| fkitsch

## Function

Fitch-Margoliash method with contemporary tips

## Description

Estimates phylogenies from distance matrix data under the "ultrametric" model which is the same as the additive tree model except that an evolutionary clock is assumed. The Fitch-Margoliash criterion and other least squares criteria, or the Minimum Evolution criterion are possible. This program will be useful with distances computed from molecular sequences, restriction sites or fragments distances, with distances from DNA hybridization measurements, and with genetic distances computed from gene frequencies.

## Algorithm

This program carries out the Fitch-Margoliash and Least Squares methods, plus a variety of others of the same family, with the assumption that all tip species are contemporaneous, and that there is an evolutionary clock (in effect, a molecular clock). This means that branches of the tree cannot be of arbitrary length, but are constrained so that the total length from the root of the tree to any species is the same. The quantity minimized is the same weighted sum of squares described in the Distance Matrix Methods documentation file.

The programs FITCH, KITSCH, and NEIGHBOR are for dealing with data which comes in the form of a matrix of pairwise distances between all pairs of taxa, such as distances based on molecular sequence data, gene frequency genetic distances, amounts of DNA hybridization, or immunological distances. In analyzing these data, distance matrix programs implicitly assume that:

- Each distance is measured independently from the others: no item of data contributes to more than one distance.
- The distance between each pair of taxa is drawn from a distribution with an expectation which is the sum of values (in effect amounts of evolution) along the tree from one tip to the other. The variance of the distribution is proportional to a power p of the expectation.

These assumptions can be traced in the least squares methods of programs FITCH and KITSCH but it is not quite so easy to see them in operation in the Neighbor-Joining method of NEIGHBOR, where the independence assumptions is less obvious.

THESE TWO ASSUMPTIONS ARE DUBIOUS IN MOST CASES: independence will not be expected to be true in most kinds of data, such as genetic distances from gene frequency data. For genetic distance data in which pure genetic drift without mutation can be assumed to be the mechanism of change CONTML may be more appropriate. However, FITCH, KITSCH, and NEIGHBOR will not give positively misleading results (they will not make a statistically inconsistent estimate) provided that additivity holds, which it will if the distance is computed from the original data by a method which corrects for reversals and parallelisms in evolution. If additivity is not expected to hold, problems are more severe. A short discussion of these matters will be found in a review article of mine (1984a). For detailed, if sometimes irrelevant, controversy see the papers by Farris (1981, 1985, 1986) and myself (1986, 1988b).

For genetic distances from gene frequencies, FITCH, KITSCH, and NEIGHBOR may be appropriate if a neutral mutation model can be assumed and Nei's genetic distance is used, or if pure drift can be assumed and either Cavalli-Sforza's chord measure or Reynolds, Weir, and Cockerham's (1983) genetic distance is used. However, in the latter case (pure drift) CONTML should be better.

Restriction site and restriction fragment data can be treated by distance matrix methods if a distance such as that of Nei and Li (1979) is used. Distances of this sort can be computed in PHYLIp by the program RESTDIST.

For nucleic acid sequences, the distances computed in DNADIST allow correction for multiple hits (in different ways) and should allow one to analyse the data under the presumption of additivity. In all of these cases independence will not be expected to hold. DNA hybridization and immunological distances may be additive and independent if transformed properly and if (and only if) the standards against which each value is measured are independent. (This is rarely exactly true).

FITCH and the Neighbor-Joining option of NEIGHBOR fit a tree which has the branch lengths unconstrained. KITSCH and the UPGMA option of NEIGHBOR, by contrast, assume that an "evolutionary clock" is valid, according to which the true branch lengths from the root of the tree to each tip are the same: the expected amount of evolution in any lineage is proportional to elapsed time.

The method may be considered as providing an estimate of the phylogeny. Alternatively, it can be considered as a phenetic clustering of the tip species. This method minimizes an objective function, the sum of squares, not only setting the levels of the clusters so as to do so, but rearranging the hierarchy of clusters to try to find alternative clusterings that give a lower overall sum of squares. When the power option P is set to a value of P = 0.0, so that we are minimizing a simple sum of squares of the differences between the observed distance matrix and the expected one, the method is very close in spirit to Unweighted Pair Group Arithmetic Average Clustering (UPGMA), also called Average-Linkage Clustering. If the topology of the tree is fixed and there turn out to be no branches of negative length, its result should be the same as UPGMA in that case. But since it tries alternative topologies and (unless the N option is set) it combines nodes that otherwise could result in a reversal of levels, it is possible for it to give a different, and better, result than simple sequential clustering. Of course UPGMA itself is available as an option in program NEIGHBOR.

