An examination of the meaning of cranial discrete traits for human skeletal biological studies.код для вставкиСкачать
An Examination of the Meaning of Cranial Discrete Traits for Human Skeletal Biological Studies ROBERT S. CORRUCCINI Division of Physical Anthropology,Smithsoninn Institution, Wtrshington, District of Columbia 20560 KEY WORDS Discrete traits . Nonmetric . Metric . Cranial morphology . Statistical analysis . White . Negro. ABSTRACT Discrete traits are of increasing interest in comparative skeletal biological research. Characteristics justifying their use have been investigated primarily in mice, however. Using 72 discrete variants, 321 human skulls from the Terry Collection of known race, sex and age have been studied. Significant sex and age differences were detected. Inter-trait correlation was found to be at a low but significant overall level. Multivariate comparison with conventional craniometric analysis was undertaken on subdivisions of the sample, and distances based on metric and nonmetric data were concordant. It is concluded, on the basis of these findings and the discontinuous variant frequency distributions, that discrete traits in isolation are not of paramount value to skeletal genetic studies, but may be vital in comparison and conjunction with other types of data in analyzing the population genetics of extinct groups. Skeletal biological studies based upon analysis of cranial discrete traits are increasing in frequency and importance (Laughlin and Jorgensen, '56; Brothwell, '59; Berry and Berry, '67, '72a,b; Anderson, '69; DeVilliers, '68; Ossenberg, '69b, 70, '71; Kellock and Parsons, '70a,b; Pietrusewsky, '71; Gaherty, '71). This topic is now a frequent basis for dissertation research (Swedlund, '69; Jantz, '70; Finnegan, '72; Ossenberg, '69a; Cybulski, '72; Wade, '70). Discrete traits were of occasional interest to earlier physical anthropologists, who treated them in a purely descriptive manner. Important early studies employing minor variants to describe populations include Le Double ('03, '06, '12), Frassetto ('04), Outes ('1 l), Akabori ('33), Sullivan ('22), Russell ('00), WoodJones ('3la,b,c, '34), and Hooton ('30). The recent revival in interest largely owes to the use of discontinuous variants by geneticists working with wild and experimental animals, primarily mice (Gruneberg, '52, '55, '63; Berry, '63, '64, '67, '68; Berry and Searle, '63; Dempster and Lerner, '50; Rees, '69). The justification for discrete trait analysis lies in several assumptions in which AM. J. PHYS. ANTHROP., 40: 4 2 5 4 4 6 they are thought to contrast with metric traits. It is claimed that discrete traits are highly genetic in nature, vary in frequency even between closely related populations, exhibit constancy under environmental variability, do not vary with age, show no sex differences, show virtually no correlation with one another, and are easily defined and standardized. Therefore archeological populations may be aggregated for analysis, maximizing sample sizes, and quick tabulation and analysis of these traits is possible. In the present author's opinion, most of these expectations exceed their experimental justification in humans. The assumptions have rarely been adequately tested, yet are taken for granted by some workers in constructing research designs. Previous investigations into these assumptions employed either laboratory rodents or archeological populations, the latter involving problems of imperfect preservation, uncertain sex and age determination, and unknown genetic relations. It is unfortunate that advocates of discrete trait analysis have not used more appropriate test samples in vanguard studies of variant distributions. Berry and Berry ('67), 425 426 ROBERT S . CORRUCCINI mated from both cadaver and skeleton. Adult skulls only were examined. To avoid biasing results by using too many of the very old specimens which dominate the collection, an upper age limit of 65 was applied. Age distribution of the selected sample is indicated in table 1. It is inferred from this sample's "skid row" source that its socioeconomic level was quite low, with health and nutrition MATERIALS lower among Blacks than Whites. The The Terry skeletal collection is ideal most prevalent cause of death among both for a study of this sort. Collected by R. groups was pulmonary tuberculosis, with Terry in St. Louis, primarily in the years alcoholism a probablecontributing factor. 