The Genetics of Shovel Shape in Maxillary Central Incisors in Man RAFAEL BLANCO AND RANAJIT CHAKRABORTY University of Texas Health Science Center, Center f o r Demographic and Population Genetics, Houston, Texas 77025
W O R D S Chilean population . Tooth morphology . Shovel shape . Genetic correlation . Heritability.
KEY
ABSTRACT From dental casts of 94 parent-offspring and 127 full-sib pairs, sampled from two Chilean populations, shovelling indices are computed to measure the degree of shovelling of maxillary central incisors quantitatively.
Genetic correlations are computed to determine the role of genetic factors in explaining the variation in this trait. Assuming only hereditary factors to be responsible for the transmission of shovel shape, 68% of total variability is ascribed to the additive effect of genes. The shovel shape character of the max- factors as measured by genetic correlaillary central and lateral incisors has been tions. studied quite extensively since the 1840s MATERIAL AND METHOD in human populations. However, until recently most of these studies focused their The data analyzed here are from dental attention on establishing this trait as a casts taken from 198 Chilean individuals racial one with a high frequency in Mon- belonging to 114 different families of Puergoloids as against relatively smaller inci- to Dominguez (73 14' W e s t 3 8 52' South) dent es among the Caucasoids (Dahlberg , and 111 individuals belonging to 67 differ'49; Lasker, '50; Pinto-Cisternas and Fi- ent families of the village of Socaire (67" gueroa, '68). The evidence of strong ge- 52' West-23" 32' South). The Puerto Donetic background of this dental feature minguez population consists of individuals has been spelled out only by a few inves- of Mapuche or Spanish origin (Palomino tigators (e.g., Lasker, '50; Turner, '67; and Pereira, '71) whereas the Socaire popPortin and Alvesalo, '74). In all these stud- ulation is considered as descendants of ies the trait has been considered as a the Atacameno Indians (Blanco et al., qualitative one with three or more degrees '73). From this combined sample of 181 of variation in shovel shape. Such quali- families, we could select only 148 unretative treatment of this trait makes the lated individuals (having no common imdifferent investigations difficult to com- mediate ancestors) of which 63 were males pare because of the lack of obtaining rigid and 85 were females. From the familial unified criteria (Dahlberg, '49) and fur- relationships, we could extract only 94 thermore, the degree of variation in the parent-offspring pairs and 127 pairs of extent of shovelling seems to be quite large full-sibs. The decomposition of these pairs in Amerindian populations where the fre- according to sex is shown in table 1. quency of this trait is one of the highest Shovel shape was measured from the found in the literature (Pinto-Cisternas dental casts in terms of shovel shape inand Figueroa, '68; Rothhammer et al., '68; dex as defined in Rothhammer et al. ('68). Rothhammer et al., '71). To determine the To arrive at this, measurements were extent to which genetic factors are respon- taken with a caliper graduated at 0.10 sible for the shovel shape character of mm on the thickness of each superior inmaxillary central incisors, we therefore cisor at the site of maximal depth in the attempt to treat this as a metric charac- palatal face and the lateral ridges at the ter. Thus we examine the role of genetic same level. The shovel shape index was O
AM. J. P H Y S . ANTHROP.,44: 233-236
O
233
234
RAFAEL BLANCO AND RANAJIT CHAKRABORTY
2 !-
z w V
CY
w
a
-
z
> V z w
3 U
w CY
1
LI
-7
0
0.3
0.6
0.9
1.2
1.5
SHOVEL SHAPE INDEX Fig. 1 Frequency distribution of shovel shape index obtained from data on 148 unrelated individuals sampled from two Chilean populations.
then obtained using the difference between the values of the mean lateral thickness and the central one. A comparison of these indices with Dahlberg's classification (referred to in Carbonell, '63) shows that an index recorded as 0.3 or less can be taken as equivalent to no shovelling for the individual concerned. All measurements reported here are on maxillary central incisors only, as earlier experiences (Rothhammer et al., '68) with measurements on lateral incisors yielded statistically significant measuremental error.
