                                  fdnapenny



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Function

   Penny algorithm for DNA

Description

   Finds all most parsimonious phylogenies for nucleic acid sequences by
   branch-and-bound search. This may not be practical (depending on the
   data) for more than 10-11 species or so.

Algorithm

   DNAPENNY is a program that will find all of the most parsimonious trees
   implied by your data when the nucleic acid sequence parsimony criterion
   is employed. It does so not by examining all possible trees, but by
   using the more sophisticated "branch and bound" algorithm, a standard
   computer science search strategy first applied to phylogenetic
   inference by Hendy and Penny (1982). (J. S. Farris [personal
   communication, 1975] had also suggested that this strategy, which is
   well-known in computer science, might be applied to phylogenies, but he
   did not publish this suggestion).

   There is, however, a price to be paid for the certainty that one has
   found all members of the set of most parsimonious trees. The problem of
   finding these has been shown (Graham and Foulds, 1982; Day, 1983) to be
   NP-complete, which is equivalent to saying that there is no fast
   algorithm that is guaranteed to solve the problem in all cases (for a
   discussion of NP-completeness, see the Scientific American article by
   Lewis and Papadimitriou, 1978). The result is that this program,
   despite its algorithmic sophistication, is VERY SLOW.

   The program should be slower than the other tree-building programs in
   the package, but useable up to about ten species. Above this it will
   bog down rapidly, but exactly when depends on the data and on how much
   computer time you have (it may be more effective in the hands of
   someone who can let a microcomputer grind all night than for someone
   who has the "benefit" of paying for time on the campus mainframe
   computer). IT IS VERY IMPORTANT FOR YOU TO GET A FEEL FOR HOW LONG THE
   PROGRAM WILL TAKE ON YOUR DATA. This can be done by running it on
   subsets of the species, increasing the number of species in the run
   until you either are able to treat the full data set or know that the
   program will take unacceptably long on it. (Making a plot of the
   logarithm of run time against species number may help to project run
   times).

  The Algorithm

   The search strategy used by DNAPENNY starts by making a tree consisting
   of the first two species (the first three if the tree is to be
   unrooted). Then it tries to add the next species in all possible places
   (there are three of these). For each of the resulting trees it
   evaluates the number of base substitutions. It adds the next species to
   each of these, again in all possible spaces. If this process would
   continue it would simply generate all possible trees, of which there
   are a very large number even when the number of species is moderate
   (34,459,425 with 10 species). Actually it does not do this, because the
   trees are generated in a particular order and some of them are never
   generated.

   This is because the order in which trees are generated is not quite as
   implied above, but is a "depth-first search". This means that first one
   adds the third species in the first possible place, then the fourth
   species in its first possible place, then the fifth and so on until the
   first possible tree has been produced. For each tree the number of
   steps is evaluated. Then one "backtracks" by trying the alternative
   placements of the last species. When these are exhausted one tries the
   next placement of the next-to-last species. The order of placement in a
   depth-first search is like this for a four-species case (parentheses
   enclose monophyletic groups):

     Make tree of first two species:     (A,B)
          Add C in first place:     ((A,B),C)
               Add D in first place:     (((A,D),B),C)
               Add D in second place:     ((A,(B,D)),C)
               Add D in third place:     (((A,B),D),C)
               Add D in fourth place:     ((A,B),(C,D))
               Add D in fifth place:     (((A,B),C),D)
          Add C in second place:     ((A,C),B)
               Add D in first place:     (((A,D),C),B)
               Add D in second place:     ((A,(C,D)),B)
               Add D in third place:     (((A,C),D),B)
               Add D in fourth place:     ((A,C),(B,D))
               Add D in fifth place:     (((A,C),B),D)
          Add C in third place:     (A,(B,C))
               Add D in first place:     ((A,D),(B,C))
               Add D in second place:     (A,((B,D),C))
               Add D in third place:     (A,(B,(C,D)))
               Add D in fourth place:     (A,((B,C),D))
               Add D in fifth place:     ((A,(B,C)),D)

   Among these fifteen trees you will find all of the four-species rooted
   trees, each exactly once (the parentheses each enclose a monophyletic
   group). As displayed above, the backtracking depth-first search
   algorithm is just another way of producing all possible trees one at a
   time. The branch and bound algorithm consists of this with one change.
   As each tree is constructed, including the partial trees such as
   (A,(B,C)), its number of steps is evaluated. In addition a prediction
   is made as to how many steps will be added, at a minimum, as further
   species are added.

