First of all, it should be noted that the data collected for the present study may contain many kinds of errors, for example, original sampling error, intra- and inter-observer errors, errors in the determination of chronological age, errors in the assignment of environmental data to the samples collected, duplication of data,¹⁾ etc.  Notwithstanding, the present study was carried out in expectation of being able to get some information which are not concealed by such errors.

Unimodal distribution of sample means and the limits of among-group variation

    It is well known that the within-group distribution of a linear measurement of the animal body is generally a normal distribution.  And the among-group distribution may not necessarily be normal depending on conditions.  In the present study, it was found that the distributions of sample means for craniofacial measurements across world human populations of the Neolithic to modern times were unimodal at least in the cases of as large number of samples as 300 or more (each sample has the size of 20 or more), as shown in Table 2 and Figs. 1 to 5.  This means that the geographical/chronological distribution of Homo sapienssapiens populations is not a uniform nor uneven distribution, and, in turn, may indicate that an appropriate morphology of our head or face has been formed through the human evolutionary process respondent to some selective pressure, and/or that all recent human populations derived from a single ancestral human population.  If the latter is the case, this finding may support the Out-of-Africa hypothesis on the origins of modern humans (e.g., Stringer and Andrews, 2005).  The validity of these hypotheses will be discussed later on the basis of the analyses of craniofacial measurements and environmental variables.

    The limits of among-group variation of Homo s. s. in each variable are shown in Tables 2 and 3.  For major craniofacial measurements (Table 3 and Fig. 6), at least, it was confirmed that the ranges between the minimum and maximum values of Homo s. s. sample means corresponded to those between the world average minus 3SD or 4SD and the world average plus 2SD or 3SD of the within-group variation in a Japanese sample.  It is also interesting that even the ultramodern skull of a Shogun of the Edo period in Japan is positioned within this range (Table 3 and Fig. 6).  On the other hand, the deviation curve for the Herto skull (Homo s. idaltu) is partially outside of the range of Homo s. s. (Fig. 6).  This seems not to be inconsistent with Figure 4b or 4c in White et al. (2003).

Comparison to within-group multivariate distributions

    How do the vectors of sample means from all over the world distribute in a within-group multivariate space?  This question was checked using two within-group variance/covariance matrices.  The results demonstrate that most of the PC score vectors for 283 sample mean vectors are placed within the ±2SD range of within-group PC scores (Figs. 7 and 8).  This means that there are certain constant limits in the craniofacial among-group covariations of Homo sapiens sapiens, as anticipated.  It was also clarified that there was no such a Homo s. s. population as a pseudo-individual with the minimum or maximum values in all eight craniofacial variables (Figs. 7 and 8).  These findings suggest some complicated system or factors controlling the coordination between substructures of the skull (or the body).  This supports Weidenreich’s (1941) idea: the body should be considered as a totality, i.e., as a unique construction in which all parts harmonize from the beginning of its organization, and every essential alteration must be accounted as a consequence of a change in the entire construction.

    In addition, two special individuals, i.e. the 160,000-154,000 year-old skull from Herto [Homo s. idaltu] (White et al., 2003) and the ultramodern skull of Iyeyoshi Tokugawa [1793-1853] (Suzuki, 1967, 1981), were plotted in the radar charts of within-group PC scores (Figs. 9 and 10).  These radar charts show that Herto partially exceeds the upper limits of the Homo s. s. range.  This is again not inconsistent with Figure 4b or 4c in White et al. (2003).  Regarding Iyeyoshi Tokugawa, it is found that he is very close to or slightly exceeds the upper or lower limits of the Homo s. s. range in a few PCs.  This is probably due to his own living environment and genetic changes in his family through aristocratic way of life for several generations, i.e. a kind of artificial selection.

General size factor and regularity in among-group variations

    Usually, a so-called general size factor (all factor loadings on this factor have the same sign) is extracted in the form of PC I from the PCA of a within-group correlation or variance/covariance matrix, as seen in Tables 4 and 5 or in many studies (e.g., Kanda and Kurisu, 1967; Mizoguchi, 1992; etc.).  In the PCAs of among-group correlations between craniofacial measurements in the present study, however, such a general size factor was not extracted (Tables 13 and 19).  This is robust evidence for a qualitative difference between within-group and among-group covariations of craniofacial measurements.  Namely, this difference is considered to result from various differences between the ontogenetic and phylogenetic processes.

