Bull. Natl. Mus. Nat. Sci., Ser. D, 39, pp. 19–46, November 22, 2013

Fractions of Variation of Neurocranial Form Associated with
Facial and Postcranial Bones: Within-group Analysis
Yuji Mizoguchi
Department of Anthropology, National Museum of Nature and Science
4–1–1 Amakubo, Tsukuba-shi, Ibaraki 305–0005, Japan
E-mail: mzgch@kahaku.go.jp

Abstract Taking into account the craniofacial and postcranial measurements supposedly associated with brain size, oxygen intake, thermoregulation, skeletal muscle mass, body size, anteroposterior head balance, and parturition, the interrelationships between such measurements and threemain neurocranial measurements were examined through principal component analyses of withingroup data to elucidate the determinants of neurocranial form. The data used are of 30 males and
20 females of modern Japanese. As a result, it was found, in both males and females, that there
was at least a common factor that was relatively strongly associated with cranial length, nasal
height, the sagittal diameter of the femoral midshaft, and the vertical diameter of the femoral head
and talar length, but not associated with body height. These ﬁndings suggest that heavier individuals who have a longer/thicker gut and a comparatively large amount of skeletal muscle (except thenuchal ones), which consume a relatively large amount of oxygen, tend to have a shorter (andprobably wider) neurocranium, regardless of brain size and body height. Furthermore, positive
associations were found between cranial breadth, the vertical diameter of the femoral head, nasal
height, and maximum pelvic breadth. This is compatible with the cold adaptation hypothesis andRuffʼs cylindrical thermoregulatory model. In order to more concretely clarify the determinants ofneurocranial form, however, multivariate among-group analyses should also be conducted using
both morphological measurements and environmental variables.
Key words : Neurocranial form, Body form, Controlling factors, Principal component analysis,
Bootstrap method

Many investigations have been conducted toclarify the causes of variation in neurocranial
form (size and shape). The present author also
carried out a series of multivariate analyses ofwithin-group correlations between three mainneurocranial maesurements (i.e., cranial lengthand breadth, and basi-bregmatic height) andpostcranial measurements to elucidate the causesof brachycephalization (Mizoguchi, 1992, 1994,
1995, 1996, 1997, 1998a, c, 1999, 2000, 2001,
2002, 2003a, b, 2004a, b, 2005, 2007b, 2008,2009) on the premise that population differences
are extensions of individual differences, as statedby Howells (1973). As a result, he found that,while cranial breadth has no consistent associations with any postcranial measurements, cranial
length is signiﬁcantly associated with many post-

cranial measurements, such as vertebral bodysize, costal chord, pelvic widths, and limb bonelengths and thicknesses, and considered that thevariation in cranial length may, in part, be related
to the degree of development of skeletal muscles
or body size and, besides, that the form of thematernal pelvic inlet may be another important
determinant of neurocranial form.
Alongside the aforementioned series of withingroup analyses, Mizoguchi (1998b) performed
among-group analyses as well, although they
were concerned only with craniofacial measurements. The results showed that, while cranial
breadth, bizygomatic breadth, upper facialheight, and nasal height always vary in parallelwith one another, cranial length and nasal
breadth vary independently of each other and of

20

Yuji Mizoguchi

the above four measurements. At that time, thepresent author could not imagine the reason why
cranial length and nasal breadth vary independently of the other cranial measurements. Later,
however, he found two interesting descriptions in
Houghton (1996): One is of Miyashita and Takahashiʼs (1971) ﬁnding based on Japanese datathat there is a strong correlation between bodymass and airway height (nasal height), and theother is of some data from Papua New Guinea
suggesting that both nasal height and nasal
breadth give a better approximation of the size ofthe nasal passage, with a high correlation being
found between body mass and nasal dimensions.
These are very suggestive in interpreting theindependent variations of nasal breadth and cranial length within the craniofacial structure.
According to Mizoguchi (2007b), there is no signiﬁcant association between these two measurements also in within-group analyses of only craniofacial measurements. Therefore, even if they
were correlated with each other through somecommon factors related to postcranial bones orbody size, the contribution of such common factors would not be so high. But they may, independently of each other, be strongly associatedwith other different factors common to postcranial characters. To conﬁrm these points, the present study attempts to ﬁnd such common factors
by combining some postcranial measurementswith a data set of craniofacial measurements
including both cranial length and nasal dimensions.
In addition, there are a few other issues to be
examined. Mizoguchi (2007a) preliminarily estimated ecological (or among-group or inter-population) correlations between neurocranial andlimb bone measurements simply using Spearmanʼs rank correlation coefﬁcient, and foundthat, in both males and females, there are signiﬁcant associations between cranial length and thethickness measurements of the radius, ulna,
femur, and tibia. It should be noted here that thelimb bone measurements signiﬁcantly associatedwith cranial length are almost always thicknesses, not lengths. In the case of within-group

analyses (Mizoguchi, 2001, 2003a, b), cranial
length is signiﬁcantly correlated with both maximum lengths and thickness measurements ofmajor limb bones. This discrepancy between theamong-group and within-group analyses suggeststhat limb bone length and thickness are associated with cranial dimensions in different ways.
Decomposing body form after Ruff (2002), it isdivided into body size and body shape. Body size
is further subdivided into body height or length(stature), body breadth (e.g., bi-iliac or maximum
pelvic breadth), and body mass (weight), while
body shape (or relative body mass) is expressedby body mass index (BMI＝weight/height2,
a.k.a. Queteletʼs Index). Using these concepts,
limb bone lengths, especially of the lower
extremities, seem to be associated with bodyheight, and limb bone thickness measurements,
to be related to body mass (Ruff et al., 1991) orskeletal muscle mass. In the present study, keeping the differential contributions of these factors
in mind, it is examined again whether multivariate within-group analyses of limb bone lengths
and thicknesses based on different combinationsof craniofacial and postcranial measurementsfrom those used in Mizoguchiʼs work (2001,
2003a, b, 2009) show the same tendencies as
those suggested by Mizoguchiʼs (2007a) bivariate
among-group analysis.
Recently, Mizoguchi (2012a) found, throughprincipal component analyses of the three dimensional structural deviations in the neighborhoodof cranial landmarks obtained by a ﬁnite element
scaling method, that the degree of occlusal wearon the maxillary ﬁrst molar (UM1) is signiﬁcantly associated with the magnitude of strain at
the inion in Japanese. This ﬁnding suggests thatcraniofacial form may vary in response tomechanical stresses from the masticatory and/or
nuchal muscles. An exaggerative extrapolation ofthis tendency further suggests the anteroposterior
elongation of both the palate and the occipitalbone in those individuals who have heavy UM1
occlusal wear (Mizoguchi, 2012b). If so, thismay support Yamaguchiʼs (1984) hypothesis ofanteroposterior head balance for brachy- andNeurocranial Form and Facial and Postcranial Bones

dolicho-cephalization. In the present study,
this hypothesis is also examined by adding facial
and maxillo-alveolar lengths to the data sets of
craniofacial and postcranial measurements tobe analyzed.
Finally, the head and body forms are wellknown to vary in response to climatic changes.
For example, Beals (1972) showed on a worldwide scale that the mean cephalic index of modern humans is higher in colder regions. Thisimplies that temperature may be one of the determinants of human neurocranial form, and is consistent with a famous ecogeographical rule,
Allenʼs rule. Later, Crognier (1981), using European, North African and Middle Eastern malesamples, quantitatively showed that not only
head and face dimensions but also body size are
signiﬁcantly correlated with temperature and precipitation. To explain the relationship of humanbody form with climatic factors, Ruff (1991,
2002) proposed the ʻcylindrical thermoregulatorymodelʼ that maintaining a constant body breadth
results in a constant surface area-to-body mass
ratio, despite changes in height, and showed that,while absolute bi-iliac breadth has little variation
within the human populations living in similar
climatic zones, this breadth changes across different climatic zones, namely, increases fromwarmer to colder climates, regardless of stature.
On the other hand, in Mizoguchiʼs (2005, 2009)
within-group analyses, the pelvic breadth is signiﬁcantly associated with cranial length. From an
obstetrical perspective, children of mothers witha wider pelvis should have longer heads. According to Ruffʼs cylindrical thermoregulatory modeland Allenʼs rule above, however, people living incolder regions must have wider pelves andshorter heads. This is also an issue to be examined.
As mentioned above, there are many candidates for the determinants of or factors controlling neurocranial form. In the present study,some candidates, particularly biomechanical factors, are ﬁrst explored by referring to previous
studies, and then, the facial and postcranial measurements that are supposedly associated with

21

such plausible factors are selected. Although theplausible factors set up in this way are hypothetical, analysis of the interrelationships between theselected measurements is considered very helpful
in understanding the formation of our morphology, especially at an early stage of research. In
the present study, multivariate within-group analyses are carried out to clarify the degree of inﬂuence of the factors plausibly affecting neurocranial form.
Materials
The data used are the cranial and postcranialmeasurements reported by Miyamoto (1924,
1925, 1927), Okamoto (1930), Kikitsu (1930),
and Hirai and Tabata (1928a, b). They wereobtained from the same adult individuals, 30 maleand 20 female modern Japanese, who lived in the
Kinai region. However, the values of “stature”(Miyamoto, 1924) are those of living stature,
except for one individual. The basic statistics forthe measurements analyzed are listed in Table 1.
Incidentally, these samples are the same as
those used in previous studies (Mizoguchi, 1994,
1995, 1996, 1997, 1998a, b, 1999, 2000, 2001,
2002, 2003a, b, 2004a, b, 2005, 2007b, 2008,2009).
Methods
First of all, candidates for the determinants ofor factors controlling neurocranial form aresearched for by referring to previous studies.
Some of them may affect ontogenetic processes,
and others may act in evolutionary processes orin both. In the present study, however, their relationships with neurocranial form are preliminarily examined through multivariate within-group
analyses on the premise that population differences are extensions of individual differences(Howells, 1973).
Candidates of the factors inﬂuencing neurocranial form
Among the plausible controlling factors that

22

Yuji Mizoguchi
Table 1. Means and standard deviations for the cranial and postcranial measurements of Japanese males andfemales used in the present study.1)
Variable2)

SKULL
1
Cranial length5
Cranial base length8
Cranial breadth17
Basi-bregmatic height31(2) Inion-opisthion chord
37(2) Cranial base angle
38
Endocranial capacity (cubic root)3)40
Facial length
45
Bizygomatic breadth
54
Nasal breadth
55
Nasal height60
Maxillo-alveolar length
70
Ramus height71
Minimum ramus breadth
THORACIC VERTEBRA VIII
4
Superior sagittal diameter of vertebral body
7
Superior transverse diameter of vertebral body
RIB IV
4Chord
HUMERUS2
Total length
6
Minimum diameter of midshaft
PELVIS
2Maximum pelvic breadth
FEMUR
1
Maximum length
6
Sagittal diameter at midshaft
18
Vertical diameter of head
TIBIA
1aMaximum length
TALUS
1
Length
BODY SIZE
StatureMales

