genetic determinants of cranio-facial morphology: a twin study

Ann. Hum. Genet., Lond. (1974), 37, 431

Printed in Great Britain 431

Genetic determinants of cranio -facial morphology : a twin study

BY MINORU NAKATA, D.D.S., D.D.Sc.,* PAO-LO YU, PH.D. ,~

BAILEY DAVIS, D.D.S.,S AND WALTER E. NANCE, M.D., PH.D.$

The use of twin studies in the analysis of cranio-facial measurements has provided a better understanding of the relative significance of hereditary and environmental factors in the determination of these traits. The ratio of intrapair variances of dizygotic (DZ) and monozygotic (MZ) twins has frequently been used to detect the significant hereditary influences on each trait by univariate statistical procedure. Although this method has resulted in considerable advances in knowledge, little is known about the basic determinants of interrelations among parts of the cranio-facial skeleton from a genetical point of view.

Kempthorne & Osborne (1961) described a method for analysing the pairwise interrelationships of multiple variables in twin data. More recently, Vandenberg (1965 a, b ) and Bock & Vandenberg (1968) introduced a new technique of multivariate analysis of interrelated traits in twins. The technique searches for correlations among intrapair differences in twins that are influenced by common genetic factors. For example, to the extent that an observed correlation in intrapair differences in intelligence and height was greater in dizygotic than in monozygotic twins, one might postulate a common genetic influence on the two variables. In this manner, a large number of variables can be grouped into sets of interrelated traits that are influenced by independent genetic factors.

An application of this method to multiple anthropological measurements based on roentgeno- graphic cephalograms will be shown and discussed in connexion with previous studies of cranio- facial morphology by multivariate analysis.

MATERIALS

Data used in this study are 33 cephalometric measurements (24 linear and 9 angular measurements), and the variables studied are listed in Table 1 and shown in Fig. 1. As an additional variable, the height was measured a t the time when X-ray photographs were taken.

The subjects for investigation were 67 monozygotic twin pairs (30 male and 37 female pairs) and 29 like-sexed dizygotic twin pairs (17 male and 12 female pairs) with the average age of 148 and 144 months, respectively. These twins are from the file of the Indiana University Twin Panel, and the zygosity was determined primarily by serologic criteria.

* Lecturer, Department of Pedodontics, Tokyo Medical and Dental University, Bunkyo-ku, Tokyo, Japan and Fogarty International Fellow, Department of Medical Genetics, Indiana University, Indianapolis, Indiana, U.S.A.

.

t Associate Professor of Medical Genetics, Indiana University School of Medicine, Indianapolis, Indiana, U.S.A.

$ Associate Professor of Pedodontics, Indiana University School of Dentistry, Indianapolis, Indiana, U.S.A. Q Professor of Medical Genetics and Medicine, Indiana University School of Medicine, Indianapolis,

Indiana, U.S.A.

432 MINORU NAKATA, PAO-LO Yu, B. DAVIS AND W. E. NANCE

Table 1. Cephalometric variables used in this study

Linear measurements

I S-N I3 Me-NL' 2 N-Ba I 4 Or-NL'

4 ANS-PNS 16 B-ML'

6 Go-Me I8 S-Gn

A r >

3 B e P N S 1.5 A-NL'

5 A-PNS I7 S-Ar

7 Ba-FL' I9 S-PNS 8 N-ANS 20 S-GO 9 N-POg 21 S-Ba

I 0 N-Me 22 Ar--Go

Ar-Gn I 1 N-NL' 23 &-Me I2 Pog-NL' 24

Angular measurements

2.5 N-S-Ba 26 N-S-Ar 27 S-N-ANS 28 S-N-A 29 NSL/FL 30 PNS-S-Be

32 NSL/NL 33 NSL/ML

31 M0-Go-h

Note : FL : Facial plane - the line through S and Pog, NL : Nasal plane - the line through ANS and PNS, NSL: Nasion-sella plane -the line through N and S, and ML: Mandibular plane - the line through Go and Me. FL', NL' and ML' are the projection from each point to the respective line.

- _ -

'----I/)".. Go Gn

Me

Fig. 1. Diagram of lateral skull X-ray used in this study. N, Nasion; S, Sella timcica; Or, Orbitare; ANS, Anterior nasal spine; A, Subspinale; PNS, Posterior nasal spine, B ; supramentale; Pog, Pogonion; Gn, Gnathion; Me, Menton; Go, Gonion; Ar, Articulare; Ba, Basion.