1910-1940, it is now housed in the Divi- These metabolic abnqrhalities affect the sion of Physical Anthropology of the Smith- microstructure of bone (Ortner, '70). The sonian Institution. Morgue cadavers were majority of skeletons are pathological in used in Washington University dissection this and other ways. Grossly pathological classes, then macerated and added to the crania were not studied. While this sample is not typical of most collection along with records documenting race, sex, age, cause of death, and mea- archeological populations, it is important surements. The collection is predominantly as a source of discontinuous variant disAmerican Caucasians and Negroes. I ex- tributions for two reasons: these are poorly cluded the few crania of Chinese and other known for Caucasians and American Neraces. Bodies were identified by sociolog- groes, and nearly absolute control can be ical, not genetic, criteria. The Whites thus exercised over preservation and over sex probably constitute a homogeneous group, and age variation. Some 72 discrete variwhile the Blacks include everything from ants were scored for every skull. I atgenetically African individuals to those tempted to include all important traits genetically Caucasian but with dark skin used in previous analyses as well as sevor other traces of Negro background. The eral innovations that appeared promising. Black sample is presumably affected by The traits are listed in tables 2 and 3. Problems rise in defining the presence approximately 15% genetic admixture with Whites (Johnston, '66; Glass and Li, and absence of traits. Although two '53; Workman, Blumberg and Cooper, '63; discontinuous states theoretically arise Roberts, '55; Howells, '70a; Adams and through threshold developmental mechanisms, many workers admit occasional Ward, '73; Reed, '69). Sex of specimens is known with 100% confusion in defining traits or drawing accuracy. Only specimens with accurate the dividing line between present and abages included in their morgue record were sent (Wood-Jones, '31a; Jantz, '70; Berry examined. Most of these ages are exact and Berry, '67; Anderson, '68a; Fenner, determinations, and the rest were esti- '39; Drennan, '30; Akabori, '39b; Thoma, for instance, rely on Egyptian and other samples of estimated age and sex and disputed relationship. The present study attempts a more rigorous and controlled investigation of assumptions underlying discrete trait analysis of human skeletal populations, using a modern, well-documented cadaver sample. TABLE 1 Age distribution of the Terry cranial sample Numbers of Age B e l o w 20 20-29 30-39 4049 50-59 Over 60 White males White females Black males Black females Total 1 7 20 26 16 7 1 3 11 20 14 13 4 23 29 24 12 7 4 20 26 20 9 4 10 53 86 90 51 31 77 62 99 83 32 1 DISCRETE TRAITS OF HUMAN SKULL ’37; Godlee, ’09; Riesenfeld, ’56; Pittard and Seylan, ’36; Kalenscher, 1893; Oetteking, ’30; Marshall, ’55; Broman, ’57; Kollmann, ’05; Misch, ’05). These difficulties are most acute for fossae, tori and tubercles, which are continuous in development. Obviously some traits are multistate rather than binary in nature. It is notable that dental traits, for which evidence of heritability is much more conclusive than for minor osteological variants, are scored with one or more intermediate states. Examples are the pit connecting presence and absence of Carabelli’s cusp, and the 3 cuspule linking 3- and 4-cusped upper molars. While dichotomous classification of traits may simplify their collection, hazards may be inherent in this simplification. Anderson (‘68b) shows that tubercles may be poorly developed in one population though present-absent variation exists. It seems these populations might for different observers have a different “threshold” location. Furthermore, the same observer might change his threshold value when confronted with another sample with greater average tubercle development and hence a different midpoint of variation. Thus for some traits the threshold may be in the eyes of the anthropologist rather than in the genetic or developmental makeup of the skeleton population. Realizing these problems, and faced with a fragmentary collection, Stewart (‘63) classified several variants as absent, slightly expressed, medium, and large, and determined the weighted percentage presence of traits. Buikstra (‘72) has also considered the problem of partial trait manifestation, stating “it is suggested that partial and complete manifestations of hyperostotic traits are products of the same or