RESULTS
Distribution of the trait As mentioned earlier, most studies of shovel shape of maxillary central incisors consider only their frequency distributions in various populations. Among the unrelated individuals of our sample, the distribution is found to be skewed (as shown in fig. 1) with no statistically significant sex dimorphism with respect to the mean values. (The mean indices for males and females are 0.553 f 0.043 and 0.461 &
235
GENETICS OF SHOVEL SHAPED INCISORS
0.059, respectively; t-value is 1.19 with < P < 0.5.) The distribution deviated quite significantly from normality also ( x z s = 24.8, P < 0.0005). The expected frequencies under normality are shown by the dotted line in figure 1. In terms of the proportion of shovelling, 66.89 & 3.87% of the individuals were with shovel shaped maxillary central incisors (with an index above 0.3). This proportion is also homogeneous in two sexes (73.0 f 5.6% in males, and 62.4 k 5.3% in females, ~ 2 = 1 1.86, P > 0.1). It may be noted here that the nonnormality of the distribution of shovel shape index is not due to non-homogeneity of the two samples. This is tested with the means (0.485 k 0.033 for Puerto Dominguez and 0.526 rt 0.043 for the Socaire sample, t-values for testing equality of means is 0.75 with 146 d.f., P > 0.4) and variances (0.101 and 0.102 for Puerto Dominguez and Socaire, respectively, Fvalue for testing equality of variances is 1.01 with 53 and 93 d.f., P > 0.25), which justifies pooling the two samples together . Familial correlation The extent to which genetic factors determine the degree of shovel shapes is studied here by considering the different familial correlations as described in table 1. Since the sample size corresponding to the different familial sets were small, we employed Fisher's bias correction (Rao, '73) for small sample sizes to obtain the pooled familial correlations in the table. The four parent-offspring correlations are seen to be statistically homogeneous (with x 2 3 = 3.78, P > 0.25; after bias correction). The homogeneity is also found among the three full-sib correlations (x** = 1.62, P > 0.25), showing the absence of sex-differ0.2
TABLE I
The familial correlations of the shovel shape index of the maxillary central incisors Number of observations
Correlation coefficient
Mother-son Mother-daughter Father-son Father-daughter Parent-offspring 1 (pooled)
28 31 22 13 94
0.4162 0.165 0.249e0.177 0.141r+_ 0.225 0.694f 0.164 0.339f 0.092
Brother-brother Brother-sister Sister-sister Full-sib 1 (pooled)
20 65 42 127
0.427e0.198 0.397k0.107 0.17820.155 0.329 0.080
Relationship
*
1 Bias correction for small and unequal sample sizes performed according to the principles indicated by Rao ('73).
ence in this trait. The full-sib correlation is not statistically different from the parent-offspring correlation ( x Z 1 = 0.01, P > 0.99), suggesting that there is no dominance deviation in the variation of shovelling indices in this population. The homogeneity of all these correlations, therefore, indicate that the hereditary factors are additive in nature. The heritability coefficient, h2 = 2rop, as estimated from parent-offspring correlation, is 0.678 f 0.186, indicating that about 68% of the variation of shovel shape index can be explained by the additive effect of genes. DISCUSSION
Although the different familial correlations as presented in table 1 are seen to be homogeneous with respect to classifications according to sex, some of them are quite small relative to their standard errors (e.g., father-son correlation is only 0.141 and sister-sister correlation only 0.178). We ascribe such fluctuations only to the small size of the samples. However,
TABLE 2
Test of hypotheses on the inheritance of shovel shaped incisors in man Variancecomponents f S.E.
Hypo thesis
d.f.
