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This study assessed regional diversity in human cranial morphology using a geometric homology model based on scan data from 148 ethnic groups around the world. This method uses template fitting technology to generate homologous meshes by performing non-rigid transformations using an iterative nearest point algorithm. By applying principal component analysis to the 342 selected homologous models, the largest change in overall size was found and clearly confirmed for a small skull from South Asia. The second largest difference is the length to width ratio of the neurocranium, demonstrating the contrast between the elongated skulls of Africans and the convex skulls of Northeast Asians. It’s worth noting that this ingredient has little to do with facial contouring. Well-known facial features such as protruding cheeks in Northeast Asians and compact maxillary bones in Europeans were reaffirmed. These facial changes are closely related to the contour of the skull, in particular the degree of inclination of the frontal and occipital bones. Allometric patterns were found in facial proportions relative to overall skull size; in larger skulls the facial outlines tend to be longer and narrower, as has been demonstrated in many Native Americans and Northeast Asians. Although our study did not include data on environmental variables that may influence cranial morphology, such as climate or dietary conditions, a large data set of homologous cranial patterns will be useful in seeking different explanations for skeletal phenotypic characteristics.
Geographical differences in the shape of the human skull have been studied for a long time. Many researchers have assessed the diversity of environmental adaptation and/or natural selection, in particular climatic factors1,2,3,4,5,6,7 or masticatory function depending on nutritional conditions5,8,9,10, 11,12. 13. . In addition, some studies have focused on bottleneck effects, genetic drift, gene flow, or stochastic evolutionary processes caused by neutral gene mutations14,15,16,17,18,19,20,21,22,23. For example, the spherical shape of a wider and shorter cranial vault has been explained as an adaptation to selective pressure according to Allen’s rule24, which postulates that mammals minimize heat loss by reducing body surface area relative to volume2,4,16,17,25. Additionally, some studies using Bergmann’s rule26 have explained the relationship between skull size and temperature3,5,16,25,27, suggesting that overall size tends to be larger in colder regions to prevent heat loss. The mechanistic influence of masticatory stress on the growth pattern of the cranial vault and facial bones has been debated in relation to dietary conditions resulting from culinary culture or subsistence differences between farmers and hunter-gatherers8,9,11,12,28. The general explanation is that decreased chewing pressure reduces the hardness of the facial bones and muscles. Several global studies have linked skull shape diversity primarily to the phenotypic consequences of neutral genetic distance rather than to environmental adaptation21,29,30,31,32. Another explanation for changes in skull shape is based on the concept of isometric or allometric growth6,33,34,35. For example, larger brains tend to have relatively wider frontal lobes in the so-called “Broca’s cap” region, and the width of the frontal lobes increases, an evolutionary process that is considered based on allometric growth. Additionally, a study examining long-term changes in skull shape found an allometric tendency toward brachycephaly (the tendency of the skull to become more spherical) with increasing height33.
A long history of research into cranial morphology includes attempts to identify the underlying factors responsible for various aspects of the diversity of cranial shapes. Traditional methods used in many early studies were based on bivariate linear measurement data, often using Martin or Howell definitions36,37. At the same time, many of the above-mentioned studies used more advanced methods based on spatial 3D geometric morphometry (GM) technology5,7,10,11,12,13,17,20,27,34,35,38. 39. For example, the sliding semilandmark method, based on bending energy minimization, has been the most commonly used method in transgenic biology. It projects semi-landmarks of the template onto each sample by sliding along a curve or surface38,40,41,42,43,44,45,46. Including such superposition methods, most 3D GM studies use generalized Procrustes analysis, the iterative nearest point (ICP) algorithm 47 to allow direct comparison of shapes and capture of changes. Alternatively, the thin plate spline (TPS)48,49 method is also widely used as a non-rigid transformation method for mapping semilandmark alignments to mesh-based shapes.
