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Cranial capacitycranial base relationships and prediction of vault form A canonical correlation analysis.

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Cranial Capacity/Cran ial Base Relationships and Prediction
of Vault Form: A Canonical Correlation Analysis
Department of Anthropology, Lehman College
of CUNY, Bronx, New York 10468
Cranial base, Cranial capacity, Canonical
correlation, Brachycephalization
Canonical correlation analysis was used to test an hypothesized
morphological relationship between vault form and cranial capacity relative to
length of the chondrocranium. Ninety-five adult male Czech skulls were measured
for vault form expressed as length, width and height of the brain case; the chondrocranium was represented by nasion-basion and basion-opisthion lengths. In terms
of explained variation, the first and most important dimension of covariation
between vault and chondrocranial variables was size. The second most significant
dimension of covariation expressed the hypothesized shape relationships-i.e.,
overall size being equal, the shorter the chondrocranial base relative to cranial
capacity, the shorter and wider the vault. Furthermore, the competing hypothesis
that vault form is determined by facial length proved untenable since facial length
was predictive of vault shape only when measured as prosthion-basion, a measure
that incorporates basal length. When corrected for basal length, facial length is
unrelated to vault form. The results are consistent with the assumption that
phylogenetic and microevolutionary trends toward brachycephaly in man stem
from changes in the relationship between two components of skull growth, the
chondrocranial base and the brain.
Many investigators have hypothesized relationships between major components of the
skull such as the face, base, neurocranium and
the brain. This research has been extensively
catologued and discussed by Riesenfeld ('67).
Historically, the relationship between face and
brain case was the dominant theme, two early
models being those of Anthony ('03; Anthony
and Pietkiewicz, '10) and Weidenreich ('41).
Anthony stressed the importance of the temporal muscles as the determinant of vault form,
while Weidenreich emphasized the expanding
brain as the motive force in a rolling-up process
of the skull producing shortening and ventral
rotation of the face and brachycephalization.
Both approaches implied a close causal relationship between face or brain and shape of
the brain case.
Despite a n occasional revival (Dokladal,
'64; Pilbeam, '721, experimental studies
(Washburn, '47; Riesenfeld, '67) disproved Anthony's masticatory hypothesis. The experiments by Young ('59) and Riesenfeld ('67)
stressed the importance of the brain in the
0092-9483/80/5301-0151$01.70 0 1980 ALAN R. LISS, INC.
determination of neurocranial form but also
suggested a degree of independence between
face and brain not envisioned by Weidenreich.
In addition, DuBrul and Laskin ('61), Sarnat
and Wexler ('66), Riesenfeld ('67), and Sarnat
('73) implicated changes in the chondrocranium as a major determinant of skull form.
In short, changes in vault morphology can be
produced by absolute increase in cranial contents (Young, '59), by increase in cranial contents relative to body size (Riesenfeld, '671, or
by removing anterior or posterior elements of
the chondro-cranium (DuBrul and Laskin, '61;
Sarnat and Wexler, '66; Riesenfeld, '67; and
Sarnat, '73).
The success of these various procedures implies that a multiplicity of causes underlies
vault morphology. The objective of the present
paper is to suggest a single principle which
unifies this seeming diversity of causes. We
reject a reductionist explanation of skull form
based on any single factor. Instead, we suggest
Received August 6, 1 9 7 9 accepted December 26, 1979.
The sample consisted of 95 adult male Czech
crania from the von Luschan collection of the
American Museum of Natural History in New
York City. There are no available records on
these specimens, but Shapiro ('29) notes that in
Central Europe graveyard space is limited and
bones are periodically disinterred and stored in
small chapels. The present series, probably datMATERIALS AND METHODS
ing from the 17th, 18th and 19th centuries, was
To explore the interrelationships between apparently acquired from such charnel houses.
cranial capacity and facial and basicranial
The study was limited to males because the
lengths on the one hand, and shape of the series did not contain enough females. Sex was
neurocranium on the other, seven dimensions assessed by a n inspectional method using sevof the skull were studied by canonical correla- eral anatomical traits such as general size and
tion analysis, a method uniquely suited to ruggedness, slope of the forehead, development
exploringcorrelations between two sets of mea- of the supraorbitals and mastoid processes, and
surements. Canonical correlation analysis is relief of the occipital lines. We used only those
the method of choice, first, because the com- skulls which each of us independently deterplexity of the interrelationships we study does mined to be male.
not admit to solution by univariate means. SecMeasurements were obtained by standard
ond, it combines some of the heuristic features craniometric procedures; i.e., cranial base
of factor analysis with the additional capability length was defined as nasion to basion, foramen
of testing the specific hypothesis that the inter- magnum length as basion to opisthion, cranial
relationships between cranial base length and height as basion to bregma, cranial length as
cranial capacity are significantly predictive of glabella to opisthocranion, cranial width as the
vault shape.
bieuryon diameter and cranial capacity as volCanonical correlation analysis (CCA) is an ume in cubic centimeters measured with millet
extension of the concept of multiple regression. seed and tested against a bronze crcine etalon.