X2
(1) No heritability h =O, k = 1:c
1
0.01
common environment (cz) remainder (1- cz)
= 0.333 0.062 = 0.667f 0.062
1
0.01
heritability (h*) remainder (1- h2)
= 0.666f 0.124
(2) Nocommon environment c = 0 , 2 = 1:h
*
=0.334f0.124
236
RAFAEL BLANCO AND RANAJIT CHAKRABORTY
the pooled correlations are significant suggesting the hereditary nature of the trait. The 0.3 index level for non-shovelling as indicated in this paper yields a shovelling rate of approximately 6 7 % , as mentioned previously. This percentage is in accordance with some other studies (e.g., Campusano et al., ’72). Of course, studies on several other populations reveal lower rates of shovelling (e.g., Pinto-Cisternas and Figueroa, ’68) in admixed samples where admixture rates are presumably higher than that in the present sample. Furthermore as a preliminary test of the hypothesis concerning the role of additive effect of genes in explaining the variation in shovelling indices in the sample, we may express the expected familial correlations (parent-offspring, OPT and sib-sib, SST) as
+
and
OPT = hz 212 c*k SST = h212 c2
+
where, h2 = heritability coefficient, c2 = proportion of variance due to common environment and z , k = scaling parameters measuring inter-generational differences in h2 and c2 (following Rao et al., ’74; see figs. 5 , 14 of their paper). Writing the likelihood function in terms of Fisher’s z-transformation of the sample correlations we obtain the results shown in table 2. Interestingly enough, while heritability alone can explain the transmission of shovel shape (hypothesis 2), so can common environment alone (hypothesis 1). Under hypothesis 1 it is implicit that common environment has the same effect on parents and children which seems unlikely for a trait like this. Hence, one may favor hypothesis 2 although a final clarification must await a more detailed segregation analysis with complete pedigree data. In view of this, the heritability estimate (68%), as obtained in the earlier section, is only a tentative one since simultaneous estimation of c and h2 is not possible from the two correlations under the assumption k = z = 1 . ACKNOWLEDGMENTS
cooperation and help during the collection of the samples, and Dr. D. C . Rao whose suggestions improved the analysis reported in the paper. This work is supported in part by a U.S. Public Health Service In tern ational Postdoctoral Research Fellowship (No. 1FO 5TW-02007-02 of which R.B. is a recipient) and U.S. National Institutes of Health Grant GM 19513 made available to R.C. LITERATURE CITED Blanco, R., F. Rothhammer, G. Olarte, H. Palomino and M. Justiniano 1973 Analisis genetico cuantitativo de cinco rasgos morfologicos dentarios. Rev. Med. Chile, 101 ; 223-226. Campusano, C., H. Figueroa, B. Lago, J. PintoCisternas and C. Salinas 1972 Some dental traits of Diaquitas Indian skulls. Am. J. Phys. Anthrop., 36; 139-142. Carbonell, V. M. 1963 Variations in the frequency of shovel shaped incisors in different populations. In: Dental Anthropology. D. R. Brothwell, ed. Pergamon Press, New York, pp. 2 11-234. Dahlberg, A. A. 1949 The dentition of the American Indian. In: The Physical Anthropology of the American Indian. The Viking Fund, Inc., New York, pp. 138-176. Lasker, G. W. 1950 Genetic analysis of racial traits of the teeth. Cold Spring Harbor Symposiaon Quantitative Biology, 1 5 ; 191-203. Palomino, H.,and G. Pereira 1971 Oral genetics among “Mapuches.” I. A study of ethnical differences in a small community. Rev. Med. Chile, 99;132-138. Pinto-Cisternas, J., and H. Figueroa 1968 Genetic structure of a population of Valparaiso. 11. Distribution of two dental traits with anthropological importance. Am. J. Phys. Anthrop., 29;339-348. Portin, P., and L. Alvesalo 1974 The inheritance of shovel-shape in maxillary centralincisors. Am. J. Phys. Anthrop., 41 ; 59-62. Rao, C. R. 1973 Linear Statistical Inference and its Applications. John Wiley, New York, pp. 435436. Rao, D. C., N. E. Morton and S. Yee 1974 Analysis of family resemblance. 11. A linear model for familial correlation. Am. J. Hum. Genet., 26; 331359. Rothhammer, F., M. Benado and G. Pereira 1971 Variability of two dental traits in Chilean Indian and mixed populations. Hum. Biol., 43: 310317. Rothhammer, F., D. Lasserre, R. Blanco, E. Covarrubias and M. Dixon 1968 Microevolution in human Chilean populations. IV. Shovel shape, mesial-palatal version and other dental traits in Peuenche Indians. 2. Morph. Anthrop., 60; 162-1_.. 69. Turner, C. G. 1967 Dental genetics and microevolution in prehistoric and living Koniag Eskimo. J. Dent. Res.,46: 911-917. ~~~
The authors are indebted to Drs. F. Rothhammer and H. Palomino for their ~
W O R D S Chilean population . Tooth morphology . Shovel shape . Genetic correlation . Heritability.