METHODS

Basic assumptions In univariate analysis we ask how much difference exists between intrapair variance of mono-

zygotic and dizygotic types of twins for each variable examined, where it is assumed that differences shown in a set of monozygotic twin pairs are attributable to environmental effects, while intrapair differences in a set of dizygotic twins pairs arise both from genetical variation in the two members and from environmental effects, the contribution of the latter being assumed to be the

Genetic determinants of cranio-facial morphology : a twin study 433

same magnitude as those acting on monozygotic twins. According to this assumption, the intrapair variances between monozygotic twin pairs (vi) should be equivalent to the portion of the intrapair variances between dizygotic twin pairs (ui) that result from environmental variation. Thus, the quantity h2, defined by h2 = (r$ - vn)/a2, is a measure of the proportion of the variance of the differences between dizygotic twins that can be attributed to genetic variation.

Following the method of Bock & Vandenberg (1968), hereditary and environmental components may be hypothesized in a multivariate analysis analogous to the univariate case:

(1) I E(M,) = Za + Z, + Z,, E(Mm) = C E + Ze, E(Me) = Z,,

where Ma, M, and Me are the covariance matrices for dizygous and monozygous twins and for measurement error, respectively; and ZG is the covariance matrix of the heritable components; Z,, the covariance matrix of the environmental components; and Z,, the covariance matrix of the measurement error.

From the equations in ( l) , the heritable covariance matrix and environmental covariance matrix can be derived from the following equations:

E(M,) -JqM,) = 20, P a ) E(M,) -E(M,) = Z,.

Xtatistical procedures" The sample quantities used for this analysis are the covariance matrices of intrapair differences,

designated M, and Ma for monozygotic and dizygotic twin pairs, respectively, and Me, the covariance matrix of measurement error which is based on duplicate measurements on the same subject (see formulae in ( I ) ) . For measured values of variablesj and k of the ith pair (Yl and Y,) in two types of twin sets (or in a set of duplicate measurements on the same subjects), let these differences be

D(i,j) = Yl(i,j) - Y,(i>j), D(i, k ) = Yl(i, k ) - Y2(i, k ) .

Then the ( j , k ) element of the covariance matrix is N

i = l Mi, = C D(i , j )D( i , k ) / 2 N ,

where N is the number of sets and may be different for each category and i = 1, . . . , N . In this manner, three different covariance matrices, M,, M,, and Me, are obtained for monozygotic and dizygotic twins and for measurement error.

The roots hi (i = 1, . . . , p ) and hj ( j = 1, . . . , t ) from the solution of determinantal equations,

lMa-hiM,I = 0, ( 3 a)

IM,-h,M,I = 0 ( 3 b ) provide a test of hypothesis that ZG = o and Z, = o in formulae (2a ) and 2 b ) , respectively.

* For additional details, the reader is referred to Bock & Vandenberg (1968) and Cooley & Lohnes (1971).

434 MINORU NAKATA, PAO-LO Yu, B. DAVIS AND W. E. NANCE Tests of significance for these roots, taking the case of C, as an example, are examined by

Bartlett's chi-square values based on the following formula:

where N, and N d are the numbers of monozygous and dizygous twin pairs and p is the number of variables. The significance of x2 is evidence of heritable variation in one or more of thep variables (i.e. Za + 0) . Subsequently, the number of significant roots, s, is tested sequentially by the chi-square test after 1 or 2 or ... or s of the largest roots have been deleted by summing from s + I to p in a modification of equation (4) as follows:

If the residual chi-square is not statistically significant, the data demonstrate no evidence of

The next step is to obtain the set of weights for the linear contribution of every variable to each heritable variation in the p - s dimensions.

root hi (i = 1, .... s, .... p ) by simultaneous solution of the following equations:

( M d - M m ) xlj = O ,

( M d - h 2 M m ) X 2 j = O , ..................... ( M d - h s M m ) % s j = OJ .....................

( M d - hp Mm) x p j = O*

This equation is solved by maximizing dizygotic variation and simultaneously minimizing monozygotic variation and the combination of variables specified by xlj, .... %sj, .... xpj (j = 1, ... ,a) is usually called the discriminant function. In other words, this function could be considered to maximize the difference between the two zygosities, as shown in 2a, which is a measure of the heritable variation.

Bock & Vandenberg (1968) proposed a technique for estimating the covariance matrix of heritable components of these variables from the resultant discriminant functions and the significant roots, by the following relationship:

h

2, = (X-1)' (A* - I) X-l,

with its diagonal elements corresponding to significant roots hi (i = 1, .... s) and ( p - s) unities.

(6)

where X-l is the inverse matrix of discriminant function coefficients and A* is a diagonal matrix

Finally, principal component analysis or rotated factor analysis is performed on this estimated heritable covariance matrix to obtain more insight into the intercorrelations of variables to each independent heritable component. The number of rotated factors must be equal to the number of significant roots ( A i ; i = 1 ..... s).

