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Copyright 0 1985 by the Genetics Society of America

GENETICS OF MANDIBLE FORM IN T H E MOUSE

WILLIAM R. ATCHLEY, A. ALISON PLUMMER AND BRUCE RISKA

Laboratory of Genetics, University of Wisconsin, Madison, Wisconsin 53706

Manuscript received March 1 1 , 1985 Revised copy accepted July 1, 1985

ABSTRACT

The underlying determination of phenotypic variability and covariability is described for 14 traits that define the morphological size and shape of the mature mouse mandible. Variability is partitioned into components due to direct additive and dominance genetic effects, indirect maternal additive genetic effects, genetic covariance between direct additive and indirect maternal additive effects and common and residual environmental effects. Multivariate analyses of the dimensionality of genetic variability indicate several complex and independent genetic components underlie the morphological form of the mandible. The multidimensional nature of the genetic components suggests a complex picture with regard to the consequences of selection on mandibular form.

NTEGRATION of development and evolution into a comprehensive theory I for morphological change is a widely recognized need in contemporary biology (BONNER 1982; RAFF and KAUFMANN 1982; GOODWIN, HOLDER and WYLIE 1983; LANDE 1983; CHEVERUD, RUTLEDGE and ATCHLEY 1983; ATCH- LEY 1984; ATCHLEY et al. 1984b). However, this integration has proven elusive because, although there is a clear and highly articulated theory of evolution, a comparable theory for development does not exist (BONNER 1982; MAYNARD SMITH 1983). Lack of an integrated theory stems partially from the inadequacy of existing models to explain developmental and morphological variability. However, resolution of important evolutionary questions about adaptive strat- egies, response to selection, rates of morphological divergence, evolutionary stasis or phylogenetic reconstruction often depends on a critical understanding of the underlying causes of variability in morphological structures.

The final form (size and shape) of complex morphological structures, such as the mammalian cranium and mandible, results from integration of growth and morphogenesis in individual components during ontogeny. Such morphogenetic integration is potentially highly intricate because the individual components of a given structure often have different embryonic origins, may be under the influence of different controlling factors and, as a result, may develop at different rates (MOORE and LAVELLE 1974; MOORE 1981; HALL 1978; SLAVKIN 1979).

Initiation, termination, rate and localization of the developmental processes underlying growth and morphogenesis are under control of gene loci whose

Genetics 111: 555-577 November, 1985.

556 W. R . ATCHLEY, A. A. PLUMMER AND B. RISKA

allelic composition varies among individuals, populations and higher taxa. Nat- ural selection acts upon genetic variability in the regulatory aspects of growth and morphogenesis to stabilize and coordinate ontogenies to produce a particular morphological form or to cause a directional change culminating in a new morphological form. Thus, a plausible causal model of variability in growth and morphogenesis must include a rigorous description of form at various points during ontogeny, elucidation of the developmental origins and ontogenies of the components of form and quantification of the underlying causes of their variability and covariability.

Considerable energy has been devoted to precise quantitative description of form (e.g., THOMPSON 1917; JOLICOEUR and MOSIMANN 1960; BLACKITH and REYMENT 197 1; BOOKSTEIN 1978, 1984; STRAUSS and BOOKSTEIN 1982; CHEV- ERUD, RUTLEDCE and ATCHLEY 1983). Further, the developmental origins and ontogenies of components of complex morphological structures, such as the mammalian cranium and mandible, are reasonably well understood (HALL 1978; MOORE 198 1 ; SLAVKIN 1979). Unfortunately, however, there has been little quantification of the underlying causal factors responsible for variability of morphological form.

A variety of genetic, hormonal, vascular, biomechanical and dietary factors have been shown to influence craniomandibular form, but few studies have quantified these causal factors and discussed their relative importance to growth and morphogenesis. In particular, the genetic component has not been systematically examined using plausible models to accurately explore the causal basis of variability. This paper describes and quantifies the underlying causes of variability and covariability in morphological form of the mandible in mature randombred mice. We examine four major aspects of morphological size and shape including (1) the underlying determination of phenotypic variability, (2) the dimensionality of genetic variability in the form of the mandible, (3) whether the genetic correlation structure among traits reflects developmental history and (4) the evolutionary impact of selection on various parts of the mandible.

A companion paper (ATCHLEY et al. 1985) examines the genetic aspects of size-related scaling in these mandible traits.

MATERIALS AND METHODS

Husbandry: ICR randombred mice obtained at 4 wk of age from Sprague-Dawley were allowed to acclimate to our laboratory for 2-3 wk. Randomly chosen males were then mated to randomly chosen females. All litters were standardized to eight individuals, four males and four females. Pups were reared in a crossfostering design where a random half of each litter was nursed by an unrelated female which had pupped on the same day. After weaning, the parents were sacrificed and the carcasses retained for analysis. A total of 3624 mice, including 931 parental generation mice and 2693 progeny, were analyzed. Because of the size of the experiment, the mice were reared as two replicates, and any resultant variation between replicates was removed statistically.

Specimen preparation and traits recorded: Progeny were weighed at weekly intervals, beginning at 2 wk after birth and continuing until 70 days of age. Growth in body weight is described by RISKA, ATCHLEY and RUTLEDCE (1984) while ATCHLEY et al. (1984a) have examined the quantitative genetics of brain and body sire association. The progeny were sacrificed at 70 days of age, and carcasses for both the parental and progeny generations were skinned, eviscerated and skele-

GENETICS OF MANDIBLE FORM 557

'14

,__. .... -".'

1

b I7 18

4

FIGURE 1 .-Outline of the mature mouse mandible denoting the position of morphological landmarks used to describe the traits presented in Table 1 .

tonized by dermestid beetles. The cleaned dentary bones were separated at the mandibular sym- physis, and the right half was placed on a glass microscope slide on the negative carrier of a photographic enlarger. The mandible image was projected onto a digitizer connected to a micro- computer, and 19 landmark points were recorded in x-y coordinate space (Figure 1) . Associated musculature for the mandible is shown in Figure 2.

Fourteen traits were chosen to represent the functional and morphogenetic aspects of the rodent mandible. Among these were Euclidean distances between points, vertical or horizontal distances relative to a horizontal reference line through points 2 and 4 and areas of polygons defined by a series of points. Table 1 gives a description of the traits, together with a code.

