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The authors have declared that no competing interests exist.

The cranium is an anatomically complex structure. One source of its complexity is due to its modular organization. Cranial modules are distinct and partially independent units that interact substantially during ontogeny thus generating morphological integration. Artificial Cranial Deformation (ACD) occurs when the human skull is intentionally deformed, through the use of different deforming devices applied to the head while it is developing. Hence, ACD provides an interesting example to assess the degree to which biomechanical perturbations of the developing neurocranium impact on the degree of morphological integration in the skull as a whole. The main objective of this study was to assess how ACD affects the morphological integration of the skull. This was accomplished by comparing a sample of non-deformed crania and two sets of deformed crania (i.e. antero-posterior and oblique). Both developmental and static modularity and integration were assessed through Generalized Procrustes Analysis by considering the symmetric and asymmetric components of variation in adults, using 3D landmark coordinates as raw data. The presence of two developmental modules (i.e. viscero and neurocranium) in the skull was tested. Then, in order to understand how ACD affects morphological integration, the covariation pattern between the neuro and viscerocranium was examined in antero-posterior, oblique and non-deformed cranial categories using Partial Least-Squares. The main objective of this study was to assess how ACD affects the morphological integration of the skull. This was accomplished by comparing a sample of deformed (i.e. antero-posterior and oblique) and non-deformed crania. Hence, differences in integration patterns were compared between groups. The obtained results support the modular organization of the human skull in the two analyzed modules. The integration analyses show that the oblique ACD style differentially affects the static morphological integration of the skull by increasing the covariance between neuro and viscerocranium in a more constrained way than in antero-posterior and non-deformed skulls. In addition, the antero-posterior ACD style seems to affect the developmental integration of the skull by directing the covariation pattern in a more defined manner as compared to the other cranial categories.

There is longstanding scientific tradition that has analyzed the complex nature of human skull using developmental [

Morphological integration and modularity has been studied in skulls by defining modules based in its differential embryological origin: the viscerocranium -derived from branchial arches-, and the neurocranium—derived from neural crest and paraxial mesoderm cells [

In the present study artificial cranial deformation (ACD) is used as a proxy for assessing the morphological integration and modularity of the human skull. ACD consists in the modification of the magnitude and direction of the normal vectors of growth and development of the skull, by using compressive forces generated by deforming devices during the early years of post-natal life [

Considering that the ACD constrains the skull’s normal ontogenetic growth direction, it would be expected that the expansion of the encephalon will continue generating internal pressures that will be redirected towards those areas of the cranial vault that are not restricted by the application of the deforming device. In fact, it has been shown that ACD typically generates some amount of compensatory growth in the sutures [

The sample comprised 269 archaeological skulls from Northern Chile (^{™} (

3D surfaces of the different cranial categories analyzed in the present paper and their corresponding anatomical views.

Origin | Antero-posterior | Non-deformed | Oblique |
---|---|---|---|

5 | 5 | 16 | |

4 | 31 | 10 | |

0 | 0 | 20 | |

8 | 4 | 5 | |

8 | 10 | 2 | |

3 | 5 | 0 | |

4 | 11 | 0 | |

0 | 2 | 1 | |

4 | 3 | 2 | |

0 | 5 | 1 | |

4 | 5 | 0 | |

8 | 3 | 1 | |

4 | 8 | 5 | |

1 | 2 | 3 | |

12 | 9 | 1 | |

4 | 11 | 4 | |

0 | 3 | 0 | |

2 | 1 | 1 | |

1 | 0 | 2 | |

2 | 0 | 3 | |

Origin of the analyzed sample (archaeological site), and type of artificial cranial deformation. Skulls are housed at Museo Arqueológico R.P. Gustavo Le Paige, San Pedro de Atacama

Chile, excluding Chorrillos (Corporación Cultural y de Turismo, Calama, Chile), and

Chunchuri (Musée de l’Homme, Paris, France).

This first step was followed by a geometric morphometrics generalized Procrustes superimposition of landmark data. This branch of shape analysis has been usually understood as the quantitative study of shape and its covariates [

An oblique artificially deformed skull from the archaeological site of Chorrillos is shown (blue = neurocranium; fuchsia = viscerocranium).