In the latter, a single dependent variable, Y, is Facial length was measured as the perpendicucorrelated with a combined predictor variable, lar distance from prosthion to the nasionx, obtained by summing the appropriately basion line; this yields a measure geometrically
weighted independent variables, XI, X2,. . .X,. independent of cranial base length. In other
In CCA we have a set of dependent variables, studies (e.g., Weidenreich, '41 and Hemmei ,
Y ,, Y2, . . .Y,, as well as the set of Xs. This set of '671, facial lenth is usually defined as prosthion
Ys is also weighted and summed to produce a to basion, but in humans this is highly correcombined outcome variable, 7.The simple cor- lated with nasion-basion length.
relation between x and 7 is the canonical correlation coefficient, R, (Harris, '75).
In many respects x and 7 can be thought of as
latent factors of their respective variable doTable 1 presents the canonical correlation
mains (Cooley and Lohnes, '71). The procedure coefficients which are statistically significant
extracts these factors, one from each variable at the 0.05 level, together with their respective
set, so as to maximize the covariance between canonical variable loadings. The first pair of
them. Usually a second pair of factors, inde- canonical factors correlate at 0.92, and the secpendent of the first, can account for the ond at 0.46. As in simple correlation analysis,
maximum residual covariance, and so forth. the coefficient of determination for the first caThus, several pairs of latent factors may be nonical (0.92') indicates that roughly 85% of
signifkantly correlated across sets, producing the variation in the outcome latent factor is
several canonical correlations of sequentially explained by variation in the predictor factor.
For the second pair, 21% of the outcome factor is
diminishing importance.
The seven dimensions divided by category explained by the predictor.
Canonical variable loadings are interpreted
were, first, cranial capacity, facial length, cranial base length and foramen magnum length as in factor analysis. That is, factor loadings are
in the conceptual domain of facebasebrain re- derived by correlating a latent factor with each
lationships; and, second, cranial height, length of the original variables. Each loading thus exand width in the conceptual domain of neuro- presses the relative importance of that variable
to the factor. Taken together, the loadings efcranial shape.
that the interrelationship between two components, brain size and cranial base length, accounts for the common results of both the comparative anatomical studies of Weidenreich
and the diverse experimental procedures discussed above.
fectively describe the observed variation; positive loadings indicate large size for those dimensions, negative loadings small size. For our
data, the factor loadings are graphically illustrated in Figures l a and lb.
Column 1of Table 1,and Figure l a indicate
that a large skull will tend to be large in all
dimensions, and the converse.The loadings are
high and positive for all the variables, and may
be interpreted as emphasizing variation in
skull size. This is similar to what generally
emerges in factor analysis, where the first latent factor usually represents “size.” The loading for cranial capacity is particularly high.
Column 2 of Table 1,and Figure l b illustrate
the set of relationships especially relevant to
the problem of brachycephalization. Here, wide
or “brachycephalic” skulls are related to a short
base and larger cranial capacity. This relationship obtains for all skulls of roughly the same
overall “size” as defined by the first canonical
correlation. Thus two equally large skulls will
vary in shape depending on the size of the brain
in relation to the length of the cranial base.
As in factor analysis each case can be assigned a score for each latent factor. Using
these scores only, we selected four cases which,
in theory, should illustrate the two extremes in
variation for shape within two sharply contrasting size categories. The four cases thus
identified are illustrated in Figures 2-4. The
two contrasting neurocranial shapes in the
“small” size group are shown in Figures 2.4 a
and b, and those for the “large” size group are
shown in Figures 2-4c and d. It is visually apparent that each size group exhibits one broad
TABLE 1 . The two Canonical correlations
significant at the 0.05 level, together with
their respective canonical variable loadings.
The seven skull variables are divided into
criterion (upper 3) and predictor domains
(lower 4).
Criterion Variable
Skull length
Skull width
Skull height
Predictor Variable
Cranial capacity
Facial length
Anterior Base
Posterior base
and one narrow skull. In each size category the
broad skull has a shorter cranial base relative
to brain size, while the narrow skull exhibits
the converse relationship.
In addition to the analysis presented above,
we conducted a second with face length defined
traditionally as prosthion to basion. The results
were essentially identical to those obtained
above: the first canonical produced a size factor
in which loadings for all variables were high
and positive; the second again represented
shape vis d uis the base length/ cranial capacity
relationship and vault form.
In this latter canonical, however, facial
length exhibits a factor loading which parallels
that for base length, suggesting that a “short”
face is associated with a wide skull. This relationship appears to us to be spurious. The
length of the face is apparently important only
insofar as it includes a significant proportion of
base length. This is demonstrated by the fact
that when face length is measured independently of base length, as in our first analysis,
face length drops out as a significantly loaded
variable related to vault shape.
