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There is one other point where this example deviates from the first as to the dialogs and prompts you meet. After the CAFCA parameters dialog you must decide whether you will add complementary sets, as described under option 3 to your strict monothetic sets. Take the default and click .
CAFCA - Mac version 1.3i (c) M.Z. 1987-1995
Date:1 AUG 1995 Time:9H35M28S
CAFCA Parameter Settings
Type of analysis ...................... Primary
Cladon option ......................... 2: Strict Monothetic Sets (SMS)
Cladogram Selection Criterion ......... Maximum Redundancy Index
Taxon on outgroup node ................
Ancestral zero's in character ......... 4 5 10
Ordered characters .................... 10
[Maximum] Number of Cladograms ........ 9
Table 3.7: Header of CAFCA output of strict monothetic sets example.
We now find 14 clada instead of 12 when using PMS (table 3.8). The group {2 3 4} is new, as well as {2 3}. They constitute alternatives for breaking down the group {2 3 4 5}, present in both PMS and SMS, in inclusive sets, due to the interaction of character state distribution 3 (or 4) and 18 with state distribution 17 and 15, respectively (table 3.2).
Strict Monothetic Sets of terminal taxa in Plant
-----------------------------------------------
1 | 1
2 | 2
3 | 3
4 | 4
5 | 5
6 | 3 4
7 | 4 5
8 | 2 3
9 | 3 4 5
10 | 1 2 3
11 | 2 3 4
12 | 2 3 4 5
13 | 1 2 3 4
14 | 1 2 3 4 5
-------------
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 15 17 18
9 | 1 3 4 7 12 18 19
10 | 1 15 17
11 | 1 3 4 17 18
12 | 1 3 4 18
13 | 1 17
14 | 1
---------------------------------------
Table 3.8: Clada with corresponding character states for strict monothetic sets example.
Using PMS (option 1), only {3 4} and {3 4 5} were available as subsets for {2 3 4 5}, due to character state 9 and 7 in the binary data matrix (table 3.2). The clada {2 3 4} and {2 3} have no unique separate character states but they do possess unique combinations of character states (table 3.8; # 8 and 11).
In general, the use of SMS as building-blocks for cladograms brings more resolving power in problems where the patterns implied by the distribution of character states over taxa do not allow for completely dichotomous cladograms.
In other cases, like the present example, the use of SMS simply adds alternatives to the set of already completely resolved cladograms, although not necessarily better ones. Nine alternative cladograms result from this analysis (table 3.9). One of them (# 6) is identical to the cladogram selected in the first example. Other criteria (e.g. number of homoplasious events) select cladogram # 5 as well.
Selection criteria for cladograms of: PlantB
Column numbers refer to numbers of cladograms
---------------------------------------------
Row 1 : Total number of homoplasous events
Row 2 : Total number of single origins (Support)
Row 3 : Corrected Extra Length (x1000; CEL: Turner + Zandee)
Row 4 : Total number of state changes (S: Steps)
Row 5 : Redundancy Quotient (x1000; RQ: Zandee + Geesink)
Row 6 : Rescaled Redundancy Quotient (x1000; RQc)
Row 7 : Consistency Index (x1000; CI), with autapomorphy correction
Row 8 : Rescaled Consistency Index (x1000; RC: Farris)
Row 9 : Average Unit Character Consistency (x1000; AUCC: Sang)
Row 10: Homoplasy Distribution Ratio (x1000; HDR: Sang)
Row 11: Compatible Character State Index (x1000; CCSI: Zandee)
1 2 3 4 5 6 7 8 9
------------------------------------------------------
1 | 2 3 5 3 0 0 2 5 6
2 | 14 13 10 12 16 16 14 10 6
3 | 3017 4033 6100 4083 1017 0 4033 7117 8183
4 | 18 19 21 19 16 15 19 22 23
5 | 492 460 449 473 487 510 471 432 437
6 | 138 84 66 107 130 170 103 37 45
7 | 727 667 571 667 889 1000 667 533 500
8 | 606 502 325 502 852 1000 502 248 178
9 | 875 860 817 902 975 1000 860 810 863
10 | 250 335 358 533 600 1000 335 401 605
11 | 682 545 455 636 682 818 500 409 500
No-Order Limit for Steps, Extra Steps, RQ, and CI:
S ES RQ CI
-------------------
26 11 410 421
Table 3.9: Selection criteria for cladograms in strict monothetic sets example.
Comparing the state changes for characters in the best and second best cladogram from the second example (table 3.6 and 3.10) we see that a priori defined polarity and order in states as those of character 10 can be changed as a result of the analysis. Character 10 in cladogram #5 departs from the sequence as originally coded, 0 -> 1 -> 2 -> 3. There is now a state change 0 > 2 present, implying two steps as character 10 is ordered. This makes cladogram # 5 one step longer than # 6, though not due to a homoplasy.
Plant: Cladogram - 5
/-- 4 Dus
/--7
| \-- 5 Eus
/--12
| | /-- 2 Bus
| \--8
| \-- 3 Cus
|
\-------- 1 Aus
PlantB: Cladogram-5 : APOMORPHIES
---------------------------
Cladon | Character | State
---------------------------
1 | 3 | 2
| 6 | 3
2 | 4 | 1
| 5 | 1
| 6 | 1
3 | |
4 | |
5 | 5 | 3
7 | 7 | 1
| 8 | 0
| 9 | 1
| 10 | 3
8 | |
12 | 2 | 2
| 4 | 2
| 5 | 2
| 10 | 2
---------------------------
PlantB:Cladogram-5: COMPATIBILITIES
---------------------------
Cladon | Character | State
---------------------------
1 | 2 | 1
| 3 | 2
| 6 | 3
2 | 4 | 1
| 5 | 1
| 6 | 1
5 | 5 | 3
7 | 7 | 1
| 8 | 0
| 9 | 3
| 10 | 3
12 | 2 | 2
| 3 | 1
| 10 | 1
14 | 1 | 1
--------------------------
Plant: Cladogram-5 : STATE CHANGES
--------------------------
Character : Cladon : Change
--------------------------
1 | |
2 | 12 | 1 -> 2
3 | 1 | 1 -> 2
4 | 2 | 2 -> 1
| 12 | 0 -> 2
5 | 2 | 2 -> 1
| 5 | 2 -> 3
| 12 | 0 -> 2
6 | 1 | 2 -> 3
| 2 | 2 -> 1
7 | 7 | 0 -> 1
8 | 7 | 1 -> 0
9 | 7 | 2 -> 1
10 | 2 | 2 -> 1
| 7 | 2 -> 3
| 12 | 0 -> 2
--------------------------
Characters and States refer to multi-state data matrix, if present.
Cladon nrs refer to the list of monothetic sets of terminal taxa.
Table 3.10: Second best cladogram with apomorphies and state changes.
Note, however, that the sequence as estimated by CAFCA although not reflecting the original coding is fully consistent (= not implying homoplasious steps) with the different topology. We may tentatively conclude that although additive binary coding of character states defines only one particular character state tree, this coding may be consistent with more than one cladogram topology, as measured by the consistency index. This is due to the insensitivity of this index to monitor the unambiguous reconstruction of (predefined) polarity and order in multi-state characters from cladograms.
