As a sizable component of the cranial vault, the parietal bone is essential for understanding the regional variation of cranial surface morphology. Predigital, traditional morphological studies have tended to underemphasize the role of parietal trait variation, particularly in identifying region-specific and/or sex-related differences in modern human populations. Consequently, the extent of morphological variation in the parietal bone among modern human populations remains insufficiently understood. In this study, we perform a three-dimensional (3D) geometric morphometric analysis of the external surface of the parietal bone, using microcomputed tomography data from 120 human crania (60 males and 60 females) sampled from European and Chinese populations. The analysis of the periosteal surface of the parietal bone reveals significant sexual dimorphism in shape space. Specifically, the biparietal distance between pterion landmarks is wider in Chinese males than in Chinese females. Regional differences in parietal bone shape are more frequently statistically significant. Parietal bones of European populations tend to be wider and shorter, with less pronounced parietal eminences, whereas those from Chinese populations are relatively narrower and longer, exhibiting more prominent parietal eminences. When 3D geometric morphometric analysis is conducted in form space, which incorporates both shape and size, additional differences between sexes and populations become evident. Males exhibit significantly larger parietal bones than females, and individuals from European populations have significantly larger parietal bones than those from Chinese populations. Ultimately, differences in form space are more pronounced than those in shape space, emphasizing the importance of considering both shape and size in morphological analyses.

The paired parietal bones are the largest bones of the human cranial vault, located on its superolateral aspects. Typically, parietal bones are nearly square in shape with a convexly curved external surface characterized by a centrally located parietal boss that marks the site of the primary ossification center. The right and left parietal bones articulate with one another at the midline via the sagittal suture. Anteriorly, they articulate with the frontal bone at the coronal suture, while posteriorly they articulate with the occipital bone at the lambdoid suture. Laterally, the parietal bones articulate with the paired temporal bones along the squamosal sutures. Collectively, these bones form the calvarium, which, among its many functions, serves to protect the internal structures of the head, including the brain (Standring, 2020).

The external, or periosteal surface of the parietal bone is relatively smooth and morphologically simple. Primary surface features include the temporal lines, which serve as attachment sites for the temporalis muscles. Additionally, a pair of parietal foramina are usually positioned opposite to each other. Compared with other cranial bones, the parietal bone is not only larger but also more commonly preserved in both fossils and forensic contexts. This preservation, combined with its size and anatomical landmarks, makes the parietal bone a valuable source of information in the fields of forensic anthropology, biological anthropology, and paleoanthropology (Gunz et al., 2005; Torres-Lagares et al., 2010).

Previous investigations of the parietal bone have largely focused on sex-based or regional variability in non-metric features, such as the parietal eminences, temporal lines, and the sagittal keel. Amongst those, the parietal eminence has proven particularly useful for sex estimation in both forensic medicine and paleoanthropology because females generally exhibit a more developed parietal eminence than males (Larnach, 1976). In fact, in certain populations, sex can be estimated with 80% accuracy based on the morphology of the parietal eminence alone (Williams and Rogers, 2006). The expression of the trait varies across populations, tending to be more pronounced in European populations and less so in African populations (Urban et al., 2016). Other non-metric traits, such as the temporal lines, have also been shown to exhibit sex-based and region-related differences in modern humans. The vertical distance between the upper and lower temporal lines is greater in males than in females, and also greater in individuals from China than in those from Europe and Africa (Yan et al., 2022). Similarly, the presence and prominence of a sagittal keel have been found to differ by sex and historical time period. Holocene males exhibit more incidence of sagittal keel than females, and when present, the keel is generally more pronounced in males (Liu et al., 2006; Wu, 2006). There are also regional differences in overall morphology of the parietal bone. Generally, European individuals tend to have shorter and wider parietal bones, East Asians exhibit intermediate length, and African populations display the longest parietal bones (Johnson et al., 1989; Zhu, 2004).

Sex-based and regional trends in metric features of the parietal bone have also been well documented. Overall, the length of the parietal bone is generally greater in males than in females (Martin, 1928; Cekdemir et al., 2021). Differences in the parietal curvature index have also been reported, with males exhibiting higher indices than females. In a Chinese population, this index allowed for sex estimation with an accuracy rate of 66.7% (Song et al., 1992), supporting findings from two-dimensional (2D) geometric morphometric (GM) analysis (Zhang et al., 2016). Additionally, the curvature of the parietal bone in the sagittal plane is higher in males than in females (Zhang et al., 2016).

Further, a study conducted in India on Indian populations revealed significant sex-based and regional differences in the cranial angles formed at intersections of the coronal, sagittal, and lambdoid sutures. While sexual dimorphism was consistent across different regions, specific angular values varied in the sample (Makandar and Kulkarni, 2013). Females in northern and southern India had smaller frontal angles compared with males from the respective regions, while lambdoid angles were larger in females than in males. Both frontal and lambdoid angles were larger in the northern Indian sample than in the southern Indian sample (Makandar and Kulkarni, 2013). In a study of a modern Japanese sample, Akimoto et al. (1995) found that males exhibited larger frontal angles, parietal sagittal chords, and parietal sagittal arcs than females. However, no significant sex-based differences were found in parietal sagittal arc indices and lambdoid angles. Finally, studies on cranial growth suggest that the parietal bone may show the most pronounced differences in postnatal growth rates between sexes, relative to other cranial bones (Gunz et al., 2005).