Number | Name | Definition | Module |
---|---|---|---|

Prostion (pr) | The most anterior point on the alveolar ridge of the maxilla between the central incisors in the median sagittal plane. | Viscerocranium | |

Nasospinale (ns) | The lowest point of the lower border of the piriform aperture, projected into the median sagittal plane. | Viscerocranium | |

Nasion (n) | Crossing point of the frontonasal suture with the median sagittal. | Viscerocranium | |

Glabella (g) | Most anterior point, in the mediansagittal, betwen the superciliary arches | Neurocranium | |

Bregma (b) | The point at which the sagittal suture meets the coronal suture. | Neurocranium | |

Lambda (l) | The point at which the two parts of the lambdoidal suture meet the sagittal suture. | Neurocranium | |

Inion (i) | The point in the median sagittal plane, in which the two superior nuchal lines join. | Neurocranium | |

Opistion (o) | The point at which the posterior border of the foramen magnum is cut by the medial sagittal plane. | Neurocranium | |

Basion (ba) | The point at which the anterior margin of the foramen magnum is cross by the median sagittal plane. | Neurocranium | |

Sphenobasion (sphba) | Intersection of the sphenooccipitalsynchondrosis with the median sagittal plane. | Neurocranium | |

Zygomaxillare (rzm) | Lowest point of the right zygomaticomaxillary suture | Viscerocranium | |

Zygoorbitale (rzo) | Upper point of the right zygomaticomaxillary suture. | Viscerocranium | |

Frontomalare orbitale (rfmo) | The only point on the lateral right orbital rim, at which it is cross by the frontozygomatic suture. | Viscerocranium | |

Auriculare (rau) | The point that is perpendicular to the center of the right porus acusticus externus located on the zygomatic root. | Neurocranium | |

Entomion (ren) | The point at which the right squamous suture passes into the right parietomastoidea suture. | Neurocranium | |

Asterion (rast) | The point at which the right lambdoidea, occipitomastoid and parieto-mastoid the sutures meet. | Neurocranium | |

Mastoideale (rms) | The most inferior point of the right mastoid process. | Neurocranium | |

Krotaphion (rk) | The posterior point of the right sphenoparietalis suture | Neurocranium | |

Sphenion (rsphn) | The anterior point of the rigth sphenoparietalis suture | Neurocranium | |

Stephanion (rst) | The point where the coronal suture meets the right temporal line | Neurocranium | |

Obelion (ob) | The point between a transverse line connecting the two parietal foramina and the sagittal suture. | Neurocranium |

Number, name, definition, and location of the landmarks used for carrying out the geometric morphometrics workflow.

Human skulls exhibit object symmetry (i.e. the axis of symmetry passes through mid-plane, and hence the left and right halves are mirror images of each other), therefore the recommendations of [

As previously mentioned, depending on the processes responsible for integration and modularity, several levels of integration can be distinguished (e.g. static, developmental, evolutionary, among others) [

From a morphometric point of view, modularity is manifested as a strong correlation within the components of a module, versus a weak covariation between modules [

In the present study, two hypothetical modules were proposed based on developmental grounds for the whole sample: the a) viscerocranium and the b) neurocranium. The two proposed modules are parts of the cranium, being consequently spatially adjacent and within the same structure. Therefore, the analysis was restricted to the generation of only spatially contiguous configurations [

The morphological integration of the skull components was analyzed by means of a partial least-squares analysis (PLS) [

Finally, in order to quantify the overall similarity of covariance matrices, matrix correlations and the associated permutation tests were computed, using procedures adapted for geometric morphometrics and object symmetry [

In geometric morphometrics, hypothesis testing is based on the linear properties of the vectors obtained after applying Procrustes analysis onto the raw data (2 o 3 dimensional landmark coordinates). Later those vectors (i.e. the shape and size components of form) are used as analogs of the traditional interlandmark ("point to point") vectors. As a result, the linearity of the shape vectors allow to apply the toolkit of standard multivariate statistical analyses in order to explore (i.e. PCA), and contrast (i.e. CVA, PERMANOVA, PLS) hypotheses for assessing the pattern of observed shape variation.