similar genotypes and should be combined when non-metrics are scored as dichotomous data.” Buikstra contends the ageregression of hyperostotic traits can be corrected in this manner. However, large numbers of these partial manifestations persist in adult crania, so they are not merely an adolescent developmental step. In studying Terry crania I scored nonmetric variants in two ways. The first was the dichotomous scoring technique outlined by Berry and Berry (’67). In addition, an ordinal mode of scoring was under- + 42 7 taken. Traits were ranked in terms of grade of development, i.e., “absent,” “trace,” “intermediate” and “present” as well as double presence in some cases, such as double bridges over a mylohyoid groove. The average of both observations was recorded for bilaterally occurring variants, rather than two readings of the trait. This further quantifies minor traits, since even truly binary traits assume three possible grades: double present, single present, and double absent. Admittedly, the same problems obtain in distinguishing between, say, “trace” and “intermediate” in the ordinal model as between present and absent in the binary model. However, the former system attempts more detailed description of variability, and scoring was standardized using an initial reference series of 20 crania. The 61 nonmetric traits showing sufficient variability to be included in analysis are listed in table 2. The additional traits are described in table 3. The definition and presence-absence criteria for these traits * follows Berry and Berry (‘67), Brothwell (‘59, ’63), Anderson (‘62, ’63, ’68b), Jantz (‘70), Wood-Jones (’31a), Kellock and Parsons (’70a), Ossenberg (’69b, ’70), Grant (‘62), Grant and Basmajian (‘65), Johnson and Whillis (‘42), Buschan (1898), Akabori (’39a), and Bass (’64). I excluded internal vault traits such as clinoid and sphenoid bridging and others (Jaenicke, 1877; Locchi, ’27; Murphy, ’55) because they are difficult and timeconsuming to observe. Bi- and tri-partite parietals have been of interest (Schwalbe, ’03; Matiegka, ’05; Hrdlicka, ’03; Aichel, ’15) but are too rare to be useful. Other significant traits (Le Double, ’06; Romiti, 1881, 1898; Loewenstein, 1895; Bolk, ’21, ’22; Jeschke, 1894; Taxman, ’63; Collins, ’27; Kollmann, ’05; Misch, ’05) were encountered too late but deserve future study. Naso-frontal and transverse palatine sutural variations were not used since their significance is in doubt (Oetteking, ’20; Stieda, 1894; Woo, ’49b). Similarly, a large class of traits referred to as “anthroposcopic” was eliminated since these are not even superficially discrete (e.g., parietal bossing, brow ridge prominence). The highest nuchal line is a trait that belongs 1 Description and scoring details on a trait-by-trait basis will be provided by the author on request 428 ROBERT S. CORRUCCINI with this group, though it has been used by discontinuous variant students. Merkel (1871) showed how this feature, though possessing muscular reality, is greatly variable and depends on the form of the superior nuchal line. Additionally, 23 standard craniometric characters were recorded for every skull for comparative purposes. These are fairly representative, traditional measurements, taken mostly from Bass (‘71). METHODS Various aspects of these data are investigated, including (a) descriptive statistics, (b) sex differences, (c) age dependence, (d) intercorrelations, and (e) the correspondence between nonmetric and metric analyses of the same populations. Emphasis is placed upon examination of the assumptions underlying nonmetrical trait usage listed in the introduction. Basic descriptive statistics First the univariate statistics for 61 discrete traits are presented. These include number and frequency of traits within each of the four subdivisions of the sample: White male, White female, Black male and Black female. In formalizing discrete trait analytical procedures for physical anthropologists, Berry and Berry (’67) contributed a framework for data reduction and population comparison, based on work by Grewal and Smith. The procedure involves angular transformation of frequencies into “Theta” coefficients : 8 = arcsin (1 - 2 0 where f is the frequency. There are a number of equivalent logistic transforms (Claringbold, Biggers and Emmons, ’53; Naylor, ’64; Cox, ’70). The variance of Theta is simply l/n. Data reduction, comparison and significance estimation are simplified using this approach, but it is only safely applied