Females

n

Mean

SD

n

Mean

SD

30
30
30
30
30
30
30
29
30
30
30
29
30
30

178.4
102.3
141.0
139.8
40.5
29.2
11.4
100.2
133.4
26.3
52.5
54.1
61.1
33.7

5.6
3.5
4.7
5.8
4.6
2.6
0.3
4.0
5.3
1.8
2.9
2.9
5.0
2.8

20
20
20
20
20
20
20
19
20
20
20
19
20
20

169.4
94.8
137.8
132.1
41.0
29.0
11.0
94.4
125.9
25.0
48.9
50.9
55.4
31.5

4.9
3.6
4.1
3.8
4.7
3.6
0.3
4.7
3.8
1.7
2.5
2.5
3.4
2.3

30
30

26.4
31.6

2.0
2.5

19
19

23.8
28.3

1.9
1.5

—

—

—

20

142.3

9.0

30
30

289.8
17.4

15.7
1.5

20
20

269.5
14.6

12.5
0.9

30

258.8

13.8

20

251.9

14.4

30
30
30

413.7
27.1
45.6

24.0
2.3
2.2

20
20
20

382.3
23.3
41.2

20.6
1.8
2.8

30

331.9

20.5

20

305.1

17.2

29

50.7

2.1

20

45.6

1.9

29

1577.172.0

191489.255.9

1)The estimates of basic statistics were recalculated here on the basis of raw data published by previous authors. Skull and stature:
Miyamoto (1924); vertebrae: Okamoto (1930); ribs: Kikitsu (1930); humerus: Miyamoto (1925); pelvis: Miyamoto (1927); femur andtibia: Hirai and Tabata (1928a); and talus: Hirai and Tabata (1928b). When measurements were available for both sides, only those fromthe right side were used.
2)
Variable number according to Martin and Saller (1957).
3)
The cubic root was calculated by the present author.

may inﬂuence neurocranial form (size andshape), the ones that ﬁrst come to mind are brain
size and shape. The problem of whether brain
form determines neurocranial form or vice versa
has been discussed for over a hundred years(Macalister, 1898; Sullivan, 1978). Althoughdata for brain shape are not given by Miyamoto(1924), he reported that for endocranial capacity,which can be used as a measure of brain size.
Furthermore, according to Kean and Houghton(1990), it is likely that the cranial base, early todevelop and stable in form because of its intimate relationship with the brain and cranial
nerves, constitutes a major architectural templatein the developing head. In the present study,
therefore, cranial base length is also considered

to reﬂect the size of the basal region of the brain.
Kean and Houghton (1990) argue that there isa clear and direct relationship between increasein airway size, in measures of lung size such asvital capacity, and that in body oxygen demand,as indicated particularly by skeletal muscle mass.
In the present study, nasal height and costal
chord are used as measures of oxygen intake.
According to Crognier (1981), both nasal heightand body weight have signiﬁcant negative associations with temperature. Therefore, nasal
height must be considered from the two viewpoints of body oxygen demand and thermoregulation.
Nasal breadth, which was suggested by Mizoguchi (1998b) in among-group analyses to be rel-

Neurocranial Form and Facial and Postcranial Bones

atively independent of other craniofacial measurements, may be regarded as a composite
measure of thermoregulation and/or humidity
regulation. Wolpoff (1968) shows that there is atendency for nasal breadth to decrease in two
populations, namely, Australian Aborigines andso-called Alaskan Eskimos, as the climate
becomes cooler and drier. In contrast with theseﬁndings, Crognier (1979, 1981) reports on thebasis of European, North African and Middle
Eastern samples that, while nose breadth certainly has a signiﬁcant positive correlation withthe mean temperature of the hottest month (onlyin females), it has a signiﬁcant negative correlation with mean precipitation (of the rainiest
month in males and, in females, of the driest
month). Incidentally, stature (in both sexes) andbody weight (only in males) have signiﬁcantnegative correlations with mean annual temperature and positive correlations with the mean precipitation of the driest month (Crognier, 1979,1981). Although Houghton (1996) suggests thatboth nasal height and nasal breadth give a better
approximation of the size of the nasal passage
and there is a high correlation between bodymass and nasal dimensions, the relationships ofnasal size (height and breadth) with body size
(height, breadth, and mass) and their relationships with temperature and humidity (or precipitation) seem to be very complicated. In the present study, nasal breadth is tentatively assumed to
be a composite measure of thermoregulation andhumidity regulation.
Mizoguchiʼs (2001, 2003a, b, 2009) multivariate within-group analyses show that both limb
bone lengths and thicknesses are signiﬁcantly
associated with cranial length. However, Mizoguchiʼs (2007a) bivariate among-group analysis
suggests that only limb bone thicknesses, notlengths, are strongly associated with cranial
length. Ruff (2002) states that lower limb articular size, especially femoral head size, is an effective predictor of body mass in humans because,
while long-bone diaphyses change their diameters in response to mechanical loading, articulardimensions are less sensitive to differences in23

activity level than diaphyseal breadth dimensions. If this is the case, the diameters of longbone midshafts may be considered to reﬂect skeletal muscle mass. In fact, Wescott (2006), using
data of prehistoric and historic North American
populations, suggested that there is signiﬁcantvariation in femur midshaft shape and robusticity
in all populations analyzed, and that, while
inferred mobility levels do not correspond consistently with femur midshaft structure in either
males or females, sexual dimorphism is generally
greater in more mobile populations. Furthermore,
Weiss (2010), observing 65 prehistoric Californian Native Americans, reported that aggregate
upper limb muscle marker value has signiﬁcantcorrelations with the aggregate cross-sectional
robusticity of the humerus (Spearmanʼs rho＝0.536; P＜0.01), cranial length (rho＝0.377;
P＜0.01), cranial breadth (rho＝0.293; P＜0.05),
and body mass calculated from femoral headbreadths (rho＝0.385; P＜0.01). Ibáñez-Gimeno
et al. (2013), using 62 upper limb specimensfrom Catalonia and the Balearic Islands, also
maintain that individuals with strongly marked
entheseal changes have increased diaphyseal
rigidities, and that large muscular scars are
related to diaphyseal shape. In the present study,
therefore, the minimum diameter of the humeral
midshaft and the sagittal diameter of the femoral
midshaft are used as measures of skeletal muscle
mass. And maximum femoral and tibial lengths
as well as total humeral length are used as measures that are associated with body height, in
addition to stature itself. As regards body mass,
not only the vertical diameter of the femoral headbut also the diameters of the vertebral body ofthe eighth thoracic vertebra and talar length areemployed as predictors of body weight.
Weijs and Hillen (1986) reported that headwidth had a signiﬁcant correlation with the crosssectional area of the masseter muscle. On theother hand, the strong association between cranial breadth and bizygomatic breadth has been
conﬁrmed in both within-group (Mizoguchi,1992) and among-group (Mizoguchi, 1998b)
analyses. From these ﬁndings, it can be inferred

24

Yuji Mizoguchithat the zygomatic arch plays an important roleas an intermediate between cranial breadth andthe amount of masticatory (masseter and temporal) muscle. In addition, as the insertion sites of
all the masticatory muscles (masseter, temporal,
and medial and lateral pterygoid muscles) arelocated on the mandibular ramus, the ramus form
must also be taken into consideration. In thepresent study, therefore, bizygomatic breadth aswell as ramus height and minimum ramus
breadth are used as measures of masticatory
muscle mass.
In Mizoguchiʼs (2001, 2003a, b, 2004b)
hypothesis, the nuchal planum plays an importantrole as an intermediate between cranial lengthand postcranial measurements. He consideredthat the degree of general development of skeletal muscles, including nuchal muscles, was acause of the strong association between cranial
length and limb bone measurements. Later, however, Mizoguchi (2008), examining direct relationships between cranial length and occipital
measurements, did not ﬁnd any signiﬁcant associations between them. Furthermore, Mizoguchi(2009) conﬁrmed on the basis of Japanese andAustralian Aboriginal data that the inion-opisthion
chord was not signiﬁcantly associated withcranial length or with any postcranial measurements. Therefore, he concluded that the inionopisthion chord at least is not an appropriate
measure for the size of the nuchal planum,presumably because of the difﬁculty in determining a landmark, the inion (Mizoguchi, 2009).
Recently, however, as was stated in the Introduction, Mizoguchi (2012a) found that the degree ofocclusal wear on the UM1 was signiﬁcantly
associated with the magnitude of strain at theinion in Japanese, and Mizoguchi (2012b)
showed that those individuals who had heavy
UM1 occlusal wear tended to have an anteroposteriorly elongated palate and occipital bone.
These ﬁndings imply that craniofacial form maychange in response to mechanical stresses fromthe masticatory and/or nuchal muscles and, at thesame time, may support Yamaguchiʼs (1984)
hypothesis of anteroposterior head balance. In

the present study, therefore, facial and maxilloalveolar lengths and the inion-opisthion chord aswell as the cranial base angle are used mainly as
measures of anteroposterior head balance. The
inion-opisthion chord is also employed to reconﬁrm the involvement of nuchal muscles in general skeletal muscles by using different sets of
craniofacial and postcranial measurements fromthose used in previous analyses. As regards cranial base angle, Kean and Houghton (1990) state
that, in Polynesians, with their large cranial baseangle, the upper facial skeleton with the contained airway is positioned in a markedly anteroinferior manner and, hence, nasal height becomeslarge relative to that of most other groups of
Homo sapiens. From this viewpoint, cranial baseangle is also regarded as a measure of oxygen
intake.
According to Ruffʼs (1991, 2002) cylindricalthermoregulatory model and Allenʼs rule, people
living in colder regions tend to have wider pelves
and shorter or wider heads. On the other hand,
Mizoguchiʼs (2005, 2009) within-group analyses
show that the pelvic breadth is signiﬁcantly associated with cranial length, suggesting that thechildren of mothers with a wider pelvis tend tohave longer heads. In the present study, therefore, maximum pelvic breadth is used as a composite measure of thermoregulation and parturition.
In summary, the candidates of controlling factors that are considered to be associated with theformation of neurocranial form and are practically taken into account in the present study are
as follows: brain size, oxygen intake, thermoregulation (cold adaptation), humidity regulation,skeletal muscle mass, body size (height, breadth,and mass or weight), anteroposterior head balance, and parturition.
Statistical analysis
Because of the statistical restriction on sample
size given the number of variables, three sets ofmeasurements to be analyzed were constructedfrom the measurements selected in the above
section. The ﬁrst set is concerned with skeletal

Neurocranial Form and Facial and Postcranial Bones

muscle mass and all the other controlling factors;
the second, with body height instead of muscle
mass; and the third, with body mass or weight.
Typical combinations of measurements areshown in Tables 2, 9, and 16. Furthermore, onlyin the case of females, the data of costal chord
are available. Therefore, the additional data sets
including costal chord were also analyzed, as
shown in Tables 7, 14, and 21.
To examine the overall relationships between
the selected measurements, principal component
analysis (Lawley and Maxwell, 1963; Okuno etal., 1971, 1976; Takeuchi and Yanai, 1972) wasapplied to their correlation matrices. The numberof principal components was determined so thatthe cumulative proportion of the variances of theprincipal components exceeded 80%. The principal components obtained were then transformedby Kaiserʼs normal varimax rotation method(Asano, 1971; Okuno et al., 1971) into different
factors in an attempt to reveal other associations
behind the measurements.
The signiﬁcance of factor loadings was tested

25

by the bootstrap method (Efron, 1979a, b, 1982;
Diaconis and Efron, 1983; Mizoguchi, 1993). In
order to estimate the bootstrap standard deviationof a factor loading, 1,000 bootstrap replications,
including the observed sample, were used. The
bootstrap standard deviation was estimated bydirectly counting the cumulative frequency forthe standard deviation in the bootstrap distribution.
The presence of common factors, such as
those represented by principal components or
rotated factors, was further tested by evaluating
the similarities between the factors obtained formales and females, that is, by estimating Spearmanʼs rank correlation coefﬁcient, rho (Siegel,1956), between the patterns of variation of factor
loadings.
Statistical calculations were executed using
programs written by the author in FORTRAN:
BSFMD for calculating basic statistics, BTPCA
for principal component analysis and Kaiserʼsnormal varimax rotation, and RKCNCT for rankcorrelation coefﬁcients. The FORTRAN 77 com-

Table 2. Principal component analysis of the correlations between three main neurocranial measurements and thecraniofacial and postcranial measurements (excluding costal chord) that are supposedly associated with brainsize, muscle mass, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (males).1)
Variable2)

Factor loadings
PC I

II
−0.02
−0.17
0.49
0.30**
−0.12
0.29*
0.20
−0.41
0.25
0.16

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.72
0.56
0.47

5
38

Cranial base length
Endocran. cap. (cub. r.)

