In statistical anthropology, when a human ‘fossil sample’ needs to be considered within the general framework of the human evolution, the comparison between this population and another, called the ‘reference sample’ is necessary. Concerning our study, we decided to limit the reference sample to modern specimens coming from Far-East Asia, the same region where our fossil sample comes from. This arbitrary choice gives the maximum chance of finding in the reference sample the same, or at least close morphological characters, as those shown by the fossil sample. The reference sample is supposed to have a biological meaning because the corresponding specimens are likely to be the descendants of the ancient populations that lived in the same area. Our reference sample consists of 100 specimens whose origins are known, represented by calvariums and mandibles. 118 metrical measurements were doubled checked and taken on each on these 100 crania. These 100 individuals come from Japan, China, Vietnam, Laos, Thailand, Cambodia, Philippines and Indonesia: six individuals from Japan (Hiogo-Kobé, Steenackers Collection registered in 1886), nine individuals from China (Soller Collection registered in 1886), forty-seven individuals from Vietnam (Canoville Collection registered in 1884), twenty-three individuals from Laos (Noël Bernard Collection registered in 1920), ten individuals from Thailand (Bel Collection registered in 1896), one individual from Cambodia (Pannetier Collection registered in 1920), one individual from Philippines (Eugène Salomon Collection registered in 1897), three individuals from Indonesia (Dumoutier Collection registered in 1874).

The fossil sample consists of 86 crania of fossil modern humans discovered in Far-East Asia from Japan to Indonesia (Fig.1) [6]. We would like to emphasize that all the measurements were taken on originals with the exception of the Chinese samples. These casts account for the Upper Cave (3 of them) samples at Zhoukoudian, since the originals disappeared in the 1940s, and the Hong Kong fossil [19] housed in the Senckenberg Museum in Frankfort. All crania are presently housed in different laboratories throughout the world with the exception of the fossils coming from Cambodia, Laos, together with some Vietnamese ones, which are stored in France. The Japanese Minatogawa, Hamakita and Mikkabi fossils are housed in the University of Tokyo. The other Chinese fossils, Liujiang, Mapa and Salawusu are stored in the Institute of Vertebrate Palaeontology and Palaeoanthropology of Beijing (IVPP). The Vietnamese fossils, Mai Da Dieu, Mai Da Nuoc and Dong Can are housed in the Institute of Archaeology of Hanoi. The Indonesian fossils are housed in the National Museum of Natural History of Leiden in The Netherlands. Fossils coming from Cambodia, Laos, and Vietnam were brought back to France at the beginning of the last century and in the 1930s by researchers working for the École Française d’Extrême Orient, the National Museum of Natural History of Paris or even for the Indochina Geological Service. All of them are nowadays housed in the Biological Anthropology Laboratory of the National Museum of Natural History in Paris (Musée de l’Homme). The conditions in which some of these ex-Indochinese fossils were re-discovered have to be mentioned: while one of us (F.D.) was doing his PhD research in 1998, he was making an inventory of all the South-East Asians fossils in the Biological Anthropology Laboratory collections, with the help of Ph. Mennecier and M. Chech. Fortunately the fossils discovered 70 years ago in Cambodia (Samrong Sen) [9], in Vietnam (Cau Giat, [5] and [8], Pho Binh Gia [21]) and from Laos (Tam Hang) [15] were identified. Such fossils had never been, or were incompletely described, in publications and some of them were in very fragmentary condition. Nevertheless, they were all gathered in several wooden boxes and then stocked in a room. This happened when the old Ethnographic Museum was replaced in 1936 by the Palais de Chaillot, where the Musée de l’Homme is at present located. This accounts for the fact that these boxes and all the material they contained were forgotten by the scientific community during more than 70 years.