Genetic model: Mammals develop under the influence of two different genotypes-the genotype of the individual and that of its mother-and both have significant effects on phenotypic variability. The mother's genotype defines the effect from the uterine and early postnatal (nursing) environ- ment. As a result, any model explaining the underlying causal components of variability must include both genotypes. Thus, the genetic model for the variance of a trait Y, a; (or its covariance with another trait X ) is

& = 6; = 040 + 2- + + U$, + CAoAm + 0% + a',

where U% = phenotypic variance, azo = direct additive genetic variance, a$. = direct dominance genetic variance, 04, = indirect maternal additive genetic variance, U$, = indirect maternal dominance genetic variance, uAAoAn = genetic covariance between Ao and Am, U: = common environmental variance including nonadditive maternal and cage effects, and a% = residual variance unique to the individual mouse.

Direct genetic effects in this model (A0 and Do) arise from the individual's own genotype, where Ao stems from the variance of average effects of alleles at loci controlling a particular trait. Do arises from the variance of combinations of alleles at these loci. Indirect effects (Am and Dm) arise from these same relationships in the mother's genotype. These indirect effects arise from genes that are active in the mother but that affect the offspring because of the maternal effect. Covar- iance between direct and indirect maternal effects (uAAoAm) can have a significant effect on the phenotypic variance in the offspring, an effect increasing or decreasing 6% depending on the sign of the covariance. Genes involved in this covariance term may affect growth and morphogenesis directly by mediating growth in the individual itself and indirectly by affecting maternal performance, which, in turn, affects growth and morphogenesis in the progeny (DICKERSON 1947; HAN- RAHAN 1976; RISKA, RUTLEDCE and ATCHLEY 1985a).

Variances (covariances) from several types of relatives were used to obtain estimates of genetic

558 W. R. ATCHLEY, A. A. PLUMMER AND B. RISKA

Muscles attaching on medial surface

Muscles attaching on lateral surface

FIGURE 2.-Attachment points for muscles on the medial and lateral surfaces of the mouse mandible. Abbreviations: AZM = anterior zygomaticomandibularis; D = digastric; G = geniohyoi- deus and genioglossus; LM = lateral masseter; LP = lateral pterygoid; MP = medial pterygoid; MY = mylohyoid; PZM = posterior zygomaticomandibularis; SM = superficial masseter; T = temporalis.

and environmental variance and covariance components. Table 2 gives the expectations for the causal components of similarity between mice of varying degrees of relatedness. These observational components are as follows: (1) cov(0, S)-covariance between sire and offspring; (2) cov(0,N # D)-covariance between nurse and offspring, where the nurse is not the genetic dam; (3) cov(0,D # N)-covariance between dam and offspring, where the offspring was nursed by an unrelated dam; (4) cov(0, D = N)-covariance between dam and offspring, where the dam is also the nurse; (5) cov(FS), D = N-covariance between full sibs nursed by their own dam; (6) cov(FS), D # N- covariance between full sibs nursed by the same unrelated dam; (7) cov(FS), D =,# N-covariance between full sibs, one nursed by the genetic dam, the other by an unrelated nurse; (8) cov(UR), N = N-covariance between unrelated individuals both nursed by the same nurse, the genetic dam of one of them; (9) cov(UR), D, = Np-covariance between unrelated individuals, each nursed by the dam of the other; (10) var(residua1)-variance among full sibs, all with the same nurse.

Statistical methodology: Estimates of the causal components of variability in sex-adjusted log- transformed data for the 14 mandible traits were obtained by simultaneous solutions, using a generalized least-squares analysis. Details of the analytical procedure are described elsewhere (RISKA, RUTLEDGE and ATCHLEY 198513). Ridge regression-like procedures were used on the variance components to assess their stability. Direct additive genetic variance and covariance estimates obtained with this design are quite stable, as shown by their small standard errors compared to other components. As a result, estimates of narrow-sense heritability and additive genetic correlation between traits are quite reliable. The other components (e.g., dominance) are less reliably estimated by this design because of high correlations between the estimates. Dominance estimates were reasonably unstable in the ridge-like analyses, suggesting that the contribution of dominance to phenotypic variability is probably underestimated because of correlation with the environmental variance estimates. Estimates of components associated with maternal performance (VA,, CAoAm, and

GENETICS OF MANDIBLE FORM

TABLE 1

Descriptions of the mandible traits employed in the genetic analyses, together with a short code

559

1. 2. 3. 4. 5. 6.

7. a.

9.

10.

1 1 .

12.

13.

14.

Posterior mandible length (P0sTMANLEN)-Euclidean distance from 1-4 Anterior mandible length (ANTMANLEN)-Euclidean distance from 4-6 Height at mandibular notch (NOTCHHIGH)-Euclidean distance from 3-1 4 Height at incisor region (INcISHIGH)-Euclidean distance from 5-8 Concavity (CONCAVITY)-VertiCal distance from 3 to a h e computed from 2-4 Height of ascending ramus (RAMUSHIGH)-VeTtiCal distance from 2 to a horizontal

Condyloid width (coNDYLwrD)-Euclidean distance from 15 to 18 Condyloid length (C0NDYLLEN)-Euclidean distance from the midpoint of a line

Coronoid height (CDRONHIGH)-VertiCal distance (perpendicular to 2-4 h e ) from

Coronoid area (CORoNSIzE)-~rea defined by the triangle ( 1 1 , 12, 14) minus the

Angular process length (ANGLJLARLEN)-EUClidean distance of a line segment from

Tooth bearing area (TOOTHAREA)-Area of a polygon defined by points (3, 4, 5 ,

Superior incisive process curve (SUPERINCIS)-ShOrteSt distance to 8 from a line

Inferior incisive process curve (INFERINCIS)-ShOrteSt distance to 5 from a line from

line at 16 parallel to the line computed from 2-4

from 16-17 to the midpoint of a line from 14-19

12-14

area of (12, 13, 14)

the midpoint of 1-2 to the midpoint 3-19

6, 7, a, 9, 11)

from 4-6

4-6

Traits are described with references to Figure 1 .

TABLE 2

Expectations for observational components of variance

Causual components and expectations

Observational components do gm ~ A ~ A ~ dsA. (a&” + 4) a;

1. cov(0, S) 112 0 114 0 0 0

2. cov(0, N # D) 0 0 314 112 0 0

3. cov(0, D # N) 1 12 0 114 0 0 0

4. cov(0, D = N) 112 0 514 112 0 0

5. cov(FS), D = N 112 114 1 1 1 0

6. cov(FS), D # N 112 114 0 1 1 0

7. cov(FS), D =,# N 1 12 114 112 0 0 0

a. CO~(UR), N = N 0 0 112 1 1 0

9. COV(UR), DI = N2 0 0 1 0 0 0

10. var(residua1) 112 314 0 0 0 1

More complete descriptions of the observational components are given in the text.

