discrete

version 3.696

# DOCUMENTATION FOR (0,1) DISCRETE CHARACTER PROGRAMS

© Copyright 1986-2014 by Joseph Felsenstein. All rights reserved. License terms here.

These programs are intended for the use of morphological systematists who are dealing with discrete characters, or by molecular evolutionists dealing with presence-absence data on restriction sites. One of the programs (Pars) allows multistate characters, with up to 8 states, plus the unknown state symbol "?". For the others, the characters are assumed to be coded into a series of (0,1) two-state characters. For most of the programs there are two other states possible, "P", which stands for the state of Polymorphism for both states (0 and 1), and "?", which stands for the state of ignorance: it is the state "unknown", or "does not apply". The state "P" can also be denoted by "B", for "both".

There is a method invented by Sokal and Sneath (1963) for linear sequences of character states, and fully developed for branching sequences of character states by Kluge and Farris (1969) for recoding a multistate character into a series of two-state (0,1) characters. Suppose we had a character with four states whose character-state tree had the rooted form:

                   1 ---> 0 ---> 2
                          |
                          |
                          V
                          3

so that 1 is the ancestral state and 0, 2 and 3 derived states. We can represent this as three two-state characters:

                    Old State           New States
                    --- -----           --- ------
                        0                  001
                        1                  000
                        2                  011
                        3                  101

The three new states correspond to the three arrows in the above character state tree. Possession of one of the new states corresponds to whether or not the old state had that arrow in its ancestry. Thus the first new state corresponds to the bottommost arrow, which only state 3 has in its ancestry, the second state to the rightmost of the top arrows, and the third state to the leftmost top arrow. This coding will guarantee that the number of times that states arise on the tree (in programs Mix, Move, Penny and Boot) or the number of polymorphic states in a tree segment (in the Polymorphism option of Dollop, Dolmove, Dolpenny and Dolboot) will correctly correspond to what would have been the case had our programs been able to take multistate characters into account. Although I have shown the above character state tree as rooted, the recoding method works equally well on unrooted multistate characters as long as the connections between the states are known and contain no loops.

However, in the default option of programs Dollop, Dolmove, Dolpenny and Dolboot the multistate recoding does not necessarily work properly, as it may lead the program to reconstruct nonexistent state combinations such as 010. An example of this problem is given in my paper on alternative phylogenetic methods (1979).

If you have multistate character data where the states are connected in a branching "character state tree" you may want to do the binary recoding yourself. Thanks to Christopher Meacham, the package contains a program, Factor, which will do the recoding itself. For details see the documentation file for Factor.

We now also have the program Pars, which can do parsimony for unordered character states.

## COMPARISON OF METHODS

The methods used in these programs make different assumptions about evolutionary rates, probabilities of different kinds of events, and our knowledge about the characters or about the character state trees. Basic references on these assumptions are my 1979, 1981b and 1983b papers, particularly the latter. The assumptions of each method are briefly described in the documentation file for the corresponding program. In most cases my assertions about what are the assumptions of these methods are challenged by others, whose papers I also cite at that point. Personally, I believe that they are wrong and I am right. I must emphasize the importance of understanding the assumptions underlying the methods you are using. No matter how fancy the algorithms, how maximum the likelihood or how minimum the number of steps, your results can only be as good as the correspondence between biological reality and your assumptions!

## INPUT FORMAT

The input format is as described in the general documentation file. The input starts with a line containing the number of species and the number of characters.

In Pars, each character can have up to 8 states plus a "?" state. In any character, the first 8 symbols encountered will be taken to represent these states. Any of the digits 0-9, letters A-Z and a-z, and even symbols such as + and -, can be used (and in fact which 8 symbols are used can be different in different characters).

In the other discrete characters programs the allowable states are, 0, 1, P, B, and ?. Blanks may be included between the states (i. e. you can have a species whose data is DISCOGLOSS0 1 1 0 1 1 1). It is possible for extraneous information to follow the end of the character state data on the same line. For example, if there were 7 characters in the data set, a line of species data could read "DISCOGLOSS0110111 Hello there").

The discrete character data can continue to a new line whenever needed. The characters are not in the "aligned" or "interleaved" format used by the molecular sequence programs: they have the name and entire set of characters for one species, then the name and entire set of characters for the next one, and so on. This is known as the sequential format. Be particularly careful when you use restriction sites data, which can be in either the aligned or the sequential format for use in Restml but must be in the sequential format for these discrete character programs.

For Pars the discrete character data can be in either Sequential or Interleaved format; the latter is the default.