With the development of practical 3D whole-body scanners since the late 20th century, many studies have used 3D whole-body scanners for size measurements50,51. Scan data was used to extract body dimensions, which requires describing surface shapes as surfaces rather than point clouds. Pattern fitting is a technique developed for this purpose in the field of computer graphics, where the shape of a surface is described by a polygonal mesh model. The first step in pattern fitting is to prepare a mesh model to use as a template. Some of the vertices that make up the pattern are landmarks. The template is then deformed and conformed to the surface to minimize the distance between the template and the point cloud while preserving the local shape features of the template. Landmarks in the template correspond to landmarks in the point cloud. Using template fitting, all scan data can be described as a mesh model with the same number of data points and the same topology. Although precise homology exists only in the landmark positions, it can be assumed that there is general homology between the generated models since the changes in the geometry of the templates are small. Therefore, grid models created by template fitting are sometimes called homology models52. The advantage of template fitting is that the template can be deformed and adjusted to different parts of the target object that are spatially close to the surface but far from it (for example, the zygomatic arch and the temporal region of the skull) without affecting each other. deformation. In this way, the template can be secured to branching objects such as the torso or arm, with the shoulder in a standing position. The disadvantage of template fitting is the higher computational cost of repeated iterations, however, thanks to significant improvements in computer performance, this is no longer an issue. By analyzing the coordinate values of the vertices that make up the mesh model using multivariate analysis techniques such as principal component analysis (PCA), it is possible to analyze changes in the entire surface shape and virtual shape at any position in the distribution. can be received. Calculate and visualize53. Nowadays, mesh models generated by template fitting are widely used in shape analysis in various fields52,54,55,56,57,58,59,60.
Advances in flexible mesh recording technology, coupled with the rapid development of portable 3D scanning devices capable of scanning at higher resolution, speed, and mobility than CT, are making it easier to record 3D surface data regardless of location. Thus, in the field of biological anthropology, such new technologies enhance the ability to quantify and statistically analyze human specimens, including skull specimens, which is the purpose of this study.
In summary, this study uses advanced 3D homology modeling technology based on template matching (Figure 1) to evaluate 342 skull specimens selected from 148 populations worldwide through geographic comparisons across the globe. Diversity of cranial morphology (Table 1 ). To account for changes in skull morphology, we applied PCA and receiver operating characteristic (ROC) analyzes to the data set of the homology model we generated. The findings will contribute to a better understanding of global changes in cranial morphology, including regional patterns and decreasing order of change, correlated changes between cranial segments, and the presence of allometric trends. Although this study does not address data on extrinsic variables represented by climate or dietary conditions that may influence cranial morphology, the geographic patterns of cranial morphology documented in our study will help explore the environmental, biomechanical, and genetic factors of cranial variation.
Table 2 shows the eigenvalues and PCA contribution coefficients applied to an unstandardized dataset of 17,709 vertices (53,127 XYZ coordinates) of 342 homologous skull models. As a result, 14 main components were identified, the contribution of which to the total variance was more than 1%, and the total share of variance was 83.68%. The loading vectors of the 14 principal components are recorded in Supplementary Table S1, and the component scores calculated for the 342 skull samples are presented in Supplementary Table S2.
This study assessed nine major components with contributions greater than 2%, some of which show substantial and significant geographic variation in cranial morphology. Figure 2 plots curves generated from ROC analysis to illustrate the most effective PCA components for characterizing or separating each combination of samples across major geographic units (e.g., between African and non-African countries). The Polynesian combination was not tested due to the small sample size used in this test. Data regarding the significance of differences in AUC and other basic statistics calculated using ROC analysis are shown in Supplementary Table S3.
ROC curves were applied to nine principal component estimates based on a vertex dataset consisting of 342 male homologous skull models. AUC: Area under the curve at 0.01% significance used to distinguish each geographic combination from other total combinations. TPF is true positive (effective discrimination), FPF is false positive (invalid discrimination).
The interpretation of the ROC curve is summarized below, focusing only on the components that can differentiate comparison groups by having a large or relatively large AUC and a high level of significance with a probability below 0.001. The South Asian complex (Fig. 2a), consisting mainly of samples from India, differs significantly from other geographically mixed samples in that the first component (PC1) has a significantly larger AUC (0.856) compared to the other components. A feature of the African complex (Fig. 2b) is the relatively large AUC of PC2 (0.834). Austro-Melanesians (Fig. 2c) showed a similar trend to Sub-Saharan Africans via PC2 with a relatively larger AUC (0.759). Europeans (Fig. 2d) clearly differ in the combination of PC2 (AUC = 0.801), PC4 (AUC = 0.719) and PC6 (AUC = 0.671), the Northeast Asian sample (Fig. 2e) differs significantly from PC4, with a relatively greater 0.714, and the difference from PC3 is weak (AUC = 0.688). The following groups were also identified with lower AUC values and higher significance levels: Results for PC7 (AUC = 0.679), PC4 (AUC = 0.654) and PC1 (AUC = 0.649) showed that Native Americans (Fig. 2f) with specific characteristics associated with these components, Southeast Asians (Fig. 2g) differentiated across PC3 (AUC = 0.660) and PC9 (AUC = 0.663), but the pattern for samples from the Middle East (Fig. 2h) (including North Africa) corresponded. Compared to others there is not much difference.