The Procustes ANOVA used to measure intra-observer error in the sub-sample showed that the mean square for individual variation exceeded measurement error, so the effect of measurement error was negligible (see

Antero-posteriorly deformed and non-deformed skulls were significantly different (Mahalanobis distance: 3.2198; P-value: <0.0001; 10.000 perm.), as well as antero-posterior and oblique deformed crania (Mahalanobis distance: 3.2177; P-value: <0.0001; 10.000 perm.) and non-deformed and oblique skulls (Mahalanobis distance: 2.8743; P-value: <0.0001; 10.000 perm.). There was only a slight overlap between them (

The ellipses represent the 90% confidence intervals.

Morphological variation was relatively widespread in the different PCs obtained from the symmetric component. The first two components accounted for 24.39% and 10.17% of the total shape variation, respectively, depicting some group separation along PC1between deformation types and non-deformed skulls (

The ellipses represent the 90% confidence intervals.

There were significant differences between the shape of the different cranial categories when comparing them using the PERMANOVA (

Cranial category | F-test | R^{2} |
Adjusted P-value |
---|---|---|---|

29.77004 | 0.16652702 | 0.003 | |

26.02839 | 0.12048598 | 0.003 | |

19.4387 | 0.09150263 | 0.003 |

Pairwise PERMANOVA tests used to test for shape differences between cranial categories.

The CR tests applied to test the null hypothesis that the human skull does not show a modular behavior between viscero and neurocranium was rejected for both the symmetric (CR: 0.846; P-value: 0.007; 10.000 perm.) and the asymmetric (CR: 0.637; P-value: 0.023; 10.000 perm.) components of variation. This null hypothesis was also rejected when running the analyses separately for each one of the categories under analysis (i.e. antero-posterior, non-deformed and oblique crania) (see

The analysis identified the characteristics of shape variation that most covary between the two blocks and highlighted their relative contribution to the total amount of covariation between blocks (Tables

The ellipses represent the 90% confidence intervals.

a) Antero-posterior; b) Non-deformed and; c) Oblique.

Type of shape component | PLS | Singular value | P-value (perm.) | % total covariance | Correlation | P-value (perm.) |
---|---|---|---|---|---|---|