Three-dimensional (3D) landmarks and GM analysis represent a powerful approach for detecting variations in the parietal bone. This method makes it possible to uncover subtle anatomical differences that may be masked when analyzing the cranium as a whole, offering new insights into specific localized morphological variations attributable to sex, ancestry, or environmental influences (Baab et al., 2012; Bruner et al., 2017; Zheng et al., 2017). Previous GM studies of the parietal bone have typically emphasized its spatial relationship with adjacent cranial structures (Zhang et al., 2016; Bruner et al., 2017), while analyses focusing exclusively on the parietal bone itself have remained relatively underexplored. The parietal bone’s simple structure and smoothly curved external surface make it particularly well suited for landmark-based GM approaches. By using dense landmark configurations, one can reduce the influence of subjective bias that may arise when selecting only a limited number of landmarks. This enhances precision in data acquisition and interpretation. 3D GM provides a robust framework for examining shape–space relationships in cranial bones such as the parietal. In the present study, we apply a 3D GM approach to evaluate sex-based and regional differences in the surface morphology of the parietal bone.

The primary aim of this study is to evaluate whether significant differences exist in the parietal bone morphology between Chinese and European populations. Additionally, we aim to determine whether these differences are primarily attributable to sex-based variation or are instead driven by region-specific morphological variations independent of sexual dimorphism. Visualizing any significant variation, either between sexes or between populations from different regions, will provide a more intuitive and comprehensive understanding of how female and male parietal bone shapes may differ across geographic regions. To achieve these aims, the study addresses the following key questions: (1) What are the primary morphological distinctions between the parietal bones of Chinese and European populations? (2) How do morphological differences vary between males and females within each population? Specifically, is sexual dimorphism expressed in a consistent manner across both regions? (3) Are regional differences in parietal bone morphology more pronounced than sex-based differences, or do these sources of variation interact in more complex ways? By addressing these questions, the study will provide valuable insights relevant to several fields, including biological anthropology, archaeology, and forensic science.

To investigate sex- and region-based differences in the morphology of the parietal bones of two modern human populations, we analyzed a total of 120 modern human crania, including 60 individuals of Chinese ancestry and 60 of European ancestry, with an equal representation of males and females in each regional sample (Table 1). The Chinese sample was sourced from Han tombs in Yunnan, China. Sex and age identifications for these individuals were based on features of the skull and pelvis (Wu and Xi, 2010). This skeletal material is curated at the Institute of Vertebrate Paleontology and Paleoanthropology (IVPP), Chinese Academy of Sciences. The European sample comprises specimens from two sources: (1) materials in the IVPP collection, originating from tombs in present-day Austria-Hungary, and (2) skeletal remains curated in the Dart Collection at the University of the Witwatersrand (Wits). The Dart Collection specimens were originally labeled as ‘Euro,’ ‘White,’ or ‘Caucasian’ in the collection records and primarily originated from hospitals in South Africa. Sex and age data for these individuals were obtained from original collection records (Dayal et al., 2009). While archaeological context was unavailable for European specimens curated at the IVPP, the Chinese individuals are definitely archaeological in origin, representing civilian agricultural burials from the 19th to 20th century. To minimize potential age-related morphological effects, individuals of advanced age (i.e. 65+ years) were excluded from the analysis. This exclusion was intended to ensure comparability in age ranges between the Chinese and European samples. Although age-related changes have been shown to affect the parietal bone less than other cranial bones (Musilová et al., 2016; Velemínská et al., 2021), we still ensure a comparable age range between samples to minimize any potential confounding effects of age on parietal morphology.

The cranial samples from the two populations were analyzed by microcomputed tomography (microCT) scanning at different voxel sizes (Table 1). To assess the potential impact of voxel size differences on surface measurements, a paired t-test was performed to determine whether systematic differences existed between the datasets acquired at different voxel sizes. Five individuals from the Dart Collection, originally scanned at a pixel size of 125–130 μm, were also reconstructed at 160 μm. Cranial measurements derived from these two different voxel size datasets did not differ significantly (P > 0.05), confirming that the voxel size differences did not adversely affect the precision or reliability of surface data in this study. Therefore, voxel-size-based variation was considered negligible for the purposes of this study. Cranial microCT data were visualized as 3D renderings and volumetric surface data for each parietal bone were exported in .ply format using Mimics 19.0 software.

Landmarks and curve-based semi-landmarks were placed on the exported surface models using Rapidform software (3D Systems, Inc., Rock Hill, SC, USA). To minimize interobserver error, all landmarks were conducted exclusively by the lead author. The configuration of landmarks and semi-landmarks defining parietal morphospace follows the methodology outlined by Natahi et al. (2021), specifically their approach for placing semi-landmarks along sutures and distributing additional semi-landmarks across the bone surface (Figure 1). Four anatomical landmarks—bregma, asterion, pterion, and lambda—were selected (yellow landmarks in Figure 1). Between these anatomical landmarks, in total 72 semi-landmarks were placed along four major curves (18 landmarks each) of sutures for each side (red landmarks in Figure 1). In addition, 18 long curves, each containing 18 equidistant semi-landmarks, were distributed across the non-sutural surface of each parietal bone (cyan landmarks in Figure 1). A single short curve, located in the posterolateral area, contained six equidistant semi-landmarks. When complex sutures or sutural bones were present, the intersection of extended sutures was taken as a landmark, and midlines of sutures were taken as curves. The sutures bordering a single parietal bone can be divided into four distinct parts: anterior (coronal suture), superior (sagittal suture), and posterior (lambdoid suture) parts, each defined by a single suture, and a more complex inferior part, which is comprised of multiple sutures such as the sphenoparietal, squamosal, and parietomastoid sutures (Figure 1). For the purposes of the present study, we combined the three sutures comprising the inferior part into a single continuous curve, with 18 equidistant points placed along this curve.