In the next step, to visually interpret highly correlated vertices, areas of the surface with high load values greater than 0.45 are colored with X, Y, and Z coordinate information, as shown in Figure 3. The red area shows high correlation with X-axis coordinates, which corresponds to the horizontal transverse direction. The green region is highly correlated with the vertical coordinate of the Y axis, and the dark blue region is highly correlated with the sagittal coordinate of the Z axis. The light blue region is associated with the Y coordinate axes and the Z coordinate axes; pink – mixed area associated with the X and Z coordinate axes; yellow – area associated with the X and Y coordinate axes; The white area consists of the X, Y and Z coordinate axis reflected. Therefore, at this load value threshold, PC 1 is predominantly associated with the entire surface of the skull. The 3 SD virtual skull shape on the opposite side of this component axis is also depicted in this figure, and warped images are presented in Supplementary Video S1 to visually confirm that PC1 contains factors of overall skull size.
Frequency distribution of PC1 scores (normal fit curve), color map of the skull surface is highly correlated with PC1 vertices (explanation of colors relative to The magnitude of opposite sides of this axis is 3 SD. The scale is a green sphere with a diameter of 50 mm.
Figure 3 shows a frequency distribution plot (normal fit curve) of individual PC1 scores calculated separately for 9 geographic units. In addition to the ROC curve estimates (Figure 2), South Asians’ estimates are to some extent significantly skewed to the left because their skulls are smaller than those of other regional groups. As indicated in Table 1, these South Asians represent ethnic groups in India including the Andaman and Nicobar Islands, Sri Lanka and Bangladesh.
The dimensional coefficient was found on PC1. The discovery of highly correlated regions and virtual shapes resulted in the elucidation of form factors for components other than PC1; however, size factors are not always completely eliminated. As shown by comparing the ROC curves (Figure 2), PC2 and PC4 were the most discriminative, followed by PC6 and PC7. PC3 and PC9 are very effective at dividing the sample population into geographic units. Thus, these pairs of component axes schematically depict scatterplots of PC scores and color surfaces highly correlated with each component, as well as virtual shape deformations with dimensions of opposite sides of 3 SD (Figs. 4, 5, 6). The convex hull coverage of samples from each geographic unit represented in these plots is approximately 90%, although there is some degree of overlap within the clusters. Table 3 provides an explanation of each PCA component.
Scatterplots of PC2 and PC4 scores for cranial individuals from nine geographic units (top) and four geographic units (bottom), plots of skull surface color of vertices highly correlated with each PC (relative to X, Y, Z). Color explanation of the axes: see text), and the deformation of the virtual form on opposite sides of these axes is 3 SD. The scale is a green sphere with a diameter of 50 mm.
Scatterplots of PC6 and PC7 scores for cranial individuals from nine geographic units (top) and two geographic units (bottom), cranial surface color plots for vertices highly correlated with each PC (relative to X, Y, Z). Color explanation of the axes: see text), and the deformation of the virtual form on opposite sides of these axes is 3 SD. The scale is a green sphere with a diameter of 50 mm.
Scatterplots of PC3 and PC9 scores for cranial individuals from nine geographic units (top) and three geographic units (bottom), and color plots of the skull surface (relative to X, Y, Z axes) of vertices highly correlated with each PC color interpretation: cm . text), as well as virtual shape deformations on opposite sides of these axes with a magnitude of 3 SD. The scale is a green sphere with a diameter of 50 mm.
In the graph showing the scores of PC2 and PC4 (Fig. 4, Supplementary Videos S2, S3 showing deformed images), the surface color map is also displayed when the load value threshold is set higher than 0.4, which is lower than in PC1 because PC2 value the total load is less than in PC1.
