifiers | Allowed values | Default
(none)

## Input file format

fpars reads discrete characters input, 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.

### (0,1) Discrete character data

These programs are intended for the use of morphological systematists who are dealing with discrete characters, or by molecular evolutionists dealing with presence-absence data on restriction sites. One of the programs (PARS) allows multistate characters, with up to 8 states, plus the unknown state symbol "?". For the others, the characters are assumed to be coded into a series of (0,1) two-state characters. For most of the programs there are two other states possible, "P", which stands for the state of Polymorphism for both states (0 and 1), and "?", which stands for the state of ignorance: it is the state "unknown", or "does not apply". The state "P" can also be denoted by "B", for "both".

There is a method invented by Sokal and Sneath (1963) for linear sequences of character states, and fully developed for branching sequences of character states by Kluge and Farris (1969) for recoding a multistate character into a series of two-state (0,1) characters. Suppose we had a character with four states whose character-state tree had the rooted form:

                   1 ---> 0 ---> 2
                          |
                          |
                          V
                          3

so that 1 is the ancestral state and 0, 2 and 3 derived states. We can represent this as three two-state characters:

                    Old State           New States
                    --- -----           --- ------
                        0                  001
                        1                  000
                        2                  011
                        3                  101

The three new states correspond to the three arrows in the above character state tree. Possession of one of the new states corresponds to whether or not the old state had that arrow in its ancestry. Thus the first new state corresponds to the bottommost arrow, which only state 3 has in its ancestry, the second state to the rightmost of the top arrows, and the third state to the leftmost top arrow. This coding will guarantee that the number of times that states arise on the tree (in programs MIX, MOVE, PENNY and BOOT) or the number of polymorphic states in a tree segment (in the Polymorphism option of DOLLOP, DOLMOVE, DOLPENNY and DOLBOOT) will correctly correspond to what would have been the case had our programs been able to take multistate characters into account. Although I have shown the above character state tree as rooted, the recoding method works equally well on unrooted multistate characters as long as the connections between the states are known and contain no loops.

However, in the default option of programs DOLLOP, DOLMOVE, DOLPENNY and DOLBOOT the multistate recoding does not necessarily work properly, as it may lead the program to reconstruct nonexistent state combinations such as 010. An example of this problem is given in my paper on alternative phylogenetic methods (1979).

If you have multistate character data where the states are connected in a branching "character state tree" you may want to do the binary recoding yourself. Thanks to Christopher Meacham, the package contains a program, FACTOR, which will do the recoding itself. For details see the documentation file for FACTOR.

We now also have the program PARS, which can do parsimony for unordered character states.

### Input files for usage example

### File: pars.dat

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

## Output file format

fpars 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.

### Output files for usage example

### File: pars.fpars

    Discrete character parsimony algorithm, version 3.6b

    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

### File: pars.treefile

    (((Epsilon:0.00,Delta:3.00):2.00,Gamma:0.00):1.00,Beta:2.00,Alpha:0.00);

## Data files

None

## Notes

None.

## References

None.

## Warnings

None.

## Diagnostic Error Messages

None.

## Exit status

It always exits with status 0.

## Known bugs

None.

## See also

Program name | Description
--- | ---
eclique | Largest clique program
edollop | Dollo and polymorphism parsimony algorithm
edolpenny | Penny algorithm Dollo or polymorphism
efactor | Multistate to binary recoding program
emix | Mixed parsimony algorithm
epenny | Penny algorithm, branch-and-bound
fclique | Largest clique program
fdollop | Dollo and polymorphism parsimony algorithm
fdolpenny | Penny algorithm Dollo or polymorphism
ffactor | Multistate to binary recoding program
fmix | Mixed parsimony algorithm
fmove | Interactive mixed method parsimony
fpenny | Penny algorithm, branch-and-bound

## Author(s)

This program is an EMBOSS conversion of a program written by Joe Felsenstein as part of his PHYLIP package.

Although we take every care to ensure that the results of the EMBOSS version are identical to those from the original package, we recommend that you check your inputs give the same results in both versions before publication.

Please report all bugs in the EMBOSS version to the EMBOSS bug team, not to the original author.

## History

Written (2004) - Joe Felsenstein, University of Washington.

Converted (August 2004) to an EMBASSY program by the EMBOSS team.

## Target users

This program is intended to be used by everyone and everything, from naive users to embedded scripts.