    As shown in Tables 13 and 19, however, some PCs or local common factors were certainly extracted from among-group correlation matrices of craniofacial measurements.  This fact is evidence for the existence of some regularity in the among-group variations between craniofacial measurements.  From these tables, it is found that, while cranial breadth, upper facial height, bizygomatic breadth, orbital height and nasal height vary in parallel with one another, cranial length and nasal breadth vary relatively independently of each other and of the above five measurements.  This supports Mizoguchi’s (1998b, c) findings from Asian samples. 

    Česnys (1991) carried out an inter-group PCA of craniofacial measurements on the basis of 70 male Central and Eastern European samples from the Late Mesolithic, Neolithic and Early Bronze Ages, and showed that the first PC was relatively highly associated with bizygomatic breadth, upper facial height, orbital breadth and nasal height, and that the second PC was relatively highly associated with cranial breadth and, at the same time, inversely associated with cranial length.  These findings are partially consistent with those of the present study (Tables 13 and 19).

Deviated distributions of environmental variables

    The data of craniofacial and postcranial measurements used here have been collected by the present author from the literature as randomly as possible in the research environment of the present author, namely in Japan.  But there are lots of bias factors affecting the amount of data for a particular character or the shape of among-group distribution of a variable.  For example, the geographical distribution of anthropologists (some people say that the number of archeological sites excavated is large in the areas where there are many universities or institutions to which archeologists belong), the research environment of a data collector, main interest of many researchers, etc. may influence on the amount of data or the shape of among-group distributions in addition to a simple sampling error due to the smallness of sample size.  In the present study, the number of samples collected for limb bone measurements is smaller than that for craniofacial measurements (Table 2).  This fact may be explained by the possibility that many anthropologists are interested in the skull more than in limb bones.

    Among the environmental variables analyzed here, only average annual temperature has a distribution which is not significantly different from normal distributions at the 5% level (Table 23 and Fig. 11).  This may be evidence that many people prefer a moderate climate, especially in temperature.

    The distributions of the other environmental variables are highly significantly different from normal distributions (Table 23 and Figs. 12 to 16).  In particular, chronological age of sample is extremely deviated.  This is, however, convincing because the older the sample is, the worse the preservation of bones is.

    Regarding the deviated distributions of precipitation, relative humidity, the absolute value of latitude, and great circle distance, various causes can be considered.  But it is not easy to identify them without other information.

Environmental influence on the craniofacial morphology

    In his studies on within-group correlations between craniofacial and postcranial measurements, Mizoguchi (e.g., 2007a) showed that, for example, cranial length was associated with many postcranial measurements.  In the beginning of this study, therefore, it was planned to carry out analyses based on the data including postcranial measurements to clarify the causes for the among-group correlations between craniofacial measurements.  As already stated, however, the number of samples collected for postcranial measurements was too small to examine the global tendency in the among-group associations between craniofacial, postcranial, and environmental variables (Tables 9, 10, 48 and 49).  Therefore, the among-group associations between only craniofacial and environmental variables are mainly discussed here.

    Major among-group associations between craniofacial measurements and environmental variables are shown in Figs. 17 to 22.  In Figs. 17 and 18, it is clear that cranial breadth, upper facial height, bizygomatic breadth, and nasal height tend to be larger in colder regions of higher latitudes, and vice versa.  The robustness of this tendency is confirmed by highly significant Spearman’s rank correlation coefficients between independent male and female samples (Figs. 17 and 18).  Crognier (1979, 1981), using “zero-order correlation coefficients” based on 85 male samples from Europe, North Africa and Near/Middle East, suggested that temperature (all of mean annual temperature, mean temperature of the coldest month, and mean temperature of the hottest month) had high inverse correlations with maximum head breadth, morphological face height, bizygomatic breadth, and nose height.  Although it is unknown whether or not Crognier took into account the premise of bi-variate normal distribution for correlation coefficient when estimating a correlation coefficient from the among-group samples, the findings are very suggestive and not inconsistent with the above results of the present study.  Guglielmino-Matessi et al. (1979) compared the PCs from 19 climatic variables on temperature and humidity with the discriminant functions based on Howells’ (1973) craniofacial data from 17 populations, and found that their PC I mainly associated with temperature had significant inverse correlations with Howells’ first discriminant function strongly associated with skull breadth and facial height in both males and females.  This is also compatible with the findings in the present study.  Gilligan and Bulbeck (2007) showed, using male data from Australian Aboriginal tribes (the number of tribal groups varies from 59 to 102 across the variables cited here), that maximum head breadth was negatively associated with temperature, but bizygomatic diameter and nasal height had no significant association with temperature.  Although their findings is not completely consistent with the present study, this does not necessarily mean that either of the two studies is wrong because Gilligan and Bulbeck’s data are derived from a local region, not from all over the world.  After all, the strong among-group associations of craniofacial measurements with temperature found in the present study are considered a result of the adaptation of local populations to their living environments.