   This is done by counting how many sites which are invariant in the data
   up the most recent species added will ultimately show variation when
   further species are added. Thus if 20 sites vary among species A, B,
   and C and their root, and if tree ((A,C),B) requires 24 steps, then if
   there are 8 more sites which will be seen to vary when species D is
   added, we can immediately say that no matter how we add D, the
   resulting tree can have no less than 24 + 8 = 32 steps. The point of
   all this is that if a previously-found tree such as ((A,B),(C,D))
   required only 30 steps, then we know that there is no point in even
   trying to add D to ((A,C),B). We have computed the bound that enables
   us to cut off a whole line of inquiry (in this case five trees) and
   avoid going down that particular branch any farther.

   The branch-and-bound algorithm thus allows us to find all most
   parsimonious trees without generating all possible trees. How much of a
   saving this is depends strongly on the data. For very clean (nearly
   "Hennigian") data, it saves much time, but on very messy data it will
   still take a very long time.

   The algorithm in the program differs from the one outlined here in some
   essential details: it investigates possibilities in the order of their
   apparent promise. This applies to the order of addition of species, and
   to the places where they are added to the tree. After the first
   two-species tree is constructed, the program tries adding each of the
   remaining species in turn, each in the best possible place it can find.
   Whichever of those species adds (at a minimum) the most additional
   steps is taken to be the one to be added next to the tree. When it is
   added, it is added in turn to places which cause the fewest additional
   steps to be added. This sounds a bit complex, but it is done with the
   intention of eliminating regions of the search of all possible trees as
   soon as possible, and lowering the bound on tree length as quickly as
   possible. This process of evaluating which species to add in which
   order goes on the first time the search makes a tree; thereafter it
   uses that order.

   The program keeps a list of all the most parsimonious trees found so
   far. Whenever it finds one that has fewer losses than these, it clears
   out the list and restarts it with that tree. In the process the bound
   tightens and fewer possibilities need be investigated. At the end the
   list contains all the shortest trees. These are then printed out. It
   should be mentioned that the program CLIQUE for finding all largest
   cliques also works by branch-and-bound. Both problems are NP-complete
   but for some reason CLIQUE runs far faster. Although their worst-case
   behavior is bad for both programs, those worst cases occur far more
   frequently in parsimony problems than in compatibility problems.

  Controlling Run Times

   Among the quantities available to be set from the menu of DNAPENNY, two
   (howoften and howmany) are of particular importance. As DNAPENNY goes
   along it will keep count of how many trees it has examined. Suppose
   that howoften is 100 and howmany is 1000, the default settings. Every
   time 100 trees have been examined, DNAPENNY will print out a line
   saying how many multiples of 100 trees have now been examined, how many
   steps the most parsimonious tree found so far has, how many trees of
   with that number of steps have been found, and a very rough estimate of
   what fraction of all trees have been looked at so far. When the number
   of these multiples printed out reaches the number howmany (say 1000),
   the whole algorithm aborts and prints out that it has not found all
   most parsimonious trees, but prints out what is has got so far anyway.
   These trees need not be any of the most parsimonious trees: they are
   simply the most parsimonious ones found so far. By setting the product
   (howoften times howmany) large you can make the algorithm less likely
   to abort, but then you risk getting bogged down in a gigantic
   computation. You should adjust these constants so that the program
   cannot go beyond examining the number of trees you are reasonably
   willing to pay for (or wait for). In their initial setting the program
   will abort after looking at 100,000 trees. Obviously you may want to
   adjust howoften in order to get more or fewer lines of intermediate
   notice of how many trees have been looked at so far. Of course, in
   small cases you may never even reach the first multiple of howoften,
   and nothing will be printed out except some headings and then the final
   trees. The indication of the approximate percentage of trees searched
   so far will be helpful in judging how much farther you would have to go
   to get the full search. Actually, since that fraction is the fraction
   of the set of all possible trees searched or ruled out so far, and
   since the search becomes progressively more efficient, the approximate
   fraction printed out will usually be an underestimate of how far along
   the program is, sometimes a serious underestimate.

   A constant at the beginning of the program that affects the result is
   "maxtrees", which controls the maximum number of trees that can be
   stored. Thus if maxtrees is 25, and 32 most parsimonious trees are
   found, only the first 25 of these are stored and printed out. If
   maxtrees is increased, the program does not run any slower but requires
   a little more intermediate storage space. I recommend that maxtrees be
   kept as large as you can, provided you are willing to look at an output
   with that many trees on it! Initially, maxtrees is set to 100 in the
   distribution copy.

  Method and Options

   The counting of the length of trees is done by an algorithm nearly
   identical to the corresponding algorithms in DNAPARS, and thus the
   remainder of this document will be nearly identical to the DNAPARS
   document.