V,) were highly variable, as evidenced by the relative sizes of their standard errors. It is not possible to estimate unbiasedly the dominance maternal genetic variance with these analyses; therefore, this source of variation is pooled with the common environmental variance.


In spite of the instability of the initial estimates of direct dominance, they are included here because little is actually known about the levels of dominance variance, particularly in skeletal traits. WRIGHT (1968, p. 418) stated that “even if linkage and interaction are treated as negligible in effect, the difficulty of obtaining sufficiently reliable data for estimation of the variance due to dominance is great . . . . The results tend to confirm the view that dominance is not a general property of minor gene differences involved in quantitative variability, but there was great uncer- tainty in each individual case.”

The underlying distributions of variance and covariance components are not well studied; therefore, for statistical inference we assume normal distribution theory. Thus, genetic statistics that differ from zero or from other numerical values by at least two standard errors are assumed to be statistically significant.

Obviously, the mandible is morphogenetically and functionally a highly integrated structure, and many of these traits will exhibit varying amounts of intercorrelation. To resolve these inter- correlations, a principal components analysis was carried out on the phenotypic data, and the resultant vectors were rotated to orthogonal simple structure using the Varimax criterion (RUMMEL 1970). The original data are projected onto the Varimax-rotated vectors to produce a new set of synthetic traits, the rotated principal components scores (RPC). These scores position each individual mouse on an axis of multivariate variability described by rotated principal component vectors. Because these scores represent new synthetic morphogenetic traits, their underlying causal components of variability can be estimated as was done with the original univariate traits.

Additive genetic and residual environmental correlations are presented for the 14 traits. Ad- ditive genetic covariance has a definition equivalent to additive genetic variance in that the indirect maternal covariance is not included. Residual environmental correlation is that correlation after postnatal maternal affects have been removed. A small number of pairwise direct dominance genetic correlations are included for the traits having the largest dominance variance. As noted above, dominance variance and covariance are not very reliably estimated with this design and the standard errors are large; thus, critical discussion and statistical tests based on these estimates are not warranted. However, in a few instances, preliminary correlation data are useful in discussions about common dominance effects among several functionally related traits that exhibit dominance.

Three different multivariate statistical procedures are used to explore the structure of the genetic and residual environmental correlations among these traits. First, a UPGMA cluster analysis is perfortned on each correlation matrix to examine hierarchical structure (SNEATH and SOKAL 1973). Second, a Varimax-rotated principal component analysis of each correlation matrix is used to examine multivariate patterns of phenotypic, additive genetic and environmental covariability. Third, the level of integration among the phenotypic, additive genetic and residual environniental correlation matrices is described by an index of integration, I (CHEVERUD et al. 1983). The formula for this index is

I = i (A, - 1)2/(n* - n ) ) L=, where A, is the ith eigenvalue and n is the number of eigenvalues or traits. In a well-conditioned matrix, the index will take values between 0 and 1, where 0 implies no integration (very low or zero correlation coefficients) and 1 is perfect integration where all the correlation coefficients are unity.

RESULTS

This paper describes four major aspects of morphological size and shape in the rodent mandible including ( 1 ) the underlying determination of phenotypic variability; (2) the dimensionality of the genetic variability in the form of the mandible; (3) whether the correlation structure among these 14 traits reflects the developmental history of the mandible; and (4) the evolutionary impact of selection on various parts of the mandible. Results relating to points 1-3 are discussed here, and their relationship to point 4 is considered in the DISCUS- SION.

GENETICS OF MANDIBLE FORM 56 1

Variance components: Table 3 provides the variance components and their standard errors for the 14 mandible traits. Proportions of the phenotypic variance due to additive direct genetic variance ( = narrow-sense heritability, h'), direct dominance genetic variance (d2) and additive maternal genetic variance (m') are also given. Negative variance estimates for d 2 and m 2 are de- noted by a blank. Since h', d 2 and m 2 are proportions, geometric rather than arithmetic means are given.

The additive genetic variance component is significantly different from zero for all traits. Narrow-sense heritability estimates range from 0.09 (CONCAVITY and CONDYLWID) to 0.44 (NOTCHHIGH), with a geometric mean of 0.19 over all 14 traits. These heritability estimates are considerably lower than previous full-sib analyses involving mandibular traits (e.g., ATCHLEY 1983a) since heritability estimates in these latter studies included '/2 U&,.

The geometric mean for d' is 0.10. In four traits-SUPERINCIS, TOOTHAREA, INFERINCIS and CONDYLWID-the estimated dominance genetic variance is a relatively large proportion of the phenotypic variance. The actual variance components for direct dominance have large standard errors, and direct dominance variance is probably underestimated with this design (RISKA, RUTLEDCE and ATCHLEY 1985b). Traits with largest dominance variance are associated with the incisor and molar region of the corpus and the area of the condylar processes. As will be shown later, most of these traits also have a large additive genetic correlation among them.

The geometric mean for m2 is 0.07 and one individual estimate (NOTCHHIGH) is significantly different from zero (m' = 0.26). The covariance between additive direct and additive maternal genetic variance is a small proportion of the phenotypic variance; however, in several instances it ranges up to about 8-9% of the variability. In a number of instances, this covariance term is negative; therefore, it has a dampening effect on the phenotypic variance.

Covariance components: Additive genetic and residual environmental correlation coefficients among these 14 traits are given in Table 4. Genetic correlations due to dominance are estimated for the seven traits with the largest dominance variance estimates (Table 5). Dominance correlation estimates for many of the remaining traits cannot be obtained because of negative variance estimates. Formulas for computing standard errors for the correlations are not available for the type of simultaneous estimation procedure used here; however, they are expected to be relatively small for the additive genetic and residual environmental correlations, but relatively large for those due to dominance.