An important use of this method will be to do a formal statistical test of the evolutionary clock hypothesis. This can be done by comparing the sums of squares achieved by FITCH and by KITSCH, BUT SOME CAVEATS ARE NECESSARY. First, the assumption is that the observed distances are truly independent, that no original data item contributes to more than one of them (not counting the two reciprocal distances from i to j and from j to i). THIS WILL NOT HOLD IF THE DISTANCES ARE OBTAINED FROM GENE FREQUENCIES, FROM MORPHOLOGICAL CHARACTERS, OR FROM MOLECULAR SEQUENCES. It may be invalid even for immunological distances and levels of DNA hybridization, provided that the use of common standard for all members of a row or column allows an error in the measurement of the standard to affect all these distances simultaneously. It will also be invalid if the numbers have been collected in experimental groups, each measured by taking differences from a common standard which itself is measured with error. Only if the numbers in different cells are measured from independent standards can we depend on the statistical model. The details of the test and the assumptions are discussed in my review paper on distance methods (Felsenstein, 1984a). For further and sometimes irrelevant controversy on these matters see the papers by Farris (1981, 1985, 1986) and myself (Felsenstein, 1986, 1988b).

A second caveat is that the distances must be expected to rise linearly with time, not according to any other curve. Thus it may be necessary to transform the distances to achieve an expected linearity. If the distances have an upper limit beyond which they could not go, this is a signal that linearity may not hold. It is also VERY important to choose the power P at a value that results in the standard deviation of the variation of the observed from the expected distances being the P/2-th power of the expected distance.

To carry out the test, fit the same data with both FITCH and KITSCH, and record the two sums of squares. If the topology has turned out the same, we have N = n(n-1)/2 distances which have been fit with 2n-3 parameters in FITCH, and with n-1 parameters in KITSCH. Then the difference between S(K) and S(F) has d1 = n-2 degrees of freedom. It is statistically independent of the value of S(F), which has d2 = N-(2n-3) degrees of freedom. The ratio of mean squares

          [S(K)-S(F)]/d1
         ----------------
              S(F)/d2

should, under the evolutionary clock, have an F distribution with n-2 and N-(2n-3) degrees of freedom respectively. The test desired is that the F ratio is in the upper tail (say the upper 5%) of its distribution. If the S (subreplication) option is in effect, the above degrees of freedom must be modified by noting that N is not n(n-1)/2 but is the sum of the numbers of replicates of all cells in the distance matrix read in, which may be either square or triangular. A further explanation of the statistical test of the clock is given in a paper of mine (Felsenstein, 1986).

The program uses a similar tree construction method to the other programs in the package and, like them, is not guaranteed to give the best-fitting tree. The assignment of the branch lengths for a given topology is a least squares fit, subject to the constraints against negative branch lengths, and should not be able to be improved upon. KITSCH runs more quickly than FITCH.

## Usage

Here is a sample session with fkitsch

    % fkitsch
    Fitch-Margoliash method with contemporary tips
    Input file: kitsch.dat
    Input tree file:
    Output file [kitsch.fkitsch]:

     inseed: 0
     jumble: false
     njumble: 1
     lengths: false
     lower: false
     negallowed: false
     power: 2.000000
     replicates: false
     trout: true
     upper: false
     usertree: false
     printdata: false
     progress: true
     treeprint: true
     mulsets: false
     datasets: true
     nummatrices: 0Adding species:
       1. Bovine
       2. Mouse
       3. Gibbon
       4. Orang
       5. Gorilla
       6. Chimp
       7. Human

    Doing global rearrangements
      !-------------!
       .............
    coordinates lengthsum: 0.000000
    Calling coordinates q->v 0.077904
    coordinates lengthsum: 0.077904
    Calling coordinates q->v 0.429227
    coordinates lengthsum: 0.507131
    Calling coordinates q->v 0.066390
    coordinates lengthsum: 0.573520
    Calling coordinates q->v 0.076377
    coordinates lengthsum: 0.649897
    Calling coordinates q->v 0.028355
    coordinates lengthsum: 0.678252
    Calling coordinates q->v 0.134600
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.134600
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.162955
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.239332
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.305722
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.734948
    coordinates lengthsum: 0.812852
    Calling coordinates q->v 0.812852
    coordinates lengthsum: 0.812852

    Output written to file "kitsch.fkitsch"

    Tree also written onto file "kitsch.treefile"

    Done.

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

## Command line arguments

       Standard (Mandatory) qualifiers:
      [-datafile]          distances  File containing one or more distance
                                      matrices
      [-intreefile]        tree       (no help text) tree value
      [-outfile]           outfile    Output file name

       Additional (Optional) qualifiers (* if not always prompted):
       -matrixtype         menu       Type of data matrix
       -minev              boolean    Minimum evolution
    *  -njumble            integer    Number of times to randomise
    *  -seed               integer    Random number seed between 1 and 32767 (must
                                      be odd)
       -power              float      Power
       -negallowed         boolean    Negative branch lengths allowed
       -replicates         boolean    Subreplicates
       -[no]trout          toggle     Write out trees to tree file
    *  -outtreefile        outfile    Tree file name
       -printdata          boolean    Print data at start of run
       -[no]progress       boolean    Print indications of progress of run
       -[no]treeprint      boolean    Print out tree

