180 



Appendix II 



FIG. 60. All nine possible fully resolved cladogram topologies for four unspecified outgroups and an 

 in group (inverted triangle). 



made a compromise between maximizing the total number of characters on the one hand 

 and using only those characters whose polarities are completely unambiguous on the other. 



Table 1 1 shows polarity inferences for all possible arrangements of four outgroups on 

 the two rerooted cladograms (Fig. 61A,C) for seven cases of character-state distribution. 

 This exhausts the possible character- state distributions for two state characters, since it is 

 the occurrence of a given state rather than its alphabetic designation that is important (e.g., 

 A/A/A/B = B/B/B/A). The following is a case-by-case discussion of possible polarity 

 inferences under different relationships of the four outgroups to the ingroup. 



Case I (A/A/Ai/A,B): For the case in which three outgroups have one condition and the 

 other has both altemative conditions, all arrangements except one require that the common 

 state be considered plesiomorphic. The lone exception is when the variable outgroup 

 attaches direcdy to the basal node of the rerooted cladogram (Fig. 62A). If resolution of 

 relationships within this outgroup requires that state B be considered plesiomorphic for this 

 group, the polarity will be equivocal. 