With the support of the Collège de France, the Prehistory Laboratory of the Human Palaeontology Institute of Paris (IPH) and the Biological Anthropology Laboratory of the National Museum of Natural History in Paris (Biological Anthropology Laboratory, Musée de l’Homme), a ¹⁴C dating program on some of these fossils was started [7]. The absolute dating results make the fossils older than their discoverers thought in the 1930s; moreover, it is interesting to note that, according to the correspondence between researchers and notably that of M. Colani, more South-East Asian archaeological sites were known in the 1930s than those that have been described in the literature up until now. Concerning Vietnam, we can mention in Hoa Binh Province the sites of Lang Kay, Da Phuc, Lang Gam, Lang Tanh, Lang Tieng, Lang Mi; in Quang Binh Province, the sites of Kim Bang, Bat Môt, Duc Thi, Xom Tham, Yên Lac sites; in Than Hoa Province, the Lang Bong site; in Ha Nam Province, the Dong Noi and Hang Oa sites; in Thai Nguyen Province, the Na Ca site; and in Ninh Binh Province, the Phu Té site.

Concerning the statistical aspect of this study, as a first step, we performed a bivariate quantitative analysis on the fossil cranium of the 86 individuals. The fragmentary aspect of 41 fossils led us to withdraw them from the statistical analysis. On the remaining 45 well-preserved fossils, we were able to take 118 measurements. For our methodology, we followed that developed by E. Peyre and C. Menin [26] and [29]. We highlighted the morphological characteristics using sigmoid profiles upon 13 variables whose presence was constant. Sigmoid profiles show morphological features of an individual considering the fossil variable compared to the reference sample in terms of sigma. This term gave the name to the graphic [27]. The ordinate axis or sigmoid scale is divided into standard deviation or σ. Only the standard deviation for each character is used as a reference. The reference sample is then represented by a base-line on the ordinate axis at the zero points (0). Starting from this point, we compare the individuals or group of individuals with this base-line. If the mean value of some characters in the selected sample is m1 and the corresponding mean value in some other sample is m2, then the quantity is represented by means of a graph: $ (\frac{\mathrm{m1-m2}}{\sigma })$ $\left(\frac{\mathrm{m}1-\mathrm{m}2}{\sigma }\right)$ where σ is the standard deviation of the sample, m1 the mean value.

In other words, we measure each m2 from m1 and divide it by the standard deviation (σ) of the reference sample.

As a second step, we used a cluster analysis to characterize the fossil sample. We wanted to check whether the database was structured and whether the individuals could be gathered by similar morphology. Consequently, we chose to use the Hierarchical Cluster Analysis (HCA). As exposed by Williams Howells [18], this method shows by the mean of a graphic, the dendrogram, the different main clusters according to an aggregation criterion. We choose the Ward criterion [40] that gathers individuals with the smallest loss of information.

In order to get rid of the ‘size’ factor and to keep only the ‘shape’ of the crania, we had to normalize our database upon Williams Howells recommendations [18]. First of all, the specimens raw measurements were rendered into standard form called Z-scores. The deviation of each score from the general mean is divided by the general standard deviation (Table 1). Then the mean of each individual’s Z-scores was calculated. It was called ‘Pensize’. Pensize = (Z1+Z2+ $ \dot{\mathrm{ }}$ $\dot{}$ $ \dot{\mathrm{ }}$ $\dot{}$ $ \dot{\mathrm{ }}$ $\dot{}$ +Zg)/G, where G is the number of measurements. Then, the Z-scored were centered once again by subtracting from each of them that individual’s Pensize (table not shown), so that the sum of these deviated scores is zero. These newly centered figures are called C-scores (table not shown).

Once the C-score database matrix is calculated, the HCA is used to study the relations among individuals. This method, which only considers the cases rather than the variables, is also called ‘Q-mode analysis’. The results of the Hierarchical Cluster Analysis, according to the Ward criterion [43], is represented by the dendrogram of Fig. 1. The meaning of the different branches is as follows: the individuals gathered on the same side have a close morphology. This hierarchy is indexed, meaning that each cut corresponds to a numeric value indicating at what level clustering happens. This index, called the aggregation level, shows the distance between clusters. The higher this aggregation level is, the less similar the morphology is.

