A new model for discrete character evolution

The paper provides an explicit justification for the principle that a uniform taxon should contribute only one datapoint in comparative analyses with discrete variables. The justification is that phylogenetic patterns in variables unincluded in the proposed test vitiate the assumption of independence, both at the level of species and at the level of branch segments. The consequence is that a uniform taxon cannot safely be counted as more than one datapoint. The arguments use a branching discrete Markov process in continuous time, with the new feature that the tested variables are only a subset of the evolving characters. This model is proposed as a useful criterion for measuring the merit of proposed tests, and illustrates the necessity for models in evaluating comparative methods.