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Preparation of craniofacial and limb bone data
To clarify the limits and regularity of
craniofacial variations and, if possible, to determine the causes of the
variations, 156 craniofacial and 78 limb bone measurement items were chosen,
and sample means and sample sizes for these measurement items have been
collected from the literature for many Homo
sapiens sapiens populations of the Neolithic to modern times in various
regions of the world (Appendices 1 and 2).
As well known, however, some measurement
items have been frequently used, analyzed, or reported, but others have not so
often. In the present study, the
measurement items frequently reported were first searched using 235 male
samples from modern human populations (because the number of the samples
collected is larger for males than for females). As a result, it was confirmed that the
craniofacial measurement items for which the sample size, or the number of
individuals, was 10,000 or more in a pooled sample consisting of the 235 samples
were as follows (the number in parentheses is a measurement item No. in Martin
and Saller [1957]): cranial length (1), cranial base length (5), minimum
frontal breadth (9), cranial breadth (8), basi-bregmatic height (17), upper
facial height (48), bizygomatic breadth (45), orbital breadth (51), orbital
height (52), nasal breadth (54), and nasal height (55). And the craniofacial measurement items for which
the sample size is 2,000 or more in the pooled sample are as follows (only
Martin’s Nos. [Martin and Saller, 1957]): 1, 5, 7, 9, 11, 8, 12, 16, 17, 23,
24, 25, 26, 27, 28, 29, 30, 31, 40, 48, 45, 43, 46, 51, 52, 54, 55, 57, 60, 61,
62, 63, 65, 66, 32, 72, and 73. In the
present study, the former is called “the first variable set of the skull,” and
the latter, “the second variable set of the skull” (Table 1). Similarly, the postcranial measurement items
for which the sample size is 750 or more in the pooled sample are as follows: maximum
length (1), maximum diameter of the midshaft (5), and minimum diameter of the
midshaft (6) for the humerus; maximum length (1) for the ulna; maximum length
(1) for the radius; maximum length (1), bicondylar length (2), sagittal
diameter at midshaft (6), transverse diameter at midshaft (7), circumference at
midshaft (8), and epicondylar breadth (21) for the femur; maximum length (1a) for
the tibia; and maximum length (1) for the fibula. This is called “the first variable set of postcranial
bones” (Table 1). The postcranial
measurement items for which the number of individuals is 500 or more in the
pooled sample are as follows: 1, 7, 9, 5, 6, and 7a for the humerus; 1, 12, and
11 for the ulna; 1, 4, and 5 for the radius; 1, 2, 6, 7, 8, 18, and 21 for the
femur; 1a, 8, 8a, 10, and 10a for the tibia; and 1, 2, and 3 for the fibula. This is “the second variable set of
postcranial bones” (Table 1).
To confirm the limits of among-group
variation in each measurement, the second variable sets were used for both the
skull and postcranial bones (Table 2).
The minimum and maximum values were sought across 527 male and 206
female samples of the Neolithic to modern times from various regions in the world. The data were separately processed for males
and females.
As shown in Table 2, the standard
deviations (SDs) in Japanese male and female samples (sample size is about 30
for males and 20 for females) seem relatively similar to those in Egyptian
samples (sample size is about 900 for males and 600 for females) for at least
20 craniofacial measurement items common to both populations, though no
significance tests are carried out. In
the present study, therefore, the SDs in the Japanese samples were used as representative
within-group SDs for a given local population of Homo s. s. because the number of measurement items is much larger
in the Japanese samples than in the Egyptian.
In the succeeding analyses, orbital breadth
(Martin’s No. 51) is excluded because of its extremely large measurement error
variance compared to those for other craniofacial measurements (Sakura and
Mizoguchi, 1983).
