J. Anat. (1977), 123, 1, pp. 111-127

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With 1 figure Printed in Great Britain

Associations in the hominoid facial skeleton W. J. MOORE Department of Anatomy, University of Leeds, Leeds LS2 9NL

(Accepted 10 December 1975) INTRODUCTION

Of the numerous studies of associations within the human skull (e.g. Pearson & Davin, 1924; Woo, 1931; Meredith & Higley, 1951; Bjork & Palling, 1954; Koski, 1964) that by Solow (1966) is particularly noteworthy in that it provides a critical examination of the methodology involved, in addition to a comprehensive survey of associations in the facial region. He distinguishes topographical correlations, found between two variables sharing common reference points, from non-topographical correlations, which arise from co-ordinated variation of reference points that are not common to both variables. A non-topographical correlation can be presumed to indicate a biological association, while a correlation between variables with common reference points does not necessarily indicate such an association. As an aid in interpreting the pattern of non-topographical correlations, Solow analysed his data (collected from 102 adult male Danes) by the factor analysis technique. He found that three groups of statistically significant associations could be recognized within the face. The first group, reflecting variation in the overall size of the head, comprised numerous associations between linear facial dimensions and body measurements such as stature and the size of limb segments. The second group was made up of associations between measurements spanning common facial regions, indicating co-ordinated variation within those regions. Thus the lengths of the jaws were positively correlated with each other and with the length of the anterior cranial base, while the widths of the jaws were similarly correlated with facial (bizygomatic) width. In addition, positive associations were found between the heights (anterior and posterior) of the maxillae and the length of the basicranial axis, but a negative association between posterior maxillary height and the angle of cranial base flexion. These measurements relate to the nasal cavity and nasopharynx, and the associations between them suggest a co-ordinated variation in the size of the upper airway and a compensatory mechanism to preserve the size of the nasopharynx despite changes in cranial base flexion. The third and largest group of associations was found between measurements of the jaws and dentition. On the basis of the factor analysis results, Solow divided this group into three sub-groups. The first was composed of positive associations between jaw measurements and the length and width of the dental arches and tooth size. The length and prognathism (a measure of antero-posterior position) of the maxillae, but not of the mandible, were associated with arch length and tooth size in both

W. J. MOORE 112 upper and lower dentitions, while face and jaw widths were correlated with dental arch width in both jaws. The second sub-group indicated the adaptation of the dental arches to the relationship between the upper and lower jaws. The correlation analysis showed that the length and prognathism of the jaws were positively correlated with incisor inclination in the opposite jaw. Mandibular inclination (relative to the anterior cranial base) was positively correlated with the heights of the alveolar processes and inclinations of occlusal planes in both jaws. There were positive correlations between the heights of upper and lower alveolar processes, and between these alveolar heights and the height of both the total face and lower face (approximately nasal floor to lower border of chin). The third sub-group consisted of associations between jaw dimensions and estimates of occlusion. Mandibular length and prognathism were correlated with overjet (negatively) and the antero-posterior relationship of upper and lower first molars (positively) but the corresponding correlations for maxillary length and prognathism were statistically insignificant. If the compensatory mechanisms between the dental arches and the jaws, which were indicated by the associations in sub-group two, were perfect, no such associations would be expected between the jaw measurements and the estimates of occlusion. It is clear from these findings that a pervasive set of relationships exists within the human facial skeleton and dentition. The object of the present study was to determine whether such a set of associations is unique to man or whether a similar pattern exists within the facial skeleton of other members of the Hominoidea. Although the measurements used here correspond broadly with those of Solow (1966), modifications have been introduced, partly to accommodate differences in the morphology of ape and human skulls, but principally to take account of recent work dealing with the analysis of facial growth (see Moore & Lavelle, 1974, for a description and bibliography of this work). The modifications are described in detail in the section on biometry. MATERIALS AND METHODS

Skulls A total of 246 hominoid skulls was measured. All were adult and with no more than moderate attrition. Their breakdown by genus and sex is given in Table 1. Biometry The cranium and mandible of each skull were articulated in full occlusion and the following measurements made, using standard osteometric procedures (see Fig. 1; also Moore & Lavelle, 1974, for methods and detailed definitions of reference points). In the case of bilateral structures, those on the left side were used for measurement. Numerous studies (e.g. Bjork, 1955; Ford, 1958) have shown that the anterior extension of the cranial base is a relatively stable zone during postnatal skull growth. Measurements of facial length and height were therefore taken parallel and perpendicular, respectively, to this segment of the cranial base. Since relating measurements to a common reference line introduces a degree of topographical correlation between them (Solow, 1966), corresponding direct measurements were also recorded in order

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Table 1. Skulls measured Species Homo sapiens (mixed stock)

Pan troglodytes

Gorilla sp. Pongo pygniaeus

Sex

Number of skulls

Male Female Male Female Male Female Male Female

43 26 21 50 38 37 16 15

NS c

ANS('*IF

>

Pr

ww~~~~~~~~

5

4 Fig. 1. The reference landmarks. 1, lateral view of upper facial skeleton; 2, lateral view of mandible; 3, frontal view of facial skeleton; 4, occlusal view of upper arch; 5, molar occlusion; 6, overjet. See text for meaning of abbreviations; numbering indicates measurements as numbered in text. Not to scale. 8

ANA I23

W. J. MOORE 114 to provide a check that any observed associations were not due solely to this topographical effect. These unprojected measurements are not included in the following list, although they were included in the factor analyses (making the total number of variables 45). Their correlations did not differ, in a statistically significant manner, from those for the projected measurements.