The environmental covariance matrix (C,) is estimated according to the same procedures, based on the covariance matrices of monozygotic twins (M,) and measurement errors (Me).


Table 2. F-ratios of M Z twins and measurement error, and DZ twins and M Z twins intrapair variances along with heritability estimates

(Ne = 45, Nm = 67, Nd = 29)

Variable

I Height

3 N-Ba 4 Be-PNS

2 S-N

5 ANS-PNS 6 A-PNS 7 Go-Me 8 Ba-FL' 9 N-ANS 10 N-Pog 11 N-Me

13 Pog-NL' 14 Me-NL' 15 Or-NL' 16 A-NL' 17 B-ML' 18 S-Ar 19 S-Gn

12 N-NL'

20 S-PNS 21 S-GO 22 S-Ba 23 Ar-Go

25 Ar-Gn 26 N-S-Ba 27 N-S-Ar

24 h-Me

28 S-N-ANS 29 S-N-A 30 NSL/FL 31 PNS-S-Ba

33 NSL/NL 34 NSL/ML

32 M e G 0 - h

7

-%b,"

2.15**

2-77 * * *

4,94* * *

- 6.67***

2.46** 3'41 *** 2.69***

4'5I*** 3'90***

4'42*** 10.69***

3'55*** 13.21*** 2.00* 2'55** 2.19** 5.36*** 8.25*** 1'37

1-57 3*28***

10.29***

3-05 *** 4.65 *** 1*96* 5.04* * * 7.82***

I 1-55*** 3*64* * *

4.93***

I0*97***

3.45***

8*74* **

F-ratio m

6.10*** g s :

3'75*** 2.43** 1*92* I'97* 2*14** 2'55*** 2.14** 2.68*** 3'58*** 4.36*** 2-55*** 3'74*** 4-21*** I40* I 2 7 6.06 * * * 2 A * *

3.87* * * 3'07***

2*46** 1.89* 1-37 2-67*** 2-58*** 2.04** 1.84* 2.64*** 2.73*** 1'93 * 2 . I I * * 2.31 ** 2-82*** 2.45**

Heritability

0.84 0.73 0'59 0.48 0.49 0.53 0.61 0'53 0.63 0.72 0.77 0.61 0.73 0.76 0'44

0.84 0.56 0.67 0.74 0.59 0.47 0.27 0.63 0.61 0.5 I 0.46 0.62 0.63 0.48 0'53 0.57 0.64 0.59

ha = (S,"-Si)/8,"

0'2 I

Note : N,, N,, iVd indicate the number of pairs for measurement errors and MZ and DZ twins, respectively. st, 4, si are intrapair variances of measurement errors and MZ and DZ twins respectively. Measurement error was not available for height. ***P < 0.001, **P < 0.01, *P < 0.05.

RESULTS

The observed F ratios between intrapair variances of MZ twins and measurement errors, and between DZ twins and MZ twins are shown in Table 2 along with the heritability estimates by Holzinger's (1929) formula based on the DZ and MZ intrapair variances.

It can be seen that all of the variables have a significant environmental component, except for two variables of S-PNS and S-Ba showing nonsignificant F ratios that may be attributed to the measuring variability for these two variables.

On the basis of F ratios of DZ over MZ twins intrapair variances, hereditary factors appear to contribute to the variation of each trait except for two variables of A-NL' and Ar-Go.

,


Table 3. Rotated factor analysis of measurement errors Factor loadings*

Variable

I S-N 2 N-Ba 3 Ba-PNS 4 ANS-PNS 5 A-PNS 6 Go-Me 7 Ba-FL’ 8 N-ANS 9 N-Pog 10 N-Me 11 N-NL’