    Incidentally, the representative samples which are placed at both extreme positions in the tendencies shown in Figs. 17 and 18 are listed in Table 50.  The three male samples with the highest scores of PC I in Fig. 17 are Yakuts [Russia; 73 YAKUT in Appendix 3], Buryats [Russia; 71 B-T-B] and Chukchi [Russia; 74 CHUK3], while the three male samples with the lowest scores are Lower Nubia [Egypt; 26 L-NB2], Naqada [Egypt; 4 NAQAD] and S. Egyptians [Upper Egypt; 3 S-EGY] (Table 50).  In Fig. 18, those with the highest scores of PC I are S. Egyptians [Upper Egypt; 4 S-EGY in Appendix 4], Naqada [Egypt; 5 NAQAD] and Lower Nubia [Egypt; 108 L-NB2], while those with the lowest scores are Buryats [176 BURYATM], Buryats [Russia; 175 B-T-B] and Yakuts [Russia; 177 YAKUT] (Table 50).  The contrast between these samples is shown in Figs. 23 and 24.  Such examples make our imagination real.

    In Figs. 19 and 20, the variation patterns of factor loadings are slightly different between males and females, as indicated by Spearman’s rank correlation coefficients.  But the results based on male samples, the number of which is much larger than that of female samples, show interesting among-group associations between craniofacial and environmental variables.  Both figures show a tendency of basi-bregmatic height and nasal breadth to be larger and, at the same time, another tendency of minimum frontal breadth to be smaller in the regions more distant from Ethiopia and of lower latitudes where average precipitation is higher and average temperature is also relatively high.

    Wolpoff (1968), using cranial samples from Australian Aboriginals and Alaska Natives, showed that nasal breadth was smaller in colder and drier regions.  Noback et al. (2011), using ten modern human population samples from five climatic groups, suggested that nasal aperture tended to be narrower and higher in cold and dry regions, and that the bony nasal cavity appeared mostly associated with temperature, and the nasopharynx with humidity.  According to Crognier (1979, 1981), however, nose breadth has a significant negative correlation with the mean precipitation of the rainiest month in males and, in females (Crognier,1979), with the mean precipitation of the driest month.  Gilligan and Bulbeck (2007), using 75 male tribal groups of Australian Aboriginals, showed that nasal breadth is positively associated with temperature and negatively with relative humidity.  As regards the association between nasal breadth and temperature, the finding in the present study is compatible with those of Wolpoff, Gilligan and Bulbeck, and Noback et al.  But Crognier’s results on precipitation and Gilligan and Bulbeck’s findings on relative humidity are not completely consistent with those of the present study.  Maddux et al. (2016) suggest that environments typically characterized as “cold-wet” actually exhibit low absolute humidities, with values virtually identical to cold-dry environments and significantly lower than hot-wet and even hot-dry environments, and that strong associations between the nasal index and absolute humidity are, potentially erroneously, predicated on individuals from hot-dry environments possessing intermediate (mesorrhine) nasal indices.  Furthermore, Maddux et al. (2017) state that only the internal nasal fossa, which is one of the four morphofunctional units of the nasorespiratory tract (external pyramid, nasal aperture, internal nasal fossa, and nasopharynx), exhibits an ecogeographic distribution consistent with climatic adaptation, with crania from colder and/or drier environments displaying internal nasal fossae that are longer, taller, and narrower (especially superiorly) compared to those from hotter and more humid environments.  Although the problems on precipitation or humidity should be investigated in more depth in the future, it is most likely that nasal breadth has been determined through adaptation to temperature to a considerable extent.

    Regarding the within-group genetic variation of nasal breadth, there is an interesting report.  Martínez-Abadías et al. (2009), using 355 pedigree-known adult skulls from Hallstatt, Austria, showed that the estimates of narrow-sense heritability for cranial length, cranial breadth, basi-bregmatic height, bizygomatic breadth, upper facial height, orbital breadth, and nasal height were between 0.24 and 0.43, while the heritability estimate for nasal breadth was 0.00.  If this can be applied to most populations, it turns out that nasal breadth is perfectly determined by genes and genetically extremely stable in diverse populations, such as the number of eyes in many animals.  If so, the connection of nasal breadth with temperature woud be very strong.

