version 3.5c


        DOLPENNY - Branch and bound to find all most parsimonious trees
                  for Dollo, polymorphism parsimony criteria


(c) Copyright  1986-1993  by  Joseph  Felsenstein  and  by  the  University  of
Washington.  Written by Joseph Felsenstein.  Permission is granted to copy this
document provided that no fee is charged for it and that this copyright  notice
is not removed.

     DOLPENNY is a program that will find all of the  most  parsimonious  trees
implied  by  your  data  when  the Dollo or polymorphism parsimony criteria are
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 DOLPENNY 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 losses.  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.

     Actually 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.  Its 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
bifurcating   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
losses (or retentions of polymorphism) is evaluated.

     The point of this is that if a previously-found tree such as ((A,B),(C,D))
required  fewer  losses,  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.

     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 the list 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 at the  beginning  of  a  run  of
DOLPENNY, two (howoften and howmany) are of particular importance.  As DOLPENNY
goes along it will keep count of how many trees it has examined.  Suppose  that
howoften is 100 and howmany is 300, the default settings.  Every time 100 trees
have been examined, DOLPENNY 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  X  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 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.


                              Methods and Options

     The counting of the length  of  trees  is  done  by  an  algorithm  nearly
identical  to the corresponding algorithms in DOLLOP, and thus the remainder of
this document will be nearly identical  to  the  DOLLOP  document.   The  Dollo
parsimony  method  was  first  suggested  in  print in verbal form by Le Quesne
(1974) and was first well-specified by Farris  (1977).   The  method  is  named
after  Louis Dollo since he was one of the first to assert that in evolution it
is harder to gain a complex feature than to lose it.   The  algorithm  explains


the  presence  of the state 1 by allowing up to one forward change 0-->1 and as
many reversions 1-->0 as are necessary to explain the pattern of  states  seen.
The program attempts to minimize the number of 1-->0 reversions necessary.

     The assumptions of this method are in effect:

     1. We know which state is the ancestral one (state 0).

     2. The characters are evolving independently.

     3. Different lineages evolve independently.

     4. The  probability  of  a  forward  change  (0-->1)  is  small  over  the
evolutionary times involved.

     5. The probability of a reversion (1-->0) is also  small,  but  still  far
larger  than  the  probability of a forward change, so that many reversions are
easier to envisage than even one extra forward change.

     6. Retention  of  polymorphism  for  both  states  (0  and  1)  is  highly
improbable.

     7. The lengths of the segments of the true tree are not  so  unequal  that
two changes in a long segment are as probable as one in a short segment.

     That these are the assumptions is established  in  several  of  my  papers
(1973a,  1978b,  1979,  1981b,  1983).   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).

     One problem can arise when using additive binary recoding to  represent  a
multistate  character  as  a series of two-state characters.  Unlike the Camin-
Sokal, Wagner, and Polymorphism  methods,  the  Dollo  method  can  reconstruct
ancestral states which do not exist.  An example is given in my 1979 paper.  It
will be necessary to check the output to make sure that this has not occurred.

     The polymorphism parsimony method was first used by me,  and  the  results
published  (without  a clear specification of the method) by Inger (1967).  The
method was published by Farris (1978a) and by me (1979).   The  method  assumes
that  we can explain the pattern of states by no more than one origination (0--
>1) of state 1, followed by retention of polymorphism along as many segments of
the  tree  as  are  necessary,  followed by loss of state 0 or of state 1 where
necessary.  The program tries to  minimize  the  total  number  of  polymorphic
characters,  where  each  polymorphism  is counted once for each segment of the
tree in which it is retained.

     The assumptions of the polymorphism parsimony method are in effect:

     1. The ancestral state (state 0) is known in each character.

     2. The characters are evolving independently of each other.

     3. Different lineages are evolving independently.

     4. Forward change (0-->1) is highly improbable over  the  length  of  time
involved in the evolution of the group.

     5. Retention of polymorphism is also improbable,  but  far  more  probable
that  forward change, so that we can more easily envisage much polymorhism than
even one additional forward change.


     6. Once state 1 is reached, reoccurrence of state 0  is  very  improbable,
much less probable than multiple retentions of polymorphism.