   This program carries out unrooted parsimony (analogous to Wagner trees)
   (Eck and Dayhoff, 1966; Kluge and Farris, 1969) on DNA sequences. The
   method of Fitch (1971) is used to count the number of changes of base
   needed on a given tree. The assumptions of this method are exactly
   analogous to those of DNAPARS:
    1. Each site evolves independently.
    2. Different lineages evolve independently.
    3. The probability of a base substitution at a given site is small
       over the lengths of time involved in a branch of the phylogeny.
    4. The expected amounts of change in different branches of the
       phylogeny do not vary by so much that two changes in a high-rate
       branch are more probable than one change in a low-rate branch.
    5. The expected amounts of change do not vary enough among sites that
       two changes in one site are more probable than one change in
       another.

   Change from an occupied site to a deletion is counted as one change.
   Reversion from a deletion to an occupied site is allowed and is also
   counted as one change. 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). Change from an
   occupied site to a deletion is counted as one change. Reversion from a
   deletion to an occupied site is allowed and is also counted as one
   change. Note that this in effect assumes that a deletion N bases long
   is N separate events.

Usage

   Here is a sample session with fdnapenny


% fdnapenny
Penny algorithm for DNA
Input (aligned) nucleotide sequence set(s): dnapenny.dat
Phylip dnapenny program output file [dnapenny.fdnapenny]:

justweights: false
numwts: 0

How many
trees looked                                       Approximate
at so far      Length of        How many           percentage
(multiples     shortest tree    trees this short   searched
of  100):      found so far     found so far       so far
----------     ------------     ------------       ------------
      1             9.0                2                0.11
      2             8.0                3                6.67
      3             8.0                9               20.00
      4             8.0                9               86.67

Output written to file "dnapenny.fdnapenny"

Trees also written onto file "dnapenny.treefile"



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

Command line arguments

Penny algorithm for DNA
Version: EMBOSS:6.2.0

   Standard (Mandatory) qualifiers:
  [-sequence]          seqsetall  File containing one or more sequence
                                  alignments
  [-outfile]           outfile    [*.fdnapenny] Phylip dnapenny program output
                                  file

   Additional (Optional) qualifiers (* if not always prompted):
   -weights            properties (no help text) properties value
   -howoften           integer    [100] How often to report, in trees (Any
                                  integer value)
   -howmany            integer    [1000] How many groups of trees (Any integer
                                  value)
   -[no]simple         boolean    [Y] Branch and bound is simple
   -outgrno            integer    [0] Species number to use as outgroup
                                  (Integer 0 or more)
   -thresh             toggle     [N] Use threshold parsimony
*  -threshold          float      [1.0] Threshold value (Number 1.000 or more)
   -[no]trout          toggle     [Y] Write out trees to tree file
*  -outtreefile        outfile    [*.fdnapenny] 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 out steps in each site
   -ancseq             boolean    [N] Print sequences at all nodes of tree

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

   "-sequence" associated qualifiers
   -sbegin1            integer    Start of each sequence to be used
   -send1              integer    End of each sequence to be used
   -sreverse1          boolean    Reverse (if DNA)
   -sask1              boolean    Ask for begin/end/reverse
   -snucleotide1       boolean    Sequence is nucleotide
   -sprotein1          boolean    Sequence is protein
   -slower1            boolean    Make lower case
   -supper1            boolean    Make upper case
   -sformat1           string     Input sequence format
   -sdbname1           string     Database name
   -sid1               string     Entryname
   -ufo1               string     UFO features
   -fformat1           string     Features format
   -fopenfile1         string     Features file name

   "-outfile" associated qualifiers
   -odirectory2        string     Output directory

   "-outtreefile" associated qualifiers
   -odirectory         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

   fdnapenny reads any normal sequence USAs

  Input files for usage example

  File: dnapenny.dat

    8    6
Alpha1    AAGAAG
Alpha2    AAGAAG
Beta1     AAGGGG
Beta2     AAGGGG
Gamma1    AGGAAG
Gamma2    AGGAAG
Delta     GGAGGA
Epsilon   GGAAAG

Output file format

   fdnapenny 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, and
   (if option 2 is toggled on) a table of the number of changes of state
   required in each character. 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. If the inferred state is a "?"
   or one of the IUB ambiguity symbols, there will be multiple
   equally-parsimonious assignments of states; the user must work these
   out for themselves by hand. A "?" in the reconstructed states means
   that in addition to one or more bases, a deletion may or may not be
   present. 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: dnapenny.fdnapenny


Penny algorithm for DNA, version 3.69
 branch-and-bound to find all most parsimonious trees


requires a total of              8.000

     9 trees in all found




  +--------------------Alpha1
  !
  !        +-----------Alpha2
  !        !
  1  +-----4        +--Epsilon
  !  !     !  +-----6
  !  !     !  !     +--Delta
  !  !     +--5
  +--2        !     +--Gamma2
     !        +-----7
     !              +--Gamma1
     !
     !              +--Beta2
     +--------------3
                    +--Beta1

  remember: this is an unrooted tree!