(a) Cranial base (1) Length of basicranial axis: pituitary point (P) - endobasion (E). Several studies (Ashton, 1957; Zuckerman, 1955) have shown that the pituitary point provides the best estimate of the anterior extremity of the basicranial axis. Since all the skulls measured were intact, this point could not be located directly. Instead, the most medial point on the left optic foramen was used, examination of sagittally sectioned human and ape skulls showing that this closely approximates to the pituitary point, when both points are projected into the median plane. (2) Length of anterior extension: P - nasion (N). In apes, the nasion was defined as the point where a line joining the upper limits of the maxillary frontal processes crosses the median plane (Ashton, 1957). (3) Angle of flexion: N - P - E.

(b) Upper facial skeleton (4) Maxillary length: prosthion (Pr) - pterygomaxillary fissure (PtM), parallel to anterior extension. (5) Anterior maxillary height: N - anterior nasal spine (ANS), perpendicular to anterior extension. (6) Posterior maxillary height: P - PtM, perpendicular to anterior extension. (7) Bizygomatic width: maximum width between external surfaces of right and left zygomatic arches. (8) Maxillary prognathism: infraorbital foramen (IF - major foramen where multiple) - N, parallel to anterior extension. In all prognathisms, distances anterior to nasion termed positive and distances posterior to nasion termed negative. (9) Maxillary alveolar prognathism: Pr - N, parallel to anterior extension. (10) Angle of maxillary inclination: the angle between lines (projected into the median plane) drawn from P to N and from IF to the inferior orbital fissure where it is joined by the infra-orbital groove (IbG). The latter line approximates to the basal unit of the maxilla as defined by Moss & Greenberg (1967). (c) Mandible (11) Length: infradentale (I) - condylion (C), parallel to anterior extension. (12) Body height: minimum height of body at the mesial root of the left first lower molar. (13) Rameal height: gnathion (G) - C, perpendicular to anterior extension. (14) Bicondylar width: width between lateral poles of right and left condyles. (15) Prognathism: mental foramen (MF -major foramen where multiple) -N parallel to anterior extension. (16) Alveolar prognathism: I - N, parallel to anterior extension.

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115 (17) Angle of inclination: the angle between lines (projected into median plane) from P to N and from MF to the mandibular foramen (MbF). The latter line approximates to the basal unit of the mandible (Moss, 1960). (d) Facial heights (18) Total height: N - G, perpendicular to anterior extension. (19) Lower height: ANS - G, perpendicular to anterior extension. (e) Dentitions (20) Upper arch length: length (in median plane) from tips of upper central incisors to a line joining distal contact areas of upper second molars. (21) Lower arch length: measured as in the upper arch (20). (22) Upper arch width: width between buccal surfaces of the right and left first upper molars. (23) Lower arch width: measured as in upper arch (22). (24) Height of upper alveolus: the perpendicular distance from the IF - IbG line to Pr. (Measurements 24-29 were projected into the median plane.) (25) Height of lower alveolus: the perpendicular distance from the MF - MbF line to I. (26) Upper incisor inclination: the angle between the long axis of the crown of the left upper central incisor and the IF - IbG line. (27) Lower incisor inclination: the angle between the long axis of the crown of the left lower incisor and the MF - MbF line. (28) Upper occlusal inclination: the angle between a line drawn from the incisal edge of the left upper central incisor to the distobuccal cusp of the left upper first molar and the IF - IbG line. (29) Lower occlusal inclination: the angle between a line drawn from the incisal edge of the left lower central incisor to the middle buccal cusp of the left lower first molar and the MF - MbF line. (30) Molar occlusion: the distance, in the occlusal plane, between the mesial surfaces of the upper and lower left first molars. (31) Overjet, the distance, in the occlusal plane, between the incisal edges of the upper and lower left first incisors. (32) Upper tooth size: sum of the mesiodistal diameters of the upper teeth (excluding third molars). (33) Lower tooth size: sum of the mesiodistal diameters of the lower teeth (excluding third molars). Measurements (26), (27), (30) and (31) are termed, collectively, the occlusal estimates.