13 Me-NL’ 14 Or-NL‘ 15 A-NL’ 16 B-ML’ 17 S-Ar 18 S-Gn 19 S-PNS

21 S-Ba

23 Ar-Me 24 Ar-Gn 25 N-S-Ba

12 Pog-NL’

20 S-GO

22 &-GO

26 N-S-Ar 27 S-N-ANS 28 S-N-A 29 NSL/FL 30 PNS-S-Ba 31 Me-Go-Ar 32 NSL/NL 33 NSL/ML

Proportion of variance

I, 21 21

- 1 2 - I 4 16 07 03 91 47 77 94

- 04 -31 I9

- I7 18 09 37

- 05 08

- I5 - I7

24 16

- 57 - 49 - 54

- I4 44 49

13.8

I 2

I 0

- 21

I&

14 91 79 I5 18

95 I3 05 06

02

I1 - 00 - 00 - I 2 06

- 30 04 01

- 02 20

74 I7 17 08 74 08 05

- 03

- 18

I1

69

I 0 - 21 13.1

I I I , Iv,

I1 02 -08 -11 34 -06 05 21

-50 -06 09 90

-04 -17 01 08

- I 0 I4 07 28

- 02 08 - I3 06

30 I 2

- 24 23 I 0 08 40 06 62 -28 80 08 23 -87 10 -24

-08 -88 09 07 11 -28

- 48 I5 - 77 I5 66 06 46 -31 48 -39

- 01 I1

-08 -01

1 0 -34 -41 -11 - 24 66

11.5 11.3

v, - 06 - 00 20

- I3 - 06 24 I 0

- 02 - 03 24

- 02 - 02 37

34 04

- I9 47 24 I5

27 81

21

02

87 02

37 I3 32 25 I3

- 02 - 21 - I 2 8.2

VI, 06

- 35 79 75 03

06 16

- 03 05 15

21

I 0

- I 0 I 0

40 60 06

- 29 - I3 26

- I4 - I4

- 05 09 16 I4

- 06 - 45 09

- 04 09

0 1

- 0 1

7‘4

VI& VIII ,

83 02 02 03 14 -02

- 03 I3 -04 -01

03 04 01 -06 04 -01

- 02 81 I1 24 04 -05

- 0 5 94 I1 48 57 -28 02 I 2 25 I9

-70 -04 - I4 06

05 -23 12 -04

-36 -03 I 5 -04

-02 -04 05 I1

- 25 07

-17 -14 -35 -24 35 I5

-13 -06 25 26 I 0 I7

6.9 6.9

21 -01

- 08 04

1x0 I1

- 07

06 06

- 18 - 07 - I9 - 06 33

- 18

53 - I5 ‘4

29

I4 09

- I5 03 09

- 04 05 04 07

0 1

01

- I1

- 01

I 1 - I 0 04 77

- 35 22

4‘7

* Decimal points omitted.

The fact that there are evidently both heritable and environmental components in examined traits justifies proceeding to the further step of multivariate analysis in order to determine whether some groups of the variables are influenced by common hereditary or environmental factors.

All of the sample information necessary for the preceding analysis is contained in the intrapair difference covariance matrices of measurement errors, MZ and DZ twins. This is shown in Appendix Tables 1-3 in the form of correlations and standard deviations.

Interrelationships of measurement errors (2,) Rotated factor analysis of the measurement error correlation matrix was carried out to identify

any interrelated measurement errors that might confound the subsequent analysis of the heritable and environmental covariance matrices (Table 3), even though the magnitude of measuring errors was negligible enough in this study. The following factors were observed:

Factor I,. High loadings for all the vertical measurements originating Nasion and negative


Table 4. Roots* obtained f r o m discriminant equations for environmental components along with eigen values and chi-square tests

Eigen Chi-square Degrees values values of

Roots (A$) (X2) freedom P

I 2

3 4 5 6 7 8 9

I 0 I 1

I 2

I 3 I4 I 5 16

148.398 89.361 68.886 48.219 39.086 31.136 25'395 22.009 14.837

9' I 20 7'292 5.767 4.887

3.694

13'223

4'324

4227.78 3895.53

3308.92

2794.26

3594'29

3045'23

2557'01

2115.55 1922'47 I 736. I 6 1571.36 1419.28 I 28027

1026.89

2332'00

I 150'29

221 I 21 I 2 2015 I 920 I 827 I736 I647 1560 I475 I392 1311

1232 1155 1080 1007 936

< 0'001 < 0'001 < 0'001 < 0'001 < 0'001 < 0'001 <O'OOI <O'OOI < 0'001 < 0'001 <O'OOI

<O'OOI < 0'001 < 0'001 < 0'001 < 0.05

* Roots significant at 5 yo level or more are shown.

loadings on angular measurements relating to them. This factor may represent a measuring error relating to Nasion.

Factor Ire. High positive loadings for all the variables including Basion, representing a measurement error related to Basion.

Factor IIIe. High loadings for vertical measurements and angles measuring mandibular prognathism involving Sella, associated with negative loadings on cranial base angles.

Factor IK. High loadings on Go-Me and negative loadings on vertical measurements from Gonion. This factor may be related to difficulty in locating the Gonion.

Factor V,. Highest loading on diagonal length of mandible, associated with some loadings on S-Gn. This factor relates to imprecision in locating Gnathion and Menton.

Factor VIe. High loadings on measurements from PNS with negative loadings on angles of PNS-S-Ba and S-PNS. This factor seemed to be related to imprecision in locating the PNS except for positive loading on B-ML'.