Figure 1. Template of anatomical, curve, and surface semi-landmarks used for geometric morphometric analysis of the parietal bones. (a) Lateral view of the left parietal bone showing four anatomical landmarks (yellow spheres): bregma, lambda, pterion, and asterion. Between these anatomical landmarks, a total of 72 curved semi-landmarks (red spheres) were placed along four major sutural curves (18 landmarks per curve) on each side. The surface of the parietal bone was populated with symmetrically distributed surface semi-landmarks (cyan spheres), arranged along 18 long curves with 18 equidistant semi-landmarks each, and one shorter curve in the posterolateral region containing six equidistant semi-landmarks. (b) Superior view of the symmetrical model, displaying both parietal bones and showing the midline sagittal suture, as well as the coronal and lambdoid sutures, each annotated with anatomical (yellow), curved (red), and surface (cyan) semi-landmarks. (c) Anterior view, highlighting the distribution of landmarks along the sagittal and coronal sutures. (d) Posterior view, highlighting the distribution of landmarks along the sagittal and lambdoid sutures. The complete model, including both right and left parietal bones, comprises 792 total landmarks: six anatomical landmarks (yellow: paired pterion and asterion; and shared bregma and lambda), 126 curve semi-landmarks on sutures (red), and 660 surface semi-landmarks on non-sutural areas (cyan).

Non-sutural semi-landmarks were included as analogous points densely distributed over the surface to improve accuracy by accounting for the entire parietal surface as opposed to using only several type I anatomical landmarks and sutural semi-landmarks. Configuration of the 660 non-sutural semi-landmarks on both parietals is largely determined by the parietal bone’s natural orientation and surface features, such as its curves and ridges, particularly the temporal lines. These surface semi-landmarks are arranged to follow the natural contours of the bone, ensuring that they accurately reflect the bone’s overall shape and structure. To minimize potential errors in the analysis, we created an initial symmetrical parietal bone model by mirroring the better-preserved side of the parietal bone. This symmetrical model served as the foundation for generating a template composed of symmetrically placed surface semi-landmarks. These semi-landmarks were subsequently used as reference points to accurately map onto the remaining parietal bone of each specimen in this study (Figure 1).

To ensure that the distribution of landmarks and semi-landmarks was statistically sound and did not exhibit patterns of spatial dependence (autocorrelation) that could bias the analysis, we conducted a Moran’s I test. Moran’s I is a measure of spatial autocorrelation, which assesses whether the values of a variable (in this case, the positions of landmarks and semi-landmarks) are spatially clustered, dispersed, or randomly distributed. A significant positive Moran’s I value would indicate clustering (where nearby points are more similar to each other than expected by chance), while a significant negative value would indicate dispersion (where nearby points are less similar than expected by chance). Results indicated that no significant spatial autocorrelations were observed (P > 0.05), suggesting that the placement of landmarks and semi-landmarks was random and unbiased, and not affected by any unintended clustering or dispersion of the points, thus ensuring robustness of the morphometric data.

Analyses of landmarks and semi-landmarks were completed in R 4.3.2, using the Morpho (Schlager, 2017), geomorph (Adams and Otárola‐Castillo, 2013), and ggplot2 (Wickham, 2011) packages. Landmark data were first subjected to generalized Procrustes analysis (GPA), with semi-landmarks slid using the bending energy criterion. Centroid size represents the size of an individual bone and is equivalent to the square root of the sum of the squared distances of all coordinates from the centroid of a bone (Klingenberg, 2016). In the resulting shape space, a GPA approach eliminates differences in size and differentiates bones according to Procrustes distances. Thus, these distances, which reflect overall differences between a given bone’s shape and the entire group’s mean shape, exclude centroid size. Shape data were then analyzed by principal components analysis (PCA) to identify the sample’s main axes of shape variation. This PCA provided insights into overall patterns of shape variation across the dataset, with each specimen represented by principal component (PC) scores.

The form of the parietal bone is obtained by combining size (e.g. centroid size) with shape, which makes it possible to examine how size affects shape. After incorporating size, a second PCA was performed on form data to explore patterns of form variation. This approach enabled investigation of how form varies between sexes and regions. For both the shape PCA and the form PCA, 3D surface changes were visualized using thin plate spline (TPS) interpolation, which facilitates precise alignment of landmarks and semi-landmarks between specimens, ultimately enabling detailed comparisons of bone morphology (Bookstein, 1989). TPS transforms landmark coordinates into surface patches. To generate these visualizations, the mean group shape was calculated, and shapes corresponding to extreme positive and negative values of selected PCs were generated. The TPS approach was then applied to these extreme shapes/forms to produce deformation grids and 3D surface models illustrating morphological changes along PC axes. These TPS visualizations provided clear representations of how parietal bones change along each PC axis, for both shape (excluding size variation) and form (including size variation). This dual approach differentiates shape differences attributed to overall size (form) from those reflecting intrinsic morphological variation of shape differences, offering a more nuanced understanding of parietal bone variation across the studied populations.