Assuming these mice are randomly mating (and, as a result, in linkage equi- librium), the additive genetic correlations describe the genetic association between pairs of traits arising from the summed additive effects of alleles at each relevant locus that impinge on both traits, i .e. , pleiotropy. Absolute values for the additive genetic correlations range from 0.01 to 1.12, with a mean of 0.32 (kO.02). Only one of the 91 estimates of additive genetic correlations is greater than unity (CONDYLWID with SUPERINCIS = 1.12). This specific estimate probably represents sampling variability around a parametric correlation of near 1.0. Three of the 21 estimated dominance correlations have values above


TABLE 3

Variance components for 14 mandible traits on ICR randombred mice

Trait V,. Vo. V,, CdoAm VC V , VP h2 d2 m2

POSTMANLEN

ANTMANLEN

NOTCHHIGH

INCISHIGH

CONCAVITY

RAMUSHIGH

CONDYI.WID

CONDYLLEN

CORONHIGH

CORONSIZE

ANGULARLEN

TOOTHAREA

SUPERINCIS

INFERINCIS

108 +27 136 +28 367 +43 259 t5 1 664

f301 196 +35 429

f214 405 +83 1161 +205 1561 +432 202 +9 1

398 +64 1232 2410 645

+177

39 +83 58

+86

70 +I40 -87 +160 -148 +941 -86 +lo9 741

+685 107

f255 206

+674 -615 k1363 133

+293 256

+205 1790

f1232 732

+555

67 +52 37

+54 22 1 +87 -101 594

-1239 +646

69 +7 1 -61 1 +429

8 f161 492

+417 -98 +837 -266 +183 187

+130

52 +759 -1 16 +341

-3 +25 26

+25 -75 +40

59 t43 329

+304 -6 f33 184

+188 -5 +72 -233 +191 -157 f390 126 +82 -79 263

-299 f337 -163 +151

-14 326 549 +61

-60 365 +49 +64 -218 474 +79 +lo4 29 863

+88 2119 1024 6658 +584 f743 -11 570 +65 +81

451 3664 +401 +523 -39 1112 +-I48 +188 -604 3516 k384 +516 77 9221

+777 f1057 150 1793

k171 +226 -87 585 f118 +152 -410 6236 +695 +934 132 2575

+316 +41Y

524 +29 562 f3 I

839 247 1022 +59 7287 +406 732 +40

4858 +272 1589 +90

4537 +262 9989 +570 2137 2120 1260 f69

8600 f486 3805 +212

0.21 0.07 0.13

0.24 0.10 0.07

0.44 0.08 0.26

0.25

0.09

0.27 0.09

0.09 0.15

0.26 0.07 0.01

0.26 0.05 0.11

0.16

0.10 0.06

0.32 0.20 0.15

0.14 0.21 0.01

0.17 0.19

nata are sex-adjusted and log-transformed. Elements in the table have been multiplied by 1000. h2 = narrow-sense heritability; d 2 = the proportion of phenotypic variance due to direct dominance; m2 = the proportion of phenotypic variance due to additive maternal genetic variance.

unity, which is expected from the greater instability in estimating of dominance effects.

As would be expected in a morphogenetically and functionally highly integrated structure like the mandible, there are several pairs of traits with high additive genetic correlations. These high correlations usually reflect developmental or functional relationships. For example, CONDYLWID has high additive genetic correlations with the curvature of the incisor, SUPERINCIS (1.12), and with other traits reflecting the development of the anterior corpus region, i . e . , INCISHIGH (0.62), ANTMANLEN (0.65) and TOOTHAREA (0.78).

CONDYLWID, SUPERINCIS, TOOTHAREA and ANTMANLEN all have reasonably

GENETICS OF MANDIBLE FORM 563 TABLE 4

Additive genetic and residual environmental correlations between 14 mandible traits

Traits z

Y P

E POSTMANLEN

ANTMANLEN

NOTCHHIGH

INCISHIGH

CONCAVITY

RAMUSHIGH

CONDYLWID

CONDYLLEN

CORONHIGH

CORONSIZE

ANGULARLEN

TOOTHAREA

SUP ER IN C I S

INFERINCIS

-

6

40

18

-4

26

41

15

10

56

58

34

21

-15

19 - 35

45

54

54

65

-9

-1 3

22

65

78

-25

50

25

20 -

33

18

50

41

-30

1

59

39

52

4

24

18

33

32 -

20

12

62

-19

-50

33

6

64

18

3

26

30

-3

18 -

42

94

-4

28

76

41

59

-14

27

46 5 20 -16 12

30 22 -1 14 9

26 8 -39 9 29

16 14 -24 19 20

52 7 1 -16 10

- 28 33 -15 12

54 - 12 -3 9

23 1 - -25 -43

-13 -24 -21 - 58

33 35 -42 3 - 12 48 I -4 54

54 78 -11 -3 50

-1 112 30 6 6

8 25 -42 -22 17

55

40

32

28

33

31

-5

13

-1

11 -

47

-5

20

40 35 -29

58 11 20

14 7 12

42 25 20

36 15 -11

30 -7 6

5 -4 17

-27 -12 -14

-4 -5 19

10 5 16

5 26 -11

- 61 21

9 - -20

47 -47 - ~~

All values have been multiplied by 100. Genetic correlations are below the diagonal, and environmental are above the diagonal.

large dominance variances (geometric mean of d 2 = 0.16). Is this high dominance variance due to a shared dominance effect; that is, do they share a high dominance correlation? With two exceptions (ANTMALEN with CONDLYWID and SUPERINCIS with INFERINCIS), CONDYLWID, ANTMANLEN, TOOTHAREA, SUPERINCIS and INFERINCIS have low intertrait dominance correlations. Thus, except for SUPERINCIS and INFERINCIS, the higher dominance variances in individual measures from the corpus region do not translate into high dominance correlations between traits from within that region. Although dominance effects in one trait are not highly correlated with dominance effects in other traits from the corpus region, this regional relationship does not seem to hold for the ramus. For POSTMANLEN, NOTCHHIGH and CONDYLWID, at least POSTMANLEN has a high correlation with the other two ramus traits; however, NOTCHHIGH and CON- DYLWID have a more modest correlation of 0.4, which is similar to that between INFERINCIS and ANTMANLEN in the corpus region.

Residual environmental correlations have lower values than the additive genetic correlations and range in value from 0.01 to 0.61. The mean of absolute values is only 0.18 (2 0.03). there are only ten coefficients in the matrix that


TABLE 5

Genetic correlations due to dominance between seven mandible traits

Traits

POSTMANLEN -

ANTMANLEN -154 -

NOTCHHIGH 83 15

CONDYLWID 98 -130 44

TOOTH AREA 99 15 94 37 - SUPERINCIS 70 2 88 -4 -34 -

INFERINClS 55 43 7 -63 35 -136 -

-

-

All values have been multiplied by 100

are >0.5 and only one trait, TOOTHAREA, that has an environmental correlation >0.5 with more than one trait.

Dimensionality of genetic variability in form Table 6 gives the Varimax-rotated principal components analysis of the phe-

notypic data. Principal component vectors are interpreted by the magnitude and sign of their coefficients. The first phenotypic vector has largest coefficients for TOOTHAREA, ANTMANLEN, INCISHIGH, CONCAVITY, ANGULARLEN and RAMUSHIGH. Thus, these traits reflect measures of the height of the mandible, particularly at the anterior or symphysial end. The remaining phenotypic principal component vectors will not be verbally described in order to conserve space.