Factor VII,. High loading on S-N and negative loading on S-Ar. Factor VIIIe. High loadings on vertical measurements from Pogonion. Factor IX,. High loading on gonial angle with some loading on Me-NL'. This factor can be

related to imprecision in locating Menton in vertical direction and might be independent of Factor V,.

Environmental variation (Z,)

Based on the procedures as previously described, the covariance matrices of measurement errors (Me) and MZ twin differences (M,) were transformed into the environmental covariance matrix, where 16 significant roots were found (Table 4) out of 33 variables, excluding height for which the measurement error was not available.

Although rotated factor analysis was performed on the resultant environmental covariance

438 M~NORU NAKATA, PAO-LO Yu, B. DAVIS AND W. E. NANCE

Table 6. Rotated factor analysis of environmental factors Factor loadings

Variable

2 N-Ba 3 Ba-PNS

I S-N

4 ANS-PNS 5 A-PNS 6 Go-Me 7 Ba-FL’ 8 N-ANS 9 N-Pog

10 N-Me 11 N-NL’ 12 Pog-NL’ 13 Me-NL’ 14 Or-NL’ 15 A-NL’ 16 B-ML’ 17 S-Ar 18 S-Gn 19 S-PNS 20 S-GO 21 S-Ba 22 &-GO 23 &-Me 24 Ar-Gn 25 N-S-Ba 26 N-S-Ar 27 S-N-ANS 28 S-N-A 29 NSL/FL 30 PNS-S-Be 31 Me-Go-Ar 32 NSL/NL 33 NSL/ML


IE

32 I8 I7 26 30 82 66

- I 2 0 1

- 04 - I 2 I9 23 I3

- 09 32

- 07 66 05 31

41 81 84

- 07 19 23 75 I2

- 30

- 50 14’5

-11

- 00

-11

I IE IIIE IV’ V E VIE

-11 24 41 67 -24 12 21 23 87 09

-05 -19 11 89 24 02

- I5

- 07

86 86

91

02

I 0

1 0

- I 2 - 08 - 24 - 18 97 38 43 97

- I9

91 21 10

91 I7 03 05 17 -10

40 57 I3 -13 -02 11

-17 -05 02 -13 -04 01

-14 -03 11

-05 -07 -08 91 -13 03 -03 -11

17 37 03 -01 45 09 -60 -05 -16 02 27 14 07 22 -02

21 -11 -14 -20 02 62 -03 21 04 -25 17 -09 08 02 -27 40 04 21 08 48 02 -13 39 27 15 36 25 34 02 30 25 33 00 32 21

-16 04 03 36 -08 38 -08 11

-01 -56 71 17 -15 -51 68 12 -08 -45 30 -06 -27 -17 IS 72 23 14 -08 -14

-04 76 -17 09 34 30 -34 -21

04 - 34 23 I4 I 0

85 86

-17 - 25 - 25 42 05 06 01

145 14‘3 11.6 11-1 7-5

VIIE

02 - 16 - I1 - I 2 - 02 - 28 - I5 03 I 5

03 I4

02

- 02 02

- 05

07 - 04 - 08

- 25 - 43

- I 2

- 48

- I 2 - I 0 - 04 05

- I 2 - 01 - 08 04 89 I 0

51

5 ‘4

VIIIE

- 05 06 07 00

02

-09 02 02 18 04 04 12

- I 0 I 5 22 I 0 22 16 91

30 08

22

- 0 1 02

- 16 - 18 09 I 5 I 3 31

- 06 - 57 - I4 5’3

I X E

03 I2 I 2

- 01 -04

04 - 04 - 07 06

- 04 - 03

13 - 73

- I1

- 21 83

-07

03

34 28

I3 - I9 - 03

08 07

- 0 5 08

- 08 5’2

I1

21

I2

I1

- 02

X E

-09

- 08 - 07 - 04 - I7 - 05

00

- 0 1 02 16

- 00 00

I4

I3

90 I3

49 31

- 03

- 16 I8

I 2

02

21

I1

-01

- 02 - 00

I 0

- I9

- I5 - 23 4’7

I1

XIE 06

- 09 - 02

02

- 04 05

- 03 - 08 09

- 08 - 05 I4

- 08 - 07 69

- 18 08

- 03 09

- I 0 - 20 - I 3 - 06 - 03 - 04 06 03

- 07 - 03 - 02 - 04 - 05 - 06 2’1

Decimal points omitted.

matrix subject to the constraint that there were 16 independently significant components, only the first 1 1 factors appeared to identify significant environmental variations and accounted for 97.7 yo of the total variance. The results are shown in Table 5 .

Factor IE. High loadings on mandibular base length and angle NSL/FL. This factor appeared to be associated with the mandibular depth factor.

