NOT APPLICABLE? NOT A PROBLEM FOR PARSIMONY

Many paleontology questions either focus on or require hypotheses of evolutionary relationships, and in paleontology that is largely done using parsimony. This parsimony approach involves counting the number of evolutionary transitions implied by particular evolutionary histories and then preferring the evolutionary histories that require the fewest assumptions of homoplasy (i.e. similarity not inherited from a common ancestor). Some characters used to compare these different evolutionary hypotheses are not applicable for certain taxa because they are logically dependent on other conditions already being observed in the taxa. The algorithms used for this reconstruction of evolutionary histories can miscount the number of inferred evolutionary steps when some taxa have inapplicable characters, possibly leading researchers to unintentionally reject more or equally parsimonious hypotheses. Several approaches to coding the characters have been proposed to avoid a possible miscount; none are without problems. We propose a simple algorithm that uses two matrices to avoid miscounting the number of inferred evolutionary steps. This algorithm works regardless of the number or arrangement of the logical dependencies between characters. The correct handling of inapplicable characters permits a wider taxon sampling that encompasses more evolutionary history while also preserving the ability to use detailed characters that only pertain to subsets of taxa. This approach has immediate applications in corals where many characters deal with colony construction, but transitions between colonial and solitary conditions have occurred multiple times.