*2.1. Materials*

In total, 58 adult endocasts, including 28 females and 30 males, were collected from the same archaeological site in Yunnan Province of Southwestern China, dated to about 300 years ago [50]. The skulls were well preserved or only minorly damaged in a way that would have no significant influence on the endocast reconstruction. The sexual assignment of specimens relied on diagnostic characteristics of the pelvis and cranium [50].

## *2.2. Endocast Reconstruction and Processing*

All of the modern human specimens investigated in this study were scanned by a 450 KV industrial CT scanner with a spatial resolution of 160 μm (designed by the Institute of High Energy Physics, Chinese Academy of Sciences, and housed at the Key Laboratory of Vertebrate Evolution and Human Origins, Institute of Vertebrate Paleontology and Paleoanthropology, Chinese Academy of Sciences) [51]. The virtual reconstruction of each endocast was performed through semi-automatic threshold-based segmentation via the Mimics v. 17.0 software (Materialise, Leuven). A three-dimensional (3D) mesh of each endocast was generated and saved as an STL file in Mimics, and then imported into MeshLab software (Bangalore, India) [52] for 'Cleaning and Repairing' and a resulting 3D surface was obtained.

Considering the presence of Yakovlevian anticlockwise torque, the cerebral longitudinal fissure is not entirely on the midsagittal plane. Thus, the central axis or central plane separating a complete left hemisphere from its right side is difficult to determine. To investigate shape differences of the endocast between the right and left hemispheres, mirrored versions of each original specimen were created via Avizo v. 8.0 (FEI Visualization Sciences Group, Houston, TX, USA) [15,25]. The left side of the original endocast corresponds to the right side of the mirrored version and vice versa, as shown in Figure 1. Therefore, a total of 116 cases of endocast surfaces were included in the following deformation analyses. In this way, we could obtain a symmetrical mean shape by averaging the original and mirrored endocast of each individual in the following steps. The shape asymmetry of endocast surfaces was analyzed by calculating the deformation between each original endocast and its mirrored endocast.

**Figure 1.** The original endocast (**A**) and the mirrored endocast (**B**) of the same individual in occipital view.

## *2.3. Diffeomorphic Surface Asymmetry*

All surfaces were superimposed and aligned in Avizo through translation, rotation, and dilation (scaling) to eliminate differences, except for shapes. The aligned surfaces were exported as PLY files and then transformed to VTK format by ParaView v. 5.6.0 software (Kitware Inc., Clifton Park, NY, USA). The set of VTK data were imported into Deformetrica v. 4.3 (Paris, France) [53] to carry out the diffeomorphic calculation. The outputs include the spatial coordinates of control points defining the deformable space (9200 in this study), the momenta vectors recording the deformation information of each control point, and a symmetric endocast configuration representing the global mean shape [45,54].

For each endocast specimen, the vector difference at each control point was calculated by subtracting the momenta vector of the mirrored one from its counterpart of the origin one. Then, the surface asymmetry was quantified by an asymmetrical matrix depositing the vector differences at all control points.

A non-center principal component analysis (PCA) using the "RToolsForDeformetrica" [55] and "ade4" v. 1.7-17 [56] packages for R v. 4.0.4 [57] was carried out on an array storing the asymmetrical matrices of all specimens. The "ggplot2" package [58] was used to visualize the result of the PCA. A scatter plot of the second principal component (PC2) against the first principal component (PC1) displayed the distributional relationship of each specimen. The deformations displaying the asymmetric patterns at the four extremes were computed via Deformetrica and visualized in ParaView v. 5.6.0. These deformations were displayed in a form of colormap from dark blue (more constricted compared to the opposite) to red (more expanded compared to the opposite).

The mean matrix averaging the asymmetrical matrices of all specimens was calculated to exhibit the general pattern of surface asymmetry. The deformation for this mean matrix was also computed via Deformetrica and visualized in ParaView v. 5.6.0.
