| fmix

## Function

Mixed parsimony algorithm

## Description

Estimates phylogenies by some parsimony methods for discrete character data with two states (0 and 1). Allows use of the Wagner parsimony method, the Camin-Sokal parsimony method, or arbitrary mixtures of these. Also reconstructs ancestral states and allows weighting of characters (does not infer branch lengths).

## Algorithm

MIX is a general parsimony program which carries out the Wagner and Camin-Sokal parsimony methods in mixture, where each character can have its method specified separately. The program defaults to carrying out Wagner parsimony.

The Camin-Sokal parsimony method explains the data by assuming that changes 0 --> 1 are allowed but not changes 1 --> 0. Wagner parsimony allows both kinds of changes. (This under the assumption that 0 is the ancestral state, though the program allows reassignment of the ancestral state, in which case we must reverse the state numbers 0 and 1 throughout this discussion). The criterion is to find the tree which requires the minimum number of changes. The Camin-Sokal method is due to Camin and Sokal (1965) and the Wagner method to Eck and Dayhoff (1966) and to Kluge and Farris (1969).

Here are the assumptions of these two methods:

1. Ancestral states are known (Camin-Sokal) or unknown (Wagner).
2. Different characters evolve independently.
3. Different lineages evolve independently.
4. Changes 0 --> 1 are much more probable than changes 1 --> 0 (Camin-Sokal) or equally probable (Wagner).
5. Both of these kinds of 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 0 --> 1 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 fmix

    % fmix
    Mixed parsimony algorithm
    hylip character discrete states file: mix.dat
    Phylip tree file (optional):
    Phylip mix program output file [mix.fmix]:

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

    Doing global rearrangements
      !---------!
       .........

    Output written to file "mix.fmix"

    Trees also written onto file "mix.treefile"

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

Example 2

    % fmix -printdata -ancfile mixancfile.dat
    Mixed parsimony algorithm
    hylip character discrete states file: mix.dat
    Phylip tree file (optional):
    Phylip mix program output file [mix.fmix]:

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

    Doing global rearrangements
      !---------!
       .........

    Output written to file "mix.fmix"

    Trees also written onto file "mix.treefile"

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    [*.fmix] Phylip mix program output file

       Additional (Optional) qualifiers (* if not always prompted):
       -weights            properties Weights file
       -ancfile            properties Ancestral states file
       -mixfile            properties Mixture file
       -method             menu       [Wagner] Choose the method to use (Values: w
                                      (Wagner); c (Camin-Sokal); m (Mixed))
    *  -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)
       -threshold          float      [$(infile.discretesize)] Threshold value
                                      (Number 1.000 or more)
       -[no]trout          toggle     [Y] Write out trees to tree file
    *  -outtreefile        outfile    [*.fmix] 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
       -ancseq             boolean    [N] Print states at all nodes of tree
       -stepbox            boolean    [N] Print out steps in each character

       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 mix program output file | Output file | <*>.fmix
Additional (Optional) qualifiers | Allowed values | Default
-weights | Weights file | Property value(s) |
-ancfile | Ancestral states file | Property value(s) |
-mixfile | Mixture file | Property value(s) |

-method

Choose the method to use

w | (Wagner)
c | (Camin-Sokal)
m | (Mixed)

Wagner

-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
-threshold | Threshold value | Number 1.000 or more | $(infile.discretesize)
-[no]trout | Write out trees to tree file | Toggle value Yes/No | Yes
-outtreefile | Phylip tree output file (optional) | Output file | <*>.fmix
-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
-ancseq | Print states at all nodes of tree | Boolean value Yes/No | No
-stepbox | Print out steps in each character | Boolean value Yes/No | No
Advanced (Unprompted) qualifiers | Allowed values | Default
(none)

## Input file format

fmix reads discrete character data. States "?", "P", and "B" are allowed.

### (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: mix.dat

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

### Input files for usage example 2

### File: mixancfile.dat

    001??1

## Output file format

fmix output is standard: a list of equally parsimonious trees, which will be printed as rooted or unrooted depending on which is appropriate, and, if the user chooses, a table of the number of changes of state required in each character. If the Wagner option is in force for a character, it may not be possible to unambiguously locate the places on the tree where the changes occur, as there may be multiple possibilities. If the user selects menu option 5, 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 "?" there will be multiple equally-parsimonious assignments of states; the user must work these out for themselves by hand.