Elongation of the frontal and occipital lobes in the sagittal direction along the Z-axis (dark blue) and the parietal lobe in the coronal direction (red) on pink), the Y-axis of the occiput (green) and the Z-axis of the forehead (dark blue). This graph shows the scores for all people around the world; however, when all samples consisting of a large number of groups are displayed together simultaneously, the interpretation of scattering patterns is quite difficult due to the large amount of overlap; therefore, from only four major geographic units (i.e., Africa, Australasia-Melanesia, Europe, and Northeast Asia), samples are scattered below the graph with 3 SD virtual cranial deformation within this range of PC scores. In the figure, PC2 and PC4 are pairs of scores. Africans and Austro-Melanesians overlap more and are distributed towards the right side, while Europeans are scattered towards the upper left and Northeast Asians tend to cluster towards the lower left. The horizontal axis of PC2 shows that African/Australian Melanesians have a relatively longer neurocranium than other people. PC4, in which the European and northeast Asian combinations are loosely separated, is associated with the relative size and projection of the zygomatic bones and the lateral contour of the calvarium. The scoring scheme shows that Europeans have relatively narrow maxillary and zygomatic bones, a smaller temporal fossa space limited by the zygomatic arch, a vertically elevated frontal bone and a flat, low occipital bone, while Northeast Asians tend to have wider and more prominent zygomatic bones. The frontal lobe is inclined, the base of the occipital bone is raised.
When focusing on PC6 and PC7 (Fig. 5) (Supplementary Videos S4, S5 showing deformed images), the color plot shows a load value threshold greater than 0.3, indicating that PC6 is associated with maxillary or alveolar morphology (red : X axis and green). Y axis), temporal bone shape (blue: Y and Z axes) and occipital bone shape (pink: X and Z axes). In addition to forehead width (red: X-axis), PC7 also correlates with the height of the anterior maxillary alveoli (green: Y-axis) and Z-axis head shape around the parietotemporal region (dark blue). In the top panel of Figure 5, all geographic samples are distributed according to the PC6 and PC7 component scores. Because ROC indicates that PC6 contains features unique to Europe and PC7 represents Native American features in this analysis, these two regional samples were selectively plotted on this pair of component axes. Native Americans, although widely included in the sample, are scattered in the upper left corner; conversely, many European samples tend to be located in the lower right corner. The pair PC6 and PC7 represent the narrow alveolar process and relatively wide neurocranium of Europeans, while Americans are characterized by a narrow forehead, larger maxilla, and a wider and taller alveolar process.
ROC analysis showed that PC3 and/or PC9 were common in Southeast and Northeast Asian populations. Accordingly, the score pairs PC3 (green upper face on the y-axis) and PC9 (green lower face on the y-axis) (Fig. 6; Supplementary Videos S6, S7 provide morphed images) reflect the diversity of East Asians. , which contrasts sharply with the high facial proportions of Northeast Asians and the low facial shape of Southeast Asians. Besides these facial features, another characteristic of some Northeast Asians is the lambda tilt of the occipital bone, while some Southeast Asians have a narrow skull base.
The above description of the main components and the description of PC5 and PC8 have been omitted because no specific regional characteristics were found among the nine main geographic units. PC5 refers to the size of the mastoid process of the temporal bone, and PC8 reflects the asymmetry of overall skull shape, both showing parallel variations between the nine geographic sample combinations.
In addition to scatterplots of individual-level PCA scores, we also provide scatterplots of group means for overall comparison. To this end, an average cranial homology model was created from a vertex data set of individual homology models from 148 ethnic groups. Bivariate plots of the score sets for PC2 and PC4, PC6 and PC7, and PC3 and PC9 are shown in Supplementary Figure S1, all calculated as the average skull model for the sample of 148 individuals. In this way, scatterplots hide individual differences within each group, allowing for clearer interpretation of skull similarities due to underlying regional distributions, where patterns match those depicted in individual plots with less overlap. Supplementary Figure S2 shows the overall mean model for each geographic unit.
In addition to PC1, which was associated with overall size (Supplementary Table S2), allometric relationships between overall size and skull shape were examined using centroid dimensions and sets of PCA estimates from non-normalized data. Allometric coefficients, constant values, t values, and P values in the significance test are shown in Table 4. No significant allometric pattern components associated with overall skull size were found in any cranial morphology at the P < 0.05 level.
