Contributions to Variance in Phalangeal Growth: Estimates from Twins RONALD K. WETHERINGTON AND GARY W. RUTENBERG Department ofAnthropology, Southern Methodist Uniuersity, Dallas, Texas, 75275 KEY WORDS Twins. Bone growth . Hand-wrist . Genetics ABSTRACT Lengths of the second metacarpal and fourth middle phalanx of a sample of 99 sets of radiographs of twins (45 MZ sets and 54 like-sex DZ sets) are subjected to variance analysis. The purpose is to examine incremental growth status between the appearance of these bones and the fusion of their epiphyses. Grouped data show higher F-ratios and H scores for males in MC2 length and for females in MP4 length. When the data are sub-divided by age (10 and under, older than 101,the later ages show uniformly higher F and H scores than the younger, and males higher than females for all measurements. I t is suggested that the influence of the environment is relatively less in later ages, and that Xchromosomal influence plays a part in determining tubular bone growth in the hand-wrist. Variation in osseous development in the hand and wrist has been the subject of several studies to assess the relative genetic and environmental influences on growth. Both the timing (Garn e t al., '61b; Garn e t al., '63) and sequence (Hertzog, et al., '69) of hand-wrist centers have revealed evidence of genetic control, as have both the timing and sequences of epiphyseal union in the metacarpals and phalanges (Garn e t al., '61a). The process and rate of incremental growth intervening between the appearance of osseous centers and their epiphyseal fusion have not been adequately studied with respect to genetic control. In light of the absence of demonstrable correlation between the earlier and later episodes of hand growth, such an investigation is important. The most valid means of estimating the contributions to bone growth of genotype and environment, relative to one another, is the comparison of monozygous and like-sex dizygous twins. While for discrete variables concordance studies are appropriate, for continuous variables such as incremental growth other methods must be applied. Since variation in incremental growth is the result of both genotype and environment (and their interaction), applicable methods of analysis seek to partition t h a t portion of total variance AM. J. PHYS. ANTHROP. (1978)48: 83-88. due to environmental variance and that due to genetic variance. Commonly used analysis of variance (anova) tests are the F-ratio and Holtzinger's heritability index (h2)with various modifications (Holzinger, '29; Cavalli-Sforza and Bodmer, '711. While anova in general and heritability in particular have been criticized for having been both misapplied and misinterpreted (Feldman and Lewontin, '75; Layzer, '74; Sanday, '72), their proper application can provide valid estimates of the relative genotypic-environmental contributions to observed phenotypic variation. METHODS AND MATERIAL In a n effort to clarify these proportionate contributions to growth variance in the hand, we applied anova to metacarpal and phalangeal dimensions in a twin sample. The subjects were drawn from the longitudinal Nebraska Child Growth Study conducted from 1958 through 1964. The collection of handwrist radiographs represents 469 children (226 males, 243 females) with a total agerange of 2 to 19 years. Included in the study are 102 sets of like-sex twins, all Caucasian and all raised by their natural families. General medical histories on each child, listing episodic illness, were collected during the 83 84 RONALD K. WETHERINGTON AND GARY W. RUTENBERG study. We thus have an opportunity to examine growth processes in children with apparently adequate nutritional backgrounds and in general good health. The study is based on 99 pairs of like-sex twins who participated in the 12-month recall examination for periods ranging from one to seven years: 47 pairs of male and 52 pairs of female twins. Among the males, 27 pairs were classified as dissimilar and 20 pairs as similar; and among the females, 27 pairs as dissimilar and 25 as similar. Thus, of the total of 99 pairs, 54 (108 individuals) may be classified as dizygous and 45 (90 individuals) as monozygous, both terms being approximate. Zygosity was estimated by parent-child and within-pair comparisons which included blood grouping (ABO, Fy, K, Le), surface morphology of the mandibular first molar, cephalometry, several postcranial anthropometrics, and overall morphological similarities. The distributions of zygosity by sex does not depart from random expectation (x' = 0.303, p > 0.005). While recognizing the possibilities of misclassification, the categories MZ and DZ will be used here. Measurements