0.71
0.69

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Min. diam. of hum. midshaft
Sag. diam. of fem. midshaft

0.70
0.69
0.45
0.56
0.73

31(2)

Inion-opisthion chord

0.07

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.15
0.65
0.52

0.05

III

IV

V

VII

0.06
−0.49*** 0.15
0.10
−0.24***−0.53**
0.45*
0.18* −0.13−0.16**−0.41** −0.37* −0.15
0.23**
0.13−0.42*** −0.09−0.05
0.15* −0.23***−0.36** −0.13
0.09−0.21*** −0.05
−0.06
0.04
0.44*** −0.04
0.07
0.14
0.13
−0.26
−0.38**
0.33***−0.05−0.41*
0.34*
0.00
0.54***
0.25
0.15
−0.20
0.53*** −0.03
0.29
0.32* −0.13
−0.12
0.12
0.62* −0.51*
0.16−0.35*** −0.23**−0.34* −0.17
−0.02
−0.03
−0.32*** −0.08−0.12−0.66*** −0.03
0.51*** 0.16
−0.14

55

Nasal height

0.40

0.83
0.10
−0.55* −0.04−0.36**
0.18
0.51*
0.35

2

Maximum pelvic breadth

0.66

−0.13

0.31** −0.01

0.20*

54

Nasal breadth

0.36

−0.33

0.44**

0.14

0.22

32.35
32.35

13.34
45.69

10.41
56.10

9.21
65.31

7.21
72.51

Total contribution (%)
Cumulative proportion (%)

VI

0.10
0.00
−0.06

Total variance
(%)
84.81
89.13
86.00
85.13
69.34
76.84
87.75
93.70
78.17
78.96
85.62
87.95
83.95
88.95

0.01

84.34

−0.26*

66.16

0.55***

0.11

81.70

6.15
78.66

4.19
82.85

82.85
82.85

−0.05

1)
Sample size is 29. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

26

Yuji Mizoguchi
Table 3. Rotated solution of the ﬁrst seven principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord)that are supposedly associated with brain size, muscle mass, antero-posterior head balance, oxygen intake,parturition, or thermoregulation (males).1)
Variable2)

Factor loadings
Fac I

II

III

IV

V

VI

VII

−0.56
0.18
0.12

−0.23
−0.06
−0.05

0.25
−0.04
−0.04

0.24
0.02
0.14

−0.03
−0.16

−0.13
−0.25

0.06
−0.12

−0.06
0.31*

−0.22
−0.03
−0.13
0.04
−0.09

0.21
−0.41
−0.13
−0.22
−0.31

0.15
−0.12
0.15
0.63**
0.23

0.28
0.22
0.92***
−0.17
0.03

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.04
0.26
0.10

−0.17
−0.84**
0.16

538

Cranial base length
Endocranial capacity (cubic root)

0.20
0.18

−0.31
−0.49

−0.58
−0.27
−0.89**−0.83*
−0.47

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Min. diam. of hum. midshaft
Sag. diam. of fem. midshaft

0.52**
0.77**−0.02
0.36
0.77**

−0.30
−0.01
−0.13
0.10
−0.13

−0.47
−0.21
−0.12
−0.41
−0.16

31(2)

Inion-opisthion chord

0.07

0.29

0.13

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.19
0.09
0.09

0.71
−0.40
−0.02

−0.40
−0.10
−0.10

−0.07
−0.07
−0.10

55

Nasal height

0.85*** −0.05

−0.04

−0.09

0.21

0.16

−0.21

2

Maximum pelvic breadth

0.32

−0.33

−0.14

−0.52

−0.20

0.33

0.08

0.09

−0.09

0.11

−0.09

−0.09

0.85***

0.22

54

Nasal breadth−0.86*** −0.04

−0.07

0.07

0.25
−0.26
−0.76**
0.14−0.92***
0.13

−0.19
0.25
−0.00

1)

Sample size is 29. Cumulative proportion of the variances of the seven principal components is 82.85%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Table 4. Principal component analysis of the correlations between three main neurocranial measurements and thecraniofacial and postcranial measurements (excluding costal chord) that are supposedly associated with brainsize, muscle mass, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (females).1)
Variable2)

Factor loadings
PC I

II

III

IV

V

VI

Total
variance (%)

1
817

Cranial length
Cranial breadth
Basi-bregmatic height

0.24
0.03
0.21

0.01
0.46*
0.62**−0.58***
0.69***
0.38**−0.48***
0.30***
0.11

0.52***−0.13
0.44***

0.01−0.22**
0.14*

89.96
84.66
79.39

5
38

Cranial base length
Endocranial capacity (cubic root)

0.79
0.09

0.31
0.61**−0.21
0.47***

−0.04
−0.06

84.08
80.64

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Min. diam. of hum. midshaft
Sag. diam. of fem. midshaft

0.80
0.05
0.67
0.27
−0.07

0.25
−0.23
−0.29
0.44**
0.62***

0.09
−0.31
−0.05
−0.67***−0.39*

0.05
0.83***
0.59***−0.18
0.20

0.28***
0.44***−0.12**
0.17−0.01−0.42***−0.35**

41.57
71.42
83.77
91.17

31(2)

Inion-opisthion chord

−0.41

0.31

0.07

−0.02

0.09

0.08
0.04
−0.15***−0.09−0.26***
0.02−0.20−0.37***

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.53
0.79
0.73

−0.31
0.18*
0.23**

0.30*−0.15*
0.02−0.01−0.14*−0.32***

0.23**
0.08
0.46***

55

Nasal height

−0.15

0.44
−0.36**
0.03
0.75***

0.12

−0.05

−0.34***

0.34***

83.34

2

Maximum pelvic breadth

0.40

0.56**−0.36**

−0.11

0.08

−0.50***

87.32

54

Nasal breadth

0.01

0.15

−0.44*

0.44**

0.28

0.52***

75.30

21.74
21.74

18.57
40.31

14.41
54.72

10.42
65.14

8.31
73.45

7.46
80.91

80.91
80.91

Total contribution (%)
Cumulative proportion (%)

74.16
88.02
94.52
91.89
74.17

1)
Sample size is 19. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Neurocranial Form and Facial and Postcranial Bonespiler 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.

27

sets possibly associated with skeletal muscle
mass are shown in Tables 2 to 5. Spearmanʼs rankcorrelation coefﬁcients between males andfemales for the variation patterns of factor loadings on the principal components (PCs) and/or
rotated factors (Facs) are listed in Table 6.
Remarkable ﬁndings are as follows. First,
male and female PC IIIs (Tables 2 and 4, respectively) indicate that cranial breadth and basi-

Results
The results of principal component analyses(PCAs) and their rotated solutions for the data

Table 5. Rotated solution of the ﬁrst six principal components extracted from the correlations between three mainneurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord) thatare supposedly associated with brain size, muscle mass, antero-posterior head balance, oxygen intake, parturition,or thermoregulation (females).1)
Factor loadings

Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Minimum diameter of humeral midshaft
Sagittal diameter of femoral midshaft

Fac I

II

0.02
−0.04
0.07
0.54*
−0.05
0.59*
−0.08
0.45
0.19
−0.22

31(2)

Inion-opisthion chord

−0.57

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.46
0.82*
0.92***

55

Nasal height2

Maximum pelvic breadth

54

Nasal breadth

III

IV

0.02
0.59*
0.88***

−0.14
−0.08
−0.03

−0.06
0.05
−0.04

0.42*
0.88***

−0.36
0.02
−0.41
0.02
−0.09
−0.85**−0.78**

0.32
−0.13
−0.02
−0.22
0.02

V

VI
0.02
−0.21*
0.14

0.20
−0.17

0.94***−0.66***−0.02
0.45**−0.02

0.23
0.83***
0.85***
−0.18
0.00

−0.00
−0.08
−0.07
0.21
−0.19

0.04
−0.02
−0.26**
0.41***
−0.11
0.18
0.21

0.19

−0.15

−0.06

−0.11

−0.13

0.03
−0.05
0.12

−0.23
0.10
−0.06

−0.13
0.15
−0.08
−0.55

−0.15
0.11
−0.17
−0.38*

0.64***−0.35***
0.05
0.32**

0.01

0.32

−0.42

−0.04

0.31

−0.77**

0.17

0.32

0.07

0.07

−0.04

0.20

0.20

−0.23
0.81***

1)

Sample size is 19. Cumulative proportion of the variances of the six principal components is 80.91%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

Table 6. Spearmanʼs rank correlation coefﬁcients between males and females in the patterns of variation of factor
loadings of the principal components and/or rotated factors obtained from the data set on cranial and postcranialmeasurements, some of which are supposedly associated with muscle mass.1)
Male
Female PC I
II
III
IV
V
VI
Fac I
II
III
IV
V
VI

PC I

II

III

IV

V

VI

VII

Fac I

II

III

IV

V

VI

VII

—
—
—
—
—
—
—
—
—
—
—
—

—
.52*
—
—
—
—
—
—
—
—
—
—

—
—
.51*
—
—
—
—
—
—
—
—
—

—
—
—
—
.58*
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
.52*
—
—
—
.57*
—

—
—
—
.69**
—
—
—
—
—
—
—
—

—
.53*
—
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
—
—
—
.62**

—
—
—
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
—
—
—
—

—
—
.59*
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
.52*
.53*
—
—

1)
Only rank correlation coefﬁcients signiﬁcant at the 5% level are listed here. The signs of rank correlation coefﬁcients are
removed because the signs of factor loadings are reversible. The original factor loadings are listed in Tables 2, 3, 4, and 5.
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed test.