The mean shape for each group corresponds to the mean 3D coordinates of all the specimens in the group in shape space and serves as a reference to visualize shape differences among groups (Bookstein, 2017). Specifically, the minimum distance between mean meshes can be calculated and visualized to intuitively illustrate morphological differences between groups (Musilová et al., 2016). Two-sample t-tests were performed on distances from all surface patches to the mean parietal shape, and P-values were visualized on the patches to identify statistically significant morphological differences between groups. All statistical tests were performed in R 4.3.2 (R Core Team, 2024), using the stats and rstatix (Kassambara, 2023) packages. Statistical significance was determined at an α level of 0.05.

The relationship between shape and size, known as allometry, is well established (Simons, 2004). The centroid sizes of study groups were tested for normality and homogeneity of variance using the Shapiro–Wilk test and Bartlett’s test (P > 0.05). A two-factor analysis of variance was then conducted to examine the interaction between sex and region. To account for the influence of size on shape, allometric regression analysis was performed using the common allometric component (CAC) method (Mitteroecker et al., 2004), which allowed for the control of allometric effects in the dataset.

To assess intra-observer error, five specimens were randomly selected, and anatomical landmarks, curve semi-landmarks, and surface semi-landmarks were placed five times on each left and right parietal bones. After performing GPA and PCA, an analysis of variance was used to evaluate differences among the five sets of landmark configurations. The non-significant P-values indicated low intra-observer error, suggesting high consistency in landmark placement.

The distribution of the parietal bone in shape space is illustrated in Figure 2. PC1–PC4 account for 26.2%, 11.6%, 8.6%, and 8.1% of the total variance, respectively, collectively explaining 54.5% of the variance in the overall sample.

Figure 2. Principal component analysis (PCA) plot of parietal bone shape variation. Plots display shape variation along the first two principal components (PC1, PC2) in the top half and the third and fourth principal components (PC3, PC4) in the bottom half. Star-shaped markers indicate the average position of each group in the PCA space, with fill colors corresponding to group identity. Parietal maps on both sides of the scatter plots (i.e. visualized as top and lateral views in each pair along an axis) indicate maximum values (rainbow visualization) and minimum values (blue visualization) along the PC y-axes (left pairs) and x-axes (right pairs). Rainbow colors indicate the distances from the minimum value to the maximum value. Negative loadings indicate contractions and positive loadings indicate expansions in these visualizations. These distances are mapped onto the maximum value to visualize deformation from the negative to positive direction. In top and lateral views, the coronal suture is located along the bottom edge of the images.

PC1 primarily reflects the length and width dimensions of the parietal bone (Figure 2). Along the negative-to-positive direction of PC1, the parietal becomes progressively wider mediolaterally and shorter anteroposteriorly. Shape variation along the sagittal suture also shows increasing contraction, particularly around the obelion–lambdoid region (Figure 2).

PC2 reflects mainly curvature differences expressed at the squamosal suture and the lateral sides of the parietal bone (Figure 2). Along the negative-to-positive direction of PC2, in top view, the parietal bone slightly contracts in the middle and expands at the mastoid angle area, with accompanying downward and inward contraction of the parietal eminences (Figure 2). In lateral view, increased curvature of the squamosal suture is observed, along with expansion of the mastoid angle area.

PC3 primarily reflects changes in the shape of sphenoid and mastoid angles of the parietal bone (Figure 2). Along the negative-to-positive direction of PC3, the parietal bone expands slightly near the sagittal suture and substantially at the lower margin of the mastoid angle, while the parietal width decreases mediolaterally, with marked contraction at the sphenoid angle area (Figure 2).

PC4 primarily captures curvature of the anterior portion and size of the posterior portion of the parietal bone (Figure 2). Along the negative-to-positive direction of PC4, the posterior end shows expansion, particularly near the mastoid angle and along the lambdoid suture, while the anterior two-thirds shows contraction, especially around the central portion of the coronal suture (Figure 2).

The distribution of the parietal bone in form space is illustrated in Figure 3. PC1–PC4 account for 40.9%, 14.0%, 7.0%, and 5.3% of the total variance, respectively, collectively explaining 67.2% of the variance in the overall sample.

Figure 3. Principal component analysis (PCA) plot of parietal bone form variation. Plots display form variation along the first two principal components (PC1, PC2) in the top half and the third and fourth principal components (PC3, PC4) in the bottom half. Star-shaped markers indicate the average position of each group in the PCA space, with fill colors corresponding to group identity. Parietal maps on both sides of the scatter plots (i.e. visualized as top and lateral views in each pair along an axis) indicate maximum values (rainbow visualization) and minimum values (blue visualization) along the PC y-axes (left pairs) and x-axes (right pairs). Rainbow colors indicate the distances from the minimum value to the maximum value. Negative loadings indicate contractions and positive loadings indicate expansions in these visualizations. These distances are mapped onto the maximum value to visualize deformation from the negative to positive direction. In top and lateral views, the coronal suture is located along the bottom edge of the images.

PC1 primarily reflects size differences, with associated variation in mediolateral and anteroposterior direction of the parietal bones. Along the negative-to-positive direction of PC1, the parietal bone shows a substantial increase in overall size, accompanied by a trend towards a mediolaterally wider and anteroposteriorly shorter shape.

In the analysis of form, PC2 mainly captures differences in parietal length and width dimensions, exhibiting a PCA distribution and visualization that are remarkably similar to those captured by PC1 in the analysis of shape, albeit with reversed axis directions. Along the negative-to-positive direction of PC2, the parietal bone exhibits progressive mediolateral contraction and anteroposterior expansion.