Table 7 provides the variance components for these multivariate patterns of variability. These four vectors represent 61 % of the total phenotypic variability in these 14 traits. The geometric means are 0.19, 0.07 and 0.06 for h 2 , d 2 and m2, respectively, for these multivariate constructs. These values for independent multivariate patterns are very similar to those averaged for the individual traits.

Four eigenvectors were extracted from the genetic correlation matrix and Varimax-rotated. The first vector reflects genetic covariation in the several measures of height or length of the mandible and has highest coefficients for CONCAVITY, ANTMANLEN, CONDYLWID, TOOTHAREA, RAMUSHIGH and ANGULAR- LEN. The second vector reflects genetic variability in the ramus, with largest coefficients for CORONSIZE, POSTMANLEN, NOTCHHIGH, ANGULARLEN and CON- DYLLEN. CONDYLLEN has an opposite sign for its coefficient, so it varies inversely relative to the other four traits.

The third genetic vector represents covariation between curvature of the

GENETICS OF MANDIBLE FORM 565 TABLE 6

Varimax-rotated principal components of the phenotypic, additive genetic and residual environmental correlations f o r 14 mandible traits from ICR randombred mice

Phenotypic Genetic Environmental

Trait 1 2 3 4 1 2 3 4 1 2 3 4

POSTMANLEN

ANTMANLEN

NOTCHHIGH

INCISHIGH

CONCAVITY

RAMUSHIGH

CONDYLWID

CONDYLLEN

CORONHIGH

CORONSIZE

ANGULARLEN

TOOTHAREA

SUPERINCIS

INFERINCIS

Variance exp. %

GI

PI 32

p2 65

ps 99

p4 56

44

73

35

68

61

54

10

0

-6

19

63

80

30

27

23 23

35 44 42

10 -26 0

65 -2 3

20 7 -18

-10 13 19

23 -6 59

28 -5 46

-32 3 74

70 6 9

81 -3 -5

11 13 27

29 0 18

1 1 79 -11

15 -81 -3

15 12 11 38 50 61

G2 G3 G4

49 84 62

31 88 86

84 57 I08

81 62 94

8 73 36 -5

84 8 -28 26

25 71 -11 20

21 30 5 82

87 21 -5 -18

67 10 12 6

79 32 53 42

18 -47 61 -12

1 20 3 -79

33 84 -9 -3

50 51 -3 -9

75 39 -7 34

4 15 94 24

40 30 5 24

38 27 23 19

GI El 54

E2 57

E3 79

E4 39

80

27

34

16

50

68

8

35

-16

12

77

13

19

-36

25

G2

59

61

43

76

25 0

48 12

9 59

51 37

31 -12

2 -6

-1 -1

-36 -62

-7 72

1 81

9 19

93 1

74 -3

13 25

22 22

Gs 73

80

106

91

-13

50

6

23

24

53

64

19

6

7

-6

20

-38

64

12

G4

90

60

87 60

All coefficients have been multiplied by 100. Below the factor matrices are matrices of the congruence between Varimax-rotated principal components solutions of the phenotypic, genetic and residual environmental correlation matrices. Congruence is given in degrees of the angles between vectors. P = phenotypic; G = additive genetic; E = residual environmental.

incisor and condyloid dimensions and has highest values for SUPERINCIS, CON- DYLLEN and CONDYLWID. The last genetic vector reflects an inverse relationship between INCISHIGH and CORONHIGH, so that the thicker the anterior portion of the mandible, the shorter the coronoid process.

Four factors were also extracted from the residual environmental correlation matrix. The first environmental vector concerns primarily the lower dimensions of the ramus and has largest coefficients on POSTMANLEN, ANGULARLEN, RAMUSHIGH and CONCAVITY. This vector may simply be describing the envi- ronmentally induced variability in the angular process. The second vector describes the environmental covariability in the corpus and has largest coefficients for TOOTHAREA, SUPERINCIS, INCISHIGH and ANTMANLEN.


TABLE 7

Variance components for phenotypic Varimax-rotated principal components scores of 14 mandible traits on ICR randombred mice

Trait V,. VD. v.4, CAoAn VC V E V P h2 d 2 m'

PI 206 10 -45 39 15 656 882 0.23 0.01 f42 +129 &U4 +4 277 +9U +49

Ps 175 112 U5 -40 -117 733 947 0.18 0.12 0.09 f40 +I13 k 8 2 +3U 275 +lo4 +54

Pa 168 255 41 -63 -51 623 972 0.17 0.26 0.04 +48 +I47 k92 +41 +U4 +110 +55

P.j 171 -66 -43 20 63 764 909 0.19 f49 f142 k87 f93 +U7 +lo4 +51

Data are sex-adjusted and log-transformed. Elements in the table have been multiplied by 1000.

The third environmental vector reflects variability primarily in the upper ramus, with large coefficients for CORONSIZE, CORONHIGH, NOTCHHIGH and CONDYLLEN. Since CONDYLLEN differs in sign, length of the condyloid process varies inversely with ramus height. The fourth vector reflects variability in INFERINCIS, CONDYLWID, RAMUSHIGH and ANTMANLEN. This suggests a pattern of environmental covariability between the length and curvature of the incisor region with the height of the ramus and width of the condyloid process.

The index of integration ( I ) for the phenotypic, additive genetic and residual environmental matrices is 0.27, 0.39 and 0.25, respectively. These values are rather low and mirror the computed average correlations given earlier. This suggests considerable heterogeneity in the correlations arising from a number of independent patterns of variability with a resultant low level of morphogenetic integration.

Do genetic and environmental factors have similar effects on the correlations between traits? The product-moment correlation between the 91 pairs of genetic and environmental correlations in Table 4 is 0.43 (P < 0.01).

Concordance between phenotypic, genetic and residual environmental vectors can be ascertained by the angle between vectors computed as the arc cosine of the cross-products of the vector coefficients divided by the square root of the product of the values. Vectors exhibiting an angle of 90" are orthogonal to each other, whereas those with a value of 0" are completely concordant. The values of vector concordance are given in Table 6. Between the phenotypic and genetic factor matrices, vectors PI with GI and P2 with G2 exhibit greatest concordance. For the genetic and residual environmental matrices, GI with E4 and GP with ES show most similarity.