Factor II,. High loadings for anterior total and lower face height. Factor I I , is interpreted as the anterior lower face height factor.

Factor III,. Highest loadings for anterior maxillary height and inclination of nasal floor. Maxillary prognathism was negatively associated with this factor. On these grounds factor I I I , is termed as the anterior maxillary height factor.

Factor IV,. High loadings on maxillary base length and maxillary prognathism. This factor is characterized as the maxillary depth factor.


Table 6. Roots* obtained from discriminant equations for heritable components along with eigen values and Chi-square tests

Eigen Chi-square Degrees values values of

Roots (A,) (X2) freedom P

43.108 27.176 22.093 16‘943 14.510 11.553 9’023 6.356 5.182

166976 1479’68 13 16.48 I 166.08 1038.08 91 136 796.80

610.56 695.04

986 924 864 806 750 696 644

546 594

< 0’001 < 0’001 <O’OOI <O’OOI

<O’OOI < 0‘001 < 0‘001 < 0.005 < 0.05

* Roots significant at 5 yo level or more are shown.

Factor V,. High loadings on cranial base dimensions with some loadings on its flexion. Factor VE is termed the cranial base length factor.

Factor VIE. High loadings on cranial base flexion, but other loadings negligible. This factor is interpreted as the cranial base Jlexion factor.

Factor VIIE. High loading on mandibular gonial angle associated with some loading on NSL/ML. Mandibular Jlexion factor is also an independent factor.

Factor VIIIE. High loading on posterior upper face height, while low negative loading for NSLINL. This factor is characterized as the posterior maxillary height factor which determined the posterior facial height, affecting the inclination of nasal floor negatively.

Factor IXE. High loading on B-ML’ and negatively on Or-NL’. Factor X,. High loading on S-Ar with some loading on 5-Go. Factor XI,. High loading on A-NL’. This factor may be associated with the position of A point.

Heritable variation Z, Since the intrapair covariance matrix of DZ twins (Md) reflects both genetic and non-genetic

variations and, on the other hand, the intrapair covariance matrix of MZ twins (M,) is attributed solely to non-genetic variation, a description of heritable variation should result when the heritable covariance matrix (C,) is estimated from these two covariance matrices. According to Bartlett’s chi-square test, nine roots were found significant out of 34 variables (Table 6); in other words, there are a t least nine independently significant heritable components. Subject to the constraint that there are only nine independent heritable components, the heritable covariance matrix (Z,) wa5 generated by solving the discriminant functions which simultaneously maximize dizygotic variation and minimize monozygotic variation.

Rotated factor analysis was finally carried out on the resultant covariance matrix of heritable components and this result is shown on Table 7.

Factor I,. High loadings on all of cranial base lengths and mandibular lengths with negative loading on NSL/ML. This factor has also positive loading on NSL/FL, but no loadings on any facial height measurements. Thus Factor .IG is interpreted as the mandibular length factor associated with cranial base dimensions.


Table 7. Rotated factor analysis of heritable factors

Factor loadings*

Variable

I Height

3 N-Ba 4 Ba-PNS

2 S-N

5 ANS-PNS 6 A-PNS 7 Go-Me 8 Ba-FL’ 9 N-ANS 10 N-Pog 11 N-Me 12 N-NL’ 13 Pog-NL’ 14 Me-NL’ 15 Or-NL’ 16 A-NL’ 17 B-ML’ 18 S-Ar 19 S-Gn 20 S-PNS 21 S-GO 22 S-Ba 23 Ar-Go 24 Ar-Me 25 Ar-Gn 26 N-S-Ba 27 N-S-Ar 28 S-N-ANS 29 S-N-A 30 NSL/FL 31 PNS-S-Ba 32 Me-Go-Ar 33 NSL/NL 34 NSL/ML