Similarity between Form PC3 and Shape PC2, and Form PC4 and Shape PC3 is also notable, with minor differences in loading distributions potentially stemming from algorithmic distinctions between form and shape (Figures 2, Figure 3). In Form PC3, changes along the negative-to-positive direction primarily involve contraction in the vicinity of the parietal eminence, expansion of the areas of mastoid angle and frontal angle, and contraction at much of the squamosal suture. Form PC4 displays changes emphasizing increasingly more contraction of the sphenoid angle area and expansion of the mastoid angle margin along the negative-to-positive direction (Figure 3).

Male and female shapes along PC1, PC3, and PC4 axes exhibit substantial overlap (Figure 2). Along the PC2 axis, female distributions tend to cluster and fall slightly more toward the negative direction compared with male distributions. This subtle separation along PC2 suggests that, on average, male parietal shapes are associated with slightly more curved squamous sutures and more expanded mastoid angle area than female parietal shapes (Figure 2).

Regional patterns of sex-based variation differ from those observed in the combined sample. Specifically, Chinese males exhibit greater variation than Chinese females in PC1–PC2 (Figure 2). European males and females display broadly similar ranges of variation in their distributions along PC1 and PC2, with European females slightly more shifted towards the positive direction along PC1 and, like Chinese females, shifted slightly more towards the negative direction along PC2. In PC3, Chinese males are shifted to a more negative direction than Chinese females. European males and females again show substantially overlapping distributions in PC3. In PC4, females of each region fall within the respective male ranges.

Sex-based differences are more pronounced in form space (Figure 3). In PC1, as with the Chinese, European males tend to be shifted more towards positive positions, while European females tend to be more shifted towards negative positions (Figure 3). This confirms that sex-based differences in form may be explained with size as the decisive factor, with males being larger than females. In contrast, PC2 shows substantially more overlap between the sexes. In PC3, females are shifted more towards negative positions than males, and in PC4, females are shifted more towards positive positions than males.

Differences in mean shapes show that the lateral edge of the female parietal bone is slightly narrower than that of males due to contraction along the inferior part in the former (Figure 4a). Also, females exhibit a parietal bone, with the area around lambda being slightly higher, and the lateral wall expanded upward and outward (Figure 4a). Areas of the parietal where these shape differences between males and females are significant occur only at the pterion area (Figure 4b). In form differences of the parietal bone, males are generally larger than females (Figure 4c), with statistical significance assigned to these differences exhibited throughout the entire parietal bone, with statistically more significant differences found at the pterion area and parietal eminence and at areas close to sagittal and coronal sutures (Figure 4d).

Figure 4. Visualization of differences in shape and form between sexes. (a) Overall sample differences in mean shapes of males and females. (b) Statistically significant differences in mean shapes of males and females. (c) Overall sample differences in mean forms of males and females. (d) Statistically significant differences in mean forms of males and females. (e) Within the Chinese sample, differences in mean shapes of males and females. (f) Within the Chinese sample, statistically significant differences in mean shapes of males and females. (g) Within the European sample, differences in mean shapes of males and females. (h) Within the European sample, statistically significant differences in mean shapes of males and females. Left three renderings in each row represent the top, lateral, and anterior views, respectively, with rainbow colors indicating the distance from the male mean to the female mean. The warm colors indicate relative expansion, while the cool colors indicate relative contraction. The fourth renderings in rows a, c, e, and g are overlays of the lateral views of male mean (blue) and female mean (red). In the right three renderings, P-values are indicated in shades of blue, while darker shades of blue indicate successively smaller P-values. In top and lateral views, the coronal suture is located along the bottom edge of the images.

When comparing sex-based differences within regions, the mean shapes of Chinese males and females reveal differences that are not present in the comparisons between European males and females. These differences are especially prominent as contraction along squamosal (dark blue) and expansion along lambdoid (dark red) sutures from male to female mean shape (Figure 4e). Compared with Chinese males, the mean shape of Chinese females’ parietals has a relatively narrower lateral wall in the mediolateral dimension and an area bordering the lambdoid suture that extends outwardly and upwardly. Statistical significance of these shape differences between Chinese males and females is restricted to the areas near the pterion and lambda (Figure 4f).

Sex-based differences in the European sample are less expressed than in the Chinese sample (Figure 4e–h). The primary differences between male and female European samples are depicted by light blue areas near the sphenoidal angle and mastoid angle (Figure 4g), where males show downward and outward expansion (i.e. the bone surface of their parietals extends further downward and outward), while females exhibit slight inward and upward contraction (i.e. the bone surface of their parietals is less extended and curves inward and upward). Additionally, the area surrounding the sagittal suture in European females is slightly lower than in European males, and the middle portion of the parietal is slightly more expanded in European females (i.e. wider breadth) than in males (Figure 4g). In European males and females, the areas of statistical significance in these shape differences are minimal (Figure 4h).

In the PCA for shape, European individuals tend to fall more in the positive direction along PC1, while Chinese individuals tend to fall more in the negative direction (Figure 2). Along PC2, Chinese males exhibit a larger range of variation than either Chinese females or both sexes of Europe. Regional patterns by sex indicate that variation among Chinese females is the smallest, tending towards the negative direction on both PC1 and PC2, while European females appear more variable, tending towards the positive direction on PC1 and being relatively evenly distributed among positive and negative directions along PC2 (Figure 2). Among males, Europeans are also shifted in the positive direction on PC1, while Chinese males tend towards the negative direction on PC1. The range of variation of European males on PC2 is encompassed within that of Chinese males (Figure 2). In PC3, regional distributions largely overlap, while in PC4 Europeans show a slightly more positive distribution than Chinese.