Statistical analysis were calculated for each pair of variables in both sex coefficients The correlation of the As sub-groups of each species. an essential aid in interpreting the very large matrices so correlation obtained, the variables were subjected to three factor analyses Principal Components, Varimax (rotated orthogonal) and Promax (rotated oblique) - the factors being extracted separately for each sex sub-group. 8-2

116 W. J. MOORE The significance level for loadings on each factor was calculated by means of the Burt-Banks Formula (Burt & Banks, 1947). The extraction of factors was terminated at an eigenvalue of 1 00. The Varimax solution was found to be the most helpful in interpreting the correlations, and it forms the basis of the subsequent description of the results. Presentation of data The correlation matrices, each consisting of 528 coefficients, and the tables of loadings of the 33 variables on between 7 and 12 factors in the factor analyses, are far too large to be included here, but are available for consultation on request to the author. In the results section, description is limited to the pattern of associations, in each species and sex sub-group, between variables not sharing common reference points. To avoid repetition, the following conventions have been adopted: (1) in the factor analysis, the direction (+ve or -ve) of the factor loadings has been given only where helpful in the subsequent interpretation of the correlation matrices; signs given in brackets are opposite to those of undesignated loadings; (2) in the correlation analysis, only statistically significant (P < 05) or highly significant (P < 0 1) correlations have been described except where non-significance is important in making intergeneric or sexual comparisons; correlations are positive unless otherwise stated. RESULTS

Homo sapiens Eleven factors were extracted for both the male and female sub-groups in the Varimax solution. In the males, the first factor had high loadings for the linear dimensions of the cranial base, the lengths, heights and widths of maxillae and mandible, total and lower facial height, the lengths and widths of the dental arches and upper and lower tooth size. Factor 2 had the highest loadings for mandibular inclination, total and lower facial heights, mandibular heights, and also high loadings for upper and lower alveolar heights and the prognathisms (negative) and moderately high loadings for maxillary heights. Factor 7 had high loadings for the angle of cranial base flexion and, of opposite sign, for maxillary and mandibular prognathisms. Factor 9 had strong associations with the two measurements of mandibular prognathism, the occlusal estimates (negative for overjet), arch lengths and tooth size. Factor 4 had high loadings for the inclination of the lower occlusal plane and for the length, posterior height (negative) and prognathisms of the maxillae. The inclination of the upper occlusal plane loaded on factor 5, together with the height of the upper alveolus (negative), maxillary inclination and maxillary prognathism (negative). Factor 6 had the highest loadings for the upper and lower arch widths. The pattern of loadings was broadly similar for the females, although the factors were not extracted in the same order. The first factor had again high loadings for the linear dimensions of the cranial base, lengths, heights and widths of the jaws, total and lower facial height and upper alveolar height. The second factor had high loadings for the linear measurements of the cranial base, maxillary and mandibular length and mandibular inclination (negative) and rather less strong associations with

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dental arch lengths, lower alveolar height (negative) and upper and lower tooth size. The angle of cranial base flexion had negative, and maxillary and mandibular alveolar prognathisms positive, loadings on factor 8, representing factor 7 in the males. Factor 4 was strongly associated with mandibular prognathism, and the occlusal estimates (negative for overjet), and is equivalent to factor 9 in the males. Factor 11 had high loadings of opposite signs for lower occlusal plane inclination and posterior maxillary height and represents factor 4 of the male sub-group. Factor 6 was strongly associated with upper occlusal plane inclination, the height of the upper alveolus (negative), maxillary inclination and maxillary prognathism (negative), being thus identical with the male factor 5. Factor 5 had the highest loadings for dental arch widths and represents factor 6 in the males. As in the factor analyses, the correspondence between the two sexes in the pattern of correlations was good although, as would be expected from the smaller sample size, the number of coefficients reaching significant levels in the female sub-group was fewer than in the males. One group of associations reflected total skull size. This included significant or highly significant correlations, in both sexes, between the linear dimensions of the cranial base, the lengths, heights and widths of the maxillae, length, body height (in the male) and width of the mandible and total facial height. A second group, not entirely distinct from the first, consisted of associations between measurements that spanned closely related regions. Thus the length and width of the upper jaw were correlated with the corresponding dimensions of the lower jaw. Significant correlations were also observed between maxillary, mandibular, total and lower facial heights and between maxillary heights and the lengths of the basicranium and its anterior extension. In the males, maxillary and mandibular inclinations were correlated with facial and mandibular heights but in the females only the correlations between mandibular inclination and facial and rameal heights reached the significant level. In both jaws, the two prognathisms were correlated. Maxillary prognathism was correlated with maxillary length and, in the males, mandibular prognathism with mandibular length. Maxillary and mandibular prognathisms were negatively correlated with the jaw inclinations. The alveolar prognathisms were negatively correlated with facial heights, except for the single instance of maxillary alveolar prognathism with lower facial height in the males where the coefficient fell just short of significance. The angle of cranial base flexion had few statistically significant associations apart from negative correlations with the mandibular prognathisms and maxillary alveolar prognathism in the males. Its negative associations with the alveolar prognathisms just failed to reach significance in the females. The third group of statistically significant associations comprised those between measurements of the jaws and dentitions. The lengths and widths of the mandible and maxillae were correlated with the corresponding dimensions of the dental arches. The lengths of the jaws and the lengths and widths of the arches were strongly associated with tooth size in the males but less so in the females. In each sex, the correlations between the prognathisms and arch and tooth size were low. Upper alveolar height was positively correlated with anterior maxillary height, rameal height and total facial height but negatively with upper occlusal, upper incisor and

W. J. MOORE 118 maxillary inclinations. Lower alveolar height had few statistically significant correlations in the females, but in the males was associated with mandibular heights, total and lower facial heights, mandibular inclination and lower occlusal inclination. Finally, the dimensions estimating occlusion had several significant correlations with jaw dimensions. Upper incisor inclination was associated with mandibular length and prognathism and, in the males, with maxillary and mandibular alveolar prognathisms. Lower incisor inclination was associated with mandibular prognathism and, in the males, with maxillary alveolar prognathism. Molar occlusion was positively correlated with mandibular prognathism while overjet was negatively correlated with both mandibular prognathisms.