on radiographs used for the present study include lengths of the second metacarpal (MC 2) and the middle fourth phalanx (MP 4). Measurements were taken a t mid-line of the diaphysis and included the epiphysis and intervening cartilage plate. All measurements were made with a Helios x-ray caliper and recorded to the nearest 0.1 mm. The choice of MC 2 and MP 4 was based on the high communalities these display in incremental growth (Roche and Hermann, '70a,b) and the utility of these bones in helping to assess other growth components (cortical thickness and density in MC 2, brachymesophalangia in MP 5-MP 4 comparisons). For each twin-pair, measurements were recorded for each radiograph in the longitudinal study, amounting to 243 pairs of radiographs. For the current study, only the first films of each twin-pair were used, totalling 99 pairs of radiographs. Longitudinal aspects of the collection are being treated elsewhere (Wetherington and Rutenberg, in preparation). FINDINGS Two procedures were used for initial data reduction: First, the initial radiographs of each twin-pair were selected and grouped according to sex and zygosity. Intra-pair means, variances and correlations were calculated for each group. From these results, Fratios' and heritability indices' were obtained. The heritability scores, with their standard errors, were calculated separately using variance and mean r . Results are indicated in table 1. In this paper H refers to the heritability calculation from variance in bone lengths, and H' refers to the calculation from correlation coefficients. Secondly, to evaluate the effects of age on the intra-pair variances, and particularly to separate pre-pubertal from pubertal effects, the data were separated by age-groups and again classified according to sex and zygosity. The same statistics were applied t o these data (table 2). Small cohort sizes prevented us from using 5-year intervals for the age-grouping. We therefore chose two cohorts, ages 2-10 representing the pre-pubertal portion of growth in the hand, and ages 11-19 representing that portion influenced by pubertal changes. In the grouped data, for both MC 3 and MP 4 lengths, within-pair variances are lower for MZ than for DZ twins, as expected under the genetic hypothesis. Likewise, the intra-pair correlations (r) are higher for MZ than for DZ twins. For MZ pairs, correlations for males and females are not significantly different, and are equivalent for both MC 2 and MP 4 lengths. However, for DZ intra-pair correlations females rank slightly higher than males for MC 2 lengths (r = 0.97 and 0.93, respectively), while males rank higher than females for MP 4 lengths (r = 0.94 and 0.86, respectively). All intra-pair correlations for the grouped age data are significant (p < 0.001). When the sample is divided by age into the pre-pubertal and pubertal/post-pubertal groups, influences of age on the growth process become apparent, despite the possibly misleading results due to some of the low numbers of pairs. Intra-pair variances among MZ males are higher in the earlier age category for both MC 2 and MP 4 lengths, and among DZ males are lower in the earlier age category 1 V,V2 = F.05 (vl,vs),where V, is intra-pair DZ variance and V1 is intra-pair MZ variance. VMZ . variance for each twin-group was calculated by = vDz ' the formula V = iZdiz, where di is the difference between twin A and twin B of a p%r.This is the unbiased variance estimator when the population mean difference is known to be equal to zero. The variance of H, or its standard error, was calculated after the method in Cavalli-Sforza and Bodmer ('71). c1 -'MP). 'MZ2 is the squared product-moment correHo= (1 - r ~ z z )' lation coefficient for munozygous twins. and WZzis the same fur dizygous twins. 85 PHALANGEAL GROWTH IN TWINS TABLE 1 Variance comparisons for twin sample: grouped data Twin type MZ males DZmales MZ females DZfemales MZ males DZmales MZ females DZfemales ?j Pairs Bone 20 27 25 27 MC2 MC2 20 27 M MP P4 4 25 MP4 MP4 27 MC2 MC2 Intra-pair variance r 0.0146 0.1764 0.0169 0.0671 0.988 o.9323 0.986 o,9683 0.0058 0.0243 0.0035 0.0524 o.8633 0.984 :::::: H1 Standard error H' 2 0.92 20.002 0.82 12.0823 0.75 20.013 0.56 3.9703 0.76 20.013 0.45 0.93 +0.001 0.875 14.971 F F 4.1903 TABLE 2 Variance comparisons for twin sample by age categories Twin pair N pairs Bone 17 15 18 14 17 15 18 14 MC2 MC2 MC2 MC2 Intra-pair variance r A Standard error H' 0.86 rtO.009 0.93 7.462 0.58 t0.340 0.65 1.245 0.755 t0.112 0.70 2.086 0.97 ?0.001 0.94 20.324' 20.002 1.000 22.326 20.017 0.931 7.043 Ages 2-10 MZ males DZ males MZ females DZ females MZ males DZ males MZ females DZ females MP4 MP4 MP4 MP4 0.0151 0.1129 0.0146 0.0182 0.0066 0.0137 0.0037 0.0756 O"" ' 0.689' :::;:: :::::' Ages 11-19 DZfemales MZ males DZ males MZ females DZ females 13 3 12 7 13 MC2 MP4 MP4 MP4 MP4 0.1232 0.0016 0.0357 0.0027 0.0190 08002 u.8" 1.000 o,712 0.97 :::!;: 0.87 ' po.01. 