Because some size factors may be included in PC estimates based on non-normalized data sets, we further examined the allometric trend between centroid size and PC scores calculated using data sets normalized by centroid size (PCA results and score sets are presented in Supplementary Tables S6) . , C7). Table 4 shows the results of the allometric analysis. Thus, significant allometric trends were found at the 1% level in PC6 and at the 5% level in PC10. Figure 7 shows the regression slopes of these log-linear relationships between PC scores and centroid size with dummies (±3 SD) at either end of the log centroid size. The PC6 score is the ratio of the relative height and width of the skull. As the size of the skull increases, the skull and face become higher, and the forehead, eye sockets and nostrils tend to be closer together laterally. The pattern of sample dispersal suggests that this proportion is typically found in Northeast Asians and Native Americans. Moreover, PC10 shows a trend toward proportional reduction in midface width regardless of geographic region.
For the significant allometric relationships listed in the table, the slope of the log-linear regression between the PC proportion of the shape component (obtained from the normalized data) and the centroid size, the virtual shape deformation has a size of 3 SD on the opposite side of the line of 4.
The following pattern of changes in cranial morphology has been demonstrated through the analysis of datasets of homologous 3D surface models. The first component of PCA relates to overall skull size. It has long been thought that the smaller skulls of South Asians, including specimens from India, Sri Lanka and the Andaman Islands, Bangladesh, are due to their smaller body size, consistent with Bergmann’s ecogeographic rule or island rule613,5,16,25,27,62 . The first is related to temperature, and the second depends on the available space and food resources of the ecological niche. Among the components of shape, the greatest change is the ratio of the length and width of the cranial vault. This feature, designated PC2, describes the close relationship between the proportionally elongated skulls of Austro-Melanesians and Africans, as well as differences from the spherical skulls of some Europeans and Northeast Asians. These characteristics have been reported in many previous studies based on simple linear measurements37,63,64. Moreover, this trait is associated with brachycephaly in non-Africans, which has long been discussed in anthropometric and osteometric studies. The main hypothesis behind this explanation is that decreased mastication, such as thinning of the temporalis muscle, reduces pressure on the outer scalp5,8,9,10,11,12,13. Another hypothesis involves adaptation to cold climates by reducing head surface area, suggesting that a more spherical skull minimizes surface area better than a spherical shape, according to Allen’s rules16,17,25. Based on the results of the current study, these hypotheses can only be assessed based on the cross-correlation of cranial segments. In summary, our PCA results do not fully support the hypothesis that cranial length-width ratio is significantly influenced by chewing conditions, as PC2 (long/brachycephalic component) loading was not significantly related to facial proportions (including relative maxillary dimensions). and the relative space of the temporal fossa (reflecting the volume of the temporalis muscle). Our current study did not analyze the relationship between skull shape and geological environmental conditions such as temperature; however, an explanation based on Allen’s rule may be worth considering as a candidate hypothesis to explain brachycephalon in cold climate regions.
Significant variation was then found in PC4, suggesting that Northeast Asians have large, prominent zygomatic bones on the maxilla and zygomatic bones. This finding is consistent with a well-known specific characteristic of Siberians, who are thought to have adapted to extremely cold climates by forward movement of the zygomatic bones, resulting in increased volume of the sinuses and a flatter face 65 . A new finding from our homologous model is that cheek drooping in Europeans is associated with reduced frontal slope, as well as flattened and narrow occipital bones and nuchal concavity. In contrast, Northeast Asians tend to have sloping foreheads and raised occipital regions. Studies of the occipital bone using geometric morphometric methods35 have shown that Asian and European skulls have a flatter nuchal curve and a lower position of the occiput compared to Africans. However, our scatterplots of PC2 and PC4 and PC3 and PC9 pairs showed greater variation in Asians, whereas Europeans were characterized by a flat base of the occiput and a lower occiput. Inconsistencies in Asian characteristics between studies may be due to differences in the ethnic samples used, as we sampled a large number of ethnic groups from a broad spectrum of Northeast and Southeast Asia. Changes in the shape of the occipital bone are often associated with muscle development. However, this adaptive explanation does not account for the correlation between forehead and occiput shape, which was demonstrated in this study but is unlikely to have been fully demonstrated. In this regard, it is worth considering the relationship between body weight balance and the center of gravity or cervical junction (foramen magnum) or other factors.