Multidimensional scaling analysis (MDS) [32] and [35] was applied to the data to graphically identify possible patterns of spatial variation. This multivariate method takes a set of dissimilarities (as in a distance matrix) and returns a set of points such that distances among the points in the plot are approximately equal to the dissimilarities. MDS is not so much an exact procedure as rather a way to ‘rearrange’ objects in an efficient manner, so as to arrive at a configuration that best approximates the observed distances.

It actually moves objects around in the space defined by the requested number of dimensions, and checks how well the distances between objects can be reproduced by the new configuration. In more technical terms, it uses a function minimization algorithm that evaluates different configurations with the goal of maximizing the goodness-of-fit (or minimizing ‘lack of fit’).

The most common measure that is used to evaluate how well (or poorly) a particular configuration reproduces the observed distance matrix is the stress measure. The raw stress value Phi of a configuration is defined by: \[ \mathrm{Phi=\Sigma \; [d}_{\mathrm{ij}}\mathrm{-f(\delta }_{\mathrm{ij}}\mathrm{)]}^{2} \] $$\mathrm{Phi}=\Sigma {[{\mathrm{d}}_{\mathrm{ij}}-\mathrm{f}\left({\delta }_{\mathrm{ij}}\right)]}^2$$

In this formula, d_ij stands for the reproduced distances, given the respective number of dimensions, and δ_ij (delta_ij ) stands for the input data (i.e., observed distances). The expression f (δ_ij) indicates a nonmetric, monotone transformation of the observed input data (distances). Thus, it will attempt to reproduce the general rank-ordering of distances between the objects in the analysis. The MDS analysis (Fig. 3 and Fig. 4 ), as well as the dendrogram (Fig. 2 ), were computed by means of the software Statistica version 5.0 by StatSoft Inc on the same Ward [42] matrix.

Geological ages of the fossils were not considered to constitute ‘same age’ groups of specimens. Although the time period covering the fossil sample age, about 67 000 (Liujiang, China upon ¹⁴C dating on the associated fauna) [44] to 1200 BP (Cambodia, Samrong Sen, upon direct ¹⁴C dating) [6] is quite large at an individual scale, it seems to have a small impact regarding the evolutionary process of modern man. This assumption is confirmed by the result in this study of the multivariate analyses, which do not isolate the Liujiuang specimen (the oldest of the fossil samples). Indeed, both dendrogram and the multidimensional scaling plot groups Liujiang with the Wadjak specimens which are known to be 9000 years old. Considering this result, one can assume that a same morphology could persist over generations and then at the same time concerning the methodology, the pertinence of grouping specimens by same age is flawed.

The dendrogram (Fig. 2) shows three main clusters of specimens or groups we called C1, C2 and C3. The first group (‘C1’, Fig. 2) consists, by construction, of specimens characterized by a high cranium, long and broad cranial vault (calva) with a high, long and fairly broad face. The second group (‘C2’, Fig. 2) consists, by construction, of specimens themselves divided into two other distinct sub-groups (‘χ’ et ‘δ’). The first sub-group ‘χ’ consists of specimens with a relatively high cranium, short, with a narrow calva. The face is low, long and very broad at the orbit level and with a narrow frontal. The second sub-group ‘δ’ consists of specimens with a rather short cranium, a narrow calva and frontal, a quite broad face and a very broad inter-orbital section. The third group (‘C3’, Fig. 5) is represented by two specimens. They show the same morphological characteristics of the previous sub-group ‘δ’ but with a very long face.

It is well known that environmental factors (mainly related to the diet), at least at an individual level, can increase the morphological variability of the skull, whose range of variation is genetically coded. To overcome the confounding effects of this source of variation it is advisable to study morphological differences by grouping several specimens in samples that are then compared. The rationale is that inter-specimen differences play a minor role and samples trends become recognizable. On the other hand, this choice may obscure some information because of a sort of ‘averaging process’ that underlies the computation of any distance matrix from a set of variables.