Our primary conclusion is that variation in
vault form is the result of a n inversely covarying relationship between brain size and length
of the chondrocranium, and that change in cranial form can be understood in terms of this
underlying relationship, obviating the need to
hypothesize direct selection for skull form per
se (cf. Weidenreich, ’45; ’46). We suggest, as
have others, that brain size and base length
possess intrinsic growth potentials which,
under normal circumstances, by and large
exempt them from environmental influences
during growth and development (for a review
see Moore and Lavelle, ’74:98-102). As such,
each may be, and has been at different times,
relatively independently influenced by natural
selection. For example, phylogenetically,
brachycephalization seems mediated primarily
by rapid expansion of the brain; whereas recent
brachycephalization, where brain size has remained constant, is dominated by reduction in
chondrocranial length.
Second, we abandon the traditional method
of measuring facial length (i.e. prosthion to basion), because this measurement includes and
is necessarily correlated with basicranial
length. In doing so we have shown that facial
length (i.e. the perpendicular distance from
prosthion to the nasion-basion line) is not corre-
Figure l a
-0.0First Canonical
Brain/ Face/ Base Variables
Brain/ Face/ Base Variables
Second Canonical Rc=0.46
- .2
- .4
- .a
Figure l b
Fig. 1. Graphic representation of the factor loadings for the predictor (braidfacebase variables) and the
criterion domains (vault variables) for the first two canonical correlation coefficients: a. the first canonical
correlationcoeficient (0.92)represents a general “size”factor;b. the second canonicalcorrelationcoefficient (0.46)
contrasts wideness of skull and larger brain with shortness of both base and skull length.
lated with vault shape. At the same time, Fig. 4
seems to show a reduced anterior projection of
prosthion in the wide skulls. What is not discernible in the two-dimensional plane of the
photograph, is the fact that this reduction is not
a simple linear decrement, but is due to ventral
rotation of the face and palate. At this stage of
our research, we are not able to say what re-
lationship this rotation bears to kyphosis of the
cranial base, but we expect to be able t o clarify
this issue in the near future.
Third, the form of the vault in Fig. 2 suggests
that we have formulated a principle which may
be applicable to the analysis of several other
areas of craniofacial study. Specifically,the extreme of long basal length associated with
Fig. 2. Frontal views of four skulls, two with extreme negative values on canonical factor 1(a and b) and two with extreme
positive values on the same factor (c and d). These extremes represent “small” and “large” skulls, respectively. Within each
size group, the left skull (a or c) represents extreme negative valuesfor canonical factor 2 6 e . longbase relative to brain size),
while the right hand skulls (b or d) represent the converse (i.e. short base relative to brain size).
Fig. 3. Vertical views of the same skulls represented in Figure 2.
Fig. 4. Basilar views of the same skulls represented in Figure 2.
small cranial capacity (Fig. 2a) may account for
the scaphoid form of this skull. The scaphoid
vault contour has been regarded variously, as a
primitive character in Homo erectus, a pathological or anamolous trait among microcephalics, and an archetype for the dolichocephalic
Australian and Eskimo skull. Additionally,
among brachycephalic populations, where
scaphocrania is uncommon, it has been considered a sexually dimorphic trait. Shapiro ('29)
for example, found ridged and scaphoid contours nearly three times as often among males
in his brachycephalic Greifenbergers. It may be
that a long chondrocranium in relation to brain
size may underly scaphocrania where ever it
occurs.Verification of the broader applicability
of this explanation is part of our on-going research.
In addition to these substantive conclusions,
one theoretical point should be noted. Evolutionary trends emerge through the operation
of natural selection on interindividual variations within populations. Our data indicate
that such variations exist vis ci vis the factors
determining vault form, and provides a basis
for understanding the observed trends in
brachycephalization in a way not possible by
experimental or comparative anatomical
methods. On the other hand, because statistical
relationships do not allow for the determination of cause, as does experimentation, a need
for feedback between these approaches seems
imperative for a full understanding of evolutionary problems. We feel that the method of
canonical correlation as employed here will
contribute significantly to this process, especially where some a priori hypothesis of causal
interrelationships can be used to structure the
data. In such circumstances cannonical correlation allows us to fully account for the complexity of the interrelationships involved,
without sacrificing the ability to test for the
plausibility of the underlying hypothesis. In
short, it possesses the versatility of factor analysis with fewer of its short-comings.
We wish to express our appreciation and
thanks to Priscilla Ward, Ian Tattersall and
Harry L. Shapiro of the American Museum of
Natural History in New York City for their
cooperation and assistance in making the materials and work space available for this research. We also thank Eric Delson for his comments and suggestions, and for use of his photographic equipment. Finally, we wish to thank
our student assistants, Vicki Lamas and Ted
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