IG

I9 85 89 50 40 46 70 90 04 I1 22

0 5 08 24 27 09

- 0 1 76 74 62 79 62 72 92 91

I9

07 53

- I5 - 24 - 40 - 65 28.0

- 38

- 0 1

IIG 16

- I 0 I1

- 37

33 09

09 94 82

97 90

33 I9 30 48

- 26 26 I3

23 27 39 45

- 29 - I5 - 54 - 18

I4 56

16.5

12

- 22

I 0

- 00

I 0

21

IIIG

I 2

- 09

03 75 66

- 20

I 2 I1

- 23 - I5 - 05 - 25 - 06 04

24 33 06 24 41

21

22 - 0 1 26 21 22

- 26 - 28 89 87 50

- 25 - 20 - 58 - 26 12.8

IVG 86

05 -31 I4

I 2

- 02 38

- I3 91 24 35 90

-11

02 18

- 26 I5 27 27

I7 I1

0 1 - 22

0 1

08 - I7 - I 3 - I5 - 25 - 20 - 36 - 45 49 07

11.7

VG

33 36 34 25

16 05 I7 05

- 0 1

- I 0 - 00 07

- I4 - 05 91

- 05 06 28

42

53

I 2

I 2

- 22 - I1 - I 2 - 76 - 71

I5 31 18

- 24 - I9 - 16

8.7

- 20

VIG

19

-09 55

- 33 -31

I5 - 27 - 07 - 23 - 30 08

- 09 - 03 - 04 - I7 - 16 - I5 - 25

- 27 37

- 09 - 06 14

- 04 06 08 I9

01

- 36

I1

78 0 1 22

- I9 6. I

VIIG VIIIG I X G

I4 01 -14 -06 -33 03 -15 -06 -00

- 35 I 7 0 5 31 -12 -08 25 -18 -13 02 -10 -48

-21 -11 -07 05 -14 -12

06 -01 - 05 29 03

32 I 7 I7 88 36 I5 - 16 29

- 23 I7

- I 0

I 0 I 0

- 03 I7 I4 07

- 21 - 21 00 I1 08

I1 - I1 07 I1 02

85 I3 16 16 30 30 44 36 I 0

I3

23

18 04

- I9

- 35 - 07

- 0 1

21

- 02

0 1

- 07 - 0 5 04

- 03 00 0 1

- 03 - 09

- I7 - 06 08

- 0 5 - 02

0 5 27

- 07 - 16

79

32

I1

-11

0 1

- 21

5 ’7 5.6 3.7

* Decimal points omitted.

Factor I&. High loadings on anterior total and lower face height, but no loading on upper face height. This factor was strongly representing the lower face height factor.

Factor IIIG. High loadings on the maxillary prognathism and maxillary depth. Some loadings were found on posterior maxillary height associated with negative loading on NSL/NL. Factor I I I , will be characterized as the maxillary depth factor.

Factor IV,. High loadings on the height and upper face height. Other loadings were found negatively on PNS-S-Ba associated with Ba-PNS. Factor IV, appeared to justify being termed the anterior upper face height factor.

Factor V,. High loadings on Or-NL’ and negatively on cranial base flexion. The considerable loadings on the variables measured from Sella suggest that Factor V, was associated with relative position of Sella to cranial base flexion, termed the cranial basejlexion factor.

Factor VIG. High loading on the distance Ba-PNS and the relating angle.


Factor VII,. Variable B-ML' appeared to be independent when the other low loadings were

Factor VIII,. A-NL' was also independently associated with Factor VIIIG, the other low

neglected.

loadings being ignored.

Factor IX,. High loading on the mandibular gonial angle.

DISCUSSIONS

Because it is unlikely that there are as many independent genetic factors as the number of characters examined, this method of multivariate analysis in twin data is advantageous for detecting the genetical interrelationships of multiple characters. Many anthropological variables are sointerrelated to each other (Howells, 1957; Landauer, 1962; Solow, 1966) that the application of this method is highly recommended. Previous applications of this technique by Bock & Vandenberg (1968) utilized psychological subtest scores, and because of the nature of the variables, empirical validation of the results is difficult. In the present study and a previous analysis of dermatographic variables (Nance et al. 1974; Nakata, Yu & Nance, 1973) we have applied the technique to interrelated anthropometric variables, with the hope that the resulting groupings of genetically related variables would be biologically meaningful. In the previous study (Nance et al. 1973), for example, we found that ridge counts from the thumbs, 5th digits, and middle digits of both hands were grouped together as three independent variables.

The results from the present study indicate that the groupings of the measurement errors have a geometric rather than a biological basis. Thus the location of the points of Nasion (Ie), Basion (IIe), Sella ( I I I J , Gonion ( I V e ) , Gnathion and Menton (E), PNS (VIJ and Pogonion (VI&) were the major sources of the variation originating from the measurement errors, and the grouping of variables that resulted from the analysis can generally be interpreted as correlated errors associated with imprecision in locating these cephalometric landmarks.

While there were major similarities in the magnitude and groupings of the genetic and environmental factors identified by the analyses, the number of significant environmental factors was greater and they appeared to a greater extent to influence individual or localized regions of the cranio-facial complex. Those findings are in general agreement with those of Bailey (1956) who observed, in a study of bone morphology in interrelated strains of mice, that genetic and environmental factors appeared to influence similar morphogenic pathways.