     7. The lengths of segments in the true tree are not so unequal that we can
more  easily  envisage  retention events occurring in both of two long segments
than one retention 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).

     The input format is the standard one, with "?", "P", "B"  states  allowed.
Most of the options are selected using a menu:


Penny algorithm for Dollo or polymorphism parsimony, version 3.5c
 branch-and-bound to find all most parsimonious trees

Settings for this run:
  P                     Parsimony method?  Dollo
  H        How many groups of  100 trees:  1000
  F        How often to report, in trees:  100
  S           Branch and bound is simple?  Yes
  T              Use Threshold parsimony?  No, use ordinary parsimony
  A   Use ancestral states in input file?  No
  M           Analyze multiple data sets?  No
  0   Terminal type (IBM PC, VT52, ANSI)?  ANSI
  1    Print out the data at start of run  No
  2  Print indications of progress of run  Yes
  3                        Print out tree  Yes
  4     Print out steps in each character  No
  5     Print states at all nodes of tree  No
  6       Write out trees onto tree file?  Yes

Are these settings correct? (type Y or the letter for one to change)

The P option toggles between the Polymorphism parsimony method and the  default
Dollo parsimony method.

     The options T, A, and M are the usual  Threshold,  Ancestral  States,  and
Multiple  Data Sets options.  They are described in the Main documentation file
and in the Discrete Characters Programs documentation file.

     Options F and H reset the variables howoften (F)  and  howmany  (H).   The
user  is prompted for the new values.  By setting these larger the program will
report its progress less  often  (howoften)  and  will  run  longer  (howmany x
often).   These  values  default  to  100 and 1000 which guarantees a search of
100,000 trees, but these can be changed.  Note that option F in this program is
not  the Factors option available in some of the other programs in this section
of the package.

     The A (Ancestral states) option works in the usual way, described  in  the
Discrete Characters Programs documentation file.  It also requires that an A be
present on the first line of the input file.  The use of the  A  option  allows
implementation  of  the  unordered  Dollo  parsimony and unordered polymorphism
parsimony methods which I have described elsewhere (1984b).  When the A  option
is  used  the  ancestor  is  not  to  be  counted as one of the species.  The O
(outgroup) option is not available since the tree produced is already rooted.



     Setting T at or below 1.0 but above  0  causes  the  criterion  to  become
compatibility   rather  than  polymorphism  parsimony,  although  there  is  no
advantage to using this program instead of PENNY to do a compatibility  method.
Setting  the  threshold  value  higher brings about an intermediate between the
Dollo or polymorphism parsimony methods and the compatibility method,  so  that
there  is  some  rationale  for  doing  that.  Since the Dollo and polymorphism
methods produces a rooted tree, the user-defined trees required by the U option
have two-way forks at each level.

     Using a threshold value of 1.0 or lower, but above 0,  one  can  obtain  a
rooted  (or,  if  the  A option is used with ancestral states of "?", unrooted)
compatibility criterion, but there is no particular  advantage  to  using  this
program  for  that  instead  of  MIX.   Higher  threshold  values are of course
meaningful and provide intermediates between Dollo and compatibility methods.

     The S (Simple) option alters a step  in  DOLPENNY  which  reconsiders  the
order in which species are added to the tree.  Normally the decision as to what
species to  add  to  the  tree  next  is  made  as  the  first  tree  is  being
constructucted;  that  ordering  of species is not altered subsequently.  The R
option causes it to be continually reconsidered.  This will probably result  in
a  substantial  increase  in  run  time,  but on some data sets of intermediate
messiness it may help.  It is included in case it might prove of  use  on  some
data sets.

     In the input file the W (Weights) option is available, as usual.   It  and
the  A (Ancestral states) option also requires the option to be declared on the
first line of the input file, and other information to be present in the  input
file.   If the Ancestral States option is used the A option must also be chosen
from the menu.  The F (Factors) option is not available in this program, as  it
would  have  no  effect on the result even if that information were provided in
the input file.