    Incidentally, Fabra and Demarchi (2011), using male samples from 17 pre-Hispanic populations in the Southern Cone of South America, suggested that, while nasal height and breadth had no significant among-group association with temperature nor with rainfall, they had significant negative correlations with altitude.  The number of samples used in their analysis is limited.  But their findings are very interesting in understanding the adaptation of the nasal structure to some environmental factors other than temperature and humidity, such as oxygen content.

    It is also interesting here that the three matric traits, i.e. nasal breadth, basi-bregmatic height and minimum frontal breadth, seem to be highly associated not only with precipitation and latitude but also with the great circle distance from Herto, Ethiopia.

    Relethford (2004) comprehensively examined the contribution of isolation by geographic distance to the present global variation patterns in three kinds of characters, i.e., red blood cell polymorphisms, microsatellite DNA markers and craniofacial measurements, and maintains, as an alternative explanation, that, since a common pattern of global gene flow mediated by geographic distance is detectable in diverse genetic and morphological data sets, the correspondence between genetic similarity and geographic distance reflects the history of dispersal of the human species out of Africa.  His conclusion seems reasonable if all the geographic distances he computed are those from Africa.  In practice, however, the distances he used contain not only distances between local populations within Africa but also those within New World, Australasia, or Eurasia in addition to the distances between the four regions.  Namely, it can also be said that his results may reflect the history of dispersal of the human species out of New World, Australasia, or Eurasia.  In any case, geographic distance is no doubt an important factor in understanding the background of evolutionary processes.

    As shown by Relethford (2004), genetic similarity between populations may decrease with geographic distance between the populations in general, and this can partly be explained by gene flow or migration.  Betti et al. (2010) assert that neutral processes (genetic drift) have been much more important than climate in shaping the human cranium, and that a large proportion of the signal for natural selection comes from populations from extremely cold regions.  In both of Figs. 19 and 20 of the present study, it is found, though only in males, that the mean values themselves of metric traits, not their differences or similarity between populations, vary in parallel with the geographic distance from Herto, Ethiopia.  Can this phenomenon be explained by gene flow (or migration) or genetic drift?  The three male samples with the highest scores of PC II in Fig. 19 are Chamorros [Mariana Islands; 30 MEDCHAMM in Appendix 3], Hawaii [Hawaiian Islands; 31 HAWAI] and Dayak [Borneo; 91 DAYAK], while the three male samples with the lowest scores are Nenets [Russia; 61 NENET], Carinthians [S.C. Austria; 102 CARIN] and Czechs [Bohemia; 110 CZECH] (Table 50).   In Fig. 20, those with the highest scores of PC II are Dayak [Borneo; 195 DAYAK in Appendix 4], Chamorros [Mariana Islands; 115 MEDCHAMM] and Hawaii [Hawaiian Islands; 116 HAWAI], while those with the lowest scores are Lapps [199 LAPPS], Čuden [Russia; 120 CUDEN] and Kaiserslautern [Germany; 96 KAISR] (Table 50).  The contrast between these samples is shown in Figs. 25 and 26.  If the Out-of-Africa hypothesis on the origins of modern humans is correct, nasal breadth, for example, must decrease toward the northeast and increase toward the southeast.  If two different critical genetic drifts happened in the process of migration and, after that, there have been no great change in the descendant populations, one of which migrated to a more distant region than the other, then such a state as shown here may have appeared.  But, if so, not only the above three metric characters but also all the other characters must change in the two directions, namely, all characters must have high correlations with geographic distance, as stated by Fabra and Demarchi (2011).  In Figs. 19 and 20, there is no such indication.  Therefore, the strong associations of the above three metric characters with geographic distance are also considered evidence of adaptation to environment in each region.  But it is not easy to imagine the mechanism of adaptation for minimum frontal breadth and basi-bregmatic height.  If the compression by temporal muscles affects the smallness of minimum frontal breadth and the largeness of basi-bregmatic height, their associations with geographic distance may be due to a difference between the ways of subsistence, such as food habits, in the high and low latitudes.