Gorilla Eleven factors were extracted for the males and 10 for the females in the Varimax factor analysis. Apart from differences in the order of extraction, the factors were generally similar in the two sexes. Factor 1 had high loadings for the linear dimensions of the cranial base, overall jaw dimensions and prognathisms, total and lower facial heights, dental arch and tooth sizes. In the females, the first factor had also high loadings for cranial base flexion and maxillary and mandibular inclinations (all of opposite sign to the measurements of length and prognathism). Cranial base flexion (negative) and maxillary prognathism loaded on factor 3 in the males. Factor 2 in the male sub-group had high loadings for jaw lengths and heights (negative), total facial height (negative), jaw inclinations (negative) and the prognathisms. Similar loadings occurred in the females, except that jaw and arch widths also loaded on this factor. These widths loaded separately on factor 7 in the males. Factors 3 in the female and 5 in the male sub-group were strongly associated with upper incisor and occlusal inclinations and (of opposite sign) upper alveolar height. Factors 8 in the females and 9 in the males were strongly associated with lower alveolar height, lower incisor inclination (of opposite sign) and lower occlusal inclination. Tooth and arch size and overjet loaded on factor 4 in the females but, in the males, tooth and arch size were more strongly associated with factor 1 and overjet loaded separately on factor 6. The highest loadings for molar occlusion occurred on factors 10 in the male and 7 in the female sub-group. The correlation matrices were generally similar for both sexes. Two major groups of statistically significant correlations were apparent representing, respectively, overall skull size and measurements spanning similar anatomical regions. Thus, many associations were found between linear dimensions of the cranial base, lengths, heights and widths of the jaws, maxillary and mandibular prognathisms, facial heights, lengths and widths of the dental arches. Maxillary heights were correlated with total facial height and mandibular heights with both total and lower facial heights. Of the associations between jaw inclinations and heights, only those with anterior maxillary height and rameal height were statistically significant in both sexes. The two prognathisms of each jaw, as well as being correlated with each other, had strong associations with jaw lengths and, in the males, with arch lengths. The alveolar prognathisms, but not the main prognathisms, of the upper and lower jaws were correlated. High negative correlations occurred between all the prognathisms

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and maxillary and mandibular inclinations but the correlations with facial heights were low, only those in the males of maxillary alveolar and mandibular prognathism with total facial height (negative) and maxillary and mandibular alveolar prognathisms with lower facial height (positive) being statistically significant. The principal correlations of the angle of cranial base flexion were negative with maxillary and mandibular prognathisms. In the female sub-group, cranial base flexion was, in addition, positively associated with both jaw inclinations and, negatively, with posterior maxillary height. The third major group of associations was made up of the many statistically significant correlations between jaw and dentitional measurements. The lengths and widths of maxillae and mandible were correlated with corresponding dimensions of the dental arches. The correlations between the overall dimensions of the jaws and tooth size, on the other hand, were generally low, the only ones to reach significance being those involving maxillary length and width in the males. The male prognathisms were associated with arch but not tooth size. Upper alveolar height in the males was positively correlated with anterior maxillary, rameal and total facial height and mandibular inclinations but negatively with maxillary, upper incisor and both occlusal inclinations; in the females only the negative correlations were significant. Lower alveolar height in the male sub-group was positively correlated with lower facial height and lower occlusal inclination while, in the females, this dimension was correlated with jaw and lower occlusal inclinations and negatively with lower incisor inclination. The associations between the measurements of the dentition were all strong, except for those involving the occlusal inclinations whose principal associations were, as just described, with alveolar heights. There were no statistically significant correlations between the estimates of occlusion and few between alveolar heights and incisor inclinations. In the female sub-group, incisor and occlusal inclinations were positively correlated in the upper dentition and negatively correlated in the lower. Pan In the Varimax solution, 12 factors were extracted for the males and 11 for the females. The solution was similar for the two sexes, despite differences in the order in which factors were extracted. Factor 1 had high loadings, in both sexes, for the

anterior extension of the cranial base, lengths, heights and widths of maxillae and mandible, upper facial height, dimensions of both arches and, in the males, maxillary and mandibular prognathisms (negative) and upper and lower tooth size. In the females, factor 1 was also strongly associated with the length of the basicranium. The second factor had high loadings in the female sub-group for cranial base flexion, jaw inclinations and, of opposite sign, all the prognathisms and jaw lengths while, in the males, this factor was associated with the length of the basicranium, jaw lengths and overjet. Jaw and facial heights in the females loaded on factor 3 as well as factor 1. Factors 3 in the males and 4 in the-females were associated with maxillary, upper incisor and upper occlusal inclinations and, of opposite sign, upper alveolar height. Similar associations were found for mandibular, lower incisor and lower occlusal inclinations and lower alveolar heights with factors 7 in the males and 10 in the females, except, in these instances, lower incisor inclination was of opposite sign