2 p 0.001 for both bones. However, intra-pair variances for both MZ and DZ females are lower in the earlier age category for MC 2 length and in the later age category for M P 4 length. For the intra-pair correlations, DZ females show a higher values for MC 2 in the earlier age category and are higher for M P 4 in the later age category. The correlation for M P 4 length in the earlier ages for females (r = 0.04) is the lowest of all values obtained and the only one showing no significance. The DZ males show the opposite age-relationship, with higher correlation for MC 2 in the later ages and for MP 4 in the earlier ages. These differences are reflected, obviously, in the F-ratios and H indices, and thus aid in their interpretation. The F-ratios for the grouped data are all significant (p < 0.001), but are higher among males for MC 2 lengths and higher among females for M P 4 lengths. The same is true for the heritability scores, with both MC 2 lengths for males and MP 4 lengths for females higher than the H scores for MC2 lengths in females (H = 0.75) and MP 4 lengths in males (H = 0.76).Heritability indices based on the intra-pair correlations are lower overall, but reflect the same relative values. 86 RONALD K. WETHERINGTON AND GARY W. RUTENBERG When the data are age-grouped, the F-ratio is higher for later than for earlier ages in both sexes for MC 2 lengths and higher in males for M P 4 lengths. I t is higher in females, however, in the earlier ages for M P 4 lengths. The H scores show the same age-related changes: increasing heritability values with increasing age for males and females, and for both MC 2 and MP 4 lengths, except for M P 4 length in females. When H' is computed on the squared intra-pair correlations, the scores for earlier and later ages for MP 4 lengths in females are essentially the same. DISCUSSION Interpretation of the anova calculations in this study depends upon the validity of assumptions made regarding both zygosity and the heritability of continuous traits. The assumption that the MZ and DZ classifications are accurate is supported, but nevertheless not fully verified, by both the blood-group data and the uniformly lower within-pair variances for the group classified as monozygous. The assumptions underlying heritability and the definition of the genetic portion of phenotypic variance have been subject to a great deal of discussion. These include the assumptions: (1) that there is a uniform distribution of the underlying genotypes across environments; that is, the correlation of environment with genotype is no different from the MZ group than for the DZ group, and (2) that the genotype-environment interactions are of equivalent phenotypic significance for both MZ and DZ twins. There is evidence (Osborne and DeGeorge, '59) that the first assumption is not validthat a t least some environmental components are more similar for MZ pairs than for DZ pairs. To the extent that such components include those affecting growth, genotypic contribution to variance will be overestimated by present methods. While we believe that these twin study limitations are more relevant to psychological than to anthropometric measurements there is a need for more thorough documentation of the evidence. If we assume that the within-pair variance in the MZ group is environmental (because of identical genotypes), the DZ portion not explained by the MZ variance is presumed to reflect the genetic contribution to that (DZ) variance. The H index reflects the difference in the contribution of genotype to phenotypic variance relative to the contribution of environment to phenotypic variance: the score will increase as either environmental or genotypic variances among dizygous twins increase. The F-ratio establishes statistical probability and reliability for this variance comparison. The value of using the H statistic here, then, lies in providing a numerical percentage indicating the ratio of the environmental-genetic contribution to observed phenotypic variation. Such values apply only to the population sample in the present study. The H values are apparently not stable through time. With the exception of M P 4 lengths among females, the values are higher for the older age group than for the pre-pubertal group, suggesting a decreasing environmental influence on variability through time for these phenotypes, contrary to previous conclusions (Vandenberg, '62). Since the two age-groups consist of different twin-pairs, the