28

Yuji Mizoguchi

bregmatic height are positively associated withendocranial capacity and, simultaneously,
inversely associated with maximum pelvic
breadth and nasal breadth in both sexes. The
Spearmanʼs rho between these two PCs is 0.51
(P＜0.05), as shown in Table 6.
Both male PC IV and female PC V (Tables 2
and 4) show that cranial length and basi-bregmatic height are inversely associated with thesagittal diameter of the femoral midshaft andnasal height. The Spearmanʼs rho between themis 0.58 (P＜0.05).
The highest rank correlation coefﬁcient inTable 6 is 0.69 (P＜0.01) between male PC VII(Table 2) and female PC IV (Table 4), whichshows that cranial length is inversely associatedwith mandibular ramus height and minimum
ramus breadth.
In Tables 7 and 8, the results of the PCA and
its rotated solution for the female data set including costal chord are shown. PC II in Table 7 (orFac V in Table 8) indicates that nasal height issigniﬁcantly associated not only with the sagittal
diameter of the femoral midshaft, as shown byfemale PC II (Table 4) and male Fac I (Table 3),
but also with costal chord.
The results on body height are shown in
Tables 9 to 12. Spearmanʼs rank correlation coefﬁcients between males and females are listed inTable 13. One of the major ﬁndings common toboth sexes is that there is a factor, as represented
by male Fac VI and female PC III (rho of 0.71
between them being signiﬁcant at the 1% level) ,which is signiﬁcantly correlated with cranial
length, maximum tibial length, and maximum
pelvic breadth, and, at the same time, inversely
correlated with cranial breadth and nasal height(Tables 10 and 11).
Another factor common to males and females(male PC VI in Table 9 and female PC V in Table
11; rho＝0.62, P＜0.05) reveals that cranial
length is signiﬁcantly associated with endocranial capacity, inion-opisthion chord, maximum
pelvic breadth, and, simultaneously, inversely

Table 7. Principal component analysis of the correlations between three main neurocranial measurements and thecraniofacial and postcranial measurements (including costal chord) that are supposedly associated with brainsize, muscle mass, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (females).1)
Variable2)

Factor loadings
PC I

II
0.22
0.17
0.45**

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.30
0.04
0.29

5
38

Cranial base length
Endocranial capacity (cubic root)

0.85
0.15

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Min. diam. of hum. midshaft
Sagittal diameter of femoral midshaft

0.81
0.03
0.61
0.38
0.04

III

IV

−0.60*** −0.45***
0.83***
0.24**
0.53***
0.04

V

VI

0.33***
0.19*
0.01−0.26***
0.44***
0.22***

84.70
84.87
80.93
87.69
77.52

44.36

0.22**
0.03
0.36***

70.65
82.54
89.32

−0.39***
0.24**
0.26*
−0.11

79.81
76.21
83.47

31(2)

Inion-opisthion chord

−0.35

−0.11
−0.04
0.23***
0.14*
0.65*** −0.11
0.37***
0.17*
0.04
0.21**
0.06−0.10*−0.17***
−0.14
−0.33
0.81***
0.30*−0.09−0.40*−0.10
0.56***
0.14−0.28***
0.54** −0.43** −0.01−0.55*** −0.02
0.65*** −0.08
0.32*−0.39** −0.22
0.38
0.12
−0.06
0.18
−0.36***

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.44
0.71
0.69

0.57*
−0.12
−0.52***
0.05−0.24
0.30**

55
4

Nasal height
Costal chord

−0.05
0.21

2

Maximum pelvic breadth

54

Nasal breadth

Total contribution (%)
Cumulative proportion (%)

0.26
0.40*

0.35*
−0.16*
0.06

0.52

0.66***
0.40**
0.02
0.66*** −0.42*** −0.17
0.59** −0.15
−0.07

0.05

0.21

20.61
20.61

19.21
39.82

Total variance
(%)

−0.05
−0.12
−0.37***

74.04
88.51
94.36
92.15
73.45

0.07

−0.43***−0.29

0.51***

0.11

0.60***

76.53

14.85
54.67

10.00
64.67

8.24
72.91

7.15
80.06

80.06
80.06

1)
Sample size is 19. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Neurocranial Form and Facial and Postcranial Bones

29

Table 8. Rotated solution of the ﬁrst six principal components extracted from the correlations between three mainneurocranial measurements and the craniofacial and postcranial measurements (including costal chord) thatare supposedly associated with brain size, muscle mass, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (females).1)
Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)

45
70
71
6
6

Bizygomatic breadth
Ramus height
Minimum ramus breadth
Min. diam. of hum. midshaft
Sag. diam. of fem. midshaft

Factor loadings
Fac I

II

III

IV

V

VI

0.06
−0.02
0.04
0.54*
−0.01
0.63*
−0.12
0.47
0.21
−0.19

0.90***−0.53
0.14
0.60***
0.03

−0.12
0.67*
0.88***

−0.11
0.09
−0.01

0.08
−0.17
−0.02

0.08
−0.27*
0.12

0.36
0.86***

0.21
−0.18

−0.20
0.04

0.13
−0.05
−0.04
0.35
−0.03

0.31
−0.12
−0.03
−0.24
0.05

0.25
0.84***
0.84***
−0.14
0.06

−0.31
0.01
−0.01
−0.82***−0.83***

0.05
−0.00
−0.26**
0.38***
−0.08
0.11
0.10
−0.22**

31(2)Inion-opisthion chord

−0.57

0.01

0.21

−0.03

−0.15

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.52
0.83*
0.91**

−0.06
0.08
−0.16

0.08
−0.07
0.15

−0.08
0.12
−0.06

55
4

Nasal height
Costal chord

−0.05
−0.25

−0.19
0.74**

0.41
0.13

−0.47
0.03

−0.36*
0.18−0.10−0.57**−0.37*

2

Maximum pelvic breadth

0.02

0.53

0.26

0.21

−0.59***

Nasal breadth

0.04

0.13

0.04

0.19

−0.08

54

0.54***−0.26**
0.10
0.22
0.02
−0.31*
0.84***

1)

Sample size is 19. Cumulative proportion of the variances of the six principal components is 80.06%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

Table 9. Principal component analysis of the correlations between three main neurocranial measurements and thecraniofacial and postcranial measurements (excluding costal chord) that are supposedly associated with brainsize, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (males).1)
Variable2)

Factor loadings
PC I

II

III

IV

V

VI

Total
variance (%)

0.23*** −0.28***
0.16** −0.09
0.06
0.10*

87.94
82.68
83.79

−0.01
−0.14***

83.12
65.18

−0.05
0.05
−0.15**
0.06
−0.05
0.04
−0.61*** −0.18*
0.54***
0.05−0.27***

79.14
96.67
90.25
73.58

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.67
0.46
0.46

0.09***
0.50***−0.26***

5
38

Cranial base length
Endocranial capacity (cubic root)2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
Stature

0.67*
0.68*
0.84**
0.88**
0.80*
0.50

0.00
0.27***−0.27***−0.35***−0.30***−0.17***

31(2)Inion-opisthion chord

0.13

−0.33

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

−0.09
0.57
0.56

55

Nasal height

0.43

2

Maximum pelvic breadth

0.73*

0.03

−0.30***

0.00

0.13*

54

Nasal breadth

0.26

0.32**−0.42**

0.09

0.57***

0.21**

72.65

34.95
34.95

14.20
49.15

11.94
61.09

8.99
70.08

7.30
77.38

5.27
82.65

82.65
82.65

Total contribution (%)
Cumulative proportion (%)

0.13***
0.53***
0.35*** −0.45***
0.69***
0.28***
0.61***
0.04
0.29***
0.07−0.07−0.18**−0.33***−0.04−0.51**

0.06
0.09*

−0.11
−0.14
−0.24*−0.20***−0.80***
0.28
0.30**
0.07
0.63*** −0.10
0.19** −0.18**
0.34*** −0.24***
0.33*** −0.29**−0.43*** −0.14−0.46***
0.44***

74.69

0.30***
0.26***
0.49***

91.41
87.38
92.49

0.21**

84.86−0.35***

76.54

1)
Sample size is 28. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

30

Yuji Mizoguchi
Table 10. Rotated solution of the ﬁrst six principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord)that are supposedly associated with brain size, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (males).1)
Variable2)

Factor loadings
Fac I

II

III

IV

V

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.16
0.18
0.10

0.12
0.53***−0.42**

0.75*
0.47
0.79*

0.20
0.05
0.03

0.15
0.10
−0.12

5
38

Cranial base length
Endocranial capacity (cubic root)−0.05
0.29**

0.83*
0.68

0.10
0.22

−0.10
0.02

2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
Stature0.26
0.24
0.79***
0.90***
0.92***
0.52**

−0.02
−0.04
0.06
0.15

0.35
0.25
0.11
0.09

0.19
0.23
0.17
0.17

−0.06
−0.14
−0.02
−0.64***

VI−0.47***
0.53***
0.09
0.22***
0.04

31(2)

Inion-opisthion chord

0.16

−0.10

−0.07

0.02

0.07

−0.07
−0.11
−0.12*−0.03−0.84***

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length−0.91***
0.35***
0.01

0.11
0.28
0.11

−0.21
0.81***
0.93***

55

Nasal height

0.09
0.10
0.22
0.76***−0.17−0.12**
0.05−0.08
0.20**

Maximum pelvic breadth

0.59***

2
54

Nasal breadth

0.16

0.02

−0.24

−0.05
0.09
0.05
0.39*

0.41**

0.32

0.09

0.10

−0.36***

0.22

−0.00

0.25

0.76***−0.13*

1)

Sample size is 28. Cumulative proportion of the variances of the six principal components is 82.65%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

Table 11. Principal component analysis of the correlations between three main neurocranial measurements andthe craniofacial and postcranial measurements (excluding costal chord) that are supposedly associated withbrain size, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation(females).1)
Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
StatureFactor loadings
PC I

II

III

IV

0.46*** −0.60***
0.16***−0.06
0.83*** −0.29***
0.28***
0.54***
0.25***
0.29
0.82***
0.05
0.09**
0.36
0.14***
0.68***
0.06
0.74*
0.46*** −0.33*** −0.10
0.86***
0.09*−0.22*** −0.03
0.86** −0.02−0.11** −0.01
0.63−0.24*** −0.02−0.48***
0.17
0.25
0.45

31(2)

Inion-opisthion chord

0.42

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.43
−0.39
−0.30

−0.43*−0.02−0.39***

VVI

0.50***
0.15**−0.04−0.19***
0.30*** −0.29***0.09*
0.25***
0.52***
0.04−0.09−0.18***−0.26*** −0.32***−0.34***
0.03−0.12***
0.39***
0.20***

Total variance
(%)
88.54
88.08
80.70
83.75
88.20
92.11
96.06
87.26
85.54

0.32***

65.83−0.10*−0.26***−0.25*** −0.05−0.42***
0.16***−0.26***
0.34***

91.96
89.36
96.39

55

Nasal height

0.47−0.51*−0.13
0.62***
0.79***
0.04−0.23***
0.73***
0.35***
0.15**−0.17***
0.51***
0.26***

2

Maximum pelvic breadth

0.63

0.42*** −0.17*** −0.21**

54

Nasal breadth

0.22

0.06

−0.05

0.74*** −0.05

0.38***

74.09

26.19
26.19

19.14
45.34

15.02
60.35

10.57
70.93

5.93
84.45

84.45
84.45

Total contribution (%)
Cumulative proportion (%)

0.18**
7.60
78.52

−0.06

75.78
67.59

1)
Sample size is 18. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Neurocranial Form and Facial and Postcranial Bones

31

Table 12. Rotated solution of the ﬁrst six principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord)that are supposedly associated with brain size, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (females).1)
Factor loadings

Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
Stature

Fac I

II

III

0.20
0.06
0.27
0.33*
−0.04
0.90***
0.96***
0.81***
0.39***

0.04−0.17
0.20**−0.02
0.66*
0.82**

0.04
−0.17
0.12

IV

0.01
−0.17*

0.31
0.92***

0.23
0.10

−0.06
−0.07
−0.32***−0.83***

0.07
0.05
0.02
−0.01

−0.02
0.06
0.30
0.03

−0.74**

0.07

−0.07

0.22
0.31**
0.34***

−0.01
−0.09
0.05

31(2)

Inion-opisthion chord

0.08

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.30**
0.02
−0.06

55

Nasal height

0.14−0.30**

0.32

0.48***−0.27*
0.23
0.61***

2

Maximum pelvic breadth

0.64***−0.20*

0.26

−0.11

54

Nasal breadth

0.03

0.11

0.03

0.82***

VVI

0.92***−0.61***−0.02
0.42***
0.03
0.29***
−0.04
−0.13
−0.12
0.00

0.06
0.10
−0.00
0.64***
0.01
0.13*−0.18**−0.11−0.06−0.31***−0.13***
0.04−0.17**−0.73***
0.85***
0.87***−0.41***−0.01

