**3. Results**

## *3.1. Principal Component Analysis*

The first two principal components account for 27.06% and 14.32% of the total shape asymmetry variation. The PC1 indicates that there is no clear directional trend for the two asymmetrical types represented by the shapes at the two extremes (Figure 2). At the positive extreme of PC1 (Figure 3A), the frontal, anterior parietal, and anterior temporal lobes in the right hemisphere are more bulged compared to the left hemisphere, whereas the occipital, posterior temporal, and posterior parietal lobes in the left hemisphere project more posteriorly and laterally than the right side. With increasing values along PC1, the left cerebellar lobe bulges and protrudes more posteriorly, while the right cerebellar lobe exhibits the opposite trend. Comparatively, the asymmetrical pattern in the negative-value end of PC1 shows a contrary trend to that at the positive end (Figure 3B).

**Figure 2.** Bivariate plot of PC2 against PC1 based on diffeomorphic surface matching (DSM) analysis for endocast shape asymmetry variation.

**Figure 3.** The virtual asymmetric shapes of endocast surfaces at the positive and negative extremes of PC1 (**A**,**B**) and PC2 (**C**,**D**) in frontal (**i**), left lateral (**ii**), occipital (**iii**), right lateral (**iv**), dorsal (**v**), and basal (**vi**) views. The colormap shows the degree of asymmetry in endocast surface shape. The dark blue and red represent the most constricted and expanded area of one hemisphere relative to the other half (in millimeter).

As shown in Figure 2, PC2 presents directional asymmetry: about 74% of the individuals are distributed in the positive-value half of PC2 and 26% in the negative-value half. The shape asymmetry pattern of the endocast at the dominant side of the distribution (positive extreme end of PC2, Figure 3C) is mainly shown as left-occipital and right-frontal petalial asymmetries. The superior and middle-frontal convolutions present a slight rightward asymmetry, while the inferior frontal convolution shows a slight leftward asymmetry. The temporal lobe presents a rightward asymmetry. The parietal-occipital lobe presents a leftward asymmetry. The cerebellum shows a double asymmetry with a leftward anterior lobe and rightward posterior lobe, but to a low degree. The negative extreme end of PC2

(Figure 3D) displays the reverse trend of the asymmetrical pattern, namely anti-symmetry of those at the positive extreme end of PC2.

## *3.2. The General Pattern of Endocast Surface Asymmetry*

The mean asymmetric shape of the endocast surface, averaging the asymmetrical deformation of all individuals, is shown in Figure 4. It reveals a directional asymmetry pattern consistent with the positive-value end of PC2 but displays more detailed local asymmetries.

**Figure 4.** The mean asymmetric shape of the endocast surface in frontal (**i**), left lateral (**ii**), right lateral (**iii**), occipital (**iv**), dorsal (**v**), and basal (**vi**) views. The colormap shows the degree of asymmetry in endocast surface shape. The dark blue and red represent the most constricted and expanded area of one hemisphere relative to the other, and the displacement within 5% from symmetric shape is shown in white (in millimeter).

In the frontal view (Figure 4i), the frontal lobe has a strip adjacent to the longitudinal cerebral fissure, showing expansion on the right hemisphere and contraction on the left side. As a result, the right hemisphere protrudes more anteriorly than the opposite side and slightly bends the anterior interhemispheric fissure towards the left. The left inferior frontal convolution (Figure 4ii), an area that includes Broca's area, is extended more anteriorly, laterally, and ventrally relative to the right side, whereas the right inferior frontal convolution (Figure 4iii) appears more flattened and elongated antero-posteriorly. Additionally, the right frontal bec is more elongated than that of the opposite hemisphere and the ventral surface of the frontal lobes in the left hemisphere is more bulged than the right (Figure 4vi).

In terms of the local shape asymmetry of the temporal lobe (Figure 4ii,iii), the posterior portion, involving all three convolutions, is more inflated in the right hemisphere than the left. The right temporal lobe protrudes more inferiorly than the left one, resulting in a right temporal petalia (Figure 4vi). Additionally, the left temporal lobe appears to be shorter and the left Sylvian fissure is displaced anteriorly to a greater extent than the right. The parietal lobe also shows complex shape asymmetry (Figure 4v): the anterior portion adjacent to the frontal lobe and the posterior portion adjacent to the occipital lobe are more bulged on the left parietal lobe than the right, while an elliptic region, roughly corresponding to the superior parietal lobule, appears to protrude more on the right hemisphere than the left. Asymmetries in the temporal and parietal lobes sugges<sup>t</sup> that the directional asymmetry in the surface of the region corresponding to Wernicke's area is in favor of the right side.

The greatest degree of local asymmetry in the endocast surface was observed in the occipital region (Figure 4iv): the portion of the left occipital lobe near the indentation of the superior sagittal sinus protrudes significantly backward while the relative position of the right hemisphere contracts inward compared to the opposite side. Additionally, the left occipital lobe extends more medially than the right, bending the posterior interhemispheric fissure towards the right.

The surface shape of the cerebellum shows bilateral asymmetry (Figure 4iv,vi): the anterior portion of the cerebellum extends more anteriorly and ventrally in the left hemisphere than the right, whereas the posterior portion of the cerebellum extends more posteriorly and superiorly in the right hemisphere than the left. The cerebellum thus has the appearance of an anticlockwise twisting torque in basal view.