Regional differences in form are particularly distinct (Figure 3). In PC1, the European groups tend to be shifted towards the positive direction compared with the Chinese groups, while in PC2 the European groups tend to be shifted more towards the negative directions. Regional differences within each sex exhibit similar patterns as those within the overall sample differences. In PC3 and PC4, the European groups are generally shifted to a more positive direction overall compared with the respective Chinese groups. For PC4 specifically, European individuals are slightly in a positive distribution compared with Chinese individuals across both sexes. In regional variation of form, size remains the primary explanatory factor, with morphology playing a secondary role.

As shown in Figure 5a, b, mean shape differences between Chinese and European samples are mainly concentrated at the coronal suture, parietal eminence, and mastoid angle area. Along the coronal suture, the parietal bone of the European sample is wider except for the pterion area, and higher in vertical height than the parietal bone of the Chinese sample. Along the sagittal suture, parietals in the European sample are shorter than those in the Chinese population and the parietal eminences indicate a more prominent condition in the Chinese sample (Figure 5a). The European sample also exhibits greater breadth between mastoid angles (Figure 5a). The mean shape of the Chinese parietal is narrow and long, with a more prominent parietal eminence. The mean shape of the European parietal, on the other hand, contrasts with this pattern in being wider and shorter, with a weaker parietal eminence. Overall, statistical differences between regional groups emphasize these same differences in mastoid angle, parietal eminence, and coronal suture between mean shapes (Figure 5b).

Figure 5. Visualization of differences in shape and form between populations. (a) Overall sample differences in mean shapes of Chinese and European groups. (b) Statistically significant differences in mean shapes between Chinese and Europeans. (c) Overall sample differences in mean forms of Chinese and Europeans. (d) Statistically significant differences in mean forms between Chinese and Europeans. (e) Differences in mean shapes of Chinese and European males. (f) Statistically significant differences in mean shapes of Chinese and European males. (g) Differences in mean shapes of Chinese and European females. (h) Statistically significant differences in mean shapes of Chinese and European females. Left three renderings in each row represent the top, lateral, and anterior views, respectively, with rainbow colors indicating distance from the Chinese mean to the European mean. The warm colors indicate relative expansion, while the cool colors indicate relative contraction. The fourth renderings in rows a, c, e, and g are overlays of the lateral views of Chinese mean (blue) and European mean (red). In the right three renderings, P-values are indicated in shades of blue, while darker shades of blue indicate successively smaller P-values. In top and lateral views, the coronal suture is located along the bottom edge of the images.

After adding centroid size into comparisons, regional differences in mean forms and the statistical significance of these form differences can be assessed again (Figure 5c, d). European individuals exhibit areas of expansion from bregma to obelion and from the lower portion of the lateral area of the parietal to the mastoid angle, with the largest differences from Chinese individuals observed at the mastoid angle area (Figure 5c). Areas of contraction in European individuals are mainly confined to the vicinity of the parietal eminence and the middle portion of the lambdoid suture, with the small area at pterion contracting posteriorly and slightly outwards.

Compared with the mean shape in Chinese males, European males have a curved coronal suture, the area near the bregma is anteroposteriorly shorter, and the mastoid angle area is expanded outward (Figure 5e). The bi-pterion width of European males was less than in Chinese males (Figure 5e). Compared with Chinese males, European males exhibit a wider mean parietal shape with the anterior portion of their parietal being shorter and raised, and its parietal eminence being less pronounced. Statistically significant shape differences between Chinese and European males are restricted to the vicinity of the parietal eminence, the mastoid angle, and along the coronal suture above the sphenoidal angle (Figure 5f).

When comparing the mean shapes of Chinese and European females, European females have a shorter and wider parietal bone, with the Chinese females having a longer and narrower one (Figure 5g). This is supported by statistically significant differences in mean parietal shapes between Chinese and European females (Figure 5h), emphasizing the significant areas of difference located above the sphenoidal angle area and continued to slightly anterior to the mastoid area (Figure 5h).

Comparing centroid sizes across the four groups (Figure 6a), European males have the largest centroid size on average, followed by European females, Chinese males, and Chinese females. Specifically, there are significant size differences between Chinese females and Chinese males (P < 0.01), Chinese females and European females (P < 0.01), Chinese females and European males (P < 0.01), and Chinese males and European males (P < 0.01). There are no significant differences between the other pairwise comparisons (i.e. between Chinese males and European females or European females and European males). Thus, significant differences in centroid size are observed between sexes and between regions, with a confidence level of 0.99; sexual dimorphism is more pronounced in the Chinese sample than in European sample (Figure 6a). Patterns in PC1 of the PCA on form parallel these patterns in the centroid sizes of groups (Figure 3).

Figure 6. Analysis of centroid size and allometry in Chinese and European populations. (a) Bar plot of centroid sizes for groups. (b) Bar plot of the common allometric component for groups. (c) Scatter plot of allometry describing the common allometric component distribution against log centroid sizes for groups. *Statistically significant at P < 0.05; **statistically significant at P < 0.01; ns, non-significant.

