POLYMORPHIC TAXA, MISSING VALUES AND CLADISTIC ANALYSIS.

Missing values have been used in cladistic analyses when data are unavailable, inapplicable or sometimes when character states are variable within terminal taxa. The practice of scoring taxa as having "missing values" for polymorphic characters introduces errors into the calculation of cladogram lengths and consistency indices because some character change is hidden within terminals. Because these hidden character steps are not counted, the set of most parsimonious cladograms may differ from those that would be found if polymorphic taxa had been broken into monomorphic subunits. In some cases, the trees found when polymorphisms are scored as missing values may not include any of the most parsimonious trees found when the data are scored properly. Additionally, in some cases, polymorphic taxa may be found to be polyphyletic when broken into monomorphic subunits; this is undetected when polymorphisms are treated as missing. Because of these problems, terminal units in cladistic analysis should be based on unique, fixed combinations of characters. Polymorphic taxa should be subdivided into subunits that are monomorphic for each character used in the analysis. Disregarding errors in topology, the additional hidden steps in a cladogram in which polymorphisms are scored as missing can be calculated by a simple formula, based on the observation that if it is assumed that polymorphic terminals include all combinations of character states, 2 - 1 additional steps are required for each taxon in which p polymorphic binary characters are scored as missing values. Thus, when several polymorphisms are scored as missing in the same taxon, very large errors can be introduced into the calculation of tree length.