Morphological phylogenetic analysis with inapplicable data

Non-independence of characters is a real phenomenon in phylogenetic data matrices, even though phylogenetic reconstruction algorithms generally assume character independence. In morphological datasets, the problem results in characters that cannot be applied to certain terminal taxa, with this inapplicability treated as \"missing data\" in a popular method of character coding. However, this treatment is known to create spurious tree length estimates on certain topologies, potentially leading to erroneous results in phylogenetic searches. Here we present a single-character algorithm for ancestral states reconstruction in datasets that have been coded using reductive coding. The algorithm uses up to four traversals on a tree to resolve final ancestral states - which are required in full before a tree can be scored. The algorithm employs explicit criteria for the resolution of ambiguity in applicable/inapplicable dichotomies and the optimization of missing data. We score trees following a previously published procedure that minimizes homoplasy over all characters. Our analysis of published datasets shows that, compared to traditional methods, our new method identifies different trees as \"optimal\"; as such, correcting for inapplicable data may significantly alter the outcome of tree searches.