When comparing CAC differences across the four groups (Figure 6b), the European groups exhibit higher CAC values than the Chinese groups, with European females having the highest values, followed by European males, Chinese males, and Chinese females. No significant sex differences are observed within either region, however. Significant differences are observed when mixing sexes and regions, e.g. comparing Chinese females and European males (P < 0.01), Chinese females and European females (P < 0.01), Chinese males and European females (P < 0.01), and Chinese males and European males (P < 0.05). It is clear that regional differences in CAC surpass those of sex differences (Figure 6b).

Allometric growth patterns exhibit different relationships between log-transformed centroid size and CAC among the four groups (Figure 6c). European females exhibit the steepest slope, whereas Chinese males and European males show similarly flatter slopes, suggesting more similar allometric effects in the two male groups. Chinese females fall between these two extremes.

In this study, we assessed external surface shape differences of the parietal bone in two modern populations (i.e. Chinese and Europeans). Our primary aim was to determine whether significant morphological differences exist between Chinese and European parietal bones, and then to investigate the extent to which these differences are influenced by sex. Our results indicate that while regional differences were observed, sex-based differences in parietal bone shape were relatively more subtle.

Significant sex differences in the shape of the parietal bone were not widely observed in the combined sample, being confined to a portion of the pterion area. That is, in the pterion area, males exhibited a smaller sphenoidal angle area and wider bi-pterion dimension, while females exhibited the opposite pattern, indicating that these two traits can have value for sex identification purposes in at least some populations. Our results contrast with those from previous studies of the 3D GM of the entire skull in which sex differences in the shape of the parietal bone were inconsistently significant (Musilová et al., 2016, 2019; Čechová et al., 2019), therefore we refrain from generalizing the sex-based differences observed in the present study to other populations.

When sexes were compared within individual regions, significant sex differences were observed again. Within the European sample, while the parietal eminence was slightly weaker in males than in females, this area was not among the few significant differences we observed (Figure 4). This finding contradicts the earlier belief that females consistently show a stronger parietal eminence than males (Larnach, 1976; Williams and Rogers, 2006). The lack of a significant difference observed in the present study may arise from different samples being investigated than those in past studies, and/or the fact that non-metric traits can be difficult to reliably quantify due to subjectivity in their classification or visual assessment (Amiel-Tison et al., 1998; Walrath et al., 2004). Within the Chinese sample, the parietal eminence of Chinese males is also only slightly more prominent than in Chinese females, again contrasting with previous research that observed a markedly more prominent parietal eminence in females than in males (Wu, 2006; Čechová et al., 2019). The observed statistically significant sex-based differences were primarily restricted to the edge of the sphenoidal angle, which was consistent with the pattern of sex-based differences in the combined region sample.

Significant sex-based differences in the Chinese region were also observed outside the vicinity of the sphenoidal angle, i.e. primarily around lambda. In this area, Chinese female parietals were slightly higher on both sides of lambda compared with those of Chinese males, with some possible influence of cranial asymmetry appearing in the color representation of the distribution differences (Figure 4e). While it has been suggested that temporalis muscles and the posterior areas of the temporal lines might influence this difference (Noback and Harvati, 2015a), it is important to note that the temporalis muscle attachments typically do not extend this far towards the midline or the posterior portion of the cranium near the lambda, so their influence in this specific area of the cranium may be limited accordingly.

Significant differences in parietal shape were documented between regional populations, mainly due to changes in length and width dimensions of the parietal bone, with some differences also expressed in their sagittal arcs. These differences are consistent with traditional anthropological assessments that generally characterize Europeans as brachycephalic, while the Han Chinese have been mainly characterized as mesocranial (Zhu, 2004; Ball et al., 2010). Previous studies have noted interregional differences in sexual dimorphism of the parietal eminence (Urban et al., 2016), but no clear interregional differences have been reported in other parts of the parietal bone. The current study reveals that the parietal eminence in a Chinese population is stronger than that expressed in a European population, a difference that warrants further exploration. The Chinese sample also exhibited slightly flattened sagittal arcs, while the European sample exhibited more tightly curved sagittal arcs, both of which corroborate the findings of a previous study (Durbar, 2014).

When regions were compared for each sex, some shape differences not observed in previous studies (Musilová et al., 2016, 2019; Čechová et al., 2019) were documented in the current study. For example, the coronal suture edge of the European male parietal is shorter, the parietal eminence is weaker, and the mastoid angle area is longer and more outwardly expanded than in Chinese males. In females, by comparison, the main regional differences included a longer and slightly higher lambdoid suture in Chinese females than in European females. The area of the parietals inferior to the parietal eminence was also straighter and narrower in Chinese females than in European females, forming a roof shape in posterior view. In contrast, the lambdoid suture in European females was shorter and slightly flatter, and the area inferior to the parietal eminence expanded outward compared with the analogous area in Chinese females. In posterior view, the cranium of European females was nearly elliptical as opposed to the more roof-shaped configuration of Chinese females.

