Comparing Dirichlet normal surface energy of tooth crowns, a new technique of molar shape quantification for dietary inference, with previous methods in isolation and in combination

Abstract

Inferred dietary preference is a major component of paleoecologies of extinct primates. Molar occlusal shape correlates with diet in living mammals, so teeth are a potentially useful structure from which to reconstruct diet in extinct taxa. We assess the efficacy of Dirichlet normal energy (DNE) calculated for molar tooth surfaces for reflecting diet. We evaluate DNE, which uses changes in normal vectors to characterize curvature, by directly comparing this metric to metrics previously used in dietary inference. We also test whether combining methods improves diet reconstructions. The study sample consisted of 146 lower (mandibular) second molars belonging to 24 euarchontan taxa. Five shape quantification metrics were calculated on each molar: DNE, shearing quotient, shearing ratio, relief index, and orientation patch count rotated (OPCR). Statistical analyses were completed for each variable to assess effects of taxon and diet. Discriminant function analysis was used to assess ability of combinations of variables to predict diet. Values differ significantly by diets for all variables, although shearing ratios and OPCR do not distinguish statistically between insectivores and folivores or omnivores and frugivores. Combined analyses were much more effective at predicting diet than any metric alone. Alone, relief index and DNE were most effective at predicting diet. OPCR was the least effective alone but is still valuable as the only quantitative measure of surface complexity. Of all methods considered, DNE was the least methodologically sensitive, and its effectiveness suggests it will be a valuable tool for dietary reconstruction.

Introducing molaR: a New R Package for Quantitative Topographic Analysis of Teeth (and Other Topographic Surfaces)

“…Dirichlet Normal Energy (DNE) in particular is worth further discussion and explanation. DNE measures the curvature and undulation of a surface (Bunn et al 2011). DNE over the whole surface is an integral equation calculated with the following formula:…”

“…The radius of the hemisphere is off-set between the Dirichlet Energy Density and the surface area components of the equation. In this way DNE is purely a measure of the surface's complexity and curvature, independent of its size and orientation, making it a valuable addition to the dental morphologist's tool kit (see also Bunn et al 2011). These new measures have proven effective for quantitatively distinguishing among the lower molar surfaces of primate species processing differing diets (Boyer 2008;Bunn et al 2011;Winchester et al 2014), and at demonstrating adaptive and presumed functional convergences among rodent and carnivoran dentitions in taxa consuming similar ratios of plant/animal matter (Evans et al 2007).…”

“…In this way DNE is purely a measure of the surface's complexity and curvature, independent of its size and orientation, making it a valuable addition to the dental morphologist's tool kit (see also Bunn et al 2011). These new measures have proven effective for quantitatively distinguishing among the lower molar surfaces of primate species processing differing diets (Boyer 2008;Bunn et al 2011;Winchester et al 2014), and at demonstrating adaptive and presumed functional convergences among rodent and carnivoran dentitions in taxa consuming similar ratios of plant/animal matter (Evans et al 2007). A promising avenue of further development for the above-mentioned measurements is their potential advantage for studying tooth crowns of mammals that lack obviously homologous features-such as rodents, multituberculates, and xenarthrans-whose highly derived crown surface structures bear only remote resemblances to the tribosphenic molar pattern of their ancestors (Bargo et al 2009;Wilson et al 2012).…”

“…However, access to software for performing these nascent analyses has lagged behind the availability of the specimens, scans, and recognition of their usefulness. Although one stand-alone open source software package capable of performing all of these measures has recently become available (MorphoTester http:// morphotester.apotropa.com; Winchester 2016); and while there are other packages capable of performing some of these metrics (e.g., Teether; Bunn et al 2011, and surfermanipulator; Evans et al 2007), there remain significant advantages to implementing these methods in the R scientific computing language (R Core Team 2015). R provides a flexible and powerful set of tools for data analysis, and offers broad accessibility across computing platforms.…”

“…R's graphics capabilities, utilized here, facilitate a greater understanding and interpretation of DNE, RFI, and OPC. Here we present molaR, a new R package that provides functions for measuring and plotting DNE (Bunn et al 2011), RFI following Boyer (2008), and a non-rasterized variant of OPC (Evans et al 2007), on three dimensional surface scans of teeth.…”