Developmental history vs. genetic correlation

UPGMA cluster analysis of the additive genetic correlations was performed on 12 of the 14 traits (Figure 3). CONCAVITY and INFERINCIS were excluded from these analyses. These latter two traits help define the overall outline of


P O S T M A N L E N

ANGULARLEN

N O T C H H I G H C O R O N S I Z E ANTMANLEN

TOOTHAREA I INCISHIGH

RAMUSHIGH

C O N D Y L W I D

SUPERINCIS

I ' CONDYLLEN

CORONHIGH

I I I I I I I 0!2 0 0.2 0.4 0.0 0.8 1.0 1.2

GENETIC CORRELATION FIGURE J.-UPGMA cluster analysis of the additive genetic correlations of 12 traits from the

mature mouse mandible. Actual correlations are given in Table 4.

the mandible, however, they are difficult to integrate into discussions about growth and morphogenesis.

One large cluster of ten traits is produced, while the remaining two traits are unrelated to the remaining ten in a genetic correlation sense. Cluster analysis is not a tool for statistical inference; that is, it is difficult to rigorously delimit clusters in a probabilistic sense, such as one might do with multiple comparisons testing of arithmetic means. As a result, it is difficult to know where to make partitions within the large cluster in Figure 3. We have chosen to be rather conservative and to delimit the clusters at a value slightly greater than 0.4.

There are three distinct clusters of two or more traits. One cluster, composed of POSTMANLEN, ANGULARLEN, NOTCHHIGH and CORONSIZE, relates to the dimensions of the ramus. POSTMANLEN and ANGULARLEN are measures of the lower portion of the ramus, and a part-whole relationship exists, in that growth in ANGULARLEN is a major contributor to POSTMANLEN. NOTCHHIGH and co- RONSIZE relate to the- height of the ramus. All four of these traits relate to posterior growth of the mandible (Fig. 4).

The second cluster includes ANTMANLEN, TOOTHAREA and INCISHIGH, and all measure various features of the corpus or distal portion of the mandible. As such, they reflect an anterior growth pattern of the mandible (Figure 4). RA- MUSHIGH measures the height of the ramus and is linked to this latter cluster of corpus traits at a genetic correlation of approximately 0.4. The third cluster describes the high correlation between CONDYLWID and SUPERINCIS, discussed previously.

The two remaining measures, CORONHIGH and CONDYLLEN, act as independent traits. They both possess significant additive genetic variance (Table 3);

568

-

W. R. ATCHLEY, A. A. PLUMMER AND B. RISKA

POSTMANLEN

ANGULARLEN

RAMUSHIGH NOTCHHIGH

INCISHIGH

CORONHIGH CORONSIZE

DISCUSSION

Mandibular growth and morphogenesis has been the subject of considerable experimental analysis (BHASKAR 1953; HALL 1978, 1982a,b, 1984; MOORE and LAVELLE 1974; MOORE 198 1 ; SPERBER 198 1 ; SLAVKIN 1979). Understanding these results is facilitated by a brief review of some aspects of mandibular growth and morphogenesis.

Origzn of the mandible: The mammalian mandible arises from neural crest- derived mesenchyme and contains four progenitor cell populations: chondro- blasts, fibroblasts, osteoblasts and myoblasts. Interplay among these cells and their derivative tissues, together with neural and vascular tissue and the teeth, will determine mandibular form. The majority of the mandible is composed of a single bone, the dentary. The body of the dentary and the basal portion of the condylar process results from intramembranous ossification. This ossi- fying membrane, together with its accompanying neural and muscular tissue, is attached to Meckel’s cartilage along the future body of the mandible. As ossification and the accompanying development of associated neural and muscular systems proceeds, secondary mandibular cartilages appear on the dermal bone at the future sites of the condylar, coronoid and angular processes (HALL 1978). Through endochondral ossification, these secondary cartilages will serve an important role in growth in the ramus of the mandible.


The causal components of skeletal growth and morphogenesis have often been referred to by developmental biologists as being of either “intrinsic” or “extrinsic” origin (MOSS 1972; THOROGOOD 1983; HINCHLIFFE and JOHNSON 1983; HALL 1984). Intrinsic factors are involved with “programming” tissue- specific morphogenesis and generating the basic form of individual skeletal elements. According to HALL (1 982a,b), intrinsic processes include the initial size of the embryonic primordia, regulation of component synthesis, the intrinsic rate and polarization of cell division, the amount of extracellular matrix deposited by each cell, how the cells interact to produce a tissue or organ of a specific shape, the extent of programmed cell death, and so on. Develop- mental variability in these processes arises from genetic as well as nongenetic causal components.

Extrinsic refers to influences on individual skeletal elements arising from adjacent developing tissues, such as muscles, nerves, blood vessels, teeth and connective and skeletal tissue. Extrinsic factors, including biomechanical and biophysical factors, hormones and functional matrices, influence final form and size of the skeletal element by acting in conjunction with intrinsic factors. In terms of their morphogenetic effects, extrinsic factors may be local (e.g., biomechanical) or systematic (e.g., hormones and vitamins). HALL (1 984) has described extrinsic influences as “epigenetic” factors; that is, epigenetic interac- tions being those where one tissue has an influence on the development of another. Further, there may be interactive and feedback loops occur between intrinsic and extrinsic factors. As in the case of intrinsic factors, variability in extrinsic or “epigenetic” factors includes both heritable and nonheritable components (HALL 1984).

Late prenatal and early postnatal mandibular growth and morphogenesis occurs by several processes that are important in clarifying the origin of variability (MOORE 198 1). Secondary cartilage associated with the coronoid, angular and condylar processes undergoes endochondral ossification. During early postnatal growth, development and maintenance of the cartilage in these mandibular processes depend on local muscle activity so that response to local mechanical stimuli produces a balance with bone deposition and resorption (HALL 1978). Extirpation of the medial pterygoid or masseter muscles causes resorption of the angular process, while removal of the temporal muscles causes a similar reduction in size of the coronoid process (HALL 1982a). Congenital paralysis of these muscles results in a considerable reduction or absence of the mandibular processes (HERRING and LAKARS 198 1). Thus, development of the secondary cartilages and their effect on these mandibular processes is compen- satory or adaptive and depends on muscle development and activity.

The condylar region is a major region of postnatal growth in the mandible. The actual direction of intrinsic growth produced by the condylar region depends on its precise shape (MOORE 1981); however, its orientation is gen- erally posterosuperior, so that increments of growth increase mandibular height and depth. Since the condyle abuts the cranial base at the temporomandibular joint, the intrinsic growth results in the mandible being displaced anteroinferiorl y.


