Nothing to it: a reply to Wheeler's "much ado about nothing"

Wheeler (Cladistics 2023, 39, 475) recently suggested that the issues with inapplicable characters in phylogenetic analysis can be dealt with directly by treating observed absences of a feature not in a separate absence/presence character but as insertion/deletion events in a complex character that describes the feature in all its variation; and that this dynamic homology view can be achieved by imposing a sequence or linear order on a set of characters and by analysing the resulting sequence character using custom alphabet tree alignment algorithms. As Wheeler observed, this approach can lead to considering inappropriate character states (such as a head state and a foot state) homologous. We show that it is also sensitive to the specific ordering assumption used and that such different character orders can lead to a preference for different trees. We present a simple four-taxon dataset with observations of absence, but no inapplicable characters or other kinds of character dependence, for which the dynamic homology framework gives different results to classic algorithms for independent characters, including an optimal tree with biologically impossible reconstructions at inner nodes (every terminal has a head but the inner nodes are headless). We show how these issues can be solved by removing the character ordering assumption that the approach requires. Doing so, the dynamic homology framework reduces in general to Maddison's (Syst. Biol. 1993, 42, 576) well-known proposal to deal with inapplicability using step matrix analysis of complex characters. If in addition costs are interpreted in terms of homology, it reduces to Goloboff et al.'s (Cladistics 2021, 37, 596) step matrix implementation for maximization of homology as applied to inapplicable characters. However, if used with homogeneous costs, as Wheeler suggested, it reduces to unordered analysis of such complex characters, which is known to treat tails that may share many observed features as irrelevant for establishing kinship when they differ in just one feature, e.g. colour.