PLS1 | 0.00033482 | <0.0001 | 73.55 | 0.85774 | <0.0001 | |

PLS2 | 0.0001568 | <0.0001 | 16.131 | 0.93347 | <0.0001 | |

PLS3 | 0.00008937 | <0.0001 | 5.24 | 0.55733 | 0.0018 | |

PLS4 | 0.00005396 | <0.0001 | 1.91 | 0.45688 | 0.0006 | |

PLS5 | 0.00003998 | <0.0001 | 1.049 | 0.38626 | 0.0027 | |

PLS6 | 0.00003208 | <0.0001 | 0.675 | 0.4065 | <0.0001 | |

PLS7 | 0.00002996 | <0.0001 | 0.589 | 0.37694 | 0.0007 | |

PLS8 | 0.00001957 | 0.0054 | 0.251 | 0.34792 | 0.0018 | |

PLS9 | 0.00001893 | <0.0001 | 0.235 | 0.31456 | 0.007 | |

PLS10 | 0.00001563 | 0.0002 | 0.16 | 0.34212 | 0.0003 | |

PLS11 | 0.00001043 | 0.2282 | 0.071 | 0.28316 | 0.0108 | |

PLS12 | 0.00000843 | 0.4457 | 0.047 | 0.22377 | 0.1982 | |

PLS13 | 0.00000753 | 0.2289 | 0.037 | 0.17127 | 0.719 | |

PLS14 | 0.00000578 | 0.5397 | 0.022 | 0.18892 | 0.2476 | |

PLS15 | 0.00000519 | 0.2268 | 0.018 | 0.20055 | 0.0414 | |

PLS16 | 0.00000437 | 0.1146 | 0.013 | 0.16144 | 0.1452 | |

PLS17 | 0.00000214 | 0.699 | 0.003 | 0.17011 | 0.0831 | |

PLS1 | 0.00004092 | < .0001 | 76.517 | 0.85205 | < .0001 | |

PLS2 | 0.0000178 | < .0001 | 14.478 | 0.64862 | < .0001 | |

PLS3 | 0.00000822 | 0.0079 | 3.089 | 0.51247 | < .0001 | |

PLS4 | 0.00000745 | 0.0001 | 2.537 | 0.28785 | 0.0584 | |

PLS5 | 0.0000058 | 0.0007 | 1.537 | 0.30112 | 0.0065 | |

PLS6 | 0.00000392 | 0.0667 | 0.703 | 0.23064 | 0.2107 | |

PLS7 | 0.00000316 | 0.0671 | 0.456 | 0.21981 | 0.205 | |

PLS8 | 0.00000237 | 0.1713 | 0.257 | 0.24704 | 0.0407 | |

PLS9 | 0.00000219 | 0.0137 | 0.218 | 0.21242 | 0.1552 | |

PLS10 | 0.00000144 | 0.3728 | 0.094 | 0.2071 | 0.0821 | |

PLS11 | 0.00000116 | 0.3329 | 0.061 | 0.1865 | 0.085 | |

PLS12 | 0.00000083 | 0.4822 | 0.032 | 0.10635 | 0.8422 | |

PLS13 | 0.00000069 | 0.0815 | 0.022 | 0.13983 | 0.2208 |

Singular values and pairwise correlations of the PLS scores between corresponding blocks (i.e. neurocranium and viscerocranium) for the complete dataset (10.000 perm.).

Cranial category | PLS | Singular value | P-value (perm.) | % total covariance | Correlation | P-value (perm.) |
---|---|---|---|---|---|---|

