Sign-oriented Dirichlet Normal Energy: alinging dental topography and dental function in the R-package molaR

Dirichlet normal energy (DNE) is a dental topography measurement aimed at capturing occlusal sharpness and has shown promise for its ability to sort primate molars according to perceived shearing ability. As initially implemented, this measurement does not differentiate concave versus convex contributions to surface sharpness. This is problematic because the DNE-signal derived from concave aspects of an occlusal surface measures a sharp ‘edge’ oriented inward towards the enamel dentine junction rather than outward towards food contact. The inclusion of concave DNE in dietary analyses of molars possessing deep occlusal sulci–such as those found among hominoids–inflates the perceived functional sharpness of these teeth. Concave-inflated DNE values can be misleading, being interpreted as indicating that a particular taxon is more adapted for processing fibrous food than is warranted. The modification of the DNE measurement introduced here ‘Sign-oriented DNE’ alleviates this problem by elimination of concave sharpness from analyses, allowing investigations to focus on features of occlusal surfaces plausibly linked to shearing, cutting, or shredding of food materials during Phases I and II of the masticatory power stroke. Convex DNE is just as effective at sorting non-hominoid primate molars into traditional dietary categories as the initial applications of the orientation-blind version of the measurement, and produces more theoretically coherent results from hominoid molars. Focusing on- and improving the connection between measurement and occlusal function will enhance the ability of dental topography to make meaningful contributions to our collective understanding of species’ dietary ecologies.