    In Figs. 21 and 22, it is found that cranial length and cranial base length are highly associated with chronological age in both males and females.  The three male samples with the highest scores of PC III in Fig. 21 are Ekven [Russia; 7 EKVEN in Appendix 3], Proto-Nordics [North Iran; 15 PN-TP] and Murray River Valley [Australia; 11 MURRY], while the three male samples with the lowest scores are Czechs [Bohemia; 110 CZECH], Vietnamese [89 VIETN] and Vorarlberger [Austria; 108 VORAR] (Table 50).   In Fig. 22, those with the highest scores of PC IV are Cernica [Romania; 3 CERNC in Appendix 4], Ekven [Russia; 9 EKVEN] and Kivutkalis [Latvia; 71 KIVUT], while those with the lowest scores are Copts [Egypt; 144 COPTS], Armenians [231 ARMEN] and Hradek b. Mikolov [Czech; 220 HRADK] (Table 50).  The contrast between these samples is shown in Figs. 27 and 28.  The time span in the male Class A samples used here is about 7,000 years, i.e. the period of the Neolithic Age and the succeeding times (Appendices 3 and 4).  The association found here between cranial length and chronological age, therefore, does not reflect the whole evolutionary or dispersion process of Homo sapiens sapiens after the event of out-of-Africa which conceivably began before 180,000 years ago (Hershkovitz et al., 2018).  Even so, however, this is an important finding to understand the background of brachycephalization.

Causes of brachycephalization

    As pointed out by Mizoguchi’s (1998b, c), cranial length and breadth vary relatively independently of each other in the among-group multivariate space.  This is reconfirmed in the present study (Tables 13 and 19).  Brachycepahlization or dolichocephalization (Weidenreich, 1945) is a phenomenon associated with time.  In Japan, Suzuki (1956) reported the first evidence of brachycephalization.  It is well known nowadays that dolichocephalization proceeded from the Kofun period (the 4th to 12th century A.D.) till the Middle Ages (the 12th to 16th c.), and then, reversely, brachycephalization started in the Middle Ages and continued to the present (Suzuki, 1956, 1969; Nakahashi, 1987).  According to Mizoguchi (1992), cranial breadth has changed in parallel with cranial index from the Kofun period up to the present, but cranial length has gradually and slightly decreased.  (Incidentally, it is said that there is no evidence for a great number of immigrants during the period between the Kofun and modern times.)  In a global scale, while cranial breadth does not have any high correlation with chronological age but with temperature (Figs. 17 and 18), cranial length has a considerably high correlation with chronological age (Figs. 21 and 22).  From these findings, it is considered that the decrease of cranial length in Japan is also part of such a world tendency.  But the reversal from dolichocepahlization to brachycephalization in Japan cannot be explained by the gradual change in cranial length.  Even if cranial breadth is strongly correlated with temperature in a global scale, there seems no evidence for a drastic change in temperature during the period between the Kofun and modern times in Japan, as far as the present author knows.

    It is well known, on the other hand, that brachycephalization and dolichocephalization have not necessarily proceeded at the same time or at the same pace in various areas of the world (e.g., Ikeda, 1982; Susanne et al., 1988; Kouchi, 1999, 2018).  What is the cause for the different patterns of fluctuation in cranial index between geographical regions or between chronological ages?

    To elucidate the causes of brachycephalization, Mizoguchi (1992, 1994, 1995b, 1996, 1997, 1998a, d, 1999, 2000a, 2001, 2002, 2003a, b, 2004a, b, 2005, 2007a, b, 2008, 2009, 2013a) carried out a series of PCAs of within-group correlations between cranial and postcranial measurements on the premise that population differences are extensions of individual differences (Howells, 1973), as mentioned above.  He found several common factors suggesting that, while cranial breadth has no consistent associations with any postcranial measurements, cranial length is significantly associated with many postcranial measurements, such as vertebral body size, costal chord, pelvic widths, and limb bone lengths and thicknesses; and considered that the variation in cranial length might, in part, be related to the degree of development of skeletal muscles or body size and, besides, that the form of the maternal pelvic inlet might be another important determinant of the neurocranial form.  On the way to proceed his study, Mizoguchi (2004b) tentatively hypothesized as follows: There are at least three possible causes for brachycephalization or dolichocephalization, i.e. diachronic changes in the amount of skeletal muscles, body size (substantially the same as the amount of skeletal muscles), and the pelvic form; and, in turn, possible causes for secular changes in body size and/or in the degree of development of skeletal muscles may be diachronic changes in quality and quantity of available nutrition, physical activity, etc.  In addition, Mizoguchi (2007b), similarly on the basis of within-group PCAs, stated that neither cranial length nor cranial breadth had any consistent associations with facial measurements across sexes, contrary to our expectations, and that the difference in the way of connecting with other characters between cranial length and breadth might be one of the reasons why brachycephalization and dolichocephalization alternately and irregularly occur in a geographic area.