  +--------------------Alpha1
  !
  !        +-----------Alpha2
  !        !
  1  +-----4  +--------Gamma2
  !  !     !  !
  !  !     +--7     +--Epsilon
  !  !        !  +--6
  +--2        +--5  +--Delta
     !           !
     !           +-----Gamma1
     !
     !              +--Beta2
     +--------------3
                    +--Beta1



  [Part of this file has been deleted for brevity]

              +--5  +--Delta
                 !
                 +-----Gamma1

  remember: this is an unrooted tree!





  +--------------------Alpha1
  !
  !              +-----Alpha2
  1  +-----------2
  !  !           !  +--Beta2
  !  !           +--3
  !  !              +--Beta1
  +--4
     !           +-----Gamma2
     !        +--7
     !        !  !  +--Epsilon
     +--------5  +--6
              !     +--Delta
              !
              +--------Gamma1

  remember: this is an unrooted tree!





  +--------------------Alpha1
  !
  !              +-----Alpha2
  1  +-----------2
  !  !           !  +--Beta2
  !  !           +--3
  !  !              +--Beta1
  +--4
     !              +--Epsilon
     !        +-----6
     !        !     +--Delta
     +--------5
              !     +--Gamma2
              +-----7
                    +--Gamma1

  remember: this is an unrooted tree!



  File: dnapenny.treefile

(Alpha1,((Alpha2,((Epsilon,Delta),(Gamma2,Gamma1))),(Beta2,Beta1)))[0.1111];
(Alpha1,((Alpha2,(Gamma2,((Epsilon,Delta),Gamma1))),(Beta2,Beta1)))[0.1111];
(Alpha1,((Alpha2,((Gamma2,(Epsilon,Delta)),Gamma1)),(Beta2,Beta1)))[0.1111];
(Alpha1,(Alpha2,((Gamma2,((Epsilon,Delta),Gamma1)),(Beta2,Beta1))))[0.1111];
(Alpha1,(Alpha2,(((Epsilon,Delta),(Gamma2,Gamma1)),(Beta2,Beta1))))[0.1111];
(Alpha1,(Alpha2,(((Gamma2,(Epsilon,Delta)),Gamma1),(Beta2,Beta1))))[0.1111];
(Alpha1,((Alpha2,(Beta2,Beta1)),(Gamma2,((Epsilon,Delta),Gamma1))))[0.1111];
(Alpha1,((Alpha2,(Beta2,Beta1)),((Gamma2,(Epsilon,Delta)),Gamma1)))[0.1111];
(Alpha1,((Alpha2,(Beta2,Beta1)),((Epsilon,Delta),(Gamma2,Gamma1))))[0.1111];

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      Create a distance matrix from a multiple sequence alignment
                    ednacomp     DNA compatibility algorithm
                    ednadist     Nucleic acid sequence Distance Matrix program
                    ednainvar    Nucleic acid sequence Invariants method
                    ednaml       Phylogenies from nucleic acid Maximum Likelihood
                    ednamlk      Phylogenies from nucleic acid Maximum Likelihood with clock
                    ednapars     DNA parsimony algorithm
                    ednapenny    Penny algorithm for DNA
                    eprotdist    Protein distance algorithm
                    eprotpars    Protein parsimony algorithm
                    erestml      Restriction site Maximum Likelihood method
                    eseqboot     Bootstrapped sequences algorithm
                    fdiscboot    Bootstrapped discrete sites algorithm
                    fdnacomp     DNA compatibility algorithm
                    fdnadist     Nucleic acid sequence Distance Matrix program
                    fdnainvar    Nucleic acid sequence Invariants method
                    fdnaml       Estimates nucleotide phylogeny by maximum likelihood
                    fdnamlk      Estimates nucleotide phylogeny by maximum likelihood
                    fdnamove     Interactive DNA parsimony
                    fdnapars     DNA parsimony algorithm
                    fdolmove     Interactive Dollo or Polymorphism Parsimony
                    ffreqboot    Bootstrapped genetic frequencies algorithm
                    fproml       Protein phylogeny by maximum likelihood
                    fpromlk      Protein phylogeny by maximum likelihood
                    fprotdist    Protein distance algorithm
                    fprotpars    Protein parsimony algorithm
                    frestboot    Bootstrapped restriction sites algorithm
                    frestdist    Distance matrix from restriction sites or fragments
                    frestml      Restriction site maximum Likelihood method
                    fseqboot     Bootstrapped sequences algorithm
                    fseqbootall  Bootstrapped sequences algorithm

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.