Errors in the input data will often be detected by the programs, and this will cause them to issue an error message such as 'BAD OUTGROUP NUMBER: ' together with information as to which species, character, or in this case outgroup number is the incorrect one. The program will then terminate; you will have to look at the data and figure out what went wrong and fix it. Often an error in the data causes a lack of synchronization between what is in the data file and what the program thinks is to be there. Thus a missing character may cause the program to read part of the next species name as a character and complain about its value. In this type of case you should look for the error earlier in the data file than the point about which the program is complaining.

## OPTIONS GENERALLY AVAILABLE

Specific information on options will be given in the documentation file associated with each program. However, some options occur in many programs. Options are selected from the menu in each program.

- The A (Ancestral states) option. This indicates that we are specifying the ancestral states for each character. In the menu the ancestors (A) option must be selected. An ancestral states input file is read, whose default name is `ancestors`. It contains a line or lines giving the ancestral states for each character. These may be 0, 1 or ?, the latter indicating that the ancestral state is unknown.

  An example is:

  001??11

  The ancestor information can be continued to a new line and can have blanks between any of the characters in the same way that species character data can. In the program Clique the ancestor is instead to be included as a regular species and no A option is available.

- The F (Factors) option. This is used in programs Move, Dolmove, and Factor. It specifies which binary characters correspond to which multistate characters. To use the F option you choose the F option in the program menu. After that the program will read a factors file (default name `factors`) which consists of a line or lines containing a symbol for each binary character. The symbol can be anything, provided that it is the same for binary characters that correspond to the same multistate character, and changes between multistate characters. A good practice is to make it the lower-order digit of the number of the multistate character.

  For example, if there were 20 binary characters that had been generated by nine multistate characters having respectively 4, 3, 3, 2, 1, 2, 2, 2, and 1 binary factors you would make the factors file be:

  11112223334456677889

  although it could equivalently be:

  aaaabbbaaabbabbaabba

  All that is important is that the symbol for each binary character change only when adjacent binary characters correspond to different mutlistate characters. The factors file contents can continue to a new line at any time except during the initial characters filling out the length of a species name.

- The J (Jumble) option. This causes the species to be entered into the tree in a random order rather than in their order in the input file. The program prompts you for a random number seed. This option is described in the main documentation file.

- The M (Multiple data sets) option. This has also been described in the main documentation file. It is not to be confused with the M option specified in the input file, which is the Mixture of methods option (yes, I know this is confusing).

- The O (outgroup) option. This has also already been discussed in the general documentation file. It specifies the number of the particular species which will be used as the outgroup in rerooting the final tree when it is printed out. It will not have any effect if the tree is already rooted or is a user-defined tree. This option is not available in Dollop, Dolmove, or Dolpenny, which always infer a rooted tree, or Clique, which requires you to work out the rerooting by hand. The menu selection will cause you to be prompted for the number of the outgroup.

- The T (threshold) option. This sets a threshold such that if the number of steps counted in a character is higher than the threshold, it will be taken to be the threshold value rather than the actual number of steps. This option has already been described in the main documentation file. The user is prompted for the threshold value. My 1981 paper (Felsenstein, 1981b) explains the logic behind the Threshold option, which is an attractive alternative to successive weighting of characters.

- The U (User tree) option. This has already been described in the main documentation file. For all of these programs user trees are to be specified as bifurcating trees, even in the cases where the tree that is inferred by the programs is to be regarded as unrooted.

- The W (Weights) option. This allows us to specify weights on the characters, including the possibility of omitting characters from the analysis. It has already been described in the main documentation file.

- The X (miXture) option. In the programs Mix, Move, and Penny the user can specify for each character which parsimony method is in effect. This is done by selecting menu option X (not M) and having an input mixture file, whose default name is `mixture`. It contains a line or lines with one letter for each character. These letters are C or S if the character is to be reconstructed according to Camin-Sokal parsimony, W or ? if the character is to be reconstructed according to Wagner parsimony. So if there are 20 characters the line giving the mixture might look like this:

      WWWCC WWCWC

  Note that blanks in the seqence of characters (after the first ones that are as long as the species names) will be ignored, and the information can go on to a new line at any point. So this could equally well have been specified by

      WW
      CCCWWCWC

## INFORMATION IN THE OUTPUT

On the line in that table corresponding to each branch of the tree will also be printed "yes", "no" or "maybe" as an answer to the question of whether this branch is of nonzero length. If there is no evidence that any character has changed in that branch, then "no" will be printed. If there is definite evidence that one has changed, then "yes" will be printed. If the matter is ambiguous, then "maybe" will be printed. You should keep in mind that all of these conclusions assume that we are only interested in the assignment of states that require the least amount of change. In reality, the confidence limit on tree topology usually includes many different topologies, and presumably also then the confidence limits on amounts of change in branches are also very broad.