    Later, Mizoguchi (2013a), also performing PCAs of within-group correlations, found positive associations between cranial breadth, the vertical diameter of the femoral head (bearing body weight), nasal height (relating to oxygen intake), and maximum pelvic breadth, and maintained that these findings were compatible with the cold adaptation hypothesis (Coon, 1962) and Ruff’s (1991, 1993, 1994, 2002) cylindrical thermoregulatory model, in which the pelvis tended to be wider in colder regions.  Miyashita and Takahashi (1971) and Houghton (1996) already pointed out that there were high correlations between body mass and nasal dimensions.  In addition, Bastir et al. (2011) showed that males had larger cranial airway passages, both absolutely and relatively, than females and that males tended to have relatively taller piriform apertures, internal nasal cavities and choanae than females, and suggested that the identified sex-specific differences in cranial airways might be linked with sex-specific differences in body size, composition, and energetics.  These findings are not inconsistent with those of Mizoguchi (2013a) and of the present study (Figs. 17 and 18).

    In summary, it was clarified in the PCAs of among-group correlations between craniofacial measurements and environmental variables that people possessing the broader neurocranium and the higher and wider face tended to live in colder regions of higher latitudes, and, independently of this tendency, that recent people tended to have anteroposteriorly shorter skulls than ancient people during the period of the Neolithic to modern times.  Various combinations of these two tendencies seem to have generated the fluctuation of brachycephalization and dolichocephaliztion in each of local regions.  If the above Mizoguchi’s findings based on within-group analyses can be utilized to explain among-group phenomena, the decrease in cranial length may be said to have been caused, in part, by the decrease of the body size or gracilization (Schwidetzky, 1980; Henneberg, 1988) from the Neolithic to the present, which may, in turn, be referred to diachronic changes of sociocultural factors, such as the development of technology, the decrease of physical activity or labor, the improvement of nutrition (Shimada, 1974; Kouchi, 2018), the change of food habits (Mizoguchi, 1993; Noback and Harvati, 2015), the decrease of biomechanical stress on the masticatory apparatus (Ringqvist, 1973; Baab et al., 2010; Mizoguchi, 2012) or the nuchal planum (Mizoguchi, 2008, 2009, 2012; Zafar et al., 2000), etc.  It can easily be noticed here that the degree of sociocultural changes varies from region to region and from times to times.  Therefore, the change only in cranial length caused by such sociaocultural factors can also explain the fluctuation of brachycephalization and dolichocephalization in some areas.  But the same logic cannot be used for the oscillation of cranial index oberved in Japan because the cranial index has changed mainly in parallel with cranial breadth.

    For the present, it can be said in general that brachycephalization or dolichocephaliztion is caused by the differential adaptations and/or acclimatizations of cranial length and breadth to our diverse natural and sociocultural environments and by the difference in the way of connecting with other characters between cranial length and breadth.

Unknown factors influencing the craniofacial morphology

    Path analysis was performed as a complementary analysis to confirm the existence of unknown factors making a relatively large contribution to each craniofacial measurement.  The results are shown in Tables 51 and 52.  It was found that cranial length had relatively high positive path coefficients on latitude, temperature, and chronological age; minimum frontal breadth had a relatively high positive coefficient with humidity and a relatively high negative coefficient with great circle distance; cranial breadth had a relatively high negative coefficient with temperature; basi-bregmatic height had relatively high positive coefficients on temperature and great circle distance; upper facial and nasal heights had very high negative coefficients with temperature; bizygomatic breadth and orbital height had relatively high negative coefficients with temperature; and nasal breadth had relatively high negative coefficients with temperature and latitude.  Namely, path coefficients from environmental variables to each craniofacial measurement indicate almost the same tendencies as found in the above PCAs.  In addition, the path analyses suggest that, for all the craniofacial measurements, there are unknown factors other than the environmental variables dealt with here.  For example, the residual variable for nasal breadth has the highest value of 0.79 of those for the craniofacial measurements (Table 51).  In the PCA based on the same data set (Tables 11), the total variance of nasal breadth explained by the five PCs or common factors is only 49.86%, the lowest value of those for the variables under consideration.  This means that there are some other unknown factors which are not negligible to explain the variation of nasal breadth.

    The existence of such unknown factors are suggested also for the other craniofacial measurements.  Needless to say, we must collect more data of various environmental factors, natural and artificial (cultural, social, etc.) and ancient and modern, to clarify the causal chain for the formation of our morphology.