version 3.6

# CONSENSE -- Consensus tree program

© Copyright 1986-2004 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.

CONSENSE reads a file of computer-readable trees and prints out (and may also write out onto a file) a consensus tree. At the moment it carries out a family of consensus tree methods called the Ml methods (Margush and McMorris, 1981). These include strict consensus and majority rule consensus. Basically the consensus tree consists of monophyletic groups that occur as often as possible in the data. If a group occurs in more than a fraction l of all the input trees it will definitely appear in the consensus tree.

The tree printed out has at each fork a number indicating how many times the group which consists of the species to the right of (descended from) the fork occurred. Thus if we read in 15 trees and find that a fork has the number 15, that group occurred in all of the trees. The strict consensus tree consists of all groups that occurred 100% of the time, the rest of the resolution being ignored. The tree printed out here includes groups down to 50%, and below it until the tree is fully resolved.

The majority rule consensus tree consists of all groups that occur more than 50% of the time. Any other percentage level between 50% and 100% can also be used, and that is why the program in effect carries out a family of methods. You have to decide on the percentage level, figure out for yourself what number of occurrences that would be (e.g. 15 in the above case for 100%), and resolutely ignore any group below that number. Do not use numbers at or below 50%, because some groups occurring (say) 35% of the time will not be shown on the tree. The collection of all groups that occur 35% or more of the time may include two groups that are mutually self contradictory and cannot appear in the same tree. In this program, as the default method I have included groups that occur less than 50% of the time, working downwards in their frequency of occurrence, as long as they continue to resolve the tree and do not contradict more frequent groups. In this respect the method is similar to the Nelson consensus method (Nelson, 1979) as explicated by Page (1989) although it is not identical to it.

The program can also carry out Strict consensus, Majority Rule consensus without the extension which adds groups until the tree is fully resolved, and other members of the Ml family, where the user supplied the fraction of times the group must appear in the input trees to be included in the consensus tree. For the moment the program cannot carry out any other consensus tree method, such as Adams consensus (Adams, 1972, 1986) or methods based on quadruples of species (Estabrook, McMorris, and Meacham, 1985).

## INPUT, OUTPUT, AND OPTIONS

Input is a tree file (called `intree`) which contains a series of trees in the Newick standard form -- the form used when many of the programs in this package write out tree files. Each tree starts on a new line. Each tree can have a weight, which is a real number and is located in comment brackets "[" and "]" just before the final ";" which ends the description of the tree. When the input trees have weights (like [0.01000]) then the total number of trees will be the total of those weights, which is often a number like 1.00. When the a tree doesn't have a weight it will each be assigned a weight of 1. This means that when we have tied trees (as from a parsimony program) three alternative tied trees will be counted as if each was 1/3 of a tree.

Note that this program can correctly read trees whether or not they are bifurcating: in fact they can be multifurcating at any level in the tree.

The options are selected from a menu, which looks like this:

    Consensus tree program, version 3.6

    Settings for this run:
     C         Consensus type (MRe, strict, MR, Ml):  Majority rule (extended)
     O                                Outgroup root:  No, use as outgroup species  1
     R                Trees to be treated as Rooted:  No
     T           Terminal type (IBM PC, ANSI, none):  ANSI
     1                Print out the sets of species:  Yes
     2         Print indications of progress of run:  Yes
     3                               Print out tree:  Yes
     4               Write out trees onto tree file:  Yes

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

Option C (Consensus method) selects which of four methods the program uses. The program defaults to using the extended Majority Rule method. Each time the C option is chosen the program moves on to another method, the others being in order Strict, Majority Rule, and Ml. Here are descriptions of the methods. In each case the fraction of times a set appears among the input trees is counted by weighting by the weights of the trees (the numbers like `[0.6000]` that appear at the ends of trees in some cases).

Strict
  A set of species must appear in all input trees to be included in the strict consensus tree.

Majority Rule (extended)
  Any set of species that appears in more than 50% of the trees is included. The program then considers the other sets of species in order of the frequency with which they have appeared, adding to the consensus tree any which are compatible with it until the tree is fully resolved. This is the default setting.

Ml
  The user is asked for a fraction between 0.5 and 1, and the program then includes in the consensus tree any set of species that occurs among the input trees more than that fraction of then time. The Strict consensus and the Majority Rule consensus are extreme cases of the Ml consensus, being for fractions of 1 and 0.5 respectively.

Majority Rule
  A set of species is included in the consensus tree if it is present in more than half of the input trees.

Option R (Rooted) toggles between the default assumption that the input trees are unrooted trees and the selection that specifies that the tree is to be treated as a rooted tree and not re-rooted. Otherwise the tree will be treated as outgroup-rooted and will be re-rooted automatically at the first species encountered on the first tree (or at a species designated by the Outgroup option).

Option O is the usual Outgroup rooting option. It is in effect only if the Rooted option selection is not in effect. The trees will be re-rooted with a species of your choosing. You will be asked for the number of the species that is to be the outgroup. If we want to outgroup-root the tree on the line leading to a species which appears as the third species (counting left-to-right) in the first computer-readable tree in the input file, we would invoke select menu option O and specify species 3.

