                                  ftreedist



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Function

   Distances between trees

Description

   Computes the Branch Score distance between trees, which allows for
   differences in tree topology and which also makes use of branch
   lengths. Also computes the Robinson-Foulds symmetric difference
   distance between trees, which allows for differences in tree topology
   but does not use branch lengths.

Algorithm

   This program computes distances between trees. Two distances are
   computed, the Branch Score Distance of Kuhner and Felsenstein (1994),
   and the more widely known Symmetric Difference of Robinson and Foulds
   (1981). The Branch Score Distance uses branch lengths, and can only be
   calculated when the trees have lengths on all branches. The Symmetric
   Difference does not use branch length information, only the tree
   topologies. It must also be borne in mind that neither distance has any
   immediate statistical interpretation -- we cannot say whether a larger
   distance is significantly larger than a smaller one.

   These distances are computed by considering all possible branches that
   could exist on the the two trees. Each branch divides the set of
   species into two groups -- the ones connected to one end of the branch
   and the ones connected to the other. This makes a partition of the full
   set of species. (in Newick notation)

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

   has two internal branches. One induces the partition {A, C | B, D, E}
   and the other induces the partition {A, C, D | B, E}. A different tree
   with the same set of species,

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

   has internal branches that correspond to the two partitions {A, C, D |
   B, E} and {A, D | B, C, E}. Note that the other branches, all of which
   are external branches, induce partitions that separate one species from
   all the others. Thus there are 5 partitions like this: {C | A, B, D, E}
   on each of these trees. These are always present on all trees, provided
   that each tree has each species at the end of its own branch.

   In the case of the Branch Score distance, each partition that does
   exist on a tree also has a branch length associated with it. Thus if
   the tree is

  (((A:0.1,D:0.25):0.05,C:0.01):0.2,(B:0.3,E:0.8):0.2)


   The list of partitions and their branch lengths is:

{A  |  B, C, D, E}     0.1
{D  |  A, B, C, E}     0.25
{A, D  |  B, C, E}     0.05
{C  |  A, B, D, E}     0.01
{A, D, C  |  B, E}     0.4
{B  |  A, C, D, E}     0.3
{E  |  A, B, C, D}     0.8

   Note that the tree is being treated as unrooted here, so that the
   branch lengths on either side of the rootmost node are summed up to get
   a branch length of 0.4.

   The Branch Score Distance imagines us as having made a list of all
   possible partitions, the ones shown above and also all 7 other possible
   partitions, which correspond to branches that are not found in this
   tree. These are assigned branch lengths of 0. For two trees, we imagine
   constructing these lists, and then summing the squared differences
   between the branch lengths. Thus if both trees have branches {A, D | B,
   C, E}, the sum contains the square of the difference between the branch
   lengths. If one tree has the branch and the other doesn't, it contains
   the square of the difference between the branch length and zero (in
   other words, the square of that branch length). If both trees do not
   have a particular branch, nothing is added to the sum because the
   difference is then between 0 and 0.

   The Branch Score Distance takes this sum of squared differences and
   computes its square root. Note that it has some desirable properties.
   When small branches differ in tree topology, it is not very big. When
   branches are both present but differ in length, it is affected.

   The Symmetric Difference is simply a count of how many partitions there
   are, among the two trees, that are on one tree and not on the other. In
   the example above there are two partitions, {A, C | B, D, E} and {A, D
   | B, C, E}, each of which is present on only one of the two trees. The
   Symmetric Difference between the two trees is therefore 2. When the two
   trees are fully resolved bifurcating trees, their symmetric distance
   must be an even number; it can range from 0 to twice the number of
   internal branches, which for n species is 4n-6.

   Note the relationship between the two distances. If all trees have all
   their branches have length 1.0, the Branch Score Distance is the square
   of the Symmetric Difference, as each branch that is present in one but
   not in the other results in 1.0 being added to the sum of squared
   differences.

   We have assumed that nothing is lost if the trees are treated as
   unrooted trees. It is easy to define a counterpart to the Branch Score
   Distance and one to the Symmetric Difference for these rooted trees.
   Each branch then defines a set of species, namely the clade defined by
   that branch. Thus if the first of the two trees above were considered
   as a rooted tree it would define the three clades {A, C}, {B, D, E},
   and {B, E}. The Branch Score Distance is computed from the branch
   lengths for all possible sets of species, with 0 put for each set that
   does not occur on that tree. The table above will be nearly the same,
   but with two entries instead of one for the sets on either side of the
   root, {A C D} and {B E}. The Symmetric Difference between two rooted
   trees is simply the count of the number of clades that are defined by
   one but not by the other. For the second tree the clades would be {A,
   D}, {B, C, E}, and {B, E}. The Symmetric Difference between thee two
   rooted trees would then be 4.

