INTRODUCTION

In the course of a revision of the fossil glirid genera Bransatoglis and Microdyromys, we observed that many authors consider the concavity of the occlusal surface to be an important diagnostic character, e.g., de Bruijn (1967), Hugueney (1967), Bahlo (1975), van der Meulen and de Bruijn (1982), Daams and de Bruijn (1995), and Vianey-Liaud (2004). However, these descriptions were based on subjective assessments of how concave the surface is, assessments which are not very precise and which may vary from author to author. In this paper, we develop a quantification of concavity, which can serve as a diagnostic tool that reveals contradictions about concavity.

For example, Hugueney (1967) described the species Bransatoglis concavidens, characterizing it as having a very strongly concave occlusal surface on M², and Bahlo (1975) described Oligodyromys planus as having a weakly concave surface on the upper and lower dentitions. Later authors considered Oligodyromys to be a junior synonym of Bransatoglis. Our comparison of the surfaces of the upper molars of these two species using a new quantitative index showed no appreciable difference in concavity. In another example, Daams and de Bruijn (1995) defined the occlusal surface of the Dryomyinae as concave, and that of the Bransatoglirinae as strongly concave; however, when we compare Eliomys quercinus, as an example of the Dryomyinae with the holotype of Bransatoglis concavidens, one is inclined to say that the occlusal surface of Eliomys quercinus is more strongly concave than that of Bransatoglis.

Our measure of concavity is relatively simple and can be applied to any structure that has an irregularly concave cross-sectional profile. We drew profiles of the teeth of many glirid species, we measured several parameters on the digitized profiles, and we used those parameters to find the radius of a circle that best fit the entire concavity. We applied our index to a wide variety of glirid species to give a picture of the degree of concavity across the group, including a general assessment of trends in concavity from the Eocene to the Oligocene.