Output is a list of the species (in the order in which they appear in the first tree, which is the numerical order used in the program), a list of the subsets that appear in the consensus tree, a list of those that appeared in one or another of the individual trees but did not occur frequently enough to get into the consensus tree, followed by a diagram showing the consensus tree. The lists of subsets consists of a row of symbols, each either "." or "*". The species that are in the set are marked by "*". Every ten species there is a blank, to help you keep track of the alignment of columns. The order of symbols corresponds to the order of species in the species list. Thus a set that consisted of the second, seventh, and eighth out of 13 species would be represented by:

              .*....**.. ...

Note that if the trees are unrooted the final tree will have one group, consisting of every species except the Outgroup (which by default is the first species encountered on the first tree), which always appears. It will not be listed in either of the lists of sets, but it will be shown in the final tree as occurring all of the time. This is hardly surprising: in telling the program that this species is the outgroup we have specified that the set consisting of all of the others is always a monophyletic set. So this is not to be taken as interesting information, despite its dramatic appearance.

Option 2 in the menu gives you the option of turning off the writing of these sets into the output file. This may be useful if you are primarily interested in getting the tree file.

Option 3 is the usual tree file option. If this is on (it is by default) then the final tree will be written onto an output tree file (whose default name is "outtree").

## Branch Lengths on the Consensus Tree?

Note that the lengths on the tree on the output tree file are not branch lengths but the number of times that each group appeared in the input trees. This number is the sum of the weights of the trees in which it appeared, so that if there are 11 trees, ten of them having weight 0.1 and one weight 1.0, a group that appeared in the last tree and in 6 others would be shown as appearing 1.6 times and its branch length will be 1.6. This means that if you take the consensus tree from the output tree file and try to draw it, the branch lengths will be strange. I am often asked how to put the correct branch lengths on these (this is one of our Frequently Asked Questions).

There is no simple answer to this. It depends on what "correct" means. For example, if you have a group of species that shows up in 80% of the trees, and the branch leading to that group has average length 0.1 among that 80%, is the "correct" length 0.1? Or is it (0.80 x 0.1)? There is no simple answer.

However, if you want to take the consensus tree as an estimate of the true tree (rather than as an indicator of the conflicts among trees) you may be able to use the User Tree (option U) mode of the phylogeny program that you used, and use it to put branch lengths on that tree. Thus, if you used DNAML, you can take the consensus tree, make sure it is an unrooted tree, and feed that to DNAML using the original data set (before bootstrapping) and DNAML's option U. As DNAML wants an unrooted tree, you may have to use RETREE to make the tree unrooted (using the W option of RETREE and choosing the unrooted option within it). Of course you will also want to change the tree file name from "outree" to "intree".

If you used a phylogeny program that does not infer branch lengths, you might want to use a different one (such as FITCH or DNAML) to infer the branch lengths, again making sure the tree is unrooted, if the program needs that.

## CONSTANTS

The program uses the consensus tree algorithm originally designed for the bootstrap programs. It is quite fast, and execution time is unlikely to be limiting for you (assembling the input file will be much more of a limiting step). In the future, if possible, more consensus tree methods will be incorporated (although the current methods are the ones needed for the component analysis of bootstrap estimates of phylogenies, and in other respects I also think that the present ones are among the best).

###

###

    TEST SET OF INPUT TREES

    (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)))));

    TEST SET OUTPUT

    Consensus tree program, version 3.6

    Species in order:

      1. A
      2. B
      3. H
      4. D
      5. J
      6. G
      7. E
      8. F
      9. I
      10. C

    Sets included in the consensus tree

    Set (species in order)     How many times out of    9.00

    .......**.                   9.00
    ..********                   9.00
    ..****.***                   6.00
    ..***.....                   6.00
    ..***....*                   6.00
    ..*.*.....                   4.00
    ..***..***                   2.00

    Sets NOT included in consensus tree:

    Set (species in order)     How many times out of    9.00

    .....**...                   3.00
    .....*****                   3.00
    ..**......                   3.00
    .....****.                   3.00
    ..****...*                   2.00
    .....*.**.                   2.00
    ..*.******                   2.00
    ....******                   2.00
    ...*******                   1.00

    Extended majority rule consensus tree

    CONSENSUS TREE:
    the numbers on the branches indicate the number
    of times the partition of the species into the two sets
    which are separated by that branch occurred
    among the trees, out of   9.00 trees

                                         +--------------------C
                                         |
                                  +--6.0-|             +------H
                                  |      |      +--4.0-|
                                  |      +--6.0-|      +------J
                           +--2.0-|             |
                           |      |             +-------------D
                           |      |
                    +--6.0-|      |                    +------F
                    |      |      +----------------9.0-|
                    |      |                           +------I
             +--9.0-|      |
             |      |      +----------------------------------G
      +------|      |
      |      |      +-----------------------------------------E
      |      |
      |      +------------------------------------------------B
      |
      +-------------------------------------------------------A

      remember: this is an unrooted tree!