PLS1 | 0.00022702 | <0.0001 | 52.957 | 0.84244 | <0.0001 | |

PLS2 | 0.00014615 | <0.0001 | 21.948 | 0.80669 | <0.0001 | |

PLS3 | 0.00009995 | <0.0001 | 10.266 | 0.59511 | 0.2154 | |

PLS4 | 0.00007074 | 0.005 | 5.142 | 0.50818 | 0.4959 | |

PLS5 | 0.00005088 | 0.1631 | 2.66 | 0.59985 | 0.0259 | |

PLS6 | 0.00004936 | 0.0045 | 2.504 | 0.55449 | 0.0557 | |

PLS7 | 0.00003657 | 0.1146 | 1.374 | 0.44052 | 0.5675 | |

PLS8 | 0.00003181 | 0.0728 | 1.039 | 0.51616 | 0.0648 | |

PLS9 | 0.00002688 | 0.0906 | 0.742 | 0.47659 | 0.147 | |

PLS10 | 0.00002189 | 0.2138 | 0.492 | 0.42679 | 0.3276 | |

PLS11 | 0.00001675 | 0.6639 | 0.288 | 0.42802 | 0.202 | |

PLS12 | 0.00001426 | 0.6423 | 0.209 | 0.35027 | 0.6087 | |

PLS13 | 0.00001172 | 0.713 | 0.141 | 0.3684 | 0.3146 | |

PLS14 | 0.00001034 | 0.4734 | 0.11 | 0.30987 | 0.5///849 | |

PLS15 | 0.00000846 | 0.4329 | 0.074 | 0.28601 | 0.5716 | |

PLS16 | 0.00000594 | 0.6884 | 0.036 | 0.31792 | 0.1609 | |

PLS17 | 0.00000413 | 0.6133 | 0.018 | 0.20155 | 0.8294 | |

PLS1 | 0.00015927 | <0.0001 | 51.948 | 0.91448 | <0.0001 | |

PLS2 | 0.00010278 | <0.0001 | 21.632 | 0.84507 | <0.0001 | |

PLS3 | 0.00007465 | <0.0001 | 11.413 | 0.621 | 0.0335 | |

PLS4 | 0.00004542 | 0.0205 | 4.225 | 0.51909 | 0.0647 | |

PLS5 | 0.00003983 | 0.0042 | 3.249 | 0.52602 | 0.0098 | |

PLS6 | 0.00003433 | 0.0016 | 2.413 | 0.43808 | 0.1617 | |

PLS7 | 0.00003128 | 0.0001 | 2.003 | 0.47722 | 0.0111 | |

PLS8 | 0.00002324 | 0.0168 | 1.106 | 0.38172 | 0.31 | |

PLS9 | 0.00001893 | 0.0671 | 0.734 | 0.35914 | 0.3731 | |

PLS10 | 0.000014 | 0.5889 | 0.402 | 0.37862 | 0.1328 | |

PLS11 | 0.00001231 | 0.4508 | 0.311 | 0.32843 | 0.3824 | |

PLS12 | 0.00001062 | 0.3832 | 0.231 | 0.33221 | 0.2094 | |

PLS13 | 0.0000077 | 0.8936 | 0.122 | 0.3121 | 0.2286 | |

PLS14 | 0.00000725 | 0.5126 | 0.107 | 0.2775 | 0.3353 | |

PLS15 | 0.00000498 | 0.9274 | 0.051 | 0.17241 | 0.9729 | |

PLS16 | 0.00000431 | 0.6768 | 0.038 | 0.18569 | 0.7411 | |

PLS17 | 0.0000028 | 0.5845 | 0.016 | 0.25283 | 0.1212 | |

PLS1 | 0.00036424 | <0.0001 | 75.467 | 0.87452 | <0.0001 | |

PLS2 | 0.00014999 | <0.0001 | 12.797 | 0.92793 | <0.0001 | |

PLS3 | 0.00007936 | 0.0258 | 3.582 | 0.67348 | 0.0249 | |

PLS4 | 0.0000714 | 0.0009 | 2.9 | 0.57496 | 0.1397 | |

PLS5 | 0.00005595 | 0.0068 | 1.781 | 0.54332 | 0.1515 | |

PLS6 | 0.00004043 | 0.2076 | 0.93 | 0.55662 | 0.0409 | |

PLS7 | 0.00003977 | 0.0046 | 0.9 | 0.46563 | 0.3604 | |

PLS8 | 0.00003243 | 0.0112 | 0.598 | 0.50844 | 0.0653 | |

PLS9 | 0.00002395 | 0.2544 | 0.326 | 0.35908 | 0.8733 | |

PLS10 | 0.00002257 | 0.0313 | 0.29 | 0.49321 | 0.0333 | |

PLS11 | 0.00001596 | 0.5815 | 0.145 | 0.43106 | 0.1573 | |

PLS12 | 0.0000148 | 0.195 | 0.125 | 0.53239 | 0.0016 | |

PLS13 | 0.00001192 | 0.3287 | 0.081 | 0.38458 | 0.2015 | |

PLS14 | 0.00000834 | 0.8654 | 0.04 | 0.37618 | 0.1294 | |

PLS15 | 0.00000618 | 0.9523 | 0.022 | 0.28098 | 0.6061 | |

PLS16 | 0.00000473 | 0.9139 | 0.013 | 0.26312 | 0.4833 | |

PLS17 | 0.00000305 | 0.7927 | 0.005 | 0.1995 | 0.8789 |

Symmetric component.

Cranial category | PLS | Singular value | P-value (perm.) | % total covariance | Correlation | P-value (perm.) |
---|---|---|---|---|---|---|

