Do meristic characters used in phylogenetic analysis evolve in an ordered manner?

The use of ordered characters in phylogenetic analysis has been inconsistent throughout the history of phylogenetic inference. It has become more widespread in recent years, and some have advocated that all characters representing continuous or meristic traits should be ordered as a matter of course. Here, using the example of dental evolution, we examine two factors that may impact on whether meristic characters actually evolve in an ordered manner: the regulatory hierarchy governing the development of teeth that allows large sections of the entire tooth-row to be supressed in a single transition, and regionalisation of the tooth row where different modules have a degree of independence in their evolution. These are studied using both empirical and simulated data. Models of evolution of such characters are examined over molecular phylogenies to see if ordered or unordered models fit best. Simulations of tooth-row evolution are designed to incorporate changes in region size and multiple levels developmental control to supress individual regions or the entire row. The empirical analyses show that in a clade with largely homodont dentition the characters evolve in an ordered manner, but if dentition is heterodont with distinct regionalisation their evolution better fits an unordered model. In the simulations, even if teeth are added and removed from the tooth row in an ordered manner, dividing the row into independently evolving modules can lead to characters covering multiple modules better fitting an unordered model of evolution. Adding the ability to suppress regions or the entire tooth row has a variable effect depending on the rates of suppression relative to the rates of addition and subtraction of individual teeth. We therefore advise not following a single policy when deciding whether to order meristic traits, but to base the decision on a priori knowledge of the focal clade's evolution and developmental biology.