KEY
ABSTRACT From dental casts of 94 parent-offspring and 127 full-sib pairs, sampled from two Chilean populations, shovelling indices are computed to measure the degree of shovelling of maxillary central incisors quantitatively.
Genetic correlations are computed to determine the role of genetic factors in explaining the variation in this trait. Assuming only hereditary factors to be responsible for the transmission of shovel shape, 68% of total variability is ascribed to the additive effect of genes. The shovel shape character of the max- factors as measured by genetic correlaillary central and lateral incisors has been tions. studied quite extensively since the 1840s MATERIAL AND METHOD in human populations. However, until recently most of these studies focused their The data analyzed here are from dental attention on establishing this trait as a casts taken from 198 Chilean individuals racial one with a high frequency in Mon- belonging to 114 different families of Puergoloids as against relatively smaller inci- to Dominguez (73 14' W e s t 3 8 52' South) dent es among the Caucasoids (Dahlberg , and 111 individuals belonging to 67 differ'49; Lasker, '50; Pinto-Cisternas and Fi- ent families of the village of Socaire (67" gueroa, '68). The evidence of strong ge- 52' West-23" 32' South). The Puerto Donetic background of this dental feature minguez population consists of individuals has been spelled out only by a few inves- of Mapuche or Spanish origin (Palomino tigators (e.g., Lasker, '50; Turner, '67; and Pereira, '71) whereas the Socaire popPortin and Alvesalo, '74). In all these stud- ulation is considered as descendants of ies the trait has been considered as a the Atacameno Indians (Blanco et al., qualitative one with three or more degrees '73). From this combined sample of 181 of variation in shovel shape. Such quali- families, we could select only 148 unretative treatment of this trait makes the lated individuals (having no common imdifferent investigations difficult to com- mediate ancestors) of which 63 were males pare because of the lack of obtaining rigid and 85 were females. From the familial unified criteria (Dahlberg, '49) and fur- relationships, we could extract only 94 thermore, the degree of variation in the parent-offspring pairs and 127 pairs of extent of shovelling seems to be quite large full-sibs. The decomposition of these pairs in Amerindian populations where the fre- according to sex is shown in table 1. quency of this trait is one of the highest Shovel shape was measured from the found in the literature (Pinto-Cisternas dental casts in terms of shovel shape inand Figueroa, '68; Rothhammer et al., '68; dex as defined in Rothhammer et al. ('68). Rothhammer et al., '71). To determine the To arrive at this, measurements were extent to which genetic factors are respon- taken with a caliper graduated at 0.10 sible for the shovel shape character of mm on the thickness of each superior inmaxillary central incisors, we therefore cisor at the site of maximal depth in the attempt to treat this as a metric charac- palatal face and the lateral ridges at the ter. Thus we examine the role of genetic same level. The shovel shape index was O
AM. J. P H Y S . ANTHROP.,44: 233-236
O
233
234
RAFAEL BLANCO AND RANAJIT CHAKRABORTY
2 !-
z w V
CY
w
a
-
z
> V z w
3 U
w CY
1
LI
-7
0
0.3
0.6
0.9
1.2
1.5
SHOVEL SHAPE INDEX Fig. 1 Frequency distribution of shovel shape index obtained from data on 148 unrelated individuals sampled from two Chilean populations.
then obtained using the difference between the values of the mean lateral thickness and the central one. A comparison of these indices with Dahlberg's classification (referred to in Carbonell, '63) shows that an index recorded as 0.3 or less can be taken as equivalent to no shovelling for the individual concerned. All measurements reported here are on maxillary central incisors only, as earlier experiences (Rothhammer et al., '68) with measurements on lateral incisors yielded statistically significant measuremental error.
