CAFCA - Manual

The fourth example again uses the same data matrix, PLANT, but now the clada used are the partial monothetic sets (PMS) of terminal taxa plus all clada resulting from valid three-taxon-statements (TTS's; table 3.15).

In comparison with the other examples run so far, many building blocks (30) for cladograms result from all possible three-taxon statement permutations as, apparently, many of these statements are valid due to independent support for their constituent clada. These building blocks give rise to 90 possible cladograms, only one of which is the shortest if we consider zero in a multi-state character to represent an ancestral state, forced to be present on the root. If we don't apply the latter option, three shortest cladograms result from the analysis, the same as from the third example (two shown in figure 3.1 [PMS + ABC]).

Partial Monothetic Sets of terminal taxa in Plant
--------------------------
  1|   1 
  2|   2 
  3|   3
  4|   4 
  5|   5
  6|   3 4
  7|   4 5
  8|   3 5
  9|   2 5
 10|   2 4
 11|   2 3
 12|   1 4
 13|   1 3
 14|   1 2
 15|   3 4 5 
 16|   1 2 3 
 17|   2 4 5 
 18|   2 3 5 
 19|   2 3 4 
 20|   1 3 4 
 21|   1 2 4 
 22|   1 4 5
 23|   1 3 5 
 24|   1 2 5 
 25|   2 3 4 5  
 26|   1 2 3 4 
 27|   1 3 4 5 
 28|   1 2 4 5 
 29|   1 2 3 5 
 30|   1 2 3 4 5 
------------------ 

Partial Monothetic Sets of character states in Plant
--------------------------
  1|    2  5 13 
  2|    6  8 11
  3| 
  4| 
  5|   10
  6|    9
  7|   14 16 20 
  8| 
  9| 
 10|
 11|
 12|
 13| 
 14|
 15|    7 12 19 
 16|   15
 17| 
 18| 
 19| 
 20|
 21| 
 22| 
 23|
 24| 
 25|    3  4 18 
 26|   17
 27| 
 28| 
 29| 
 30|    1
---------------- 

Table 3.15: Clada, with corresponding character states, from valid three-taxon-statements.

As we can see from this table, many of the sets of taxa generated, do not have a character state by which they can be uniquely recognised. If we use theStrict Sets option in the Print menu to generate the unique combinations of character states for these sets of taxa, we see that many of them even lack these (table 3.16). For instance the sets # 9 {= 2 5}, 17 {= 2 4 5}, 18 {= 2 3 5}, and 25 {= 2 3 4 5} are all characterised by the combination of character states {1 3 4 18}, corresponding to characters 11, 22, 31, and 101.

Strict Monothetic Sets of character states in Plant
---------------------------------------------------
  1|    1  2  5 13 15 17  
  2|    1  3  4  6  8 11 15 17 18 
  3|    1  3  4  7  9 12 15 17 18 19
  4|    1  3  4  7  9 12 14 16 17 18 19 20 
  5|    1  3  4  7 10 12 14 16 18 19 20
  6|    1  3  4  7  9 12 17 18 19 
  7|    1  3  4  7 12 14 16 18 19 20
  8|    1  3  4  7 12 18 19 
  9|    1  3  4 18  
 10|    1  3  4 17 18  
 11|    1  3  4 15 17 18 
 12|    1 17   
 13|    1 15 17  
 14|    1 15 17  
 15|    1  3  4  7 12 18 19   
 16|    1 15 17  
 17|    1  3  4 18  
 18|    1  3  4 18  
 19|    1  3  4 17 18  
 20|    1 17
 21|    1 17 
 22|    1 
 23|    1   
 24|    1   
 25|    1  3  4 18 
 26|    1 17 
 27|    1  
 28|    1 
 29|    1 
 30|    1  
     --------------------------------------- 

Table 3.16: List of unique combinations of character states (= strict monothetic sets) for the sets of taxa listed in table 3.15.

You could, as an alternative, also use option 4 with three-taxon-statements according to Nelson and Platnick (1991). In that case the monothetic sets of terminal taxa (clada) generated from the data matrix will be supplemented with all clada derived from all three-taxon statements implied by the original characters. Remember that in contrast to Nelson and Platnick's original implementation in CAFCA the original data matrix is not replaced by the TTS's, except when the data matrix is exported. Table 3.17 shows the version in NEXUS format as exported by CAFCA (Utilities menu, export data matrix option).

#NEXUS 
BEGIN DATA;
	DIMENSIONS NTAX=5 NCHAR=60; 
	FORMAT missing=? symbols="0~9";
	MATRIX
      Aus 0??0??0??0??0?0?0?0?0?0?11??110?0?0?0000000000001?1??1000000
      Bus ?0??0??0??0??0?0?0?0?0?01111???0?0?01?1??11?1??111??1?1?1??1
      Cus 111??0??0??011??1111??11??111111??1111??1?11??1??111??11??1?
      Dus 1111111111111111??1111??0?0?0?1111???111???111?????111?111??
      Eus ??0111111111??1111??1111?0?0?0??1111???111???111000000???111
end;
BEGIN ASSUMPTIONS;
	OPTIONS deftype=unord;
end;

Table 3.17: Data matrix for Nelson and Platnick three-taxon statements in NEXUS format suitable to be run by PAUP

The data matrix with extensions for three-taxon statements according to the Nelson and Platnick (1991) definition generates 27 clada which give rise to 54 cladograms, one of which is most parsimonious with 15 steps. It is identical to the one found by the PMS option alone. Note that CAFCA's definition of three-taxon-statements generates more clada (30 vs 27) and as a consequence more cladograms (90 vs 54) than the Nelson and Platnick definition. This is due to the fact that N&P only consider all pairs of terminal taxa to perform as units in TTS's, while CAFCA also uses units consisting of larger sets of terminal taxa.

An analysis of the data from table 3.17 with PAUP generates 15 most parsimonious cladograms (60 steps) without an included all-zero ancestor and 105 including an ancestor. That means that all trees for the taxa involved are possible. The replacement of the original data with all three-taxon statements according to Nelson and Platnick's definition, in this case appears to render the data phylogenetically useless (without any information as to phylogenetic structure). Using the three-taxon statements as a source for clada (components) only, instead as a replacement for the original data, as is done in the CAFCA implementation of N&P's definition, appears to make more sense.

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© M. Zandee 1996