   Although the examples we have discussed have involved fully bifurcating
   trees, the input trees can have multifurcations. This does not cause
   any complication for the Branch Score Distance. For the Symmetric
   Difference, it can lead to distances that are odd numbers.

   However, note one strong restriction. The trees should all have the
   same list of species. If you use one set of species in the first two
   trees, and another in the second two, and choose distances for adjacent
   pairs, the distances will be incorrect and will depend on the order of
   these pairs in the input tree file, in odd ways.

Usage

   Here is a sample session with ftreedist


% ftreedist
Distances between trees
Phylip tree file: treedist.dat
Phylip treedist program output file [treedist.ftreedist]:


Output written to file "treedist.ftreedist"

Done.



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

   Example 2


% ftreedist -dtype s
Distances between trees
Phylip tree file: treedist2.dat
Phylip treedist program output file [treedist2.ftreedist]:


Output written to file "treedist2.ftreedist"

Done.



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

Command line arguments

Distances between trees
Version: EMBOSS:6.2.0

   Standard (Mandatory) qualifiers:
  [-intreefile]        tree       Phylip tree file
  [-outfile]           outfile    [*.ftreedist] Phylip treedist program output
                                  file

   Additional (Optional) qualifiers:
   -dtype              menu       [b] Distance type (Values: s (Symmetric
                                  difference); b (Branch score distance))
   -pairing            menu       [a] Tree pairing method (Values: a
                                  (Distances between adjacent pairs in tree
                                  file); p (Distances between all possible
                                  pairs in tree file))
   -style              menu       [v] Distances output option (Values: f (Full
                                  matrix); v (Verbose, one pair per line); s
                                  (Sparse, one pair per line))
   -noroot             boolean    [N] Trees to be treated as rooted
   -outgrno            integer    [0] Species number to use as outgroup
                                  (Integer 0 or more)
   -[no]progress       boolean    [Y] Print indications of progress of run

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

   "-outfile" associated qualifiers
   -odirectory2        string     Output directory

   General qualifiers:
   -auto               boolean    Turn off prompts
   -stdout             boolean    Write first file to standard output
   -filter             boolean    Read first file from standard input, write
                                  first file to 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 and exit. 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
   -version            boolean    Report version number and exit


Input file format

   ftreedist reads one input tree file. If the number of trees is given,
   it is actually ignored and all trees in the tree file are considered,
   even if there are more trees than indicated by the number. There is no
   maximum number of trees that can be processed but, if you feed in too
   many, there may be an error message about running out of memory. The
   problem is particularly acute if you choose the option to examine all
   possible pairs of trees in an input tree file. Thus if there are 1,000
   trees in the input tree file, keep in mind that all possible pairs
   means 1,000,000 pairs to be examined!

  Input files for usage example

  File: treedist.dat

(A:0.1,(B:0.1,(H:0.1,(D:0.1,(J:0.1,(((G:0.1,E:0.1):0.1,(F:0.1,I:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(D:0.1,((J:0.1,H:0.1):0.1,(((G:0.1,E:0.1):0.1,
(F:0.1,I:0.1):0.1):0.1,C:0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(D:0.1,(H:0.1,(J:0.1,(((G:0.1,E:0.1):0.1,(F:0.1,I:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,(G:0.1,((F:0.1,I:0.1):0.1,((J:0.1,(H:0.1,D:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,(G:0.1,((F:0.1,I:0.1):0.1,(((J:0.1,H:0.1):0.1,D:0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,((F:0.1,I:0.1):0.1,(G:0.1,((J:0.1,(H:0.1,D:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,((F:0.1,I:0.1):0.1,(G:0.1,(((J:0.1,H:0.1):0.1,D:0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,((G:0.1,(F:0.1,I:0.1):0.1):0.1,((J:0.1,(H:0.1,
D:0.1):0.1):0.1,C:0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,((G:0.1,(F:0.1,I:0.1):0.1):0.1,(((J:0.1,H:0.1):0.1,
D:0.1):0.1,C:0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,(G:0.1,((F:0.1,I:0.1):0.1,((J:0.1,(H:0.1,D:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(D:0.1,(H:0.1,(J:0.1,(((G:0.1,E:0.1):0.1,(F:0.1,I:0.1):0.1):0.1,
C:0.1):0.1):0.1):0.1):0.1):0.1);
(A:0.1,(B:0.1,(E:0.1,((G:0.1,(F:0.1,I:0.1):0.1):0.1,((J:0.1,(H:0.1,
D:0.1):0.1):0.1,C:0.1):0.1):0.1):0.1):0.1);