RESULTS
Distribution of the trait As mentioned earlier, most studies of shovel shape of maxillary central incisors consider only their frequency distributions in various populations. Among the unrelated individuals of our sample, the distribution is found to be skewed (as shown in fig. 1) with no statistically significant sex dimorphism with respect to the mean values. (The mean indices for males and females are 0.553 f 0.043 and 0.461 &
235
GENETICS OF SHOVEL SHAPED INCISORS
0.059, respectively; t-value is 1.19 with < P < 0.5.) The distribution deviated quite significantly from normality also ( x z s = 24.8, P < 0.0005). The expected frequencies under normality are shown by the dotted line in figure 1. In terms of the proportion of shovelling, 66.89 & 3.87% of the individuals were with shovel shaped maxillary central incisors (with an index above 0.3). This proportion is also homogeneous in two sexes (73.0 f 5.6% in males, and 62.4 k 5.3% in females, ~ 2 = 1 1.86, P > 0.1). It may be noted here that the nonnormality of the distribution of shovel shape index is not due to non-homogeneity of the two samples. This is tested with the means (0.485 k 0.033 for Puerto Dominguez and 0.526 rt 0.043 for the Socaire sample, t-values for testing equality of means is 0.75 with 146 d.f., P > 0.4) and variances (0.101 and 0.102 for Puerto Dominguez and Socaire, respectively, Fvalue for testing equality of variances is 1.01 with 53 and 93 d.f., P > 0.25), which justifies pooling the two samples together . Familial correlation The extent to which genetic factors determine the degree of shovel shapes is studied here by considering the different familial correlations as described in table 1. Since the sample size corresponding to the different familial sets were small, we employed Fisher's bias correction (Rao, '73) for small sample sizes to obtain the pooled familial correlations in the table. The four parent-offspring correlations are seen to be statistically homogeneous (with x 2 3 = 3.78, P > 0.25; after bias correction). The homogeneity is also found among the three full-sib correlations (x** = 1.62, P > 0.25), showing the absence of sex-differ0.2
TABLE I
The familial correlations of the shovel shape index of the maxillary central incisors Number of observations
Correlation coefficient
Mother-son Mother-daughter Father-son Father-daughter Parent-offspring 1 (pooled)
28 31 22 13 94
0.4162 0.165 0.249e0.177 0.141r+_ 0.225 0.694f 0.164 0.339f 0.092
Brother-brother Brother-sister Sister-sister Full-sib 1 (pooled)
20 65 42 127
0.427e0.198 0.397k0.107 0.17820.155 0.329 0.080
Relationship
*
1 Bias correction for small and unequal sample sizes performed according to the principles indicated by Rao ('73).
ence in this trait. The full-sib correlation is not statistically different from the parent-offspring correlation ( x Z 1 = 0.01, P > 0.99), suggesting that there is no dominance deviation in the variation of shovelling indices in this population. The homogeneity of all these correlations, therefore, indicate that the hereditary factors are additive in nature. The heritability coefficient, h2 = 2rop, as estimated from parent-offspring correlation, is 0.678 f 0.186, indicating that about 68% of the variation of shovel shape index can be explained by the additive effect of genes. DISCUSSION
Although the different familial correlations as presented in table 1 are seen to be homogeneous with respect to classifications according to sex, some of them are quite small relative to their standard errors (e.g., father-son correlation is only 0.141 and sister-sister correlation only 0.178). We ascribe such fluctuations only to the small size of the samples. However,
TABLE 2
Test of hypotheses on the inheritance of shovel shaped incisors in man Variancecomponents f S.E.
Hypo thesis
d.f.