If the Camin-Sokal parsimony method is invoked and the Ancestors option is also used, then the program will infer, for any character whose ancestral state is unknown ("?") whether the ancestral state 0 or 1 will give the fewest state changes. If these are tied, then it may not be possible for the program to infer the state in the internal nodes, and these will all be printed as ".". If this has happened and you want to know more about the states at the internal nodes, you will find helpful to use MOVE to display the tree and examine its interior states, as the algorithm in MOVE shows all that can be known in this case about the interior states, including where there is and is not amibiguity. The algorithm in MIX gives up more easily on displaying these states.

If the A option is not used, then the program will assume 0 as the ancestral state for those characters following the Camin-Sokal method, and will assume that the ancestral state is unknown for those characters following Wagner parsimony. If any characters have unknown ancestral states, and if the resulting tree is rooted (even by outgroup), a table will also be printed out showing the best guesses of which are the ancestral states in each character. You will find it useful to understand the difference between the Camin-Sokal parsimony criterion with unknown ancestral state and the Wagner parsimony criterion.

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 invented by Kishino and Hasegawa (1989), and uses the mean and variance of step differences between trees, taken across characters. 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 highest one, the variance of that quantity as determined by the step differences at individual characters, 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 binary characters are evolving independently, which is unlikely to be true for many suites of morphological characters.

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.

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.

### Output files for usage example

### File: mix.fmix

    Mixed parsimony algorithm, version 3.6b

    Wagner parsimony method

         4 trees in all found

               +--Epsilon
         +-----4
         !     +--Gamma
      +--2
      !  !     +--Delta
    --1  +-----3
      !        +--Beta
      !
      +-----------Alpha

      remember: this is an unrooted tree!

    requires a total of      9.000

         +--------Gamma
         !
      +--2     +--Epsilon
      !  !  +--4
      !  +--3  +--Delta
    --1     !
      !     +-----Beta
      !
      +-----------Alpha

      remember: this is an unrooted tree!

    requires a total of      9.000

         +--------Epsilon
      +--4
      !  !  +-----Gamma
      !  +--2
    --1     !  +--Delta
      !     +--3
      !        +--Beta
      !
      +-----------Alpha

      remember: this is an unrooted tree!

    requires a total of      9.000

         +--------Gamma
      +--2
      !  !  +-----Epsilon
      !  +--4
    --1     !  +--Delta
      !     +--3
      !        +--Beta
      !
      +-----------Alpha

      remember: this is an unrooted tree!

    requires a total of      9.000

### File: mix.treefile

    (((Epsilon,Gamma),(Delta,Beta)),Alpha)[0.2500];
    ((Gamma,((Epsilon,Delta),Beta)),Alpha)[0.2500];
    ((Epsilon,(Gamma,(Delta,Beta))),Alpha)[0.2500];
    ((Gamma,(Epsilon,(Delta,Beta))),Alpha)[0.2500];

### Output files for usage example 2

### File: mix.fmix

    Mixed parsimony algorithm, version 3.6b

    5 species, 6 characters

    Wagner parsimony method

    Name         Characters
    ----         ----------

    Alpha        11011 0
    Beta         11000 0
    Gamma        10011 0
    Delta        00100 1
    Epsilon      00111 0

        Ancestral states:
                 001?? 1

    One most parsimonious tree found:

      +-----------Delta
    --3
      !  +--------Epsilon
      +--4
         !  +-----Gamma
         +--2
            !  +--Beta
            +--1
               +--Alpha

    requires a total of      8.000

    best guesses of ancestral states:
           0 1 2 3 4 5 6 7 8 9
         *--------------------
        0!   0 0 1 ? ? 1

### File: mix.treefile

    (Delta,(Epsilon,(Gamma,(Beta,Alpha))));

## 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
fmove | Interactive mixed method parsimony
fpars | Discrete character 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.