0.36***

0.14

0.22*

−0.05

1)

Sample size is 18. Cumulative proportion of the variances of the six principal components is 84.45%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

Table 13. Spearmanʼs rank correlation coefﬁcients between males and females in the patterns of variation of factor loadings of the principal components and/or rotated factors obtained from the data set on cranial and postcranial measurements, some of which are supposedly associated with body height.1)
Male
Female PC I
II
III
IV
V
VI
Fac I
II
III
IV
V
VI

PC I

II

III

IV

V

VI

Fac I

II

III

IV

V

VI

—
.55*
—
—
—
—
.50*
—
—
—
—
—

.73**
.54*
—
—
—
—
.62*
—
—
—
—
.72**

—
—
—
—
—
—
—
—
—
—
—
—

.56*
—
—
—
—
—
—
.56*
—
—
—
—

—
—
—
.52*
.52*
—
—
—
—
—
—
—

—
—
—
.52*
.62*
—
—
.65**
—
.51*
—
—

.71**
—
—
—
—
—
.58*
.58*
—
—
—
—

—
—
—
—
—
—
—
—
—
.51*
—
—

—
.61*
—
—
.52*
—
—
—
—
—
—
.52*

—
.58*
—
—
—
—
—
—
—
—
—
—

.50*
—
—
—
—
—
.53*
—
—
—
—
—

—
—
.71**
—
—
—
—
—
—
—
—
—

1)
Only rank correlation coefﬁcients signiﬁcant at the 5% level are listed here. The signs of rank correlation coefﬁcients are
removed because the signs of factor loadings are reversible. The original factor loadings are listed in Tables 9, 10, 11, and 12.
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed test.

associated with cranial base angle, facial length,
maxillo-alveolar length, and nasal height.
In Tables 14 and 15, the results of the female
data set on body height including costal chord
are shown. Fac VI in Table 15 indicates thatnasal height and costal chord are signiﬁcantly
associated with the maximum tibial length andstature. These associations except for costal
chord are already indicated by female Fac II in

Table 12 and male PC IV in Table 9.
The results of the analyses on body mass orweight are shown in Tables 16 to 19. Spearmanʼsrank correlation coefﬁcients between males andfemales are listed in Table 20. One of the notableﬁndings common to males and females (male PC
IV in Table 16 and female PC II in Table 18;
rho＝0.50, P＜0.05) is that cranial breadth, thevertical diameter of the femoral head, talar

32

Yuji Mizoguchi
Table 14. Principal component analysis of the correlations between three main neurocranial measurements andthe craniofacial and postcranial measurements (including costal chord) that are supposedly associated withbrain size, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation(females).1)
Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
Stature31(2)Inion-opisthion chord

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

55
4Nasal height
Costal chord2

Maximum pelvic breadth

54

Nasal breadth

Total contribution (%)
Cumulative proportion (%)

Factor loadings
PC I

II

III

IV

V

VI

Total
variance (%)

0.49*** −0.56***
0.16***−0.14**
0.86*** −0.29***
0.22***
0.59***
0.25***
0.37
0.80***
0.11**
0.09**
0.30
0.06
0.71***
0.06
0.77**
0.41*** −0.18*** −0.10
0.84**
0.03
−0.08
−0.03
0.84** −0.08*
0.01
−0.01
0.64
−0.28***
0.00−0.48***
0.39−0.46*−0.01−0.39***

0.43*** −0.15**−0.07−0.19***
0.27*** −0.25***
0.17***
0.28***
0.48*** −0.20***

86.22
91.00
76.68

−0.24***−0.41***−0.40***−0.01
0.16***−0.26***−0.30***−0.05
0.42***

92.62
97.27
88.36
89.32

−0.14***

56.63−0.53*−0.12
0.62***
0.81***
0.08−0.23***
0.72***
0.39***
0.15**−0.24***
0.52***
0.26***
0.14*−0.31*** −0.00
0.38*** −0.08−0.21**−0.12** −0.06−0.26*** −0.06−0.36***
0.20***−0.10
0.55***
0.28***
0.31***

85.99
90.19
94.90

0.28
0.13
0.42

0.40
−0.34
−0.30
0.42
0.74*
0.67*

0.14**

0.21

0.04

−0.01

0.74*** −0.08

27.36
27.36

18.14
45.50

14.72
60.21

9.95
70.17

7.44
77.61

90.85
87.29

88.27
82.81

0.03

66.11

−0.03

59.68

6.17
83.78

83.78
83.78

1)
Sample size is 18. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Table 15. Rotated solution of the ﬁrst six principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (including costal chord)that are supposedly associated with brain size, body height, antero-posterior head balance, oxygen intake, parturition, or thermoregulation (females).1)
Variable2)

Factor loadings
Fac I

II

III

IV

V

VI

0.10
0.16
0.18

0.01
0.00
0.09

−0.07
0.72
0.81*

0.11
−0.28
0.21

0.82***−0.49***
0.14*

0.17
−0.04
0.86***
0.96***
0.85***
0.40***

0.56***
−0.07

−0.04
−0.00

0.67***
0.09
0.39***
0.08
0.06
0.19*

−0.40***
0.23***
0.03
0.19***
0.10

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)2
1
1a

Total humeral length
Maximum femoral length
Maximum tibial length
Stature31(2)Inion-opisthion chord

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

55
4Nasal height
Costal chord2

Maximum pelvic breadth

0.07
0.34*
0.50***

54

Nasal breadth

0.08

1)

0.26
0.92***
0.08
0.08
0.06
−0.04

0.00
0.16
0.18
−0.33

0.26**

0.12

−0.24

−0.03

0.10***

0.21*
0.06
−0.05

−0.42
0.81***
0.96***

−0.04
−0.05
0.10

0.78***−0.40*
−0.03

−0.08
0.04
−0.09

0.00
−0.22**

0.29
−0.02

0.30
0.07

0.16***−0.28***
0.08
0.83***
0.32***

0.01

0.19

−0.17

0.13

0.08

0.75***

Sample size is 18. Cumulative proportion of the variances of the six principal components is 83.78%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

−0.09
0.04
0.31***
0.65***

0.09
−0.14
−0.16
−0.41***−0.64*−0.07
0.75***
0.57***
0.11

0.12
0.01

Neurocranial Form and Facial and Postcranial Bones

33

Table 16. Principal component analysis of the correlations between three main neurocranial measurements andthe craniofacial and postcranial measurements (excluding costal chord) that are supposedly associated withbrain size, body mass (weight), antero-posterior head balance, oxygen intake, parturition, or thermoregulation(males).1)
Variable2)

Factor loadings
PC I

II

III

IV

V

VI

VII

0.21*
0.25**
0.41*** −0.02
0.03−0.58** −0.23*
0.16* −0.11−0.20**−0.39
0.31** −0.10
0.08
0.23***
0.21−0.45**
0.16
0.23**
0.15* −0.17*−0.08−0.25**
0.10
0.16* −0.24*** −0.04
0.40*
0.22
−0.07
0.27
−0.30*
0.08
0.04
0.25
0.27
−0.08
0.31*
0.11
0.01
0.08
−0.24** −0.50*** −0.17
0.02
0.26** −0.16−0.37*** −0.38*** −0.14
0.21*

Total
variance (%)

1
817

Cranial length
Cranial breadth
Basi-bregmatic height

0.76
0.11
0.51 −0.36
0.53
0.54*

86.01
85.60
88.79

5
38

Cranial base length
Endocranial capacity (cubic root)

0.69
0.73

84.90
69.61

4
7
18
1

Sup. sag. diam. of vert. b. (Th.VIII)
Sup. tr. diam. of vert. b. (Th.VIII)
Vertical diameter of femoral head
Talar length

0.66
0.68
0.72
0.63

31(2)

Inion-opisthion chord

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

55

Nasal height

0.13

0.77*

0.26

−0.11
0.85*
0.59 −0.62**
0.54 −0.40**
0.29

0.07
0.03
0.22
−0.01

0.27

0.01

0.07

0.23
−0.12
0.28* −0.05
0.37** −0.43***−0.65**
0.04

82.11
71.43
86.18
83.86

−0.35*** −0.34***

91.86−0.18**−0.27***−0.17−0.44***

92.25
88.46
89.34

0.29**
0.05
0.18
0.44*

2

Maximum pelvic breadth

0.71 −0.09

0.29

0.16

72.63

54

Nasal breadth

0.31 −0.34

0.39

−0.24

0.27

0.48***

0.36**

85.03

33.11
33.11

11.38
58.49

8.54
67.02

6.48
73.50

6.21
79.70

4.93
84.64

84.64
84.64

Total contribution (%)
Cumulative proportion (%)

13.99
47.10

0.02

−0.04

96.16

−0.32**

1)
Sample size is 29. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Table 17. Rotated solution of the ﬁrst seven principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord)that are supposedly associated with brain size, body mass (weight), antero-posterior head balance, oxygen
intake, parturition, or thermoregulation (males).1)
Variable2)
1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)

4
7
18
1

Sup. sag. diam. of vert. b. (Th.VIII)
Sup. tr. diam. of vert. b. (Th.VIII)
Vertical diameter of femoral head
Talar length

Factor loadings
Fac I

II

III

IV

V

VI

VII

0.73***
0.01
0.48
−0.63
0.68**
0.46
0.84***
0.03
0.68*
−0.31
0.59**
0.05
0.39
0.26
0.14
−0.09
0.26
0.02

0.37
−0.29
−0.25

−0.08
−0.18
−0.37

−0.23
−0.12
−0.03

0.36**
−0.11
−0.08

−0.17
0.05

−0.12
−0.28

−0.17
−0.22

−0.04
−0.01

0.05
−0.29**
0.11−0.26*
0.02

−0.40
0.12
−0.24
−0.51*−0.82*** −0.36−0.87***
0.01
−0.04

−0.08

0.05
0.00
−0.19

0.12
−0.22*−0.79***
0.10−0.91***
0.10

31(2)

Inion-opisthion chord

−0.06

0.14

0.51
0.09
0.13
−0.06
0.94***

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.13
0.28
0.06

0.89**
−0.42
−0.02

0.11
0.02
0.04

0.19
0.41**
0.03
0.02
−0.01

−0.00
0.01
−0.12
−0.13
−0.04

55

Nasal height

0.07

0.08

0.05

−0.20

0.06

0.14

−0.21*−0.01
0.06−0.94***

2

Maximum pelvic breadth

0.24

−0.21

0.27

−0.53

−0.17

0.47**

−0.13

−0.13

0.89*** −0.11

54

Nasal breadth
1)

−0.01

−0.13

−0.02

−0.01

Sample size is 29. Cumulative proportion of the variances of the seven principal components is 84.64%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

34

Yuji Mizoguchi
Table 18. Principal component analysis of the correlations between three main neurocranial measurements andthe craniofacial and postcranial measurements (excluding costal chord) that are supposedly associated withbrain size, body mass (weight), antero-posterior head balance, oxygen intake, parturition, or thermoregulation(females).1)
Variable2)

Factor loadings
PC I

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.30
0.32
0.65

5
38

Cranial base length
Endocranial capacity (cubic root)

0.64*
0.52

4
7
18
1

Sup. sag. diam. of vert. b. (Th.VIII)
Sup. tr. diam. of vert. b. (Th.VIII)
Vertical diameter of femoral head
Talar length