PLS1 | 0.00006503 | <0.0001 | 74.488 | 0.89509 | <0.0001 | |

PLS2 | 0.00003158 | <0.0001 | 17.57 | 0.69941 | 0.0005 | |

PLS3 | 0.00001375 | 0.3215 | 3.332 | 0.47458 | 0.2284 | |

PLS4 | 0.00001025 | 0.45 | 1.85 | 0.48418 | 0.0982 | |

PLS5 | 0.00000868 | 0.2264 | 1.327 | 0.53345 | 0.0086 | |

PLS6 | 0.00000586 | 0.7514 | 0.606 | 0.42417 | 0.184 | |

PLS7 | 0.00000414 | 0.9481 | 0.303 | 0.35894 | 0.4781 | |

PLS8 | 0.00000377 | 0.6266 | 0.25 | 0.31224 | 0.7608 | |

PLS9 | 0.00000258 | 0.948 | 0.117 | 0.40304 | 0.1411 | |

PLS10 | 0.00000199 | 0.9701 | 0.07 | 0.2755 | 0.803 | |

PLS11 | 0.00000157 | 0.9498 | 0.044 | 0.21466 | 0.9477 | |

PLS12 | 0.00000145 | 0.5391 | 0.037 | 0.18816 | 0.9472 | |

PLS13 | 0.00000062 | 0.9791 | 0.007 | 0.24791 | 0.3926 | |

PLS1 | 0.00003401 | <0.0001 | 70.459 | 0.83665 | <0.0001 | |

PLS2 | 0.00001627 | <0.0001 | 16.118 | 0.68219 | <0.0001 | |

PLS3 | 0.00000932 | 0.1208 | 5.287 | 0.43128 | 0.1304 | |

PLS4 | 0.00000723 | 0.2256 | 3.18 | 0.42484 | 0.0507 | |

PLS5 | 0.00000574 | 0.3121 | 2.005 | 0.35483 | 0.2513 | |

PLS6 | 0.00000421 | 0.6866 | 1.08 | 0.32847 | 0.2929 | |

PLS7 | 0.00000375 | 0.3475 | 0.858 | 0.20194 | 0.989 | |

PLS8 | 0.00000251 | 0.8762 | 0.383 | 0.3035 | 0.2943 | |

PLS9 | 0.00000205 | 0.8267 | 0.257 | 0.3019 | 0.2034 | |

PLS10 | 0.00000173 | 0.6797 | 0.183 | 0.23182 | 0.6427 | |

PLS11 | 0.00000129 | 0.7887 | 0.102 | 0.19566 | 0.7694 | |

PLS12 | 0.00000105 | 0.5824 | 0.067 | 0.15091 | 0.9182 | |

PLS13 | 0.00000059 | 0.8039 | 0.021 | 0.12506 | 0.9397 | |

PLS1 | 0.00003953 | <0.0001 | 67.032 | 0.85317 | <0.0001 | |

PLS2 | 0.0000171 | 0.1233 | 12.547 | 0.58171 | 0.0527 | |

PLS3 | 0.00001355 | 0.1152 | 7.871 | 0.52199 | 0.0853 | |

PLS4 | 0.00001037 | 0.2228 | 4.615 | 0.49875 | 0.0577 | |

PLS5 | 0.00000889 | 0.0825 | 3.391 | 0.36861 | 0.6503 | |

PLS6 | 0.00000649 | 0.3315 | 1.807 | 0.35462 | 0.6034 | |

PLS7 | 0.00000511 | 0.4062 | 1.121 | 0.31515 | 0.7753 | |

PLS8 | 0.00000426 | 0.2876 | 0.779 | 0.30781 | 0.7411 | |

PLS9 | 0.00000266 | 0.9539 | 0.303 | 0.34745 | 0.3425 | |

PLS10 | 0.00000244 | 0.6727 | 0.256 | 0.2689 | 0.7634 | |

PLS11 | 0.00000199 | 0.5659 | 0.17 | 0.27819 | 0.4924 | |

PLS12 | 0.00000133 | 0.7774 | 0.076 | 0.13281 | 0.9981 | |

PLS13 | 0.00000087 | 0.6378 | 0.032 | 0.18318 | 0.8439 |

Asymmetric component

The overall integration of shape variation component measured using the r-PLS was 0.826 (P-value: 0.001; 10.000 perm.), whilst the PLS1 axes explained 76.52% of the total covariance of the sample (P-value: <0.001; 10.000 perm.). This value was relatively similar to the ones obtained for the antero-posterior (r-PLS: 0.879; P-value: 0.001; 10.000 perm.) and oblique (r-PLS: 0.868; P-value:0.001; 10.000 perm.) crania, while the non-deformed skulls showed a lower integration value (r-PLS: 0.735; P-value:0.001; 10.000 perm.). Both oblique (PLS1: 67.03% of explained covariance; P-value: <0.001; 10.000 perm.) and non-deformed skulls (PLS1: 70.46% of explained covariance; P-value: <0.001; 10.000 perm.) exhibited a similar distribution of explained covariance by their PLS axes. However, the antero-posterior deformed crania a higher level of integration in their first PLS axes (PLS1: 74.49% of explained covariance; P-value: <0.001; 10.000 perm.) (

From all the possible comparisons between the paired singular axes between non-deformed skulls and the antero-posterior and oblique crania, only a few of them were significant. Below are presented the comparisons that were significant for the two PLS axes that accounted for the majority of the total covariance for the symmetric component.

