*2.2. Cerebellar Metrics*

Due to lacking prominent anatomical features, homologous landmarks on the cerebellar lobe are difficult to recognize and define. Although previous studies used transverse sinus and sigmoid sinus defining measurements of the cerebellum [1], the grea<sup>t</sup> variation suggests that the sinus was not an adequate reference.

Considering the ellipsoid shape of the cerebellar lobe, the size and shape can be best depicted by the major axis and two points it passes through (as illustrated in Figure 1). Here, we define the major axis as a straight line that divides the cerebellar lobe into two halves from both the inferior view and the posterior view. The point that the major axis passes through at the anterior part is defined as the most lateral and inferior point (LI point), which in most cases is medial to the sigmoid sinus. The point that the major axis passes through at the posterior part is defined as the most medial and superior point (MS point), which is close to the internal occipital protuberance point and is often asymmetric because of the occipital petalia. With the endocast at the standard position using the front pole to occipital pole as the horizontal plane [1], four measurements were defined upon the major axis (as illustrated in Figure 1, Table 2), namely, the cerebellar length, cerebellar height, sagittal orientation (the orientation of the major axis relative to the sagittal plane), and horizontal orientation (orientation of the major axis relative to the horizontal plane). Asymmetric parameters were also calculated as the difference between the left and right sides of the same measurement (L–R) [15], namely, the ML.lr, H.lr, Sagi.lr, and Hori.lr. The determination of the landmarks and the measurements were performed in Rapidform XOR3.


**Table 2.** Definition and abbreviation of measurements.

## *2.3. Descriptive Statistics of the Asymmetries*

To demonstrate overall asymmetries of the cerebellum, all the measurements were summarized regarding different populations and measurements, with mean value, standard deviation, and coefficient of variation (CV) being presented. Paired *t*-test was conducted to test the difference between the two sides with bootstrap considering the small sample size.

## *2.4. Analysis of Covariance*

Cerebellar size and shape may be influenced by occipital petalia and brain size (allometry) [49]. Therefore, those two factors were recorded and analyzed in this study. Endocasts

with left occipital petalia, right occipital petalia, or equally bilateral situation are recorded as L, R, and B, respectively. To test how cerebellar asymmetries were influenced by those two factors, analysis of covariance (ANCOVA) was conducted within each population group, with asymmetric parameters as the dependent variable, natural log-transformed cranial capacity as the covariate, and occipital petalia as the independent variable.

The statistical analysis and plotting were carried out in R [50], with packages "plyr", "tidyverse" and "ggplot2" [51].

**Figure 1.** Diagram of major axis and four measurements of cerebellum on endocast from inferior (**a**) and posterior view (**b**). MLL and MLR, cerebellar length on the left and right side; MS point, medial-superior point; LI point, lateral-inferior point; SagiL and SagiR, orientation of major axis relative to sagittal and horizontal plane; HL and HR, cerebellar height on left and right side.