The variables for which the number of male
samples of the Neolithic to modern times totaled up to 350 or more (in the case
of “Sample size of 20 or more” in Table 2) were, furthermore, selected from the
second variable set of the skull for the succeeding multivariate analyses. They are Nos. 1, 9, 8, 17, 48, 45, 52, 54,
and 55. This set is called “the third
variable set of the skull” (Table 1).
Similarly, “the third variable set of postcranial bones” was made up on
the basis of the male samples. This
consists of Nos. 1, 7, 5, and 6 of the humerus and Nos. 1, 6, 7, and 8 of the
femur (Table 1). However, the number of samples
for these postcranial variables (in the case of “Sample size of 20 or more” in
Table 2) is as small as about 40 or 50.
In addition to the above variable sets, the
fourth variable set of the skull (Table 1) was made up to confirm the
differences in cranial morphology between Homo
sapiens sapiens and Herto [Homo sapiens idaltu] (White et
al., 2003) by excluding minimum frontal breadth (No. 9) from the third variable
set. Namely, it
consists of Martin’s Nos. 1, 8, 17, 48, 45, 52, 54, and 55. Using this fourth variable set, the
ultramodern skull of Iyeyoshi Tokugawa (Suzuki, 1967, 1981) was also compared
with various samples from all over
the world.
Finally, it was checked whether or not
samples were practically usable in among-group multivariate analyses. The conditions for selection of samples are
the following three: 1) both average sample size and minimum sample size across
variables are equal to or more than 25 (Class A in Table 1); 2) the average
sample size is 25 or more and the minimum sample size is 10 or more (Class B in
Table 1); and 3) the average sample size is 20 or more and the minimum sample
size is 5 or more (Class C in Table 1).
Preparation of environmental data
For each sample of craniofacial and
postcranial measurements, data on average annual temperature (degree Celsius),
average annual precipitation (mm), average annual relative humidity (%),
chronological age (years before 2000 A.D.), latitude (degree), and longitude
(degree) were also collected from other sources. As regards the temperature, precipitation,
and relative humidity in the site from which each sample was derived, the data
were mainly obtained from CantyMedia (2017).
For latitude and longitude, the data were acquired from MY NASA DATA
(2016-2017) and www.Latlong.net (2016-2017).
The data on these variables are, however, not so strict because of the
rough assignment to samples by the present author. But the most serious problem on these data is
the fact that they are all modern data.
This should always be kept in mind.
The data of chronological age is also not
so strict. The starting point for count
is A.D. 2000. Therefore, 5000 B.P., for
example, is converted to 5050 years before 2000 A.D. When the date of a modern sample is not described
or unknown, the year of publication is used as the chronological age. If the date is younger than or equal to A.D.
2000, the chronological age is set to zero.
In addition to the above, the great circle
distance (km) from Kamoya’s hominid site (Omo-Kibish I), Ethiopia (Shea, 2008)
to a site under consideration was also calculated according to the following
formula:
D12 = R cos-1
{sin lat1 sin lat2 + cos lat1 cos lat2 cos (long1
- long2)},
where D12 is a great circle distance in km; R (km) is equivalent to one degree of
the great circle distance in degrees based on the average of the equatorial and
polar radii of the earth (National Astronomical Observatory of Japan, 2017),
i.e., 111.13287 km; lat1
and long1 as well as lat2 and long2 are the latitude and
longitude in degrees for Site 1 as well as for Site 2, respectively. This formula is equivalent to that shown in
Spuhler (1972).
As a starting point for great circle
distances, the latitude and longitude (5.40N, 35.93E) of Kamoya’s hominid site
(Omo-Kibish I), Ethiopia (Shea, 2008) was preliminarily chosen because
Omo-Kibish I (Omo I) has been said to be the oldest (196±5
ka) anatomically modern Homo sapiens
(Hammond et al., 2017), although a much older date, about 300,000 years ago,
was very recently reported for the newly discovered fossils of Homo
sapiens from Jebel Irhoud, Morocco (Richter et al., 2017; Hublin et al.,
2017). To a site in the Americas, the
total of two great circle distances was assigned: the distance from Kamoya’s
hominid site to Naukan (66.03N, 169.70W), Chukchi Peninsula, Russia, plus the
distance from Naukan to the site in question.