Another important component with great variability is related to the development of the masticatory apparatus, represented by the maxillary and temporal fossae, which is described by a combination of scores PC6, PC7 and PC4. These marked reductions in cranial segments characterize European individuals more than any other geographical group. This feature has been interpreted as a result of decreased stability of facial morphology due to the early development of agricultural and food preparation techniques, which in turn reduced the mechanical load on the masticatory apparatus without a powerful masticatory apparatus9,12,28,66. According to the masticatory function hypothesis, 28 this is accompanied by a change in the flexion of the skull base to a more acute cranial angle and a more spherical cranial roof. From this perspective, agricultural populations tend to have compact faces, less protrusion of the mandible, and a more globular meninges. Therefore, this deformation can be explained by the general outline of the lateral shape of the skull of Europeans with reduced masticatory organs. However, according to this study, this interpretation is complex because the functional significance of the morphological relationship between the globose neurocranium and the development of the masticatory apparatus is less acceptable, as considered in previous interpretations of PC2.
The differences between Northeast Asians and Southeast Asians are illustrated by the contrast between a tall face with a sloping occipital bone and a short face with a narrow skull base, as shown in PC3 and PC9. Due to the lack of geoecological data, our study provides only a limited explanation for this finding. A possible explanation is adaptation to a different climate or nutritional conditions. In addition to ecological adaptation, local differences in the history of populations in Northeast and Southeast Asia were also taken into account. For example, in eastern Eurasia, a two-layer model has been hypothesized to understand the dispersal of anatomically modern humans (AMH) based on cranial morphometric data67,68. According to this model, the “first tier”, that is, the original groups of Late Pleistocene AMH colonizers, had more or less direct descent from the indigenous inhabitants of the region, like the modern Austro-Melanesians (p. First stratum). , and later experienced large-scale admixture of northern agricultural peoples with northeast Asian characteristics (second layer) into the region (about 4,000 years ago). Gene flow mapped using a “two-layer” model will be needed to understand Southeast Asian cranial shape, given that Southeast Asian cranial shape may depend in part on local first-level genetic inheritance.
By assessing cranial similarity using geographic units mapped using homologous models, we can infer the underlying population history of AMF in scenarios outside of Africa. Many different “out of Africa” models have been proposed to explain the distribution of AMF based on skeletal and genomic data. Of these, recent studies suggest that AMH colonization of areas outside Africa began approximately 177,000 years ago69,70. However, the long-distance distribution of AMF in Eurasia during this period remains uncertain, since the habitats of these early fossils are limited to the Middle East and the Mediterranean near Africa. The simplest case is a single settlement along a migration route from Africa to Eurasia, bypassing geographical barriers such as the Himalayas. Another model suggests multiple waves of migration, the first of which spread from Africa along the Indian Ocean coast to Southeast Asia and Australia, and then spread into northern Eurasia. Most of these studies confirm that AMF spread far beyond Africa around 60,000 years ago. In this respect, the Australasian-Melanesian (including Papua) samples show greater similarity to African samples than to any other geographic series in principal components analysis of homology models. This finding supports the hypothesis that the first AMF distribution groups along the southern edge of Eurasia arose directly in Africa22,68 without significant morphological changes in response to specific climates or other significant conditions.
Regarding allometric growth, analysis using shape components derived from a different data set normalized by centroid size demonstrated a significant allometric trend in PC6 and PC10. Both components are related to the shape of the forehead and parts of the face, which become narrower as the size of the skull increases. Northeast Asians and Americans tend to have this feature and have relatively large skulls. This finding contradicts previously reported allometric patterns in which larger brains have relatively wider frontal lobes in the so-called “Broca’s cap” region, resulting in increased frontal lobe width34. These differences are explained by differences in sample sets; Our study analyzed allometric patterns of overall cranial size using modern populations, and comparative studies address long-term trends in human evolution related to brain size.
Regarding facial allometry, one study using biometric data78 found that facial shape and size may be slightly correlated, whereas our study found that larger skulls tend to be associated with taller, narrower faces. However, the consistency of biometric data is unclear; Regression tests comparing ontogenetic allometry and static allometry show different results. An allometric tendency towards a spherical skull shape due to increased height has also been reported; however, we did not analyze height data. Our study does show that there is no allometric data demonstrating a correlation between cranial globular proportions and overall cranial size per se.
