**4. Discussion**

## *4.1. Global Endocast Asymmetry*

In this study, we performed surface matching using diffeomorphisms to quantify and visualize the asymmetry of human endocasts. We found that two types of lobar asymmetries categorize the majority of the global asymmetry variation. These two types of lobar asymmetries correspond to the clockwise and counterclockwise distortion of the global brain, with the cerebrum and cerebrum being consistent in the deformation trends. Previous studies revealed that the right frontal, right parieto-temporal, and the left occipital lobes have larger surface areas than the contralateral sides [4]. Measurement of lobe volumes using MRI found rightward asymmetries for the frontal and temporal lobes, and leftward asymmetries for the parietal and occipital lobes in right-handed twin pairs [20]. Here, we find that the rightward asymmetries of frontal, anterior parietal, and anterior temporal lobes, and leftward asymmetries of occipital, posterior temporal, and posterior parietal lobes have a roughly equivalent distribution compared to the reverse asymmetry pattern in this population. This indicates that the lobar asymmetry has a more complicated pattern of shape, surface area, and volume asymmetry.

## *4.2. Local Asymmetries of the Cerebrum*

The shape at the positive-value extreme of PC2 and the deformation-based mean asymmetric shape both show a similar pattern of directional asymmetry. This directional asymmetry pattern is about three times as common as its anti-symmetry in the modern population. The general asymmetry pattern illustrated here is similar to the results of the previous study using geometric morphometrics to quantify hominid endocranial asymmetry [15] but reveals more details about the local asymmetries.

The petalia asymmetry pattern of endocasts in modern humans is typically characterized by the right frontal and left occipital lobes protruding outward more than the opposite side. Deformation results in the present study indicate that the leftward occipital petalia is much more prominent than the rightward frontal petalia, which is consistent with analyses of geometric morphometrics and linear measurements in endocasts of humans [15,59]. The temporal lobe presents a right petalia projecting inferiorly, which has not been observed in previous studies.

We found that the asymmetry in the posterior part of the temporal lobe favors the right side and the local asymmetries of the parietal lobe are complex depending on the mean asymmetric shape. In this context, the surface of Wernicke's area is primarily skewed to the right. Previous MRI research showed a complicated asymmetry in the temporal lobe. Kitchell and colleagues [5] have reported that the superior temporal sulcus is rightwardasymmetric while the planum temporale is leftward-asymmetric. A rightward asymmetry in the depth of the superior temporal sulcus ventral to Heschl's gyrus is known to be widely present in modern humans but rare in chimpanzees [60]. Due to the fact that the planum temporale and superior temporal sulcus are internal anatomical structures, it is difficult to define the contour of these area on an endocast. Therefore, the asymmetry of Wernicke's area discussed here is roughly based on the surface shape of the posterior parts of superior and middle-temporal convolutions.

A leftward asymmetry of Broca's area in the inferior frontal convolution has been identified as a feature commonly found in hominins and related to the brain lateralization associated with language [11,29]. Indeed, quantitative measurements revealed that the Broca's cap is larger in the right but more clearly defined in the left in modern humans [25,28,32]. In the present study, the inferior frontal convolution is more flattened and elongated antero-posteriorly in the right hemisphere, while the left inferior frontal convolution extends more laterally, anteriorly, and ventrally relative to the right side. As a result, the left Broca's cap appears to be more globular. In the quantitative study of *H. sapiens* endocast by Balzeau and colleagues [32], the left Broca's cap was also found to be more globular than the right side, but the length and the size of the third frontal convolution displayed a rightward asymmetry. This observation is supported and upheld by the results of the present study. Wada and colleagues [37] measured the visible cortical area on the frontal operculum (including both the pars opercularis and a posterior portion of the pars triangularis) and found that the left side was smaller than the right. However, Falzi and colleagues [61] measured the cortical surface area of Broca's area (including both the extra-sulcal and intra-sulcal cortex) and revealed that the left Broca's area was significantly larger than the right one. The difference in these results is due to the deeper fissure of the cortex in the left Broca's area [62] and perhaps leads to the larger size on the right but more globular shape on the left Broca's area.

## *4.3. Asymmetry of the Cerebellum*

The cerebellum is responsible for controlling movement and coordinating balance, as well as for regulating cognition and emotion through information circuits with the non-motor cortex in the prefrontal and posterior parietal [63–65]. Previous studies have found a leftward asymmetry of the anterior cerebellum and a rightward asymmetry of the posterior cerebellum [25]. Here, the cerebellum shows a double asymmetry in which the right posterior cerebellar lobe extends more posteriorly and superiorly than the left, and across the midline, whereas the left anterior cerebellar lobe extends more anteriorly and ventrally. Therefore, the surface shape of the cerebellum appears as a twisting effect in the opposite direction relative to the Yakovlevian anticlockwise torque of the cerebrum. There is evidence that the motor and non-motor cortex in the left and right hemispheres of the cerebrum show strong preferential correlations with the related functional areas in the contralateral cerebellum [66–68]. In addition, the region and degree of functional lateralization in the cerebellum are correlated with that of lateralization in the cerebrum [6]. With that in mind, the cerebellum may possess roughly similar asymmetrical patterns of function and structure to the cerebrum [6].

