A comparison of relief estimates used in three-dimensional dental topography

Objectives Topographic estimates of dental relief are now commonly used to make dietary inferences from the teeth of extant and extinct primates. We thoroughly compared commonly used relief estimates in an effort to help researchers decide which variable best suits their objectives. Materials and methods We combined a total of three datasets: five theoretical models built to compare the effect of tooth complexity and basin depth on relief estimates, a dataset of 110 lower molars of prosimians, and a dataset of 25 upper molars of apes. We investigated intra-mesh variation and tooth average relief, estimated from slope and three different relief indices, according to four criteria: (1) the ability to map relief on topographic maps, (2) the correlation with other relief estimates, (3) the ability to separate high-relief molars of folivores from deep-relief molars of insectivores in prosimians, and (4) the influence of surface complexity on relief estimates in apes. Results We found that polygon slope and relief index are linked by a mathematical relation. Tooth average slope and all relief indices are strongly correlated. In contrast, relief estimates are moderately correlated to cusp elevation. One relief index of four relief estimates had an excellent ability to separate high-relief from deep-relief molars in prosimians, whereas slope could not separate them. No significant effect of tooth complexity on dental relief could be detected in apes. Conclusions Because slope and relief indices are highly correlated, it is strongly recommended not to combine them in multivariate analysis. Still, slope and relief indices show interesting differences in scaling, graphical representation, computation method, and ability to separate high-relief and deep-relief molars. Our results also suggest that slope and relief indices can vary independently of tooth complexity and are moderately affected by mean cusp elevation in apes.