Autapomorphies and the retention index: Solving a limit via l’Hôpital-Bernoulli’s rule

Abstract

ABSTRACT The retention index (r or ri) is used to compute the amount of similarity in a character that can be interpreted as a synapomorphy on a given cladogram. In the case of autapomorphies, the retention index assumes the form 0 / 0, which is a mathematically indeterminate form. Originally, this issue was resolved by assigning a value of one to the retention index in such cases. However, some authors did not follow this original interpretation and assumed that, in this case, the retention index must assume a value of zero. In this note, we present two arguments supporting the original definition. The first argument is an application of the concept of limit from calculus to determine the assumed value of the retention index function in this specific situation. The second argument is a biological one that invokes the original definitions of autapomorphy and synapomorphy.

Keywords

• Calculus
• homology
• homoplasy
• indeterminate form
• mathematically undefined
• synapomorphy