possibility of relative differences in genotypes influencing the observed values cannot be ruled out, but is unlikely in view of the consistency of the value differences. The incorporation of the longitudinal films should clarify this possibility, and preliminary data support the hypothesis of reduced relative environmental contribution with increasing age. Also significant is the fact that the H values for males in the later age-group are significantly higher than for females, and with the exception of MP 4 lengths, also higher in the earlier age-group. The degree to which postfusion growth status affects these age differences is not easily interpreted from these data due to small sample sizes. Osborne and DeGeorge ('59) included only post-adolescents for their study, and for both hand length and middle finger length show higher F ratios for males. Their computed H scores for middle finger length (males = 0.87, females = 0.74) are similar to our results. This supports a growing body of evidence for X-Chromosomal influence on osseous development (Garn and McCreery, '70; Garn et al., '63; Garn e t al., '69). Since female DZ twins share identical paternal X chromosomes, each X-linked genotype for a twin-pair has one allele in common, reducing the genotypic variance of DZ females relative to DZ males. If any such genotypes contribute to epistatic influence on bone growth, inter-group phenotypic differences (MZ-DZ)for females will be less than that for males. This will result in lower PHALANGEAL GROWTH IN TWINS F-ratios and H scores in the intra-pair comparisons, as in the study. The fact that this is not indicated in the earlier age-group for MP 4 length may further indicate relatively higher environmental influence prior to puberty. Pending further and broader analysis, then, two conclusions may tentatively be drawn for the present population sample: (1) The relative contributions of genotype and environment to variance in MC 2 and MP 4 lengths change through time, reflecting decreased environmental influence on final phenotype; (2) There is in general a greater inter-group difference between MZ and DZ males than between MZ and DZ females. A possible explanation for this is that for MC 2 and MP 4 lengths, interim incremental growth between appearance and fusion is partially under the influence of x-linked loci. In a continuing study, longitudinal films for available twin-pairs are being age-standardized and analyzed for heritability in rates of change. ACKNOWLEDGMENTS We wish to thank Doctor Harold J. Hietala, Department of Anthropology and Statistics, Southern Methodist University, for his helpful suggestions in the statistical applications, and Doctor Edward I. Fry for making available the data from the Nebraska study. LITERATURE CITED Cavalli-Sforza, L. L., and W. F. Bodmer 1971 The Genetics of Human Populations. W. H. Freeman, San Francisco. 87 Feldman, M. W., and R. C. Lewontin 1975 The heritability hangup. Science, 190: 1163-1168. Garn, S. M., and L. D. McCreery 1970 Variability of postnatal ossification timing and evidence for a “dosage” effect. Am. J. Phys. Anthrop., 32: 139-144. Garn, S. M., C. G. Rohmann and B. Apfelbaum 1961a Complete epiphyseal union of the hand. Am. J. Phys. Anthrop., 19: 365-372. Garn, S. M., C. G. Rohmann, and M. Robinow 1961b Increments in hand-wrist ossification. Am. J. Phys. Anthrop., 19: 45-54. Garn, S. M., C. G. Rohmann, and A. A. Davis 1963 Genetics of hand-wrist ossification. Am. J. Phys. Anthrop.,21: 3340. Garn, S. M., C. G. Rohmann and K. P. Hertzog 1969 Apparent influence of the X chromosome on timing of 73 ossification centers. Am. J . Phys. Anthrop., 30: 123-128. Hertzog, K. P., F. Falkner and S. M. Garn 1969 The genetic determination of ossification sequence polymorphism. Am. J. Phys. Anthrop., 30: 141-144. Holzinger, K. 1929 The relative effect of nature and nurture in influences on twin differences. J. Educ. Psychol., 20: 241-248. Layzer, David 1974 Heritability analyses of IQ scores: science or numerology? Science, 183: 1259-1266. O s brne , R. H., and F. V. DeGeorge 1959 Genetic Basis of Morphological Variation; an evaluation and application of the twin study method. Harvard University Press, Cambridge. Roche, A. F., and R. F. Hermann 1970a Association between the rates of elongation of the short bones of the hand. Am. J. Phys. Anthrop., 32: 83-88. 1970b Rates of change in width and length-width ratio of the diaphyses of the hand. Am. J. Phys. Anthrop., 32: 89-96. Sanday, P. R. 1972 On the causes of IQ differences between groups and implications for social policy. Human Org., 31: 411-424. Vandenberg, S. G. 1962 How “stable” are heritability estimates? 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