Study of the K-S distance on skulls from different modern populations for sex and ancestry determination

Our dataset contained a total of 637 male and 341 female skulls, derived from four different populations (see Matin [ 10] for additional information).

Skulls were only included in the dataset if a defect on the bone had not led to any distortion of the entire skull, if sex, origin, age or year of birth, year of death, country of birth of the skull were known and if the distance between sphenion and krotaphion was calculable. Every skull underwent a measuring process described hereafter, which was the same for all data of the skulls used for our study. Experience of both anthropologists and forensic pathologists show that digital data acquisition using technique, such as a 3D digitizer is to be superior concerning intra- and inner observer errors.

The first step of the measurement process was the inspection of the skull. Any defects on the skull were to be documented, especially those that led to distortions and shifts of landmarks. The data of the skulls (sex, age, origin and year of death) were investigated in mortuary books as well as inventory lists and further registered. The landmarks were marked with a pencil on the surface of the bone and the whole skull was afterwards fixed on three columns of modelling clay on a table. The digital acquisition took place with a Microscribe 3‑D digitizer (RSI 3D-Systems, Oberursel, Germany) with a multijointed arm: Microscribe digitizers are routinely used in 3D measurement technology among many fields to capture geometric characteristics of objects. The stylus allows the user to quickly trace over the contours of a physical object with ease to obtain quick 3D measurements. Using the Microscribe we captured points in the 3 spatial axes, relative to the zero position of the arm. After acquiring all values, a 3‑D reconstruction and a measurement of the distances between individual landmarks were possible. Digital data acquisition was done using the software 3Skull (The software was produced by Steve Ousley from the University of Tennessee, Department of Anthropology in 2014), which was able to calculate the distance between different landmarks by the measured coordinates.

Figs.  2 and  3 show fixation and measuring of the skull.

Since there were exact X, Y and Z coordinates for each measurement point acquired by Microscribe and 3Skull, the distance between the landmarks krotaphion and sphenion was determined by calculating the Euclidean distance between the two points. The formula for calculating the Euclidean distance between 2 points (dP1, P2) is as follows:

Afterwards, the following statistical analyses were carried out with the data acquired:

A comparison of the mean values of the krotaphion-sphenion distance showed that there was certain symmetry in all groups, since the mean values of the two sides were close to each other (Table  1).

The smallest average value was found among the Rwandan population (left 8.73mm, right 8.70mm). The biggest average value of the krotaphion-sphenion distance was found on the left side among the German skulls (15.64mm).

The analysis with the Shapiro-Wilk test for normal distribution showed the following distribution:

Left krotaphion-sphenion distance:

Normal distribution:

Non-normal distribution:

Right krotaphion-sphenion distance:

In the Shapiro Wilk test of the right K‑S distance, only the German population was found to be normally distributed with a  p-value of 0.18. The p-value in the remaining 3 populations was <0.05; the distribution of these three populations differed significantly from a normal distribution.

Independent samples T‑test:

In our dataset containing a total of 634 male and 341 female skulls, the mean krotaphion-sphenion distance of the left side was larger in male skulls (14.17 mm) than in female skulls (13.27 mm). The median krotaphion-sphenion distance on the right side was also larger in male skulls (13.52 mm) than in the female skulls (12.53 mm).

For investigating sex differences, Levene’s test and the T‑test were performed. Levene’s test assumed that variances were homogeneous and there was no statistically significant difference between the groups. The F value of the test for the left side of the skull was 0.51 and the significance value was 0.82, which was higher than a  P-value of 0.05. This means that the variances are homogeneous. The T value was 2.548 with a  P-value of 0.011, which was smaller than the error probability of 0.05. Thus, the differences in the krotaphion-sphenion distance between the two sex groups were statistically significant.

Table  2 shows that the F value of the Levene’s test was large (2.038) with a significance value of 0.154 and the variances were homogeneous.

The two tests that do not make any assumptions about the variances or allow heterogeneity of the variances of each group are the Welch test and the Brown-Forsythe test: these tests also showed a statistically significant difference for the left krotaphion-sphenion distance.

All three test methods showed that there was difference between the groups, but not where exactly this difference was to be found or which group was different from the others. To test these differences, two post hoc tests were performed:

Levene’s test showed a  P-value >0.05 for the right krotaphion-sphenion distance. Therefore, there was no inequality between the variances of the individual groups. The results of the analysis of variance returned an F‑value of 45.11 with a  P-value <0.05. Therefore, there was a statistically significant difference between the ancestral groups. The assumption of homogeneity for the ANOVA analysis as tested by the Levene’s test was met. The ANOVA results were now statistically robust enough.