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to the remainder. Factor 4 in the males was most strongly associated with cranial base flexion. Factors 5 in the female and 11 in the male sub-group were associated with dental arch lengths; the female factor 5 was also associated with upper and lower tooth size. Arch widths loaded on factor 6 in the females and 12 in the males. Molar occlusion loaded separately on factor 10 in the males and 11 in the females while overjet in the latter sub-group loaded on factor 7. Although there was considerable similarity between the pattern of correlations in the two sexes, more of the coefficients reached statistical significance in the much larger female sample. One large group of significant correlations represented coordinated variation in total skull size. A second group was made up of associations between measurements related to similar anatomical regions. These two groups included correlations between linear dimensions of the cranial base, overall jaw dimensions and prognathisms, facial heights and dental arch size. The corresponding dimensions of maxillae and mandible were also highly correlated. Maxillary and mandibular heights were all strongly correlated with total facial height but corresponding correlations with lower facial height were much weaker. In the females, maxillary heights were associated with the length of the basicranial axis and its anterior extension; in the males only the correlation between the anterior extension and posterior maxillary height was significant. The inclinations of the two jaws were correlated with anterior maxillary height and rameal height in both sexes. Mandibular inclination was also correlated with total facial height but the corresponding association with maxillary inclination was significant in only the males. The prognathisms were all highly correlated in the females. In the males, the coefficients between maxillary prognathism and the 2 mandibular prognathisms were significant. The mandibular prognathisms were strongly associated with mandibular length and, negatively, with mandibular inclination. Of the corresponding correlations in the upper jaw only those for alveolar prognathism in the female skulls were significant. Both mandibular prognathisms were negatively correlated with rameal height and total facial height while mandibular alveolar prognathism was positively correlated with lower facial height. Negative correlations were observed between maxillary prognathism and anterior maxillary height but the correlations with lower facial height were positive. Cranial base flexion, in the female sub-group, was positively correlated with jaw inclinations and negatively with all the prognathisms and also with posterior maxillary height. In the males, the data were insufficient to establish these associations as statistically significant. The associations between the jaws and dentitions, making up the third group, included those between jaw and arch widths and, in the females, maxillary length and both arch lengths (the remainder of the correlations between jaw and arch lengths were insignificant). The correlations between jaw dimensions and tooth size were low, as were those between the prognathisms and arch and tooth size. Upper alveolar height was positively associated with anterior maxillary height, rameal height, total facial height and mandibular inclination and negatively with upper occlusal inclination and, in the females, maxillary, lower occlusal and upper incisor inclinations. Lower alveolar height was positively associated with both mandibular heights, both facial heights, mandibular inclination and lower occlusal inclination

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and, in the females, negatively with lower incisor inclination. Statistically significant correlations between dentitional measurements were sparse. Arch lengths and widths and tooth size in the upper jaw were correlated with the corresponding dimensions in the lower jaw but the associations between arch size and tooth size were low, the only ones to reach significance being between arch lengths and tooth sizes in the females. Molar occlusion had no statistically significant correlations whatever, while overjet had very few. Incisor inclinations also had few significant correlations in the males, but in the females, in addition to those with alveolar heights already noted, upper incisor inclination was positively correlated with mandibular prognathisms and both occlusal inclinations and negatively with mandibular inclination while lower incisor inclination was positively associated with arch lengths and negatively with both occlusal inclinations.

Pongo The Varimax solution extracted 7 factors for the males and 11 for the females. In the male sub-group, the basicranial axis, the linear dimensions and prognathisms of the jaws, all arch dimensions and lower alveolar height loaded heavily on factor 1. Maxillary and mandibular lengths and prognathisms and the basicranial axis also loaded on factor 2, together with, but of opposite sign, the jaw inclinations and cranial base flexion. Tooth size, molar occlusion and, to a lesser extent, arch lengths loaded on factor 3. Alveolar heights and lower occlusal inclination loaded negatively and incisor and upper occlusal inclinations positively on factor 4. Factor 5 was associated with overjet and the length of the anterior extension. Cranial base flexion had its greatest loading on factor 7. For the female skulls, jaw lengths, heights, prognathisms and inclinations, the basicranial axis and anterior extension, and cranial base flexion loaded on factor 2, the anterior extension, jaw lengths and prognathisms and posterior maxillary height being of opposite sign to the remainder. Factor 1 was most strongly associated with arch and tooth dimensions. Maxillary width and prognathism, facial heights (negative) and overjet loaded on factor 3. The basicranial axis loaded most heavily on factor 5, which also had strong associations with maxillary and mandibular lengths. Factor 6 represented mandibular width. Mandibular alveolar prognathisms loaded on factor 10. The associations between alveolar heights, occlusal and incisor inclinations were less clear cut than in the males. Upper alveolar height loaded on factor 3; lower alveolar height loaded oR factor 4 together with upper incisor and lower occlusal inclinations and, of opposite sign, lower incisor and maxillary inclinations; upper occlusal and incisor inclinations loaded on factor 7 together with molar occlusion (negative). Cranial base flexion and maxillary prognathism were strongly associated with factor 8. As would be expected from the contrasts seen in the factor analysis, there were considerable sexual differences in the pattern of correlations. Many of the coefficients for the linear dimensions of the facial skeleton and dental arches in the male correlation matrix were of very high value and so reached the significant or highly significant level despite the smallness of the sample. Far fewer reached significance in the female sub-group. In both sexes, a large proportion of the significant correlations reflected variation