MDS analysis of inter-specimen differences and inter-sample differences are shown in Fig. 3 and Fig. 4, respectively. Both analyses show a clear differentiation between sea-border and inner-land excavated sites. At an individual level (Fig. 3) the two groups can be distinguished, roughly on each side of the y axis, as follows. The first group (Fig. 3), composed of specimen from Lang Cuom (‘Lcuom 4/5/10/13/1/8’), Dong Thuoc (‘Dthuoc’), Pho Binh Gia (‘PBG1’, ‘PBG2’), Mai Da Nuoc (‘MDN’), Minatogawa (‘Minat 1’, ‘Minat 2’), Liujiang, Wadjak (‘Wadjak 1’, ‘Wadjak 2’), Upper Cave (‘Ucave 1’, ‘Ucave 2’), Samrong Sen (‘SronSen’), Cau Giat (‘Cgiat 1/2/A4’), and Dong Can. All these individuals come from coastal sites previously described by the ‘C1’ morphology (Fig. 2). The second group is composed of specimen from Tam Hang (‘THS3’, ‘THS13’, ‘THS11’, ‘THS10’, ‘THS14’, ‘THS4’, ‘THS22’, ‘THS2’, ‘THN3’, ‘THTTA’), Than Hoa (‘THOA DB’), Tam Pong (‘TP1’), Ban Kao (‘BKVII’, ‘BKLSII’, ‘BKKBSP’, ‘BKInconnu’), Mai Da Dieu (‘MDD’), Lang Cuom (‘Lcuom C9’, ‘Lcuom 11’), Upper Cave (‘UC3’) and Minatogawa (‘Minat4’). Besides the individuals belonging to Jinchuan and Zhiyang, that clearly appear to be outlier, the absence of clusters of specimens (Fig. 3) or samples (Fig. 4) was observed. Except the five individuals (‘Mai Da Dieu’, ‘UC3’, ‘Minat4’, ‘Lcuom9’ and ‘LCuom11’), all the other individuals come from inner-land sites described by the ‘C2’ morphology.

The Multidimensional Scaling (MDS) scatterplot shows (Fig. 3 and Fig. 4) a continuous range of variation that is not related to geographic distances. The absolute lack of association between biometrical differences and geography was assessed by the Mantel test [24]. Cross correlations between pairs of specimen, or pairs of samples, and their associated geographic distance is neither correlated nor significant. This result suggests the presence of discontinuities in the pattern of variation between samples that may be visualized as boundaries. To visualize barriers that separate samples, we applied the Monmonier’s maximum difference algorithm [28] on four distance matrices corresponding to the length (Fig. 5A), height (Fig. 5B), width (Fig. 5C), and mastoid height (Fig. 5D) of the studied fossil skulls. The rationale for this choice is to provide a more reliable analysis of the fossils studied in this paper.

This approach raises a question on the informative power of each of the different biometrical measures taken on skulls. If, in a given set of different measurements only a few are shown to be variable (among specimen or samples), then the distance matrix computed from all these measures will actually reflect the variability of this single variable measure and can be defined as being not robust. The separate analysis (Fig. 5 A/B/C/D) shows that strong boundaries encompass specimen of Jinchuan and Wadjak that, as in the MDS analysis (Fig. 3 and Fig. 4), show the most significant differences compared with other samples. With the exception of matrix 4 (Fig. 5D), a boundary isolates Jinchuan and Wadjak that are shown to be very different one from each other. The other barriers differ in their patterns, even though a certain longitudinal differentiation between coastal (sea-border) and inner-land samples appears. In Fig. 5A it can be seen that samples of Tam Hang (9) and Tam Pong (10) are on the left side of a boundary that splits them from costal samples as Cau Giat (2), Dong Can (3). In this respect Lang Cuom (5) seems to be more isolated from these two groups (Fig. 5B). Likewise, Liujiang (6) is put apart from neighbouring samples even though this datum is supported only by data characterizing cranium width (Fig. 5C). Concluding, even the individual of Samrong Sen (8) is set apart from different boundaries (Fig. 5D and, partially, 5C) thus indicating its biometrical difference from neighbouring samples.