     The output format is also standard.  It includes a rooted tree and, if the
user  selects  option  4, a table of the numbers of reversions or retentions of
polymorphism necessary in each character.  If any of the ancestral  states  has
been specified to be unknown, a table of reconstructed ancestral states is also
provided.  When reconstructing the placement of forward changes and  reversions
under  the  Dollo method, keep in mind that each polymorphic state in the input
data will require one  "last  minute"  reversion.   This  is  included  in  the
tabulated counts.  Thus if we have both states 0 and 1 at a tip of the tree the
program will assume that the lineage had state 1 up to  the  last  minute,  and
then state 0 arose in that population by reversion, without loss of state 1.

     A table is available to be 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 A option is used, then the program will infer,  for  any  character
whose  ancestral state is unknown ("?") whether the ancestral state 0 or 1 will
give the best tree.  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 DOLMOVE to display the tree and
examine its interior states, as the algorithm in DOLMOVE shows all that can  be
known  in  this case about the interior states, including where there is and is
not amibiguity.  The algorithm in DOLPENNY gives up more easily  on  displaying
these states.




     At the beginning of the program are a series of constants,  which  can  be
changed  to  help  adapt the program to different computer systems. Two are the
initial values of howmany and howoften, constants "often" and "many".  Constant
"maxtrees"  is  the  maximum  number  of  tied  trees  that  will be stored and
"nmlngth" is the length of the species names.

-------------------------------TEST DATA SET----------------------------

    7    6
Alpha1    110110
Alpha2    110110
Beta1     110000
Beta2     110000
Gamma1    100110
Delta     001001
Epsilon   001110

------- TEST SET OUTPUT (with all numerical options turned on) ---------

Penny algorithm for Dollo or polymorphism parsimony, version 3.5c
 branch-and-bound to find all most parsimonious trees

Dollo parsimony method




requires a total of              3.000

    3 trees in all found




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


 reversions in each character:
         0   1   2   3   4   5   6   7   8   9
     *-----------------------------------------
    0!       0   0   1   1   1   0

From    To     Any Steps?    State at upper node
                             ( . means same as in the node below it on tree)

root      2         yes    ..1.. .
  2    Delta        yes    ..... 1
  2       3         yes    ...11 .
  3    Epsilon      no     ..... .


  3       6         yes    1.0.. .
  6    Gamma1       no     ..... .
  6       1         yes    .1... .
  1    Alpha2       no     ..... .
  1       4         no     ..... .
  4       5         yes    ...00 .
  5    Beta2        no     ..... .
  5    Beta1        no     ..... .
  4    Alpha1       no     ..... .





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


 reversions in each character:
         0   1   2   3   4   5   6   7   8   9
     *-----------------------------------------
    0!       0   0   1   1   1   0

From    To     Any Steps?    State at upper node
                             ( . means same as in the node below it on tree)

root      2         yes    ..1.. .
  2    Delta        yes    ..... 1
  2       3         yes    ...11 .
  3    Epsilon      no     ..... .
  3       6         yes    1.0.. .
  6    Gamma1       no     ..... .
  6       4         yes    .1... .
  4       5         yes    ...00 .
  5    Beta2        no     ..... .
  5    Beta1        no     ..... .
  4       1         no     ..... .
  1    Alpha2       no     ..... .
  1    Alpha1       no     ..... .





  +-----------------Delta
  !
--2  +--------------Epsilon
  !  !
  +--3  +-----------Gamma1
     !  !


     !  !        +--Beta2
     +--6     +--5
        !  +--4  +--Beta1
        !  !  !
        +--1  +-----Alpha2
           !
           +--------Alpha1


 reversions in each character:
         0   1   2   3   4   5   6   7   8   9
     *-----------------------------------------
    0!       0   0   1   1   1   0

From    To     Any Steps?    State at upper node
                             ( . means same as in the node below it on tree)

root      2         yes    ..1.. .
  2    Delta        yes    ..... 1
  2       3         yes    ...11 .
  3    Epsilon      no     ..... .
  3       6         yes    1.0.. .
  6    Gamma1       no     ..... .
  6       1         yes    .1... .
  1       4         no     ..... .
  4       5         yes    ...00 .
  5    Beta2        no     ..... .
  5    Beta1        no     ..... .
  4    Alpha2       no     ..... .
  1    Alpha1       no     ..... .