Antero-posterior PLS2 v/s non-deformed PLS2 (θ = 62.762°; P-value = 0.00094)

Antero-posterior PLS1 v/s oblique PLS1 (θ = 61.069°; P-value = 0.00043)

Antero-posterior PLS1 v/s oblique PLS2 (θ = 64.017°; P-value = 0.00164)

Non-deformed PLS1 v/s oblique PLS2 (θ = 14.579°; P-value <0.00001)

Non-deformed PLS2 v/s oblique PLS1 (θ = 41.117°; P-value <0.00001)

From all the possible comparisons between the paired singular axes between non-deformed skulls and the antero-posterior deformed and oblique crania, just few of them were significant. Below are presented the comparisons that were significant for the two PLS axes that accounted for the majority of the total covariance for the asymmetric component.

Antero-posterior PLS1 v/s non-deformed PLS1 (θ = 39.064°; P-value <0.00001)

Antero-posterior PLS2 v/s non-deformed PLS2 (θ = 42.940°; P-value <0.00001)

Antero-posterior PLS1 v/s oblique PLS1 (θ = 28.325°; P-value <0.00001)

Non-deformed PLS1 v/s oblique PLS1 (θ = 30.414°; P-value <0.00001)

The PC’s and PLS axes of the complete dataset were compared using the same procedure outlined above in order to test whether the observed pattern of variation (PC’s) followed a similar trend as the observed patterns of covariation between viscero- and neurocranium (PLS axes). In a similar fashion, from all the possible comparisons only a few of them were significant (Symmetric component: θ PC1 v/s PLS1 = 13.361°, P-value <0.00001; Asymmetric component: θ PC1 v/s PLS1 = 34.190°, P-value <0.00001; θ PC2 v/s PLS2 = 49.545°, P-value <0.00001).

The matrix correlation between the covariance matrices for the symmetric and asymmetric components of variation for the complete dataset was 0.638 (P-value: < 0.0001; 10.000 perm.). Below are presented the pairwise matrix correlation results for the different cranial categories for both the symmetric and asymmetric component of variation.

Antero-posterior v/s non-deformed: 0.618 (P-value: < 0.0001; 10.000 perm.).

Antero-posterior v/s oblique: 0.592 (P-value: < 0.0001; 10.000 perm.).

Non-deformed v/s oblique: 0.750 (P-value: < 0.0001; 10.000 perm.).

Antero-posterior v/s non-deformed: 0.754 (P-value: < 0.0001; 10.000 perm.).

Antero-posterior v/s oblique: 0.745 (P-value: < 0.0001; 10.000 perm.).

Non-deformed v/s oblique: 0.873 (P-value: < 0.0001; 10.000 perm.).

The PCA showed that even though there is morphological continuum ranging from one deforming type to the other (with non-deformed individuals relatively in between), it is possible to notice differences between the analyzed cranial categories. This was confirmed when running the pairwise PERMANOVAs and CVA analysis since highly significant differences between the two deforming styles and the non-deformed crania were observed. There was a slight overlap between the groups that was expected and coherent with the morphological continuum outlined above. It is interesting that in spite of the several proposed classifications to define deforming styles [

The null hypothesis stating that there was no modular behavior on the skull based on two different developmental origins was rejected. For the symmetric component of variation, the CR coefficient was significantly lower than one, thus suggesting that there was a degree of independence between the two modules. The asymmetric component also showed a lower and significant CR value, which suggest a strong degree of independence between the two modules. Thus, there is support for the hypothesis that the human cranium displays significant modularity when compared to the null hypothesis of no modular structure. It is relevant to keep in mind that modularity and integration are not two ends of the same continuum, thus it is perfectly possible to have both modularity and integration in the same dataset as in the present case. Modularity implies greater covariation of variables within modules than between them, whereas integration means that two modules are more correlated than it would be expected from chance by random arrangements of pairs of observations from each module. Hence, it is possible to have both integration between modules and modularity within them.

