We measured the CA and FA of the orbital plane (Cartmill, 1970, 1972, 1974) for 68 carnivoran taxa (37 extant and 31 fossil species), examining 442 specimens. To define the orbital plane we captured three-dimensional landmark data using a G2X three-dimensional digitizer (Immersion Microscribe, San Jose, CA, USA) (Goswami, 2006a,b). The orbital plane was defined using three landmarks: (1) the post-orbital process, (2) the dorsal suture of the jugal and maxilla, and (3) the ventral suture of the jugal and maxilla (Fig. 1). Although using the post-orbital process of the zygomatic would more closely correspond to the orbital plane, the zygomatic arch posterior to the jugal–maxilla suture is often incomplete or distorted in fossil specimens, which would severely restrict our ability to incorporate fossil taxa into our analysis. Because this plane does not directly correspond to the orbital plane, the angles measured in this study are not directly comparable to those in other data sets (e.g. Cartmill, 1970, 1972; Ross, 1995; Noble et al. 2000; Heesy, 2005). However, these data do distinguish more and less convergent or frontated orbits, and can be used to study the impact of changes in relative volume of the braincase on the orientation of the orbits. We also defined two reference planes in the skull: the mid-sagittal plane (defined using three to six landmarks, as some fossil specimens were missing some of the six mid-sagittal plane landmarks) and the basal plane (defined using four landmarks; Fig. 1) (Goswami, 2006a,b). Using routines written in Mathematica (Wolfram Research, Inc., Champaign, IL, USA), we calculated the measures of the dihedral angles between the orbital and reference planes; the angle between the orbital plane and the mid-sagittal plane of the skull measured the CA and the angle between the orbital plane and the basal plane of the skull measured the FA. A larger CA indicates more anteriorly-oriented orbits, when viewed from above, whereas a larger FA indicates more vertically-oriented orbits, when viewed from the side.
We evaluated the relationship of orbit orientation angles to both skull length and encephalization. Skull length was used as a proxy for body size (Van Valkenburgh, 1990) and we estimated this using the chord length between the occipital condyle lateral margin and the premaxilla–maxilla anterior lateral suture (Goswami, 2006a,b), averaging over measurements of both the left and right sides. To calculate encephalization, we used an extensive database of adult body masses and endocranial volume estimates for living and fossil carnivorans (Finarelli, 2008a,b; Finarelli & Flynn, 2006, 2007), measuring the logarithm of the encephalization quotient (logEQ) (e.g. Marino et al. 2004; Finarelli & Flynn, 2007), calculating the encephalization quotient relative to the brain volume/body mass allometry for extant Carnivora. We used the base-2 logarithm, such that log2EQ = 1 indicates a brain double the expected volume for a given body mass, whereas log2EQ = –1 indicates a volume half as large as expected. Body masses, brain volumes, skull lengths and orbit orientation angles are reported in Table 1.