0.56
0.59
0.73*
0.54

31(2)

Inion-opisthion chord

0.10

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.16
0.08
0.23

55

Nasal height

0.46

2

Maximum pelvic breadth

0.76**

54

Nasal breadth

Total contribution (%)
Cumulative proportion (%)

II

III

VI

Total
variance (%)

0.21***
0.19***−0.09**

88.16
89.91
74.85

−0.01
0.24***
0.19**−0.27***−0.08−0.25***
0.74***

87.10
84.97

0.25*** −0.40***
0.04
−0.01
0.33*** −0.18***
0.50***
0.03

91.15
87.74
90.32

0.00

0.08

74.30

IV

V

0.37***
0.63***
0.16*** −0.44***−0.35*** −0.78*** −0.17** −0.08−0.16*** −0.35***
0.27*** −0.31***
***
0.63
0.04
0.26*** −0.06*−0.21*** −0.44***
0.24*** −0.47***
***
***
0.47
0.30
0.18
0.42***
0.05
0.08−0.26***
0.06−0.21***
0.23*** −0.39***0.16**
***
*
***
−0.44
0.10
−0.38
−0.25***−0.40*
0.18
0.11
0.24***−0.64***
0.34*
0.36***
0.84*** −0.32*** −0.25***
0.63*** −0.54***0.16**
***
***
−0.44
−0.29
0.37***

86.86
49.86
82.08
76.65
82.46

87.80

0.08

0.36*** −0.15*

−0.07

0.07

0.11

0.79*** −0.22*−0.22***

73.61

22.93
22.93

19.05
41.98

13.98
55.96

10.44
66.40

7.03
81.74

81.74
81.74

8.31
74.70

1)
Sample size is 18. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

Table 19. Rotated solution of the ﬁrst six principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (excluding costal chord)that are supposedly associated with brain size, body mass (weight), antero-posterior head balance, oxygen
intake, parturition, or thermoregulation (females).1)
Variable2)

Factor loadings
Fac I

II

III

IV

V

VI
0.07
0.13*
−0.10*

0.06
0.03
0.10
0.11

−0.92***
0.57***−0.05−0.48***−0.08−0.34**
−0.02
0.01
0.01

−0.06

0.10

−0.02

0.06
0.05
−0.13
−0.34

0.91***−0.65***−0.16
0.57**

0.06
0.00
0.25**
0.42***

−0.12

0.02

−0.37***

0.20*

−0.19

0.51*

−0.40***−0.22***

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.15
0.13
0.24

0.06
−0.03
0.16

−0.01
−0.71*−0.78**

−0.10
−0.19
0.20

5
38

Cranial base length
Endocranial capacity (cubic root)

0.22
0.07

−0.26
−0.91***

−0.07
−0.02

4
7
18
1

Sup. sag. diam. of vert. b. (Th.VIII)
Sup. tr. diam. of vert. b. (Th.VIII)
Vertical diameter of femoral head
Talar length

0.31
0.65***
0.88***
0.73***

0.72***−0.01
0.73***
0.20
0.06−0.34**

0.13
−0.09
−0.07
−0.29

31(2)

Inion-opisthion chord

−0.01

−0.13

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.21*
−0.01
−0.10

−0.19
0.60***
0.85***

55

Nasal height

0.16

0.32**

2

Maximum pelvic breadth

0.71***

0.23*

54

Nasal breadth−0.46**

0.14

1)

Sample size is 18. Cumulative proportion of the variances of the six principal components is 81.74%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

−0.10
0.10
0.32***−0.16*
0.15*−0.12*
0.89***
0.03−0.30***−0.26***
0.37***

Neurocranial Form and Facial and Postcranial Bones

length, and nasal height are positively associatedwith one another, and, at the same time, inversely
associated with cranial length, facial length, andmaxillo-alveolar length.
The pattern of variation in factor loadings ofthe above male PC IV in Table 16 is also similar

35

to that of female Fac VI in Table 19 (rho＝0.55,
P＜0.05), as shown in Table 20. These factors
indicate that cranial breadth, the vertical diameter of the femoral head, nasal height, and maximum pelvic breadth are positively associatedwith one another, and, at the same time, inversely

Table 20. Spearmanʼs rank correlation coefﬁcients between males and females in the patterns of variation of factor loadings of the principal components and/or rotated factors obtained from the data set on cranial and postcranial measurements, some of which are supposedly associated with body mass (weight).1)
Male
Female PC I
II
III
IV
V
VI
Fac I
II
III
IV
V
VI

PC I

II

III

IV

V

VI

VII

Fac I

.56*
—
—
—
—
—
—
—
—
—
.55*
—

—
.50*
—
—
—
—
—
—
—
.71**
—
—

—
—
.55*
—
—
—
—
—
.56*
—
—
—

—
.50*
—
—
—
—
—
—
—
—
—
.55*

—
—
—
—
—
.58*
—
—
—
—
.60*
—

—
—
—
—
—
.65**
—
—
—
—
—
.52*

—
—
—
—
.50*
—
—
—
—
—
.54*
—

—
—
—
—
.55*
—
—
—
—
—
—
—

II

III

IV

V

—
— .81*** —
—
—
—
.62*
—
—
—
.73**
—
—
—
—
—
—
—
—
—
—
—
—
**
—
—
—
.74
—
—
—
—
**
—
—
—
.69
—
—
.65**
.71**
—
—
—
—
—
—
—
.54*

VI

VII

—
—
—
—
—
—
—
—
—
—
—
—

—
—
—
—
—
—
—
—
—
—
—
—

1)
Only rank correlation coefﬁcients signiﬁcant at the 5% level are listed here. The signs of rank correlation coefﬁcients are
removed because the signs of factor loadings are reversible. The original factor loadings are listed in Tables 16, 17, 18, and 19.
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed test.

Table 21. Principal component analysis of the correlations between three main neurocranial measurements andthe craniofacial and postcranial measurements (including costal chord) that are supposedly associated withbrain size, body mass (weight), antero-posterior head balance, oxygen intake, parturition, or thermoregulation(females).1)
Variable2)

Factor loadings
VI

Total
variance (%)

0.14***
0.23***−0.08**

83.47
88.71
75.11

−0.02
0.21***
0.16**−0.25***−0.13*−0.25***

89.33
83.97

0.73***

82.89−0.65*** −0.28
0.30***
0.26*** −0.44***0.85***
0.33*** −0.21***
0.04
0.03
0.65***
0.57***
0.20**
0.33*** −0.17**
0.42−0.42***
0.35***
0.38***
0.51***
0.02
0.70* −0.03−0.47***
0.13
−0.01
0.14*
0.80**
0.10*−0.17** −0.22**
0.00
0.03

90.63
87.35
92.53

PC I

II

III

IV

V

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

0.40
0.18
0.60

5
38

Cranial base length
Endocranial capacity (cubic root)

0.65*
0.43

4
7
18
1

Sup. sag. diam. of vert. b. (Th.VIII)
Sup. tr. diam. of vert. b. (Th.VIII)
Vertical diameter of femoral head
Talar length

0.61
0.58
0.71*
0.54

0.37*** −0.57***
0.08*−0.44***−0.32***
0.83*** −0.08−0.08−0.14***
0.43***
0.30*** −0.31***0.64***
0.02
0.25*** −0.06*−0.19***
0.52***
0.27*** −0.47***
0.48*** −0.21*
0.13
0.42***
0.06
0.06−0.29***
0.06−0.19***
0.01−0.46***
0.16**−0.42***
0.07−0.41*** −0.25***31(2)Inion-opisthion chord

0.18−0.40*

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.24
−0.01
0.09

55
4

Nasal height
Costal chord2

Maximum pelvic breadth

54

Nasal breadth

Total contribution (%)
Cumulative proportion (%)

−0.19

0.11

0.24***

86.10
49.84
79.69
76.52

87.80
75.05
72.18

−0.03

0.06

−0.18

0.76*** −0.21*−0.27***

73.02

23.85
23.85

17.94
41.79

14.55
56.34

9.95
66.28

6.73
80.83

80.83
80.83

7.82
74.10

1)
Sample size is 18. Number of principal components was determined so that the cumulative proportion of the variances of theprincipal components exceeded 80%.
2)
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

36

Yuji Mizoguchi
Table 22. Rotated solution of the ﬁrst six principal components extracted from the correlations between threemain neurocranial measurements and the craniofacial and postcranial measurements (including costal chord)that are supposedly associated with brain size, body mass (weight), antero-posterior head balance, oxygen
intake, parturition, or thermoregulation (females).1)
Variable2)

Factor loadings
Fac I

II

III

IV

0.07
−0.06
−0.02
0.89***
0.17
0.04
0.73*
−0.52*
0.22
0.14
0.78**
0.15*
***
0.19
0.65
0.24
0.60**
0.05−0.02
0.91***
0.09
0.28
0.65*** −0.14
0.48*
0.65***
0.19
0.09
0.13
0.87***
0.03
0.08
0.05
0.73*** −0.35**
0.30
0.02

1
8
17

Cranial length
Cranial breadth
Basi-bregmatic height

5
38

Cranial base length
Endocranial capacity (cubic root)

4
7
18
1

Sup. sagit. diam. of vertebral body (Th.VIII)
Sup. trans. diam. of vertebral body (Th.VIII)
Vertical diameter of femoral head
Talar length31(2)Inion-opisthion chord

−0.03

−0.19

0.07

0.08

37(2)
40
60

Cranial base angle
Facial length
Maxillo-alveolar length

0.19
0.01
−0.07

−0.00
0.01
−0.19

55
4

Nasal height
Costal chord

−0.23
−0.06
0.65*** −0.05
***
0.90
0.14
0.32**
0.35
0.02
0.05

2

Maximum pelvic breadth

54

Nasal breadth

0.17
0.36*
0.67***−0.50**−0.27
0.67**

V

VI

−0.18
−0.13
0.21*

−0.03
0.19**
−0.08

−0.07
−0.02

−0.10
0.07

0.07
0.05
0.11
0.11
0.09

0.32***
−0.12
0.12
−0.12
0.88***

0.90***
0.01−0.62*** −0.25***−0.11−0.22******
0.62
0.40***
0.26*
0.31***

0.16

0.12

0.46

0.01

0.08

0.17

0.39

0.47*** −0.28***

0.16

1)

Sample size is 18. Cumulative proportion of the variances of the six principal components is 80.83%.
Variable number according to Martin and Saller (1957).
* P＜0.05; ** P＜0.01; *** P＜0.001, according to a two-tailed bootstrap test.

