Cranial capacitycranial base relationships and prediction of vault form A canonical correlation analysis.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 53:151-158 (1980) Cranial Capacity/Cran ial Base Relationships and Prediction of Vault Form: A Canonical Correlation Analysis JAMES V. TAYLOR AND ROBERT DIBENNARDO Department of Anthropology, Lehman College of CUNY, Bronx, New York 10468 KEY WORDS Cranial base, Cranial capacity, Canonical correlation, Brachycephalization ABSTRACT 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. 151 152 J.V. TAYLOR AND R. DIBENNARDO 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). RESULTS 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. VAULT FORM, CRANIAL CAPACITY AND CRANIAL BASE LENGTH 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). R C R: Criterion Variable Loadings Skull length Skull width Skull height Predictor Variable Loadings Cranial capacity Facial length Anterior Base (nasion-basion) Posterior base First Second 0.92 0.84 0.46 0.21 0.85 0.71 0.64 -0.38 0.68 0.01 0.94 0.38 0.76 0.33 0.07 -0.62 0.41 -0.16 153 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. DISCUSSION 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- 154 J.V. TAYLOR A N D R. DIBENNAFDO 1.0 .a n Figure l a .6 p-! .4 .2 .- 0 0 -0.0First Canonical &=0.92 Brain/ Face/ Base Variables Vault Variables Brain/ Face/ Base Variables Vault Variables 1.0 8 - 6 4 2 0 0 r c e s Second Canonical Rc=0.46 -.I x 1 i 0.0 - .2 t n A r 4- OJ E 82 .I m x z - 0 - .4 -.6 - .a Figure l b -1.0 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 VAULT FORM, CRANIAL CAPACITY AND CRANIAL BASE LENGTH 155 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. 158 J.V. TAYLOR AND R. DIBENNARDO 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. ACKNOWLEDGEMENTS 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 Povenelli. 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