Appendix III 

 Polarity Determination for Lower Level Analysis 



The polarities of 19 characters could not be determined using basiliscines, crotaphytines, 

 morunasaurs, and oplurines as outgroups. Therefore, I attempted to determine the 

 polarities of these characters for a less inclusive ingroup (node 3, Fig. '46), using 

 Brachylophus and Dipsosaurus as outgroups. The problem of determining polarities for 

 these characters is similar to that described in Appendix II, except that there are two 

 outgroups instead of four. With only two outgroups whose relationships to the ingroup are 

 uncertain, there are only two possible cladogram topologies (Fig. 63A,B). When rerooted 

 at the outgroup node (Fig. 63C,D), the two resulting topologies are equivalent for the 

 purposes of this analysis. The assessment of the condition at the outgroup node in Figure 

 63D must be the same as that for the node linking the two outgroups, since there are no 

 intervening nodes. Thus, both rerooted cladograms effectively have the two outgroups 

 attached direcdy to the basal (outgroup) node. 



Table 12 summarizes polarity inferences for all possible arrangements of two outgroups 

 on the rerooted cladogram (Fig. 63C) for four cases of character-state distributions among 

 the outgroups. This exhausts the possible cases for a two-state character. Case I is 

 unambiguous: the state found in both outgroups is plesiomorphic. In case II, state A is 

 considered plesiomorphic, although resolution of relationships within the variable outgroup 

 can render the polarity equivocal. In case III, the polarity is equivocal, but resolution of 

 relationships within one or both variable outgroups may require that either state A or state B 

 be considered plesiomorphic. Case IV is completely ambiguous: no polarity inference can 

 be made. Because Cases I and 11 are the only cases in which only one of the two states can 

 be considered plesiomorphic under all possible arrangements of the outgroups on the 

 rerooted cladogram (Fig. 63C), I consider polarity to be determinable only for these two 

 cases. However, none of the characters whose polarities were undeterminable at the level 

 of all iguanines exhibits a Case II distribution. Thus, polarities are only determinable for 

 characters with Case I distributions. 



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