In addition, there are numerous regional surface remodeling changes that serve to maintain the proportions of the mandible as it increases in size (MOORE 1981). Bone deposition occurs at the posterior border of the ramus and the anterior end of the symphysial region. Resorption of bone occurs along the anterior border of the ramus (coronoid process) and in the alveolar region. These deposition and resorption patterns produce a posteriorly directed component of growth that is superimposed upon the intrinsic growth of the mandible and matches the posterior component of growth at the condylar cartilage.

Causal components of mandibular size and shape: The patterns in the components of phenotypic variability in mandibular dimensions reflect both the heritable and nonheritable ontogenetic history of these traits (ATCHLEY 1983a; NONAKA and NAKATA 1984; BAILEY 1985). All mandible dimensions exhibit significant amounts of direct additive genetic variance, and heritabilities range from 10-44%. Traits representing the major dimensions of the bone usually had reasonably large heritabilities; however, traits where some of the variability more obviously arises from extrinsic biomechanical factors had a larger proportion of phenotypic variability due to environmental rather than additive genetic effects. Three such traits are cONDYLWID, CORONSIZE and ANGULARLEN, and the geometric mean of the heritability for these three traits is 0.1 1, compared with 0.22 for the remaining 11 traits.

The level of dominance variance estimated for some traits is rather unex- pected in view of the often-made assumption of no significance levels of dominance in quantitative genetics studies of skeletal traits. Obviously, at least in the mandible, dominance can be an important component of phenotypic variability, occasionally exceeding the proportional contribution of direct additive genetic variance. Traits related to the shapes of certain functional components of the mandible seemed to have reasonably large fractions of their genetic variability in the dominance component. Included here are incisor shape, condylar dimensions and area of the mandible associated with the molars.

Dimensionality of the variability: The mandible appears to be a single bone, but it can actually be partitioned into several developmental and functional skeletal units (Figure 5 ) including the basal unit (inferior alveolar neurovascular bundle), the condylar (temporomandibular joint and lateral pterygoid muscle), the coronoid (temporalis muscle), the angular (masseter and medial pterygoid muscle), the coronoid (temporalis muscle), the angular (masseter and medial pterygoid muscles), the alveolar (mandibular dentitions), and the symphysial (facial and genial muscles) (MOORE 1973, 1981). Each skeletal unit is influenced by the growth pattern of its own functional unit.

In view of this embryologic heterogeneity, the mandible should show a number of distinct morphogenetic patterns of variability belying the unitary ap- pearance of this bone. This is, in fact, what the results demonstrate. For example, the cluster analyses indicate the existence of a number of clusters of traits. However, the level of correlation at which the various clusters are joined suggests a number of independent genetically controlled developmental processes reflecting patterns of morphological variability based on embryologic origin, functional specialization or anatomical continguity.


MURINE MANDIBLE DEVELOPMENT

Neural C r e s t

F i rst Arch of -

57 1

Meckel ’s Cart i lage

Incisor Alveolar Process

A n t e r i o r Q r o r r l h

Symphyseal Secondary Car t i l age

SuDe.rlor G r o w t h Molar Alveolar Process

, P o s I e r i o r G r o w t h

Suppositions about the complexity of the underlying control of mandibular size and shape are supported by the dimensionality of the phenotypic correlation matrix as shown by the Varimax-rotated phenotypic principal components. Each vector reflects an independent pattern of morphological variability, and all four vectors have significant amounts of genetic variance. Further, the patterns of direct additive us. direct dominance differed considerably between eigenvectors. Finally, both the additive genetic and residual environmental correlation matrices also had multiple and independent patterns of covariability.

Additional evidence for the complexity in the underlying causal components stems from comparison of genetic integration values for skeletal traits from various regions of the body relative to the complexity of their development. Numerical values of the integration statistic, I , are provided describing the homogeneity of pairwise phenotypic, genetic and residual environmental correlations. The higher the correlation among traits, the fewer independent dimensions of variability and the closer Z will be to unity. Although integration of the mandible dimensions is judged to be low, no Z values were given for other body regions to judge the appropriateness of this statement. Table 8 provides Z values for sets of traits from several rodent body regions arising from both static and ontogenetic data. As will be seen, I values parallel complexity in embryologic origin of the structures. Further, integration is less in the mandible than in almost any other set of dimensions.

Comparison of integration in 19 measurements from the rat scapula and humerus (LEAMY and ATCHLEY 1984) is of interest because the scapula is

Angular Process

c


TABLE 8

Index of integration (I) for phenotyfiic (P), genetic (G) and residual environmental (E) correlation matrices from various static and ontogenetic studies in rats and mice

1 2 3 4 5 6 7

I P 0.27 0.36 0.44 0.56 0.65 0.65 0.64

IC 0.39 0.62 0.62 0.69 0.78 0.78 0.85

1, 0.25 0.19 0.31 0.48 0.40 0.53 0.32 ~

Studies are labeled as 1-7 and are identified as follows: ( 1 ) mouse mandible (14 traits)-this study; (2) mouse pelvis (8 traits)-L. A. P. KOHN and W. R. ATCHLEY (unpublished results); (3) rat pelvis (8 traits)-L. A. P. KOHN and W. R. ATCHLEY (Unpublished results); (4) rat scapula and humerus (19 traits)-LEAMY and ATCHLEY 1984; (5) rat body weight through Ontogeny-CHEV- ERUD, RUTLEDGE and ATCHLEY 1983; (6) rat tail length through ontogeny-CHEVERUD, RUTLEDGE and ATCHLEY 1983; (7) mouse live body measurements during ontogeny (5 traitS)-LEAMY and CHEVERUD 1984.

analogous to the mandible in that it also appears in the adult organism as a single bone with extensive associated musculature. Further, the scapula devel- ops from several ossification centers. However, Z values for phenotypic, genetic and residual environmental correlations are considerably higher for the scap- ular traits than for the mandible. IC is about 40% higher for the scapula compared with that for the mandible.

L. A. P. KOHN and W. R. ATCHLEY (unpublished results) examined eight dimensions from the pelvis of mice and rats. The mice are a subset of those used in this study. Zp and Z,, are comparable between the pelvis and mandible; however, 1, in the mandible data is approximately 40% less than Z, from the pelvis of both the mouse and the rat.

LEAMY and CHEVERUD (1984) examined the genetic correlation of age-specific values of the same trait followed through postnatal ontogeny. They give ontogenetic I values for five traits at five postnatal ages in sibs of the mice used in the present study. The traits include body weight, head length, trunk length, trunk circumference and tail length. The values for Z for each trait, as well as the averages over all traits, are higher than those given here for the mandible.