Although our current study does not deal with data on extrinsic variables represented by climate or dietary conditions that are likely to influence cranial morphology, the large data set of homologous 3D cranial surface models used in this study will help evaluate correlated phenotypic morphological variation. Environmental factors such as diet, climate and nutritional conditions, as well as neutral forces such as migration, gene flow and genetic drift.
This study included 342 specimens of male skulls collected from 148 populations in 9 geographic units (Table 1). Most groups are geographically native specimens, while some groups in Africa, Northeast/Southeast Asia and the Americas (listed in italics) are ethnically defined. Many cranial specimens were selected from the cranial measurement database according to the Martin cranial measurement definition provided by Tsunehiko Hanihara. We selected representative male skulls from all ethnic groups in the world. To identify members of each group, we calculated Euclidean distances based on 37 cranial measurements from the group mean for all individuals belonging to that group. In most cases, we selected the 1–4 samples with the smallest distance from the mean (Supplementary Table S4). For these groups, some samples were randomly selected if they were not listed in the Hahara measurement database.
For statistical comparison, the 148 population samples were grouped into major geographic units, as shown in Table 1. The “African” group consists only of samples from the sub-Saharan region. Specimens from North Africa were included in the “Middle East” along with specimens from West Asia with similar conditions. The Northeast Asian group includes only people of non-European descent, and the American group includes only Native Americans. In particular, this group is distributed over a vast area of the North and South American continents, in a wide variety of environments. However, we consider the US sample within this single geographic unit, given the demographic history of Native Americans considered to be of Northeast Asian origin, regardless of multiple migrations 80 .
We recorded 3D surface data of these contrasting skull specimens using a high-resolution 3D scanner (EinScan Pro by Shining 3D Co Ltd, minimum resolution: 0.5 mm, https://www.shining3d.com/) and then generated a mesh. The mesh model consists of approximately 200,000–400,000 vertices, and the included software is used to fill holes and smooth edges.
In the first step, we used scan data from any skull to create a single-template mesh skull model consisting of 4485 vertices (8728 polygonal faces). The base of the skull region, consisting of the sphenoid bone, petrous temporal bone, palate, maxillary alveoli, and teeth, was removed from the template mesh model. The reason is that these structures are sometimes incomplete or difficult to complete due to thin or thin sharp parts such as pterygoid surfaces and styloid processes, tooth wear and/or inconsistent set of teeth. The skull base around the foramen magnum, including the base, was not resected because this is an anatomically important location for the location of the cervical joints and the height of the skull must be assessed. Use mirror rings to form a template that is symmetrical on both sides. Perform isotropic meshing to convert polygonal shapes to be as equilateral as possible.
Next, 56 landmarks were assigned to the anatomically corresponding vertices of the template model using HBM-Rugle software. Landmark settings ensure the accuracy and stability of landmark positioning and ensure the homology of these locations in the generated homology model. They can be identified based on their specific characteristics, as shown in Supplementary Table S5 and Supplementary Figure S3. According to Bookstein’s definition81, most of these landmarks are Type I landmarks located at the intersection of three structures, and some are Type II landmarks with points of maximum curvature. Many landmarks were transferred from points defined for linear cranial measurements in Martin’s definition 36. We defined the same 56 landmarks for scanned models of 342 skull specimens, which were manually assigned to anatomically corresponding vertices to generate more accurate homology models in the next section.
A head-centric coordinate system was defined to describe the scan data and template, as shown in Supplementary Figure S4. The XZ plane is the Frankfurt horizontal plane that passes through the highest point (Martin’s definition: part) of the superior edge of the left and right external auditory canals and the lowest point (Martin’s definition: orbit) of the lower edge of the left orbit. . The X axis is the line connecting the left and right sides, and X+ is the right side. The YZ plane passes through the middle of the left and right parts and the root of the nose: Y+ up, Z+ forward. The reference point (origin: zero coordinate) is set at the intersection of the YZ plane (midplane), XZ plane (Frankfort plane) and XY plane (coronal plane).