W. J. MOORE 122 in total skull size or were between measurements related to common anatomical regions. In the males, basicranial length was correlated with jaw lengths and widths, facial and posterior maxillary heights and also with all four prognathisms. The maxillary lengths, heights and widths were highly correlated with corresponding dimensions of the mandible. The lengths and heights of both jaws were correlated with facial heights and arch lengths and jaw widths with arch widths. Of the correlations between the two jaw inclinations and facial heights, only those with anterior maxillary and rameal height were significant. Very high correlations were observed between both prognathisms of each jaw, the prognathisms of opposite jaws and between all four prognathisms and jaw lengths. All the prognathisms were negatively correlated with jaw inclinations and positively with lower facial height. Neither the anterior extension nor the flexion of the cranial base had significant correlations with any other dimensions. In the female skulls, basicranial length was associated with only mandibular prognathism and heights. Far fewer of the jaw dimensions were associated than in the males, significant correlations being found for only maxillary length with mandibular length and upper arch length, anterior maxillary height with rameal height, posterior maxillary height and mandibular body height with facial heights and rameal height with total facial height. There were no significant correlations between the various width dimensions. The maxillary prognathisms had few associations while the mandibular prognathisms, as well as being correlated with each other, were correlated with mandibular length and inclination. Maxillary prognathism and mandibular alveolar prognathism were associated with cranial base flexion. The two jaw inclinations were correlated with anterior maxillary, rameal and total facial height. Prominent amongst the many associations between jaws and dentition in the males, were the high correlations between jaw and tooth size already noted. There were, in contrast, no significant correlations between the prognathisms and arch size nor between tooth size and any of the jaw measurements. Upper alveolar height was positively associated with mandibular and lower occlusal inclinations and negatively with incisor and upper occlusal inclinations. Lower alveolar height was positively correlated with facial heights but had no associations with dentitional measurements. The only statistically significant correlations between corresponding dimensions of jaws and dentitions in the females were between maxillary length and upper arch length and, negatively, between maxillary inclination and mandibular alveolar prognathism, on the one hand, and lower occlusal inclination, on the other. Within the dentitions, there were highly significant correlations between arch and tooth size in the females but not in the males. In both sexes, all arch dimensions were correlated. The estimates of occlusion had few significant correlations with other dimensions in either sex. The principal exceptions, in addition to those already described for incisor inclinations, being between molar occlusion and mandibular prognathisms in the females, and between incisor and occlusal inclinations (positive in upper jaw, negative in lower) in both sexes.

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DISCUSSION

The pattern of associations for the human skulls of both sexes was closely similar to that reported by Solow (1966) for living male subjects. In each sex sub-group, as in Solow's sample, two major, and not entirely separable, groups of associations could be distinguished, the first reflecting co-ordinated variation in total skull size, the second co-ordination between measurements spanning common anatomical regions. Solow was able to demonstrate low, but statistically significant, correlations between many of the linear dimensions of these two groups and measurements of body size, but this was not possible in the present study because of the lack of associated ctanial and postcranial material. The design of the measurements allowed associations belonging to the second group to be identified additional to those described by Solow. Of particular prominence were negative associations between the angles at which the basal units of the maxillae and mandible are set, relative to the anterior cranial base, and the degree of prognathism of the jaws; and positive associations between these inclinations and facial heights. Hence, the more steeply inclined the jaws, the taller but less projecting the face. As might be expected, prognathism and facial height were negatively associated, although not all the correlations between the estimates of these two attributes were statistically significant. In addition to the strong associations between corresponding dimensions of the upper and lower jaws, high correlations were found between maxillary heights and the lengths of the basicranium and its anterior extension, dimensions representing the heights and depths of the nasopharynx and nasal cavity. Solow reported a negative correlation between cranial base flexion and posterior maxillary height and suggested that this indicated a compensatory mechanism to preserve the size of the nasopharynx despite changes in the orientation of its roof (i.e. the basicranium). Negative correlations between these dimensions occurred in the present data but did not reach the significant level. A third group of associations comprised those of measurements of the jaws with measurements of the dentition. As in Solow's study, the factor analysis suggested that this group should be divided into three sub-groups. The first of these was made up of associations between the lengths and widths of the jaws, on the one hand, and arch and tooth size, on the other. Unlike Solow, however, no statistically significant correlations were found between prognathism and arch or tooth size. The second sub-group reflected the adaptation of the arches and dentition to the relationship of the upper and lower jaws. The negative association of maxillary inclination with upper alveolar height indicates a tendency for changes in the angle at which the maxillae are set within the facial skeleton to be offset by variation in the height of their anterior alveolar processes, an increase in the angle, for example, being accompanied by a decrease in the height of the process. In the lower jaw, the reverse relationship holds true, the alveolar process tending to become taller to compensate for increases in mandibular inclination and vice versa. In this way, the effects of changes in jaw inclination on the orientation of the occlusal plane are minimized, a conclusion supported by the strong positive association between jaw and occlusal plane inclinations (the latter being measured with respect to the basal units of the jaws).