       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 deaths

Standard (Mandatory) qualifiers | Allowed values | Default
--- | --- | ---
[-datafile] (Parameter 1) | File containing one or more distance matrices | Distance matrix |
[-intreefile] (Parameter 2) | (no help text) tree value | Phylogenetic tree |
[-outfile] (Parameter 3) | Output file name | Output file | <sequence>.fkitsch
Additional (Optional) qualifiers | Allowed values | Default

-matrixtype

Type of data matrix

s | (Square)
u | (Upper triangular)
l | (Lower triangular)

s

-minev | Minimum evolution | Boolean value Yes/No | No
-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
-power | Power | Any numeric value | 2.0
-negallowed | Negative branch lengths allowed | Boolean value Yes/No | No
-replicates | Subreplicates | Boolean value Yes/No | No
-[no]trout | Write out trees to tree file | Toggle value Yes/No | Yes
-outtreefile | Tree file name | Output file |
-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
Advanced (Unprompted) qualifiers | Allowed values | Default
(none)

## Input file format

fkitsch requires a bifurcating tree, unlike FITCH, which requires an unrooted tree with a trifurcation at its base. Thus the tree shown below would be written:

         ((D,E),(C,(A,B)));

If a tree with a trifurcation at the base is by mistake fed into the U option of KITSCH then some of its species (the entire rightmost furc, in fact) will be ignored and too small a tree read in. This should result in an error message and the program should stop. It is important to understand the difference between the User Tree formats for KITSCH and FITCH. You may want to use RETREE to convert a user tree that is suitable for FITCH into one suitable for KITSCH or vice versa.

### Input files for usage example

### File: kitsch.dat

        7
    Bovine      0.0000  1.6866  1.7198  1.6606  1.5243  1.6043  1.5905
    Mouse       1.6866  0.0000  1.5232  1.4841  1.4465  1.4389  1.4629
    Gibbon      1.7198  1.5232  0.0000  0.7115  0.5958  0.6179  0.5583
    Orang       1.6606  1.4841  0.7115  0.0000  0.4631  0.5061  0.4710
    Gorilla     1.5243  1.4465  0.5958  0.4631  0.0000  0.3484  0.3083
    Chimp       1.6043  1.4389  0.6179  0.5061  0.3484  0.0000  0.2692
    Human       1.5905  1.4629  0.5583  0.4710  0.3083  0.2692  0.0000

## Output file format

fkitsch output is a rooted tree, together with the sum of squares, the number of tree topologies searched, and, if the power P is at its default value of 2.0, the Average Percent Standard Deviation is also supplied. The lengths of the branches of the tree are given in a table, that also shows for each branch the time at the upper end of the branch. "Time" here really means cumulative branch length from the root, going upwards (on the printed diagram, rightwards). For each branch, the "time" given is for the node at the right (upper) end of the branch. It is important to realize that the branch lengths are not exactly proportional to the lengths drawn on the printed tree diagram! In particular, short branches are exaggerated in the length on that diagram so that they are more visible.

### Output files for usage example

### File: kitsch.fkitsch

       7 Populations

    Fitch-Margoliash method with contemporary tips, version 3.6b

                      __ __             2
                      \  \   (Obs - Exp)
    Sum of squares =  /_ /_  ------------
                                    2
                       i  j      Obs

    negative branch lengths not allowed

                                               +-------Human
                                             +-6
                                        +----5 +-------Chimp
                                        !    !
                                    +---4    +---------Gorilla
                                    !   !
           +------------------------3   +--------------Orang
           !                        !
      +----2                        +------------------Gibbon
      !    !
    --1    +-------------------------------------------Mouse
      !
      +------------------------------------------------Bovine

    Sum of squares =      0.107

    Average percent standard deviation =   5.16213

    From     To            Length          Height
    ----     --            ------          ------

       6   Human           0.13460         0.81285
       5      6            0.02836         0.67825
       6   Chimp           0.13460         0.81285
       4      5            0.07638         0.64990
       5   Gorilla         0.16296         0.81285
       3      4            0.06639         0.57352
       4   Orang           0.23933         0.81285
       2      3            0.42923         0.50713
       3   Gibbon          0.30572         0.81285
       1      2            0.07790         0.07790
       2   Mouse           0.73495         0.81285
       1   Bovine          0.81285         0.81285

### File: kitsch.treefile

    ((((((Human:0.13460,Chimp:0.13460):0.02836,Gorilla:0.16296):0.07638,
    Orang:0.23933):0.06639,Gibbon:0.30572):0.42923,Mouse:0.73495):0.07790,
    Bovine:0.81285);

## 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
--- | ---
distmat | Creates a distance matrix from multiple alignments
efitch | Fitch-Margoliash and Least-Squares Distance Methods
ekitsch | Fitch-Margoliash method with contemporary tips
eneighbor | Phylogenies from distance matrix by N-J or UPGMA method
ffitch | Fitch-Margoliash and Least-Squares Distance Methods
fneighbor | Phylogenies from distance matrix by N-J or UPGMA method

## 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.