We used HBM-Rugle software (Medic Engineering, Kyoto, http://www.rugle.co.jp/) to create a homologous mesh model by performing template fitting using 56 landmark points (left side of Figure 1). The core software component, originally developed by the Center for Digital Human Research at the Institute of Advanced Industrial Science and Technology in Japan, is called HBM and has functions for fitting templates using landmarks and creating fine mesh models using partitioning surfaces82. The subsequent software version (mHBM) 83 added a feature for pattern fitting without landmarks to improve fitting performance. HBM-Rugle combines mHBM software with additional user-friendly features including customizing coordinate systems and resizing input data. The reliability of software fitting accuracy has been confirmed in numerous studies52,54,55,56,57,58,59,60.
When fitting an HBM-Rugle template using landmarks, the template’s mesh model is superimposed on the target scan data by rigid registration based on ICP technology (minimizing the sum of the distances between the landmarks corresponding to the template and the target scan data), and then by non-rigid deformation of the mesh adapts the template to the target scan data. This fitting process was repeated three times using different values of the two fitting parameters to improve the accuracy of the fitting. One of these parameters limits the distance between the template grid model and the target scan data, and the other penalizes the distance between template landmarks and target landmarks. The deformed template mesh model was then subdivided using the cyclic surface subdivision algorithm 82 to create a more refined mesh model consisting of 17,709 vertices (34,928 polygons). Finally, the partitioned template grid model is fit to the target scan data to generate a homology model. Since the landmark locations are slightly different from those in the target scan data, the homology model was fine-tuned to describe them using the head orientation coordinate system described in the previous section. The average distance between corresponding homologous model landmarks and target scan data in all samples was <0.01 mm. Calculated using the HBM-Rugle function, the average distance between homology model data points and target scan data was 0.322 mm (Supplementary Table S2).
To explain changes in cranial morphology, 17,709 vertices (53,127 XYZ coordinates) of all homologous models were analyzed by principal component analysis (PCA) using HBS software created by the Center for Digital Human Science at the Institute of Advanced Industrial Science and Technology. , Japan (distribution dealer: Medic Engineering, Kyoto, http://www.rugle.co.jp/). We then tried to apply PCA to the unnormalized data set and the data set normalized by centroid size. Thus, PCA based on nonstandardized data can more clearly characterize the cranial shape of the nine geographic units and facilitate component interpretation than PCA using standardized data.
This article presents the number of detected principal components with a contribution of more than 1% of the total variance. To determine the principal components most effective in differentiating groups across major geographic units, receiver operating characteristic (ROC) analysis was applied to principal component (PC) scores with a contribution greater than 2% 84 . This analysis generates a probability curve for each PCA component to improve classification performance and correctly compare plots between geographic groups. The degree of discriminatory power can be assessed by the area under the curve (AUC), where PCA components with larger values are better able to discriminate between groups. A chi-square test was then performed to assess the level of significance. ROC analysis was performed in Microsoft Excel using Bell Curve for Excel software (version 3.21).
To visualize geographic differences in cranial morphology, scatterplots were created using PC scores that most effectively distinguished groups from major geographic units. To interpret principal components, use a color map to visualize model vertices that are highly correlated with principal components. In addition, virtual representations of the ends of the principal component axes located at ±3 standard deviations (SD) of the principal component scores were calculated and presented in the supplemental video.
Allometry was used to determine the relationship between skull shape and size factors assessed in the PCA analysis. The analysis is valid for principal components with contributions >1%. One limitation of this PCA is that shape components cannot individually indicate shape because the non-normalized data set does not remove all dimensional factors. In addition to using unnormalized data sets, we also analyzed allometric trends using PC fraction sets based on normalized centroid size data applied to principal components with contributions >1%.
Allometric trends were tested using the equation Y = aXb 85 where Y is the shape or proportion of a shape component, X is the centroid size (Supplementary Table S2), a is a constant value, and b is the allometric coefficient. This method basically introduces allometric growth studies into geometric morphometry78,86. The logarithmic transformation of this formula is: log Y = b × log X + log a. Regression analysis using the least squares method was applied to calculate a and b. When Y (centroid size) and X (PC scores) are logarithmically transformed, these values must be positive; however, the set of estimates for X contains negative values. As a solution, we added rounding to the absolute value of the smallest fraction plus 1 for each fraction in each component and applied a logarithmic transformation to all converted positive fractions. The significance of allometric coefficients was assessed using a two-tailed Student’s t test. These statistical calculations to test allometric growth were performed using Bell Curves in Excel software (version 3.21).
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Post time: Apr-02-2024