Regarding the static morphological integration of the human cranium, it seems that the different categories analyzed here show relatively similar overall levels of integration as observed in their r-PLS values. Nevertheless, the oblique deforming style appears to constrain the strength of static covariation between the viscero and the neurocranium in a more defined direction as compared with both the antero-posterior crania and the non-deformed skulls (

Conversely, the developmental integration analysis showed that non-deformed skulls exhibit an overall lower level of integration as compared to the deformed skulls as shown by their r-PLS values. This might mean that the deforming styles increase the covariation between the asymmetric components of the neuro and viscerocranium. This means that an increased asymmetry in one of these cranial parts would generate a stronger increase of the asymmetry of the other skull compartment as compared to the non-deformed skulls, or a decreased asymmetry in one block would produce a stronger decrease of the asymmetry of the other cranial portion. In addition, the antero-posterior deformed crania showed a higher level of developmental integration in their first PLS axes (PLS1: 74.488% of explained covariance; P-value: <0.001; 1,000 perm.), which suggests that this particular deforming style directs the covariation between the two cranial blocks in a more directed way (i.e. it is less distributed in other directions of covariation).

ACD affects the morphological integration of the skull, showing a particular covariation trend depending on the deforming style [

Another perhaps more important explanation to the different degree of integration between modules in deformed and non-deformed crania, is the change in the normal loads acting on cranial bones during ACD. There is an important role of mechanical loads in bone growth and development [

When quantitatively testing if the observed covariation patterns were similar or not depending on the analyzed cranial category, the angular comparison between the PLS vectors shown that the majority of them were dissimilar (i.e. their angular difference was near 90°). However, there were some significant similarities between some PLS axes that could be related to the fact that despite the differences in the intensity of the covariation, the overall covariation pattern could be relatively similar. The angular comparison analyses also showed that there was a significant relationship between the PC’s and the PLS axes, thus indicating that the patterns of observed variation are in concordance with the observed covariation patterns between viscero and neurocranium. This could mean that the observed variation in cranial shape is due to the morphological integration of the skeletal face and cranial vault.

Finally, the matrix correlation analysis between the symmetric and asymmetric components of variation showed a moderate-to-high value. When carried out the matrix correlations by separating the different cranial categories it was observed that for both the symmetric and asymmetric components of variation, non-deformed skulls are more similar to the oblique crania. This seems to indicate that in spite of the increased static covariation observed in PLS1 of the oblique crania, they are more similar to the non-deformed condition. These results are concordant with the CVA results that showed that antero-posterior deformed skulls are the most different of the three cranial categories.

The results from this research show that there is a modular organization of the human skull (i.e. neuro and viscerocranium). Furthermore, the present results show that the strength of the morphological integration between the neurocranium and viscerocranium is differentially augmented depending on the applied force vectors on the skull (i.e. oblique deforming style). Compressive forces onto the parietal bones (i.e. oblique ACD) increases the static morphological integration between these two anatomical regions, while compressive forces onto the occipital and frontal bones (i.e. antero-posterior ACD), increases the developmental integration of the skull. Although the underlying cause of this phenomenon is still unknown, it could be related with the specific mechanisms constraining the normal expansion of the brain and how this affects the normal growth and development of the skull. Further analyses are required to get a better insight of the possible effects of ACD on human biology. One interesting approach would be to use the present results to carefully design a biomechanical simulation of the growing skull while simulating compressive forces as proxies for the different deforming devices.

Individual numbers and complete repository information, including museum name and geographic location.

(CSV)

Mean squares values, degrees of freedom (df), F statistic, and statistical significance (P value) of intra-observer error.

(CSV)

Linear Discriminant Analysis using the Procrustes coordinates of the first 11 PCs after a broken-stick model for 3 classes /'Antero-Posterior', 'Non.deformed', 'Oblique'/.

(CSV)

CR coefficients obtained from permutation tests (999 rounds) of alternative partitions of a) the complete dataset, b) antero-posterior deformed skulls, c) non-deformed crania and d) the oblique sample, with the observed CR coefficients designated by a red arrow. Both the symmetric and asymmetric components of shape variation were analyzed.

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a) the Complete dataset, as welll as for the different cranial categories under analysis b) Antero-posterior; c) Non-deformed and; d) Oblique.

(PDF)

We would like to thank Manuel Arturo Torres (Museo Arqueológico R.P. Gustavo Le Paige, San Pedro de Atacama and Corporación Cultural y de Turismo, Calama) and Philippe Mennecier (Musée de l'Homme, Paris) for the access to the specimens under his care. TP is also grateful with Hugo Benítez and Elis Damasceno for their useful comments about the analyses carried out in the present study. We also thank the anonymous reviewers for their contributions.