The limits of phylogenetic analysis: identifying analytical hallucinations

Phylogenetic analysis strives to construct graphs, such as trees or networks, that encapsulate the historical structure of a set of terminal taxa. This process is based on comparative character data and an optimality criterion by which these graphs are evaluated. Whether there is structure in the data or not, phylogenetic analytical methods will produce a collection of heuristically optimal graphs. The question examined here is how to determine when a data set, or components of a data set, possess sufficient shared information to yield results founded in historical phylogenetic structure, and where "hallucinatory" patterns are conjured from a lack of information. A method is described to identify mutually analysable data components based on shared information and to distinguish them from components that cannot be meaningfully analysed.