2)

associated with basi-bregmatic height, facial
length, and maxillo-alveolar length.
In Tables 21 and 22, the results of the female
data set on body mass (weight) including costal
chord are shown. Fac VI in Table 22 indicatesthat nasal height and costal chord are signiﬁcantly associated with cranial breadth, the superior sagittal diameter of the vertebral body (Th.
VIII), and inion-opisthion chord, and, at the sametime, inversely associated facial length, maxilloalveolar length, and nasal breadth. These associations except for costal chord are already indicated by female Fac VI in Table 19, although, inmales, there is no corresponding PC or rotatedfactor that has a similar pattern of variation offactor loadings.
Discussion
The purpose of a series of within-group analyses by Mizoguchi (1994, 1995, 1996, 1997,
1998a, b, 1999, 2000, 2001, 2002, 2003a, b,
2004a, b, 2005, 2007b, 2008) was to clarify theinterrelationships of three main neurocranialmeasurements, that is, cranial length and breadth,and basi-bregmatic height, with postcranial measurements, facial measurements, and neurocranial measurements other than the three main neurocranial ones. In these analyses, however,mutual relationships across all the measurementsfrom various bones could not be examinedbecause of the statistical restriction on sample
size given the number of variables. Therefore,
Mizoguchi (2009) attempted to conﬁrm the overall relationships between the limited number ofmeasurements that have been found to bestrongly associated with one or more of the threemain neurocranial measurements in each of theprevious analyses. As a result, he found that all
representative measurements of the vertebral
body, humerus, pelvis, femur, and tibia were signiﬁcantly associated with one another and withcranial length. These ﬁndings seem to support
the present authorʼs previous hypothesis thatvariation in cranial length is related to the degreeof development of skeletal muscles or body size
(Mizoguchi, 2001, 2003a, b, 2004b). In Mizoguchiʼs (2009) analyses, however, the importantNeurocranial Form and Facial and Postcranial Bones

measurements of another kind, such as nasal
height and the size of the femoral head whichhave been considered in general to be associatedwith oxygen intake, body weight, and so on,were not taken into consideration. Therefore, inthe present study, some additional measurementsthat were supposedly associated with factors possibly controlling neurocranial form were newly
examined to elucidate their relationships withneurocranial form.
Nasal height and costal chord
Before discussing the associations of neurocranial form with facial and postcranial bones, itwould be worth noting the intimate connection
between nasal height and costal chord. In all
analyses of the female data sets including costal
chord (PC II in Table 7, Fac VI in Table 15, andFac VI in Table 22), nasal height and costal
chord were found to be signiﬁcantly associatedwith each other and, furthermore, with one ormore measurements that were assumed to be correlated with skeletal muscle mass (the sagittal
diameter of the femoral midshaft and inion-opisthion chord), body height (maximum tibial
length and stature), or body mass (the superior
sagittal diameter of the vertebral body of theeighth thoracic vertebra). These ﬁndings arecompatible with Kean and Houghtonʼs (1990)
assertion that there is a clear and direct relationship between increase in airway size, in measuresof lung size such as vital capacity, and that inbody oxygen demand, as indicated particularly
by skeletal muscle mass. In fact, Hall (2005)
shows, using anthropometric and physiological
data, that a factor representing linear and bulk
measures of body size and a factor representing
lean body mass explain subjectsʼ variation innose volume, resting volume of oxygen consumed, and resting ventilation volume better thansubjectsʼ sex does, while, during exercise, sex
explains the volume of oxygen consumed andventilation volume better than body size factors
do. (She considers that this difference between
the conditions of rest and exercise is because
hormone-mediated muscularity in males pro-37

duces greater work output).
Thus, the strong associations found here areconsidered robust evidence that nasal height andcostal chord are appropriate indices of oxygen
intake.
Cranial length/breadth, nasal height/breadth,and limb bone lenghts/thicknesses
In the present study, three sets of measurements were constructed because of the statistical
restriction on sample size given the number ofvariables. Each of the three sets includes themeasurements possibly relating to skeletal muscle mass, body height, or body weight, and all
the other controlling factors mentioned above.
Namely, the measurements that are supposedly
associated with brain size, oxygen intake, thermoregulation (cold adaptation), humidity regulation, anteroposterior head balance, and parturition are common to all the three sets ofmeasurements.
Across these three sets of measurements, aremarkable tendency was found. Speciﬁcally,
there was a tendency for cranial length todecrease (and, in most cases, for cranial breadth
to increase) whenever nasal height increases.
This is clearly shown by male PC IV and female
PC V in Tables 2 and 4, respectively, and Fig. 1;
male Fac VI and female PC III in Tables 10 and
11 and Fig. 2; and male PC IV and female PC II
in Tables 16 and 18 and Fig. 3. The common factor correlated with these measurements is alsosigniﬁcantly correlated with the sagittal diameterof the femoral midshaft (Fig. 1) and the vertical
diameter of the femoral head and talar length(Fig. 3), but not strongly correlated with limb
bone lengths or stature (Fig. 2). Furthermore, thiscommon factor is not consistently correlated in
the same direction with endocranial capacity(brain size) or with inion-opisthion chord (skeletal
muscle mass/anteroposterior head balance), as
shown in Figs. 1, 2, and 3. From these ﬁndings, it
is inferred that there is a common factor that is
relatively strongly associated with cranial length(neurocranial form), nasal height (oxygen
intake), the sagittal diameter of the femoral mid-38

Yuji Mizoguchi

Fig. 1. Factor loadings on male PC IV (Table 2) and female PC V (Table 4) extracted from the data set including
the measurements supposedly associated with skeletal muscle mass.

Fig. 2. Factor loadings on male Fac VI (Table 10) and female PC III (Table 11) extracted from the data set
including the measurements supposedly associated with body height.

shaft (skeletal muscle mass), and the vertical
diameter of the femoral head and talar length(body weight), but not associated with bodyheight. According to Striedter (2005), the gut
consumes the most energy, about 70% of thetotal energy supply, and an average human brain
draws about 16% of the entire bodyʼs energy consumption. If so, the present ﬁndings suggest thatheavier individuals who have a longer/thicker gut
and a comparatively large amount of skeletal
muscle (except the nuchal ones), which consume
a relatively large amount of oxygen, tend to havea shorter (and probably wider) neurocranium
regardless of brain size and body height.
This suggestion from the within-group analyses
does not seem to be inconsistent with the cold

Neurocranial Form and Facial and Postcranial Bones

39

Fig. 3. Factor loadings on male PC IV (Table 16) and female PC II (Table 18) extracted from the data set
including the measurements supposedly associated with body mass (weight).

adaptation hypothesis (Coon, 1962). In fact, Crognier (1979, 1981) has reported that, at least in
males, mean annual temperature has high inverse
correlations with body weight, maximum headbreadth, and nose height; and low inverse correlations with standing height and maximum headlength. Wells (2012), using data from the literature for nonindustrialized populations excluding
Polynesians, also shows that mean annual temperature is signiﬁcantly negatively correlatedwith body weight and BMI (body mass index) at
the 0.01% level, while, with height, temperature
is not correlated in males and weakly negatively
correlated in females at the 5% level.
Another remarkable factor relating to femoral
head size, frequently used as an indicator of bodymass (Ruff, 2002; Weiss, 2010), is suggested bymale PC IV in Table 16 and female Fac VI in
Table 19. This local common factor indicates thatcranial breadth, the vertical diameter of the femoral head, nasal height, and maximum pelvic
breadth are positively associated with one
another, and they are inversely associated withbasi-bregmatic height, facial length, and maxilloalveolar length.
Male PC IV in Table 16, however, has a pattern of variation of factor loadings similar to
those of female Fac VI in Table 19 and of female
PC II in Table 18, with Spearmanʼs rho being

0.55 for the former and 0.50 for the latter (Table
20). In general, there is a possibility that a realcommon factor may be expressed by a PC in a
PCA (a factor in a factor analysis) or a rotatedfactor in another analysis (PCA or factor analysis
and a succeeding rotation of the solution). If wehave no external criterion for determining thereality of a factor extracted, we are obliged todepend on the reproducibility of a possible factor
in two or more samples. In the case of the present study, an indicator of the reproducibility is
Spearmanʼs rank correlation coefﬁcient between
the patterns of variation of factor loadings of two
PCs or rotated factors. As shown above, theSpearmanʼs rank correlation coefﬁcients of male
PC IV in Table 16 with female Fac VI in Table
19 and with female PC II in Table 18 are nearly
equal. Therefore, both the associations suggestedby the two sets of factors, one of which is common, must be interpreted. As the correspondencewith female PC II in Table 18 was already discussed above, the correspondence with female
Fac VI in Table 19 is discussed here.
First, the positive associations of cranial
breadth (neurocranial form) with the vertical
diameter of the femoral head (body weight),
nasal height (oxygen intake), and maximum pelvic breadth (body breadth) are all acceptablefrom the viewpoints of the cold adaptation

40

Yuji Mizoguchi

hypothesis (Coon, 1962) and Ruffʼs (1991, 1993,
1994, 2002) cylindrical thermoregulatory model.
In fact, these are, again, well compatible with
Crognierʼs (1979, 1981) report based on maledata that mean annual temperature has highinverse correlations with maximum head breadth,body weight, nose height, bi-iliocristal diameter,
and bizygomatic breadth (incidentally, meanannual temperature has low inverse correlations
with standing height and maximum head length,
and a low positive correlation with nose breadth).
The positive association between facial lengthand maxillo-alveolar length is understandablefrom their disposition. However, it is difﬁcult to
explain the negative associations between these
two measurements and the above set of measurements likely relating to cold adaptation. Holton
and Franciscus (2008) argue that more variationin nasal breadth can be explained throughbasion-prosthion length (facial length) rather
than anterior palatal breadth dimensions. MalePC IV in Table 16 and female Fac VI in Table 19,
however, show no consistent association between
facial length and nasal breadth.
Although it is stated in the above section thatnasal height and costal chord are signiﬁcantly
associated with each other and with the sagittal
diameter of the femoral midshaft and inion-opisthion chord (skeletal muscle mass), maximum
tibial length and stature (body height), or thesuperior sagittal diameter of the vertebral body
(body mass), it should be noted that this is indicated by a different common factor (suggested by
PC II in Table 7 or Fac V in Table 8, PC II in
Table 4 and Fac I in Table 3; Fac VI in Table 15,
Fac II in Table 12 and PC IV in Table 9; and Fac
VI in Table 22 and Fac VI in Table 19) from thefactor suggested by the PCs or Facs discussed inthis section (PC IV in Table 2 and PC V in Table
4; Fac VI in Table 10 and PC III in Table 11; andPC IV in Table 16 and PC II in Table 18).
Namely, it may be said that there are at least two
different common factors that explain two different fractions of the variation of nasal height.
Similarly, the signiﬁcant associations between
cranial length and limb bone lengths and thick-nesses indicated by the ﬁrst PCs extracted in
Mizoguchiʼs (2001, 2003a, b, 2009) multivariate
within-group analyses may also be due toanother common factor that differs from theabove-mentioned two factors that are associatedwith nasal height, the sagittal diameter of thefemoral midshaft, and so on because a so-called
general size factor (usually extracted as the ﬁrst
PC) can also be seen in some cases of the present
analyses, for example, in Tables 2 and 9,
although their factor loadings are hardly statistically signiﬁcant.
In Mizoguchiʼs (2007a) bivariate among-group
analyses for males and females, Spearmanʼs rankcorrelation coefﬁcients show that cranial lengthis signiﬁcantly associated with some thickness
measurements of the humerus (only in females),radius, ulna, femur, tibia, and ﬁbula (only inmales), but not associated with any lengths of allthese limb bones except the male ulna. In addition, regarding cranial breadth, a similar tendency can be found: it is signiﬁcantly associatedwith some thickness measurements of thehumerus (only in males), ulna, femur (only inmales), and tibia, but not associated with any
lengths of all these limb bones but the female
ulna. Although it cannot be judged only fromthese results of bivariate analyses whether or not
the factor causing the former associations and thefactor causing the latter ones are the same, atleast the factor causing the latter associations canbe the same factor that is suggested by the PCs or
Facs discussed above (PC IV in Table 2 and PC
V in Table 4; Fac VI in Table 10 and PC III in
Table 11; and PC IV in Table 16 and PC II in
Table 18). This interpretation is, of course, possible only when variations among groups areextensions of within-group variations. Recently,
Weiss (2010), observing 65 prehistoric Californian Native Americans, reported that the aggregate cross-sectional robusticity of the humerus issigniﬁcantly positively correlated with cranial
length (Spearmanʼs rho＝0.438; P＜0.01) andbody mass calculated from femoral headbreadths (rho＝0.732; P＜0.01), but not correlated with cranial breadth (rho＝0.225; P＞0.05);