To sum up, six variables, i.e., average
annual temperature, average annual precipitation, average annual relative
humidity, chronological age, absolute value of latitude, and great circle
distance from Kamoya’s hominid site are conveniently dealt with as
environmental variables in the present study, though, strictly speaking, the
latter three are not environmental factors.
Multivariate Statistical analysis
To elucidate the limits of the multivariate distribution of sample means from
world human populations, principal component analysis (Lawley
and Maxwell, 1963; Okuno et al., 1971, 1976; Takeuchi and Yanai, 1972) was first applied to the within-group correlation
matrices of two different samples available at hand: a
Japanese male sample from the Kinai district (Miyamoto, 1924) and an Australian
Aboriginal male sample of 4000-100 B.P. from Murray River Valley (Brown, 2001). From
these principal component analyses (PCAs), the coefficients of the simultaneous
linear equations for prediction of principal component scores (PC scores) were
obtained. The number of
principal components (PCs) was
so determined that the cumulative proportion of the variances of the PCs exceeded 85%. The PC score
vector for a sample mean vector was calculated on the basis of the world
average vector, i.e., the grand mean vector of all sample mean vectors used (Table
2), and the SDs of original variables as well as the coefficients of the
simultaneous linear equations from either of the above two samples.
The
significance of factor loadings was tested by the bootstrap method (Efron, 1979a, b, 1982; Diaconis and Efron, 1983;
Mizoguchi, 1993). To estimate the bootstrap standard
deviation of a factor loading, 1,000 bootstrap replications, including the
observed sample, were used. The
bootstrap standard deviation was estimated by directly counting the cumulative
frequency for the standard deviation in the bootstrap distribution. As noted by Diaconis
and Efron (1983), however, when a statistic like correlation coefficient has an extreme value, e.g. 1, in an observed sample, most
bootstrap values of the statistic would be nearly equal to 1, and, therefore, the
width of the interval associated with 68% [within ± 1 SD in a normal
distribution] of the bootstrap samples would be approximately zero. In such a case, the bootstrap SD is
incorrect. This is a point to be cautioned.
Also for among-group analyses, PCA was
used. The PCs obtained were further
transformed by Kaiser's normal varimax rotation method (Asano, 1971; Okuno et
al., 1971) into different factors to reveal other possible associations behind
the measurements. The statistical
significance of factor loadings on both PCs and rotated factors (Facs) was
again tested by the bootstrap method.
The presence of common factors, such as PCs or Facs, was furthermore
tested by evaluating the similarity between the factors obtained for two different data sets of the same kind, that is, by estimating Spearman's rank
correlation coefficient, rho (Siegel, 1956), between the patterns of variation of factor loadings.
Finally, path analysis (Wright, 1934; Li,
1956, 1975; Kempthorne, 1969; Yasuda, 1969; Mizoguchi, 1978, 1986, 2010) was
carried out to get a piece of information on some unknown factors which can
influence the among-group variations of craniofacial measurements. The model used here is a very simple one, the
same as that described in Mizoguchi (1978).
Craniofacial measurements were regarded as endogenous variables, and
environmental variables, as exogenous variables.
Methods of calculation
Statistical
calculations were executed using programs written by the present author in FORTRAN: BSFMD for
calculating basic statistics, BTPCA and
PCAFPP
for principal component analysis and Kaiser's normal varimax rotation, RKCNCT
for rank correlation coefficients, and
PATHAN for path analysis.
The FORTRAN 77 compiler used was
FTN77 for personal computers, provided by Salford Software Ltd. To increase efficiency during programming and
calculation, a GUI for programming, CPad, provided by “kito,” was used.
 RESULTS
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PAPER 2