## **5. Significance and Conclusions**

Here, we quantified and visualized the asymmetry of endocast surface shapes in a modern human population using landmark-free DSM. Like previous studies, we have found the dominant asymmetry pattern to have left-occipital and right-frontal petalias, a more globular left Broca's area compared to the right, and a double asymmetry in the cerebellum. In addition, our results reveal more information of the asymmetry pattern in parietal and temporal lobes. Brain structural asymmetry is extensively involved in previous studies and often associated with functional lateralization. For example, the left hemisphere is generally dominant for language, with a more prominent Broca's area and a larger planum temporale [26,69]; besides, right-handed individuals often exhibit a more pronounced left-occipital and right-frontal petalias asymmetry than non-right-handed individuals [2]. Additionally, the cortical thickness asymmetry in a specific region of the postcentral gyrus correlated with hand preference, where right-handers dominated by the left hemisphere had a less rightward/more leftward shift of neural resources [9].

Our findings support previous MRI studies and confirm the validity of endocasts for obtaining valuable information on encephalic asymmetries [1,10,15,20,37,59]. Specifically, we find that the surface shape of the temporal language comprehension area (i.e., Wer-

nicke's area) presents a rightward asymmetry, which is different from the asymmetrical pattern of the motor speech area (i.e., Broca's area). Thus, the hemisphere dominance for language in terms of shape asymmetries, reflected by the endocast surface, might not be completely leftward. Furthermore, a rightward temporal petalia and a complex asymmetry pattern of the parietal lobe were also revealed. Whether these asymmetry features in the endocast surface can be correlated with a function of the brain needs to be investigated in combination with MRI studies as well as other morphological and functional studies in the future.

The evolution of the unique structure of the human brain has long been explored by analyzing the evolutionary sequence of endocasts and comparing humans and other primates [3,40,70,71]. A detailed understanding of the asymmetric patterns of the brain structure in modern humans is central to this topic. The PCA results presented in this study demonstrate that modern humans present a fluctuating asymmetry on the endocast surface, as represented by two balanced components of left parietal/right occipital lobes or right parietal/left occipital lobes. On the other hand, the non-center PCA results and the average asymmetric shapes show that most individuals exhibit a prevalent directional asymmetry, as discussed earlier in this paper. According to previous studies, the brain of grea<sup>t</sup> apes shows a similar right-frontal and left-occipital directional asymmetry in the width of lobes, and a similar but less variable and low-degree fluctuating asymmetry in components of the petalias [3,15,23]. Moreover, Balzeau and colleagues [32] have found that *Pan paniscus* shares a common pattern of asymmetries in the third frontal convolution with *Homo sapiens* through the quantitative study of endocasts. Great apes have also been shown to have leftward asymmetries in the size of the planum temporale and Broca's area [72,73]. Additionally, previous studies have revealed that levels of brain asymmetry varied in the evolution process of *Homo* species, especially when the common ancestor of *Homo heidelbergensis*, *Homo neanderthalensis*, and *Homo sapiens* emerged [40]. This study reveals that modern humans have a more complex pattern of endocast asymmetry than previously understood, which involves both fluctuating and directional asymmetry in different lobes. Considering this new understanding of endocast asymmetry, it is necessary to assess whether the asymmetry pattern in modern humans is also present in non-human primates and whether it is present in particular stages of hominin evolution.

**Author Contributions:** Conceptualization, S.X. and S.L.; methodology, Y.Z. and S.X.; software, S.L.; validation, S.L., Y.Z. and S.X.; formal analysis, S.L.; investigation, S.L.; resources, S.X.; data curation, S.L. and S.X.; writing—original draft preparation, S.L.; writing—review and editing, S.X.; visualization, S.L.; supervision, S.X.; project administration, S.X.; funding acquisition, S.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (no. XDB26000000) and the National Natural Science Foundation of China (41872030).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data supporting this study are available from the corresponding author on reasonable request.

**Acknowledgments:** The authors thank Yemao Hou and Jing Zuo for their help in CT scanning and 3D reconstruction processing. Xiujie Wu provided the Mimics files of 3D reconstruction. Mackie O'Hara-Ali helped us in revising the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
