
                                 fdnapenny 



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 sequence: dnapenny.dat
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             8.0                3                0.95

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

   Standard (Mandatory) qualifiers:
  [-sequence]          seqsetall  File containing one or more sequence
                                  alignments
  [-outfile]           outfile    Output file name

   Additional (Optional) qualifiers (* if not always prompted):
   -weights            properties (no help text) properties value
   -howoften           integer    How often to report, in trees
   -howmany            integer    How many groups of trees
   -[no]simple         boolean    Branch and bound is simple
   -outgrno            integer    Species number to use as outgroup
   -thresh             toggle     Use threshold parsimony
*  -threshold          float      Threshold value
   -[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
   -stepbox            boolean    Print out steps in each site
   -ancseq             boolean    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 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
   [-sequence]
   (Parameter 1) File containing one or more sequence alignments Readable
   sets of sequences
   [-outfile]
   (Parameter 2) Output file name Output file <sequence>.fdnapenny
   Additional (Optional) qualifiers Allowed values Default
   -weights (no help text) properties value Property value(s)
   -howoften How often to report, in trees Any integer value 100
   -howmany How many groups of trees Any integer value 1000
   -[no]simple Branch and bound is simple Boolean value Yes/No Yes
   -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 1.0
   -[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
   -stepbox Print out steps in each site Boolean value Yes/No No
   -ancseq Print sequences at all nodes of tree Boolean value Yes/No No
   Advanced (Unprompted) qualifiers Allowed values Default
   (none)

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 3.6b
 branch-and-bound to find all most parsimonious trees


requires a total of              8.000

     9 trees in all found




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

  remember: this is an unrooted tree!





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



  [Part of this file has been deleted for brevity]

     !              +--Beta2
     +--------------5
                    +--Beta1

  remember: this is an unrooted tree!





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

  remember: this is an unrooted tree!





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

  remember: this is an unrooted tree!


  File: dnapenny.treefile

(Alpha1,(((((Delta,Epsilon),Gamma2),Gamma1),(Beta2,Beta1)),Alpha2))[0.1111];
(Alpha1,((((Delta,Epsilon),(Gamma2,Gamma1)),(Beta2,Beta1)),Alpha2))[0.1111];
(Alpha1,(((((Delta,Epsilon),Gamma1),Gamma2),(Beta2,Beta1)),Alpha2))[0.1111];
(Alpha1,((((Delta,Epsilon),Gamma2),Gamma1),((Beta2,Beta1),Alpha2)))[0.1111];
(Alpha1,(((Delta,Epsilon),(Gamma2,Gamma1)),((Beta2,Beta1),Alpha2)))[0.1111];
(Alpha1,((((Delta,Epsilon),Gamma1),Gamma2),((Beta2,Beta1),Alpha2)))[0.1111];
(Alpha1,(((((Delta,Epsilon),Gamma2),Gamma1),Alpha2),(Beta2,Beta1)))[0.1111];
(Alpha1,((((Delta,Epsilon),(Gamma2,Gamma1)),Alpha2),(Beta2,Beta1)))[0.1111];
(Alpha1,(((((Delta,Epsilon),Gamma1),Gamma2),Alpha2),(Beta2,Beta1)))[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
   ednacomp DNA compatibility algorithm
   ednadist Nucleic acid sequence Distance Matrix program
   ednainvar Nucleic acid sequence Invariants method
   ednaml Estimates phylogenies from nucleic acid sequence Maximum
   Likelihood
   ednamlk Estimates phylogenies from nucleic acid sequence Maximum
   Likelihood with molecular 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 pasimony algorithm
   frestboot Bootstrapped restriction sites algorithm
   frestdist Computes 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.