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That the adaptation between jaws and dentition is not complete is shown by the associations, comprising the third group, between jaw dimensions and the estimates of occlusion as well as by the weak associations, already noted, between the prognathisms and arch and tooth size. The correlations between upper and lower prognathisms were not high (averaging 0 466), and the mechanisms for compensating for discrepancies between the two, by variations in arch and tooth size, appear to have been insufficient to prevent disturbances of the normal occlusal relationships. The factor analyses indicated that the associations in the facial skeleton of each of the three apes could be grouped and sub-grouped in the same manner as those in the human face. Despite this broad similarity, numerous generic and sex contrasts were found amongst the associations making up the first and second groups. The most prominent of these was the generally much higher value of the correlation coefficients in the apes, suggesting a much tighter co-ordination of facial growth. The contrast was especially marked in the correlations between jaw dimensions, where the coefficients were, in many instances, close to 1. The very strong associations found between the prognathisms of the maxillae and those of the mandible indicate that variations in jaw position are well co-ordinated and produce little disturbance of the occlusion, further evidence for this conclusion being provided by the generally weak association of the prognathisms with molar occlusion and overjet in the ape skulls. In the gorilla and chimpanzee there were no great sexual differences in this respect but, in the orang utan, the correlations between the prognathisms tended to be lower, and the association between prognathism and molar occlusion correspondingly stronger, in the female sub-group. The absence of a mechanism to compensate for discrepancies in the antero-posterior relationship of the upper and lower jaws by variation in the size of the dental arches is apparent from the low correlations found between the prognathisms and arch and tooth size in all the genera. Therefore, if the association between upper and lower prognathism is relatively weak as in man and the female orang utan, the normal occlusal relationship is liable to be disturbed by poorly co-ordinated variation in the position of one or other of the jaws. Following Huxley (1863), the angle of cranial base flexion has often been used as an indication of the position of the face relative to the braincase in comparative studies of the hominoid skull (e.g. Duckworth, 1915; Ashton, 1957; Ashton, Flinn & Moore, 1975). The validity of this assumption is confirmed by the high correlations found between this angle and the degree of facial prognathism in the present study. The mandible (which articulates at the temporomandibular joints with the lateral extensions of the basicranium) showed stronger associations in this respect than did the upper face (which articulates with the anterior cranial base), especially in man. In none of the genera was cranial base flexion strongly associated with measurements of jaw lengths. It seems, therefore, that variation in the angle between the basicranial axis (with its lateral extensions) and the anterior cranial base influences the degree to which the mandible protrudes or retrudes relative to the nasion. Since the correlation between upper and lower prognathism is high in the apes and moderate in man, this variation also influences the degree of maxillary protrusion or retrusion. There appears to be no effective mechanism, operating through changes in jaw lengths, to offset variation in cranial base flexion. The weaker association between upper and lower prognathisms in man, than in the apes, accounts for the more marked contrast,

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in this genus, between the influence of cranial base flexion upon mandibular prognathism than upon maxillary prognathism. Variation in cranial base flexion might, therefore, be expected to modify the occlusal relationship in man. In fact, the correlations between molar occlusion and cranial base flexion were not large (-0 112, male; -0-310, female) but still considerably greater than in the apes (average - 0050). Cranial base flexion had negative correlations with posterior maxillary height in each of the apes, although these attained statistical significance in only the female gorilla and chimpanzee. Solow's suggestion of a compensatory mechanism adjusting the height of the nasopharynx to the slope of its roof thus gains some support from the present findings, the mechanism appearing to operate weakly throughout the genera studied. A further generic difference in the associations of the first and second groups was found in the relationship between prognathisms, jaw inclinations and facial height. In the apes, as in man, jaw inclinations were negatively correlated with maxillary and mandibular prognathism. However, of the associations between jaw inclinations and facial heights, only half of those with total facial height reached statistical significance, while none of those with lower facial height reached this level. Indeed, 9 out of the 12 correlations in the latter group were negative.Although not statistically significant, the consistency of this finding suggests that such an inverse relationship might well exist if larger samples were available. Correspondingly, the prognathisms tended to be negatively associated with total facial height but positively with lower facial height. This is in sharp contrast to man, where the associations of both facial heights with jaw inclinations and prognathisms were entirely consistent in their direction. An explanation of this generic difference in the case of maxillary inclination may lie in a stronger negative association between this attribute and upper alveolar height in the apes than in man. Thus the more inclined the maxillae, the greater the total facial height, but the less its inferior subdivision due to the associated reduction in alveolar height. Neither the validity of this suggestion nor the reason for the negative association of mandibular inclination with lower facial height are apparent from the present data, but would require ontogenetic investigation. The pattern of correlations between jaw and dentitional measurements, which make up the third group of associations, showed a remarkably close similarity in the genera studied. In the apes, as in man, the factor analyses indicated that this group is divisible into three sub-groups. It was only in the third sub-group, comprising the correlations between jaw dimensions and occlusal estimates, that any major contrast was found between man and the apes. The significance of this contrast has already been discussed with the co-ordination of jaw position. In the first (associations between jaw, arch and tooth dimensions) and second (adaptation of dental arches to the relationship of upper and lower arches) sub-groups, there was great consistency in the findings for each genus, suggesting that the co-ordination of growth in the jaws and dental arches is similar throughout the Hominoidea. Correlation studies of the adult form do no more than define patterns of coordination; they cannot provide direct evidence of the nature of the underlying controlling mechanisms. For this, recourse must be made to growth studies. Nonetheless, knowledge of the adult correlations forms a valuable first stage in unravelling

