21 



of independence is sufficient for a cladistic analysis. As well, mere word play can 

 apparently increase the degree of independence of a group of otherwise highly correlated 

 features. For example, we examined four features of the incisive foramina in this study 

 (roughly size, shape, location, and number; see Character Analysis). But, by redefining 

 these characters in terms of other variables (e.g., size of the nasopalatine nerve passing 

 through the foramina, presence of a down-growth of the premaxilla or not, ...), they cease 

 being incisive foramina characters at first glance. Finally, recent evidence indicates that 

 character independence for a single structure may, in some cases, be greater than 

 previously presumed. Atchley & Hall (1991) suggest that the single mammalian dentary 

 bone (as evidenced by the mouse) may, in fact, be composed of up to six separate centres 

 of ossification or condensation, one for each of the ramal, incisor, molar, condyloid 

 process, coronoid process, and angular process regions. Thus, there is at least the potential 

 for each to be acted upon independently during ontogeny, and thus phylogeny. In other 

 words, the mammalian mandible could justifiably be represented by up to six characters 

 (one from each of the regions above) and not violate the independence criterion. Therefore, 

 in selecting a set of characters, the best solution is likely to represent all body regions as 

 much as possible (within the constraints of their relative information content), and not to 

 over-represent any one region or feature to any great extent. 



One clarification is required with respect to the phrase "equal weighting". PAUP's 

 algorithms essentially weight characters in proportion to the number of states they possess, 

 thereby artificially attaching greater importance to multistate characters (Swofford 1993). 

 To correct for this, all characters were inversely weighted (base weight = 100) according 

 to the number of states each possessed. So, "equally" weighted will, hereafter, be taken 

 to mean inversely weighted, and not unweighted (i.e., where all characters share some 

 identical weight "x"). Unfortunately, inverse weighting creates rather unwieldy tree 

 lengths, obfuscating discussion and comparison of less than most parsimonious solutions. 

 To compensate for this, discussion is directed towards the number of character state 

 changes (or, equivalently, the number of synapomorphies, both of which equal the number 

 of unweighted steps) along a branch, and not the branch lengths derived from inverse 

 weighting. When this is not possible, "corrected steps" were devised and are referred to. 

 These are simply the absolute number of inversely weighted steps divided by the average 

 character weight of the inversely weighted character set (= 69), rounded up to the next 

 whole number. Both methods appear to be roughly equivalent (i.e., corrected steps appear 

 to be a reasonable estimator of the number of character state changes), based on 

 preliminary comparisons when both were available. 



Unordered characters (i.e., Fitch parsimony) were likewise used, as we could not 

 conclusively identify the exact sequence of character transformations based on criteria set 

 out by Hauser & Presch (1991). Thus, all possible transformations were allowed and were 

 considered to be equally probable. In any case, the supposed advantages of ordered 

 characters (e.g., increased resolution and stability, and fewer equally most parsimonious 

 solutions) may be overstated. While ordering may be advantageous for a single character, 

 such is not necessarily the case over an entire matrix due to the interaction of all characters 

 (Hauser & Presch 1991). 