In a general factor analysis on 630 subjects treated as unrelated individuals (Nakata, Yu & Nance, 1973) and using the same variables as in this study, we found that the resulting factors could generally be expressed as a compound of one or more of the genetic and environmental factors identified in the present analysis. Thus it seems likely that the phenotypic associations among multiple traits having the same hereditary determinant can also be jointly influenced by common environmental factors.

In general, there appeared to be an independent genetic determination of the upper and lower halves of the cranio-facial complex. As for the upper part of the face, it will be noteworthy that even within the upper jaw there appeared to be independent genetic influences on maxillary height and depth. The former factor was also strongly associated with stature which is of interest in view of t'he important role of the septa1 cartilage in the prenatal and postnatal development of

29-2

442 MINORU NAKATA, PAO-LO Yu, B. DAVIS AND W. E. NANCE middle facial structures (Scott, 1953; Sarnat, 1963; Muller, 1963) and the role of chondral growth and epiphyses of axial bones in the determination of skeletal height,

The determinants of mandibular growth appear to include at least two genetic factors, la and IX,, and two environmental factors, IE and VIIE. Factor la also influences the length of the cranial base, while Factor lXa appears to influence only the mandibular angle. In contrast, the two environmental factors specific to the mandible appear to influence only mandibular size and the flexion angle respectively. The finding that multiple hereditary factors influence the growth of the upper and lower jaw in an independent manner may have relevance to the etiology of some forms of malocclusion.

Since the projected lengths from menton and pogonion to the nasal plane measure the portion of the cranio-facial complex lying between the maxilla and the mandible, these measurements are profoundly influenced by the size and orientation of the dentition as well as the underlying skeletal structure. Factors Ila and 11, have high loadings on these two measurements alone, a fact which may reflect the aggregate effects of genetic and environmental factors influencing dentition (Osborne, Horowitz & DeGeorge, 1958; Asano, 1965). To the extent that the dentition of the upper and lower jaw may have independent genetic determinants (Potter, Yu & Nance, 1973), environmental modification may be required to permit occlusion. The well-known plasticity of the alveolar bones of the maxilla and mandible (Scott, 1967) and the strong association between dentitional and jaw measurements (Solow, 1966) support our interpretation of these factors, although the inclusion of dental measurements in the analysis would be indicated to confirm this hypothesis.

It would clearly be an oversimplification to equate the genetic factors identified in this analysis with single gene effects. However, in the case of the first genetical factor (la), single gene mutations are known which profoundly affect the development of the lower jaw. Similarly, in the case of the fourth genetical factor (IVQ), monogenic traits, such as classical achondroplasia, are known to have a dramatic effect on both the overall stature and the anterior maxillary height (Rischbieth & Barrington, 1912; Maroteaux & Lamy, 1964).

It is clear that morphogenesis cannot result from the independent genetic control of individual cells: Macagno, Lopresti & Levinthal(1973) have shown, for example, that although the position and gross connectivity of omatidial nerve cells in isogenic clones of Daphnia magna are remarkably similar, considerable individual and bilateral variation is observed when the branching patterns and synaptic connexions of individual cells are compared. Thus the number of independent genetic factors which control differentiation must be far fewer than the number of unitary structures involved. In the'present context, we found evidence that only nine independent genetic factors and eleven independent environmental factors influence a total of thirty-four cephalometric variables. Given an infinitely large sample of twins, we would expect that as more cranio- facial measurements were added, the number of independent genetic factors identified by the analysis would tend to converge while the number of environmental factors might well increase without limit. In this regard, as noted previously, in multivariate analyses of cranio-facial measurements in unrelated individuals the genetic effects appear to dominate and relatively few factors are identified; and in a previous study (Solow, 1966) employing as many as forty-eight cephalometric variables only seven independent factors were identified.

Multivariate analysis of interrelated cephalometric variables in twins can provide insight into the independent morphogenic pathways that determine cranio-facial differentiation. Further


validation of the factors identified in this study might be obtained by a comparison of similar measurements in patients with specific dysmorphogenic syndromes, or through a further analysis of factor scores in relatives of various degree.

SUMMARY

Multivariate analysis of twin data proposed by Vandenberg was applied on 33 cephalometric measurements and height data from 67 sets of MZ twins and 29 sets of like-sexed DZ twins. As a result, nine independently significant components of heritable variation and eleven independently significant factors of environmental variation were found. It was shown that this type of analysis was effective for the study of interrelated heritable traits such as anthropological measurements.

This work was supported by a grant from the John A. Hartford Foundation and was completed during the tenure of a Fogarty International Fellowship to M.N. Linear and angular measurements were transformed from X-Y co-ordinate values which were recorded using the Digital Analyser at the University of Michigan. The authors are indebted to Drs J. E. Harris and G. F. Walker for their courtesy.

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