  Input files for usage example 2

  File: treedist2.dat

(A,(B,(H,(D,(J,(((G,E),(F,I)),C))))));
(A,(B,(D,((J,H),(((G,E),(F,I)),C)))));
(A,(B,(D,(H,(J,(((G,E),(F,I)),C))))));
(A,(B,(E,(G,((F,I),((J,(H,D)),C))))));
(A,(B,(E,(G,((F,I),(((J,H),D),C))))));
(A,(B,(E,((F,I),(G,((J,(H,D)),C))))));
(A,(B,(E,((F,I),(G,(((J,H),D),C))))));
(A,(B,(E,((G,(F,I)),((J,(H,D)),C)))));
(A,(B,(E,((G,(F,I)),(((J,H),D),C)))));
(A,(B,(E,(G,((F,I),((J,(H,D)),C))))));
(A,(B,(D,(H,(J,(((G,E),(F,I)),C))))));
(A,(B,(E,((G,(F,I)),((J,(H,D)),C)))));

Output file format

   If any of the four types of analysis are selected, the user must
   specify how they want the results presented.

   The Full matrix (choice F) is a table showing all distances. It is
   written onto the output file. The table is presented as groups of 10
   columns. Here is the Full matrix for the 12 trees in the input tree
   file which is given as an example at the end of this page.

Tree distance program, version 3.6

Symmetric differences between all pairs of trees in tree file:



          1     2     3     4     5     6     7     8     9    10
      \------------------------------------------------------------
    1 |   0     4     2    10    10    10    10    10    10    10
    2 |   4     0     2    10     8    10     8    10     8    10
    3 |   2     2     0    10    10    10    10    10    10    10
    4 |  10    10    10     0     2     2     4     2     4     0
    5 |  10     8    10     2     0     4     2     4     2     2
    6 |  10    10    10     2     4     0     2     2     4     2
    7 |  10     8    10     4     2     2     0     4     2     4
    8 |  10    10    10     2     4     2     4     0     2     2
    9 |  10     8    10     4     2     4     2     2     0     4
   10 |  10    10    10     0     2     2     4     2     4     0
   11 |   2     2     0    10    10    10    10    10    10    10
   12 |  10    10    10     2     4     2     4     0     2     2

         11    12
      \------------
    1 |   2    10
    2 |   2    10
    3 |   0    10
    4 |  10     2
    5 |  10     4
    6 |  10     2
    7 |  10     4
    8 |  10     0
    9 |  10     2
   10 |  10     2
   11 |   0    10
   12 |  10     0


   The Full matrix is only available for analyses P and L (not for A or
   C).

   Option V (Verbose) writes one distance per line. The Verbose output is
   the default. Here it is for the example data set given below:

Tree distance program, version 3.6

Symmetric differences between adjacent pairs of trees:

Trees 1 and 2:    4
Trees 3 and 4:    10
Trees 5 and 6:    4
Trees 7 and 8:    4
Trees 9 and 10:    4
Trees 11 and 12:    10

   Option S (Sparse or terse) is similar except that all that is given on
   each line are the numbers of the two trees and the distance, separated
   by blanks. This may be a convenient format if you want to write a
   program to read these numbers in, and you want to spare yourself the
   effort of having the program wade through the words on each line in the
   Verbose output. The first four lines of the Sparse output are titles
   that your program would want to skip past. Here is the Sparse output
   for the example trees.

1 2 4
3 4 10
5 6 4
7 8 4
9 10 4
11 12 10


  Output files for usage example

  File: treedist.ftreedist


Tree distance program, version 3.69

Branch score distances between adjacent pairs of trees:

Trees 1 and 2:    2.000000e-01
Trees 3 and 4:    3.162278e-01
Trees 5 and 6:    2.000000e-01
Trees 7 and 8:    2.000000e-01
Trees 9 and 10:    2.000000e-01
Trees 11 and 12:    3.162278e-01

  Output files for usage example 2

  File: treedist2.ftreedist


Tree distance program, version 3.69

Symmetric differences between adjacent pairs of trees:

Trees 1 and 2:    4
Trees 3 and 4:    10
Trees 5 and 6:    4
Trees 7 and 8:    4
Trees 9 and 10:    4
Trees 11 and 12:    10

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
                    econsense     Majority-rule and strict consensus tree
                    fconsense     Majority-rule and strict consensus tree
   ftreedistpair    Distances between two sets of trees

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.
