On the relationship between enamel band complexity and occlusal surface area in Equids (Mammalia, Perissodactyla)

Enamel patterns on the occlusal surfaces of equid teeth are asserted to have tribal-level differences. The most notable example compares the Equini and Hipparionini, where Equini have higher crowned teeth with less enamel-band complexity and less total occlusal enamel than Hipparionini. Whereas previous work has successfully quantified differences in enamel band shape by dividing the length of enamel band by the square root of the occlusal surface area (Occlusal Enamel Index, OEI), it was clear that OEI only partially removes the effect of body size. Because enamel band length scales allometrically, body size still has an influence on OEI, with larger individuals having relatively longer enamel bands than smaller individuals. Fractal dimensionality (D) can be scaled to any level, so we have used it to quantify occlusal enamel complexity in a way that allows us to get at an accurate representation of the relationship between complexity and body size. To test the hypothesis of tribal-level complexity differences between Equini and Hipparionini, we digitally traced a sample of 98 teeth, one tooth per individual; 31 Hipparionini and 67 Equini. We restricted our sampling to the P3-M2 to reduce the effect of tooth position. After calculating the D of these teeth with the fractal box method which uses the number of boxes of various sizes to calculate the D of a line, we performed a t-test on the individual values of D for each specimen, comparing the means between the two tribes, and a phylogenetically informed generalized least squares regression (PGLS) for each tribe with occlusal surface area as the independent variable and D as the dependent variable. The slopes of both PGLS analyses were compared using a t-test to determine if the same linear relationship existed between the two tribes. The t-test between tribes was significant (p < 0.0001), suggesting different D populations for each lineage. The PGLS for Hipparionini was a positive but not significant (p = 0.4912) relationship between D and occlusal surface area, but the relationship for Equini was significantly negative (p = 0.0177). λ was 0 for both tests, indicating no important phylogenetic signal is present in the relationship between these two characters, thus the PGLS collapses down to a non-phylogenetic generalized least squares (GLS) model. The t-test comparing the slopes of the regressions was not significant, indicating that the two lineages could have the same relationship between D and occlusal surface area. Our results suggest that the two tribes have the same negative relationship between D and occlusal surface area but the Hipparionini are offset to higher values than the Equini. This offset reflects the divergence between the two lineages since their last common ancestor and may have constrained their ability to respond to environmental change over the Neogene, leading to the differential survival of the Equini.