Neurocranial Form and Facial and Postcranial Bonesthat aggregate upper limb muscle marker value
has signiﬁcant correlations with cranial length(rho＝0.377; P＜0.01), cranial breadth (rho＝0.293; P＜0.05), and body mass (rho＝0.385;
P＜0.01); and that aggregate cranial muscle
marker value has a signiﬁcant correlation withcranial length (rho＝0.248; P＜0.05), but is notcorrelated with cranial breadth (rho＝0.074;
P＞0.05) or with body mass (rho＝0.190;
P＞0.05). The stronger associations of muscle
markers with cranial length than with cranial
breadth are very suggestive, especially in interpreting the strong associations between cranial
length and limb bone lengths and thicknesses
suggested by the ﬁrst PCs extracted in Mizoguchiʼs (2001, 2003a, b, 2009) analyses. To conﬁrm
the identity of within-group and among-groupcontrolling factors, however, multivariate
among-group analyses should further be conducted for a similar set of craniofacial and postcranial measurements.
Inion-opisthion chord and facial/maxillo-alveolar length
Regarding the association between cranial
length and inion-opisthion chord, Mizoguchi(2001, 2003a, b, 2004b) hypothesized that thenuchal planum plays an important role as anintermediate between cranial length and postcranial measurements. However, Mizoguchi (2009)
conﬁrmed that the inion-opisthion chord was not
signiﬁcantly associated with cranial length orwith any postcranial measurements. At that time,
therefore, he concluded that inion-opisthion
chord at least is not an appropriate measure forthe size of the nuchal planum, presumably
because of the difﬁculty in determining a landmark, the inion (Mizoguchi, 2009). However,
Mizoguchi (2012a), using the ﬁnite element scaling method, found that the degree of occlusal
wear on the UM1 was signiﬁcantly associatedwith the magnitude of strain at the inion, andMizoguchi (2012b) showed that those individuals who had heavy UM1 occlusal wear tended tohave an anteroposteriorly elongated palate andoccipital bone. Here, if craniofacial form changes

41

in response to mechanical stresses from the masticatory and/or nuchal muscles, it is expected thatthe inion-opisthion chord is correlated not onlywith cranial length but also with some measurements supposedly associated with skeletal muscle mass or body size (height, breadth, or
weight). The above-mentioned male PC VI andfemale PC V (Tables 9 and 11) show that, while
the inion-opisthion chord is signiﬁcantly associated with cranial length and maximum pelvic
breadth (body breadth), it has no consistent association with any of the limb bone lengths andstature in the same direction. In addition, in theother PCAs of the present study, there is no factor that is simultaneously correlated with cranial
length, inion-opisthion chord, and the measurements supposedly associated with skeletal muscle mass or body size. For the present, therefore,
we may be obliged to accept the above-mentioned conclusion of Mizoguchi (2009).
Also from the viewpoint of anteroposterior
head balance (Yamaguchi, 1984), the inion-opisthion chord is expected to have some positive
correlation with facial length or maxillo-alveolar
length. However, male PC VI and female PC V
(Tables 9 and 11) show that the inion-opisthion
chord and cranial length have negative associations with facial length and maxillo-alveolar
length. Therefore, the present result does not support Yamaguchiʼs (1984) hypothesis of anteroposterior head balance. However, this problem
should be examined further, particularly throughmechanical experiments.
Cranial, nasal, and pelvic breadths
Male and female PC IIIs (in Tables 2 and 4,
respectively) are signiﬁcantly correlated withcranial breadth, basi-bregmatic height and endocranial capacity and, simultaneously, inversely
correlated with maximum pelvic breadth andnasal breadth. These two PCs from males andfemales suggest the existence of a local common
factor that is, at least, associated with the tendencies for the breadth and height of the brain caseto increase and, at the same time, for pelvic andnasal breadths to be narrow with the increase of42

Yuji Mizoguchi

brain size. It is very difﬁcult, however, to interpret this local common factor. In Mizoguchiʼs(2005) analyses on the three main neurocranial
and many pelvic measurements, the male ﬁrst PC
and a female rotated factor, which have similar
patterns of variation of factor loadings, suggested
that cranial length has strong associations withmaximum pelvic and anterior upper spinal
breadths as well as with innominate height.
These associations can be conﬁrmed by the maleand female ﬁrst PCs or a general size factor
extracted from the three main neurocranial andvarious representative postcranial measurements(Mizoguchi, 2009), which are partly different
from the measurements used in the present study.
In addition to this general size factor, there isanother local common factor in the results of
Mizoguchiʼs (2009) PCAs, which has high factor
loadings of more than 0.60 for cranial breadthand endocranial capacity, but not for pelvic
height or breadth, in both males and females,
although the factor loadings are not statisticallysigniﬁcant. This local common factor, together
with the factor suggested by male and female PC
IIIs (Tables 2 and 4) in the present study, points
to a stronger connection of brain size with cranial
breadth than with cranial length.
Another aspect shown by these male andfemale PC IIIs (Tables 2 and 4) is a signiﬁcant
positive association between maximum pelvic
breadth and nasal breadth. Previously, Mizoguchi(1998c, 2005) had considered the interrelationship between cranial length and pelvic breadth asfollows: the shapes of the neurocranium andmaternal pelvis have been formed, mutuallyaffecting each other, through the human evolutionary process and, in modern human populations, the close correspondence between neurocranial and pelvic forms is ﬁxed as a population
characteristic. Later, Mizoguchi (2009) further
analyzed the correlations between the three mainneurocranial and various representative postcranial measurements, and found that pelvic breadthand height had signiﬁcant associations not onlywith cranial length but also with the size of thevertebral body as well as with the lengths andthicknesses of the humerus, femur, and tibia,
although they have no association with stature.
From these ﬁndings, he concluded that bearing
body weight might be a more important functionof the pelvis than obstetric function, that is, compatibility with the neurocranium in terms ofshape.
On the other hand, according to Crognier(1979, 1981), nose breadth has a signiﬁcant positive correlation with the mean temperature of thehottest month (only in females) and a signiﬁcantnegative correlation with the mean precipitationof the rainiest month in males and, in females, ofthe driest month. In addition, bi-iliocristal diameter (in males) and maximum head breadth (inmales and females) have signiﬁcant negative correlations with mean annual temperature and themean temperatures of the coldest and hottest
months, and positive correlations with meanannual precipitation (except for female headbreadth) and the mean precipitations of the rainiest and driest months. (Incidentally, maximum
head length of males and females has a signiﬁcant negative correlation only with the mean
temperature of the hottest month and a signiﬁcant positive correlation only with the mean precipitation of the driest month.) As the variables
regarding temperature are negatively correlatedwith the variables regarding precipitation in Crognierʼs samples, the above Crognierʼs ﬁndings
imply that populations inhabiting colder andrainier/snowier regions tend to have a narrower
nose and a wider head and wider pelvis. The
combination of wider pelvis and colder regions iswell compatible with Ruffʼs (1991, 1993, 1994,
2002) cylindrical thermoregulatory model of thehuman body.
The negative association between nasal
breadth and cranial breadth indicated by maleand female PC IIIs in Tables 2 and 4 is compatible with Crognierʼs ﬁndings above from amonggroup comparisons. However, the results indicated by the same PCs that maximum pelvic
breadth is positively associated with nasal
breadth and negatively associated with cranial
breadth do not seem to be consistent with Cro-

Neurocranial Form and Facial and Postcranial Bonesgnierʼs ﬁndings.
Another factor suggested by male PC VI andfemale PC V (Tables 9 and 11) shows a positive
association between maximum pelvic breadthand cranial length as well as negative associations of maximum pelvic breadth with nasal
height and cranial base angle. The former association has already been pointed out by Mizoguchi(2005, 2009). Recently, Takamuku (2011), using
Japanese female samples from the Jomon period
to the present, directly conﬁrmed that the temporal changes of the pelvic inlet shape were correlated with the temporal changes of the cranial
shape. His ﬁnding supports the present authorʼsprevious hypothesis (Mizoguchi, 2005, 2009)that children of mothers with a wider pelvis tend
to have longer heads. The latter associations may
be related to thermoregulation or cold adaptation.
According to Kean and Houghton (1990), cranialbase angle must be correlated with nasal height,
and may, therefore, be regarded as another measure of oxygen intake. It should be noted here,
however, that Kean and Houghtonʼs (1990) ʻcranial base angleʼ is the angle of nasion-sellabasion, not equivalent to Martinʼs ʻNo. 37 (2) cranial base angleʼ (Martin and Saller, 1957).
Nevertheless, Martinʼs cranial base angle wasalso found to be signiﬁcantly positively associated with nasal height. The inverse association
between maximum pelvic breadth and nasal
height is, however, not compatible with the negative correlation between nasal height and temperature estimated by Crognier (1981) if Ruffʼs(1991, 1993, 1994, 2002) cylindrical thermoregulatory model, in which the pelvis tends to be
wider in colder regions, is correct.
All of the above ﬁndings demand moredetailed investigation of the functions of nasal
height and breadth and of the interrelationships
between cranial, nasal, and pelvic breadths.
Summary and Conclusions
Assuming in advance that some craniofacialand postcranial measurements are supposedly
associated with some factors controlling neuro-

43

cranial form, the interrelationships between suchmeasurements and three main neurocranial
mesurements, namely, cranial length and breadthand basi-bregmatic height, were newly examinedthrough principal component analyses of withingroup data and varimax rotation of the solutions
to elucidate the determinants of neurocranialform.
The results show that there is at least a common factor that is relatively strongly associatedwith cranial length (neurocranial form), nasal
height (oxygen intake), the sagittal diameter ofthe femoral midshaft (skeletal muscle mass), andthe vertical diameter of the femoral head andtalar length (body weight), but not associatedwith body height. This suggests that the heavier
individuals who have a longer/thicker gut and acomparatively large amount of skeletal muscle(except the nuchal ones), which consume a relatively large amount of oxygen, tend to have ashorter (and probably wider) neurocranium
regardless of brain size and body height.
In addition, positive associations were foundbetween cranial breadth (neurocranial form), thevertical diameter of the femoral head (bodyweight), nasal height (oxygen intake), and maximum pelvic breadth (body breadth). This is
acceptable from the viewpoints of the cold adaptation hypothesis and Ruffʼs cylindrical thermoregulatory model.
In the present multivariate within-group analyses, many other interrelationships between thethree main neurocranial and craniofacial/postcranial measurements were found. However, mostof them could not simplistically be interpreted
from the viewpoints of biomechanics, metabolism, thermoregulation, humidity regulation, parturition, anteroposterior head balance, and so on.
In order to clarify the determinants of neurocranial form, multivariate among-group analyses
should also be conducted using both morphological measurements and environmental variables.
Acknowledgments
I would like to thank Emeritus Professor Taka-44

Yuji Mizoguchi

hiro Nakahashi of Kyushu University for his
helpful suggestions and comments. I am also
grateful to Salford Software Ltd. and “kito” forkindly providing their very useful software,
FTN77 and CPad, respectively, via the Internet.
This work was partly supported by a Grant-inAid for Scientiﬁc Research (C) from the Japan
Society for the Promotion of Science (ProjectNo. 22570224). The manuscript was copyedited
by Medical English Service, Kyoto.
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