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the growth of complex structures in that it gives a basis for planning a rational scheme of ontogenetic investigation. The results of the present study provide such a basis for investigating the comparative growth of the hominoid facial skeleton. The next step, now being taken, is to determine how the identified generic differences in facial co-ordination arise during the growth period. SUMMARY

A comparative study has been made of the correlations between numerous linear and angular dimensions of the facial skeleton of man and the three great apes. The Varimax (rotated orthogonal) factor analysis was found to be an essential aid in analysing the very large correlation matrices obtained. It indicated that three groups of association can be identified in the hominoid skull. The first reflects co-ordinated variation in total skull size; the second, co-ordinated variation within common anatomical regions; the third, co-ordination between the jaws and dentition. A broadly similar pattern was found in each group for all four genera. The principal contrasts between man, on the one hand, and the apes, on the other, were found in groups 1 and 2. The most prominent of these was a generally much tighter degree of association between the size and position of upper and lower jaws in the apes, and a consequently reduced tendency for disruption of the occlusal relationship of the teeth. I should like to thank Professor J. T. Eayrs and the Trustees of the Powell Cotton Museum for permission to measure skulls in their care. I am deeply indebted to Dr Martin Farally for his help with the statistical analysis.

REFERENCES ASHTON, E. H. (1957). Age changes in the basicranial axis of the Anthropoidea. Proceedings of the Zoological Society 120, 715-721. ASHTON, E. H., FLINN, R. M. & MooRE, W. J. (1975). The basicranial axis in some fossil hominoids. Journal of Zoology 176, 577-591. BJORK, A. (1955). Cranial base development. American Journal of Orthodontics 41, 198-225. BJORK, A. & PALLING, M. (1954). Adolescent age changes in sagittal jaw relation, alveolar prognathy, and incisal inclination. Acta odontologica scandinavica 12, 201-232. BURT, C. & BANKS, C. (1947). A factor analysis of body measurements for British adult males. Annals of Eugenics 13, 238-256. DUCKWORTH, W. L. H. (1915). Morphology and Anthropology, 2nd edn. Cambridge University Press. FoRD, E. H. R. (1958). Growth of the human cranial base. American Journal of Orthodontics 44, 498-506. HUXLEY, T. H. (1863). Evidence as to Man's Place in Nature. London: Williams & Norgate. KoSKI, K. (1964). The Finnish female face in norma lateralis. Transactions of the European Orthodontic Society, 463-469. MEREDITH, H. V. & HIGLEY, L. B. (1951). Relationships between dental arch widths and width of the face and head. American Journal of Orthodontics 37, 193-204. MOORE, W. J. & LAVELLE, C. L. B. (1974). The Growth of the Facial Skeleton in the Hominoidea. London: Academic Press. Moss, M. L. (1960). Functional analysis of human mandibular growth. Journal of Prosthetic Dentistry 10, 1149-1159. Moss, M. L. & GREENBERG, S. N. (1967). Functional cranial analysis of the human maxillary bone. I. Basal bone. Angle Orthodontist 37, 151-164.

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PEARSON, K. & DAVIN, A. (1924). On the biometric constants of the human skull. Biometrika 16, 328-363. SOLOW, B. (1966). The pattern of craniofacial association. Acta odontologica scandinavica 24 (supplement 46), 1-174. Woo, T. L. (1931). On the asymmetry of the human skull. Biometrika 22, 324-352. ZUCKERMAN, S. (1955). Age changes in the basicranial axis of the human skull. American Journal of Physical Anthropology 13 (n.s.), 521-539.

Associations in the hominoid facial skeleton.

J. Anat. (1977), 123, 1, pp. 111-127 111 With 1 figure Printed in Great Britain Associations in the hominoid facial skeleton W. J. MOORE Department...
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