X2
(1) No heritability h =O, k = 1:c
1
0.01
common environment (cz) remainder (1- cz)
= 0.333 0.062 = 0.667f 0.062
1
0.01
heritability (h*) remainder (1- h2)
= 0.666f 0.124
(2) Nocommon environment c = 0 , 2 = 1:h
*
=0.334f0.124
236
RAFAEL BLANCO AND RANAJIT CHAKRABORTY
the pooled correlations are significant suggesting the hereditary nature of the trait. The 0.3 index level for non-shovelling as indicated in this paper yields a shovelling rate of approximately 6 7 % , as mentioned previously. This percentage is in accordance with some other studies (e.g., Campusano et al., ’72). Of course, studies on several other populations reveal lower rates of shovelling (e.g., Pinto-Cisternas and Figueroa, ’68) in admixed samples where admixture rates are presumably higher than that in the present sample. Furthermore as a preliminary test of the hypothesis concerning the role of additive effect of genes in explaining the variation in shovelling indices in the sample, we may express the expected familial correlations (parent-offspring, OPT and sib-sib, SST) as
+
and
OPT = hz 212 c*k SST = h212 c2
+
where, h2 = heritability coefficient, c2 = proportion of variance due to common environment and z , k = scaling parameters measuring inter-generational differences in h2 and c2 (following Rao et al., ’74; see figs. 5 , 14 of their paper). Writing the likelihood function in terms of Fisher’s z-transformation of the sample correlations we obtain the results shown in table 2. Interestingly enough, while heritability alone can explain the transmission of shovel shape (hypothesis 2), so can common environment alone (hypothesis 1). Under hypothesis 1 it is implicit that common environment has the same effect on parents and children which seems unlikely for a trait like this. Hence, one may favor hypothesis 2 although a final clarification must await a more detailed segregation analysis with complete pedigree data. In view of this, the heritability estimate (68%), as obtained in the earlier section, is only a tentative one since simultaneous estimation of c and h2 is not possible from the two correlations under the assumption k = z = 1 . ACKNOWLEDGMENTS
cooperation and help during the collection of the samples, and Dr. D. C . Rao whose suggestions improved the analysis reported in the paper. This work is supported in part by a U.S. Public Health Service In tern ational Postdoctoral Research Fellowship (No. 1FO 5TW-02007-02 of which R.B. is a recipient) and U.S. National Institutes of Health Grant GM 19513 made available to R.C. LITERATURE CITED Blanco, R., F. Rothhammer, G. Olarte, H. Palomino and M. Justiniano 1973 Analisis genetico cuantitativo de cinco rasgos morfologicos dentarios. Rev. Med. Chile, 101 ; 223-226. Campusano, C., H. Figueroa, B. Lago, J. PintoCisternas and C. Salinas 1972 Some dental traits of Diaquitas Indian skulls. Am. J. Phys. Anthrop., 36; 139-142. Carbonell, V. M. 1963 Variations in the frequency of shovel shaped incisors in different populations. In: Dental Anthropology. D. R. Brothwell, ed. Pergamon Press, New York, pp. 2 11-234. Dahlberg, A. A. 1949 The dentition of the American Indian. In: The Physical Anthropology of the American Indian. The Viking Fund, Inc., New York, pp. 138-176. Lasker, G. W. 1950 Genetic analysis of racial traits of the teeth. Cold Spring Harbor Symposiaon Quantitative Biology, 1 5 ; 191-203. Palomino, H.,and G. Pereira 1971 Oral genetics among “Mapuches.” I. A study of ethnical differences in a small community. Rev. Med. Chile, 99;132-138. Pinto-Cisternas, J., and H. Figueroa 1968 Genetic structure of a population of Valparaiso. 11. Distribution of two dental traits with anthropological importance. Am. J. Phys. Anthrop., 29;339-348. Portin, P., and L. Alvesalo 1974 The inheritance of shovel-shape in maxillary centralincisors. Am. J. Phys. Anthrop., 41 ; 59-62. Rao, C. R. 1973 Linear Statistical Inference and its Applications. John Wiley, New York, pp. 435436. Rao, D. C., N. E. Morton and S. Yee 1974 Analysis of family resemblance. 11. A linear model for familial correlation. Am. J. Hum. Genet., 26; 331359. Rothhammer, F., M. Benado and G. Pereira 1971 Variability of two dental traits in Chilean Indian and mixed populations. Hum. Biol., 43: 310317. Rothhammer, F., D. Lasserre, R. Blanco, E. Covarrubias and M. Dixon 1968 Microevolution in human Chilean populations. IV. Shovel shape, mesial-palatal version and other dental traits in Peuenche Indians. 2. Morph. Anthrop., 60; 162-1_.. 69. Turner, C. G. 1967 Dental genetics and microevolution in prehistoric and living Koniag Eskimo. J. Dent. Res.,46: 911-917. ~~~
The authors are indebted to Drs. F. Rothhammer and H. Palomino for their ~
