2.1 Imaging

Each skull was photographed on high resolution in standardised ventral view with a digital camera. Images were captured with a Nikon^® D70 digital camera (image resolution of 2,240 × 1,488 pixels) equipped with a Nikon AF Nikkor^® 28–200 mm telephoto lens. Scale was given for each photograph by placing a ruler. The images were then stored in JPG format.

2.2 Landmark selection

To analyse both segments of the sphenoid bone [corpus ossis (basi- et pre-)sphenoidalis], we used a set of 2 landmarks on the sagittal line and 24 paired semilandmarks for the contours (Figure 1). The x and y coordinates of chosen points were digitised using TpsDig 2.04 v. 1.40 (Rohlf, 2015). The file to determine the sliding direction of the semilandmarks was created in TpsUtil v. 1.70 (Rohlf, 2015). Since error can account for a significative fraction of between-side variance and alter the results, digitalisations were made twice by second author.

2.3 Statistical analysis

A Procrustes ANOVA with three factors (individual, side and interaction individual*side) was done to assess asymmetries and error. Comparison of sizes was done with a Mann–Whitney U test. Regressions of shape versus size, expressed as centroid size (log-transformed, and tested with 10,000 permutations), allowed the detection of allometries. Centroid size is defined as ‘the square root of the sum of the squared distances between each landmark and the centroid of the form’ (Webster & Sheets, 2010). A canonical variate analysis (CVA) determined whether both groups were statistically distinct for shape. A principal component analysis (PCA) was then run on the shape coordinate data for two groups to visualise the morphometric variation between them. Finally, thin plate spline deformation grids were obtained to visualise shape variation between both species.

Morphometric and statistical analyses were conducted using the MorphoJ v. 1.06c (Klingenberg, 2011) and PAST v. 2.17c (Hammer et al., 2001) packages. Confidence level was established at 95%.

3.1 Measurement error and asymmetries

In the Procrustes ANOVA, where three factors (individual, side and interaction individual*side) were analysed, error was very low, with a mere 7.2% (Table 1), for example it indicated a high degree of repeatability of the measurements. Side and the interaction of individuals and sides showed significant differences (p < .05), and Pillai's trace confirmed their presence (p < .0001). Ulterior analysis was then done using the symmetric component.

3.2 Size differences

Mann–Whitney test reflected statistical differences between two species (U = 676, p = .0002106), being Ovis aries’ sphenoids clearly bigger.

3.3 Allometry

The multivariate regression of Procrustes coordinates of symmetric component (dependant variable) on size (log CS as independent variable) showed a significant influence of allometry for both species (17.0% and 18.4% for Ovis and Capra, respectively, p < .0001), so for the rest of analysis, residual regressions scores were used.

3.4 Canonical variate analysis

The separation achieved by the CVA is illustrated in Figure 2.

3.5 Principal component analysis

According to the results pf PCA, PC1 and PC2 represented a total of 60.24% (PC1 + PC2 = 41.20% + 19.04%) (Table 2). Changes were found greatest on length of rostral presphenoides [os praesphenoidale] (coordinates on horizontal axis x2, x14 and x26) and on width of medium part of basisphenoid [os basisphenoidale] (coordinates on vertical axis y6, y7, y18 and y19). Coordinates are shown in Table 3. The wider and shorter sphenoid bone of sheep compared to goats was finally corroborated visually by the thin plate splines (Figure 3).