These data suggest that the genetic components underlying rodent mandible size and shape are more heterogeneous than those involved in other complex skeletal structures. Neither the rodent scapula nor pelvis seem to have the degree of extrinsic control on bone development found in the mandible.

Developmental history: Does the pattern of genetic correlations among these traits reflect the developmental history of the mandible? This intriguing ques- tion arises because the additive genetic correlations are a reflection of the genetic similarity arising from pleiotropy among the traits. It has been sug- gested (ATCHLEY 1984) that the additive genetic correlation itself has a strong developmental component because the genes affecting a pair of traits jointly are not simply those acting only at that particular time. The genetic correlation also will include genetic associations occurring at earlier periods in ontogeny, because many developmental processes are hierarchical and also depend on


A I

C h

573

C o n d y l a r P r o c e s s

g u l a r P r o c e s s

FIGURE 6.--Schematic illustration of the functional units of the mandible. (Redrawn from SPER- BER 1981).

processes occurring at different times. Thus, are higher genetic correlations the result of more common developmental processes?

The developmental history of the rodent mandible is reasonably well-known (BHASKAR 1953; HALL 1978, 1982a,b; MOORE 1981), and much of this information is summarized in Figure 5. The skeletal structure of the mandible contains two different developmental “lineages” representing intramembra- neous us. endochondral patterns of ossification of cartilage; that is, ossification of primary or secondary cartilage, respectively. Considering the so-called functional units of the mandible described in Figure 6, the body of the dentary and basal portion of the condylar process is derived by intramembrane ossification. The other “lineages,” associated with the ossification of secondary cartilage, include the angular and coronoid processes and the remainder of the condyloid process. The prenatal and early postnatal developmental history of these various lineages are different. Further, the lineage containing those structures derived from secondary cartilage is heterogeneous in terms of the underlying causal factors (different groups of biomechanical factors stimulating their development).

Part of the problem with discussing a developmental history as reflected by the pattern of genetic correlations among these traits is that some include more than one functional unit. For example, TOOTHAREA includes portions of the mandible from the body as well as the alveolar process, whereas POSTMAN- LEN includes skeletal material from the body and angular process. However, in spite of these difficulties, in several instances, the hierarchical pattern of genetic correlations as reflected by the cluster analysis does represent ontogenetic history. For example, ANTMANLEN, TOOTHAREA and INCISHIGH cluster together, as do ANGULARLEN and POSTMANLEN.

However, the similarity in genetic correlations between pairs of traits can be the result of a form of parallelism in development because high genetic cor-


relations between unrelated pairs of traits can be achieved by quite different developmental patterns. ATCHLEY et al. (1985) describe several examples of the diversity in origin of high genetic correlations between these mandible traits and adult body weight. The coordination of growth trajectories, which is one source of high genetic correlations, may occur by compensating processes that accelerate growth at one period of development and retard it at others (RISKA, ATCHLEY and RUTLEDGE 1984; ATCHLEY 1984). Further, structures of embryologically heterogeneous origins can exhibit high genetic correlations simply because of a simultaneous response to a common growth stimulating factor, e .g . , growth hormone or somatomedins (ATCHLEY et al. 198413). This may be the reason for the high genetic correlation between mandible dimensions and femur length in rats (ATCHLEY 1983a).

Selection: An evolutionary consequence of the diversity of morphogenetic patterns and resultant low genetic integration is that selection on some parts of the mandible will invoke a heterogeneous response in other mandibular dimensions. The direct response to selection in a single trait is a function of the heritability and intensity of selection. However, associated with a direct response to selection for a trait is a correlated response in other traits possess- ing significant additive genetic covariance with the trait under selection (FAL- CONER 1981). Indeed, the effect of selection for a single mandible dimension on the remainder of the mandible is defined by the additive genetic and phenotypic variance-covariance matrices. Thus, selection to alter the size and/ or shape of different regions of the mandible might require different selection indices.

Individual traits associated with the overall dimensions of the mandible

and ANTMALEN) had the greatest proportion of additive genetic variance. All things being equal, one would expect that the overall dimensions of the mandible would respond readily to selection. Incisor shape and condylar width (SUPERINCIS, INFERINCIS and CONDYLWID) are dimensions with a greater proportion of their genetic variance in the form of direct dominance variance and, as a result, would be expected to be less responsive to selection. These conclusions are reinforced by the multivariate results.

The cluster analysis of the genetic correlations in conjunction with the individual correlation coefficients aids in the speculation about the morphogenetic effects of selection. INFERINCIS, CORONHIGH and CONDYLLEN would be expected to behave independently. These three traits possess additive genetic variance; however, they exhibit little additive genetic correlation with the remaining mandible dimensions. The correlation structure of the remaining 11 traits is such that selection on any of them would produce some level of correlated response in the others, the magnitude being a function of the heritability and genetic correlation.

However, this discussion relates to selection and response in adult traits only and ignores the fact that there may be a significant ontogenetic component to genetic variance-covariance structure among these traits. If the variance-covariance structure changes during ontogeny, then the response to selection

(NOTCHHIGH, TOOTHAREA, RAMUSHIGH, CONDYLHIGH, CONDYLLEN, INCISHIGH


might be expected to vary as well, depending on when during ontogeny selection occurred, and on which traits. Based on genetic correlations between these traits in adult mice and body weight and weight gain during postnatal ontogeny, ATCHLEY et al. ( 1 985) suggest that the genetic variance-covariance structure among these traits may have a significance ontogenetic component. ANT- MANLEN and POSTMANLEN at 70 days of age have similar genetic correlations with body weight at 14 days of age and body weight gain between conception and 14 days of age. However, the correlation of these traits with body weight at 70 days of age is quite different, and they arrive at this divergence correlation by different relationships with weight gain after 28 days of age.

Thus, the genetic variance-covariance matrix may not be as stable during ontogeny as has been supposed. The result is that accurate predictions of response to selection in the adults may need to be modified to include information about the genetic variance-covariance structure at other points during ontogeny.

We are indebted to our colleague JACK RUTLEDCE for many suggestions and critical comments while the research was in progress. BRIAN K. HALL, SUSAN W. HERRING, JAMES M. CHEVERUD and LUCI A. KOHN made numerous important constructive comments on the manuscript and provided us with timely assistance on matters of development and anatomy. We are particularly grateful to SUSAN HERRING who provided the information in Figure 5. This research was supported by National Science Foundation grant DEB-8109904 and by the College of Agriculture and Life Sciences of the University of Wisconsin, Madison. Contribution 2820 from the Laboratory of Genetics, University of Wisconsin.

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