Interpopulation shape differences in the neurocranium have been primarily attributed to genetic factors and are considered by some to be less influenced by climate (von Cramon-Taubadel, 2014). Others have concluded that cranial morphology is largely attributable to dietary habits and geographical distance along with other factors such as climate (Noback and Harvati, 2015b). For example, nomadic populations tend to have temporalis muscles with more anteriorly and relatively higher positioned attachment areas, whereas agricultural populations tend to have more posteriorly positioned and relatively long temporalis muscles (Noback and Harvati, 2015a). Tougher food items require more forceful mastication, potentially leading to differences in cranial morphology (Chalk et al., 2011; Toro-Ibacache et al., 2016). Thus, differences in masticatory stress, e.g. the amount of chewing cycles and forcefulness of individual bites, may contribute to some of the regional shape differences in parietal bones that were observed in the present study. Although the populations in the present study are all from agricultural backgrounds, the late Qing dynasty Chinese lived in poverty with more limited food resources and lower proportions of animal protein compared with modern white South Africans and Central European farmers (Hu, 2014). Additionally, there are cultural differences in dietary practices between East and West populations, with the Han Chinese diet being predominantly carbohydrate-based (Ge, 2011). Thus, these types of factors may also contribute to some of the observed shape differences in parietal bone morphology between the Chinese and European regional groups.

There are significant differences in centroid size between sexes and between regions represented in the sample. Sex-based differences are similar to the differences expressed in comparisons of traditional quantitative measurement data, in which males are overall larger than females (Martin, 1928; Zhu, 2004). In terms of regional differences, compared with overall sex-based comparisons across the regions, the centroid size of individuals comprising the European sample is larger than that comprising the Chinese sample.

After incorporating centroid size, the intergroup differences in form space are much greater than those in shape space, consistent with earlier findings (Musilová et al., 2016; Cekdemir et al., 2021). This may indicate that parietal bone linear measurements reflect greater intergroup differences than the indices. Other features of the parietal bone, such as the parietal eminence, express significant intergroup differences in shape data, but not in form data. In traditional studies of regional cranial differences (Martin, 1928; Zhu, 2004), fewer metric measurements have been used and non-metric traits of the parietal bone have also been considered. Most studies have used multivariate discriminant function analysis to investigate cranial differences, with fewer investigating differences specific to the parietal bone (Johnson et al., 1989; Song et al., 1992). Compared to evaluations that have relied on a cranial index (Zhu, 2004), the present study corroborates previous findings that Chinese individuals exhibited a parietal that was narrower and longer than the parietal of European individuals.

In East Asian agricultural societies, females generally obtain fewer and lower-quality food resources than males (Wu and Li, 2011). The Chinese sample studied here may reflect more unequal resource distribution between the sexes, while the same possibility cannot be fully evaluated in the European sample. If disparities differed between regions, this may have contributed to greater sexual dimorphism in centroid size among the Chinese than the Europeans. Additionally, skeletal robusticity also could have partly explained these differences, or body size differences between the sexes may have contributed to the observed variations in centroid size. It is important to consider that male masticatory muscles tend to be more developed than female masticatory muscles due to general sex-based tendencies in overall musculoskeletal robusticity, so the shorter and more inwardly contracted pterion area of Chinese female crania may partly be influenced by different states of development in their temporalis muscles.

The greater variance observed in European samples may be influenced by the broader geographic and age distributions of these samples. In other words, the imbalanced diversity of the regional samples may be a limitation in this study, which may have influenced the study outcomes to some extent. In future studies, we encourage more balanced and representative subsamples to better control for such potential confounds. The sample in the present study also does not account for a broad range of dietary habits, or include a diverse representation of the global population. While this was not part of the current study design, we encourage future research on parietal shape and form to expand the breadth of regional samples to address these potential limitations. Additionally, visual observation errors were not investigated in this study. For example, when combined with size, the prominence and development of the parietal eminence may be influenced by observer bias when recording visual observations, ultimately resulting in measurement errors. This type of measurement error may explain some of the inconsistencies that were found when evaluating the results of sex-based differences in the present study and those of earlier investigations (Williams and Rogers, 2006; Suazo and Zavando, 2012; Urban et al., 2016). Finally, a comparison between methods used in the present study and traditional methods was insufficiently explored here. Future work should employ traditional research methods in parallel with the methods adopted in the present study and target using the same samples to facilitate a more comprehensive evaluation of trade-offs between the different approaches. Finally, we note that comparative studies of cranial bone morphology, as performed here, would be worth extending to other bones of the skull besides the parietal bone.

Significant morphological differences are present in the parietal bones of Chinese and European groups. Sex-based differences in the parietal bone are more related to form than shape, with males having absolutely larger parietal bones than females. After removing size from form, sex-based differences in parietal bone shape are predominantly non-significant, although localized differences are still apparent. For example, in terms of mean parietal shape, Chinese females exhibit more contraction at the sphenoidal angle area compared with Chinese males, while there are no significant differences expressed between European females and males. Compared with sex-based differences, regional differences in the parietal bone are more visible, with both shape and form showing significant regional differences. For example, the parietal bone of the Chinese sample is smaller and narrower, with more prominent parietal eminences and a starker transition between the superior and lateral areas, while the parietal bone of the European sample is larger and wider, with a more continuous rounded contour in the superior and lateral areas.

This study was supported by National Key Research and Development Program of China (2023YFF0804502) and the National Natural Science Foundation of China (grant number 42372001).

The authors declare that they have no conflicts of interest.

We thank Xuan Zhang and Yameng Zhang for their efforts in CT scanning the specimens. We would also like to thank the staff of the Dart Collection and the IVPP Collection for their contributions. We extend our gratitude to the editor Dr Reiko Kono for her rigorous editorial review and constructive editorial suggestions.

Yi Yan: conceptualization, methodology, formal analysis, validation, visualization, writing—original draft.

Tea Jashashvili: methodology guidance, writing—review and editing.

Kristian J. Carlson: methodology guidance, writing—review and editing.

Xiujie Wu: supervision, writing—review and editing, resources, funding acquisition.

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