In addition to the table showing numbers of events, a table may be printed out showing which ancestral state causes the fewest events for each character. This will not always be done, but only when the tree is rooted and some ancestral states are unknown. This can be used to infer states of occurred and making it easy for the user to reconstruct all the alternative patterns of the characters states in the hypothetical ancestral nodes. In Pars you can, using the menu, turn off this dot-differencing convention and see all states at all hypothetical ancestral nodes of the tree.

If you select the proper menu option, a table of the number of events required in each character can also be printed, to help in reconstructing the placement of changes on the tree.

This table may not be obvious at first. A typical example looks like this:

     steps in each character:
             0   1   2   3   4   5   6   7   8   9
         *-----------------------------------------
        0!       2   2   2   2   1   1   2   2   1
       10!   1   2   3   1   1   1   1   1   1   2
       20!   1   2   2   1   2   2   1   1   1   2
       30!   1   2   1   1   1   2   1   3   1   1
       40!   1

The numbers across the top and down the side indicate which character is being referred to. Thus character 23 is column "3" of row "20" and has 2 steps in this case.

I cannot emphasize too strongly that just because the tree diagram which the program prints out contains a particular branch MAY NOT MEAN THAT WE HAVE EVIDENCE THAT THE BRANCH IS OF NONZERO LENGTH. In some of the older programs, the procedure which prints out the tree cannot cope with a trifurcation, nor can the internal data structures used in some of my programs. Therefore, even when we have no resolution and a multifurcation, successive bifurcations may be printed out, although some of the branches shown will in fact actually be of zero length. To find out which, you will have to work out character by character where the placements of the changes on the tree are, under all possible ways that the changes can be placed on that tree.

In Pars, Mix, Penny, Dollop, and Dolpenny the trees will be (if the user selects the option to see them) accompanied by tables showing the reconstructed states of the characters in the hypothetical ancestral nodes in the interior of the tree. This will enable you to reconstruct where the changes were in each of the characters. In some cases the state shown in an interior node will be "?", which means that either 0 or 1 would be possible at that point. In such cases you have to work out the ambiguity by hand. A unique assignment of locations of changes is often not possible in the case of the Wagner parsimony method. There may be multiple ways of assigning changes to segments of the tree with that method. Printing only one would be misleading, as it might imply that certain segments of the tree had no change, when another equally valid assignment would put changes there. It must be emphasized that all these multiple assignments have exactly equal numbers of total changes, so that none is preferred over any other.

I have followed the convention of having a "." printed out in the table of character states of the hypothetical ancestral nodes whenever a state is 0 or 1 and its immediate ancestor is the same. This has the effect of highlighting the places where changes might have occurred and making it easy for the user to reconstruct all the alternative patterns of the characters states in the hypothetical ancestral nodes. In Pars you can, using the menu, turn off this dot-differencing convention and see all states at all hypothetical ancestral nodes of the tree.

On the line in that table corresponding to each branch of the tree will also be printed "yes", "no" or "maybe" as an answer to the question of whether this branch is of nonzero length. If there is no evidence that any character has changed in that branch, then "no" will be printed. If there is definite evidence that one has changed, then "yes" will be printed. If the matter is ambiguous, then "maybe" will be printed. You should keep in mind that all of these conclusions assume that we are only interested in the assignment of states that requires the least amount of change. In reality, the confidence limit on tree topology usually includes many different topologies, and presumably also then the confidence limits on amounts of change in branches are also very broad.

In addition to the table showing numbers of events, a table may be printed out showing which ancestral state causes the fewest events for each character. This will not always be done, but only when the tree is rooted and some ancestral states are unknown. This can be used to infer states of ancestors. For example, if you use the O (Outgroup) and A (Ancestral states) options together, with at least some of the ancestral states being given as "?", then inferences will be made for those characters, as the outgroup makes the tree rooted if it was not already.

In programs Mix and Penny, if you are using the Camin-Sokal parsimony option with ancestral state "?" and it turns out that the program cannot decide between ancestral states 0 and 1, it will fail to even attempt reconstruction of states of the hypothetical ancestors, printing them all out as "." for those characters. This is done for internal bookkeeping reasons -- to reconstruct their changes would require a fair amount of additional code and additional data structures. It is not too hard to reconstruct the internal states by hand, trying the two possible ancestral states one after the other. A similar comment applies to the use of ancestral state "?" in the Dollo or Polymorphism parsimony methods (programs Dollop and Dolpenny) which also can result in a similar hesitancy to print the estimate of the states of the hypothetical ancestors. In all of these cases the program will print "?" rather than "no" when it describes whether there are any changes in a branch, since there might or might not be changes in those characters which are not reconstructed.

For further information see the documentation files for the individual programs.