As for the left krotaphion-sphenion distance, the Tukey HSD and the Games-Howells tests as post hoc tests were performed for the right side of the skull:

The examined krotaphion-sphenion distance in our study showed a statistically significant sex-specific difference and was greater in male skulls than in female skulls. This trend was observed on both sides of the skull; on the left side there was a mean distance of 14.2 mm for male skulls and only 13.3 mm for female skulls. The krotaphion-sphenion distance on the right side was smaller overall, so that a pure comparison of the mean values showed an asymmetry. The T‑test showed a statistically significant difference between the sexes on the left side. Both the right and the left krotaphion-sphenion distances were 1 mm longer among male skulls than female skulls (male 13.5 mm, female 12.5 mm). In the T‑test a statistically significant difference between the sexes was also shown on the right side of the skull. Assuming that the krotaphion-sphenion distance can be used as a measurement of skull size, the data are consistent with the general assumption that male skulls are larger and more robust than female skulls [ 11, 12].

Our results reflect the frequency of the sphenoparietal variant, which the anthropological researcher Murphy had already found in his morphological analysis on skulls of Aborigines: Murphy performed his study to thoroughly analyze pterion types and correlation with cranial indices, but without looking for gender or ancestral differences. A relevant difference to our study is that for quantitative analyses Murphy included all variants of the pterion region in the study except the epipteric variant. The distribution of his results showed two maxima: the first peak in the distribution curve was between +4 mm and +9 mm, the second peak was between −11 mm and −6 mm in the frontotemporal variant. On average, the krotaphion-sphenion distance in the frontotemporal variant was 11.2 mm long with a standard deviation of 4.2 mm. Murphy explained the distribution with two maxima either with an inhomogeneous data set or with a still unknown factor, which led to a preponderance of the frontotemporal variant with a krotaphion-sphenion distance of 8–11 mm [ 13]. By comparing the results of Murphy to ours, the different ethnic evolution of both Aborigines and the other examined populations, such as African-Americans has to be considered. Nevertheless, the average krotaphion-sphenion distance presented by Murphy matches the average distance that the African-Americans showed in our study (right side: 11.19 mm with SD 5.15 mm; left side: 11.03 mm with SD 4.95 mm).

In terms of ancestry differences, the skulls of the German population showed the greatest asymmetry; the mean for the krotaphion-sphenion distance was 15.6 mm on the left and 14.5 mm on the right, a difference of 1.2 mm. The Rwandan population had the smallest mean krotaphion-sphenion distance with a mean of 8.7 mm left and right, showing the strongest symmetry with respect to the krotaphion-sphenion distance. This agrees with literature so far as the occurrence of the frontotemporal variant of the pterion is highest among African populations [ 14]. Asala and Mbajiorgu postulated that the frequency of frontotemporal articulation, in combination with other non-metric parameters, could be used as a distinguishing feature of African descent [ 15]. Hauser and De Stefano [ 16] summarized the frequencies of the frontotemporal variant of different populations: The most common incidence of the frontotemporal variant was found in Melanesians (present day New Guinea, New Caledonia and Solomon Islands) and African populations. The lowest incidence was found in European populations (British, Dutch, Italian).

The ANOVA analysis performed in our study showed a statistically significant difference between the individual populations in the krotaphion-sphenion distance, both on the left and the right side of the skull. In further analyses (Tukey HSD and Games-Howells tests), it can be stated that the African-American and Rwandan populations differed from all other groups. The German and Euro-American populations differed only from the Rwandan and African-American populations. This trend could be observed on the right and left side and is further supported by the fact that although the African-American populations are very heterogeneous in modern times; African-American descent can be primarily attributed to the African continent [ 17]. Thus, the analysis indicates that there is less difference between the African-American and Rwandan populations than between African-Americans and Germans or between Rwandans and Germans. Additionally, we saw less differences between German and Euro-American populations than between Germans and African-Americans or Rwandans.

In summary we can state that our study showed a statistically significant difference in the krotaphion-sphenion distance between the four populations studied.

Morphometric analysis of the pterion region has so far rarely been reported in the literature; in consequence no suitable comparative data were available for our study. Vivaan et al. examined 78 skulls from an Indian population from the Institute of Anatomy in Begaluru (India) capturing the krotaphion-sphenion distance by digital measuring. Here, a mean distance of 14.06 mm and 14.58 mm was determined for each of the right and left sides. Further analyses of the statistical differences between sex or other populations were not performed in the study [ 18]. While interpreting these results in comparison to ours, they are nearest to our measured data from Euro-American and German skulls. As an attempted explanation for this, many factors next to historical components have to be taken into account: in general, both genetics and environment have an impact on cranial morphology. The exact control mechanisms for formation of the different variants of pontic stenosis, asymmetry, sex and ancestry-specific differences in krotaphion-sphenion distance are still not exactly known. For a population limited to a particular geographical area, there have to be different factors influencing growth and development of the skull; however, there is a closely linked genetic component [ 19] as morphological skull characteristics are inherited and thus cause ancestry-specific differences. Abbie [ 20] showed the human skull as a physical mosaic of independent inherited traits. The mosaic for each ancestral group is determined by its own genetic pool. Liu et al. for example discovered the MSX2 gene, which encodes a transcription factor and is active in craniofacial morphogenesis, especially at cranial sutures. Overexpression of this gene led to early occlusion of the cranial sutures and thus deformation of the skull [ 21]. Furthermore, the development of the neurocranium strongly correlates with the growth of the brain and is dependent on interactions between different types of tissue involved in the sutures [ 22].