when frequencies do not range below f = 0.05. The standard method of data reduction is described in detail by Berry and Berry (‘67), Rees (‘69), and Kellock and Parsons (‘70a), and involves accumulation of average squared Theta difference between samples, adjusted by sampling variance, to yield a measure of overall divergence. Sanghvi, Kirk and Balakrishnan (‘71), Edwards and Cavalli-Sforza (’64), Edwards (‘71), Steinberg, Bleibtreu, Kurczynski, Martin and Kurczynski (‘67), Kurczynski (‘70), Balakrishnan and Sanghvi (‘68), Afifi and Elashoff (’69), Martin and Bradley (‘72) and Goodman (’72) offer other models for multivariate discrete distances, some of which can incorporate multi-state data. The better-known Theta-square distance is used in the present study. The standard deviation of the distance can be derived to test the significance of divergence, assuming independent traits. Sex differences Lack of sex difference in nonmetric frequencies is one of the claims underlying their use. Berry and Berry (’67) attempted to test this hypothesis in humans. They lumped all samples under study into grand male and female samples and tested the Theta-squared sex distance. Since the result was not significant, Berry and Berry concluded that sex differences were absent. Several subsequent studies cite this test as adequate demonstration of the nonnecessity of testing sex difference in other racial samples, but the Berrys’ procedure is questionable. The purpose of testing sex variation is to determine whether males and females may be lumped into a reasonably homogeneous sample without distorting comparisons through combining different frequencies. The Berrys did not recognize the converse of this principle in aggregating racial samples of varying fiequencies into two heterogeneous sex series. Sex variation over different samples could be cancelled out by summing them. Simpson (’51) and Lindley (’64; cf. Cox, ’70: 109) explain this point in detail. If different sexes must be separated to test population differences, it is obligatory to separate different populations to test sex differences. Several analyses contradict Berry and Berry in finding significant inter-sex variation (Jantz, ’70; Finnegan, ’72; Sublette, ’66; Humphreys, ’71). Jantz (‘70) excluded dimorphic variants and coalesced sexes for the remaining variants. This strategy is undesirable since the most dimorphic traits tend also to be the most valuable for discriminating populations (Finnegan, ’72). Finnegan’s solution was to keep num- 429 DISCRETE TRAITS OF HUMAN SKULL TABLE 2 Busic descriptive statistics of craniul discrete traits in four samples. Asterisk bilateral variant with actual sample size of 2 N ~ Caucasian Trait Males N=77 No. (freq.) Mandibular torus Genial tubercles Accessory mental f.'% Mylohyoid bridge :; Access. mylohyoid f. '% Gonial eversion Palatine torus Palatine bridging * Maxillary torus Mult. lesser pal. ff." Acc. infraorbital f.+ Sutural infraorb. f.'* Nasal sill sharp Ant. ethmoid f. exsut.'* Posterior ethmoid f. :> Orbital osteoporosis Trochlear spur %' Trochlear f." Supraorbital f. * Frontal f." Metopism Frontal grooves ::' Pterion X or K ?' Zygo-facial f. * Zygo-maxillary tub. :* 0 s japonicum trace '> Epipteric bone Parietal notch bone :; Ossicle at lambda Sup. lambdoid ossicle Inf. lambdoid ossicle %' Asterion ossicle >: Sub-asterionic as." Parietal f.': Inion salience Huschke f.::' Marginal meatal f.'> Mastoid f.:% Exsutural mast. f.'! 1 Mastoid grooves ':' Mastoid notch Postcondylar c a n a l %: Intermed. cond. canal :: Hypoglossal bridge >: Bifaceted condyles i:i Precondylar tubercle " Postcondylar tub. Jugular f. bridge :* Pharyngeal fossa Lat. pterygoid perf." Pterygoid f. $' Pterygoid spurs * f. Civinnini :' Pterygo-basal bridge >: f. Vesalium :> Spino-basal bridge '* Complete f. ovale ': f. ovale spine " Ovale-spinosum cont. * Open f. spinosum " Accessory f. spinosum ::i " 1 5(0.065) 66(0.857) 23(0.149) 16(0.104) 56(0.364) 9(0.117) 1l(0.143) 14(0.091) 4(0.052) 125(0.812) 14(0.091) 22(0.143) 60(0.779) 75(0.487) 131(0.851) 6(0.078) 25(0.162) 43(0.279) 27(0.175) 25(0.162) 5(0.065) 37(0.240) 0(0.000) 130(0.844) 44(0.286) 4(0.026) 18(0.117) 17(0.110) 7(0.091) 18(0.117) 41 (0.266) 18(0.117) 4(0.026) 78(O.50 7) 24(0.312) 34(0.221) 89(0.578) 131(0.851) 82(0.626) 125(0.812) 37(0.240) 81(0.526) 4910.31 8) 27(0.175) 35(0.227) 21(0.136) 12(0.156) 26(0.169) 1l(0.143) 20(0.130) 118(0.766) 52(0.338) 4(0.026) 2(0.013) 54(0.351) 12(0.078) 145(0.942) 20(0.130) 76(0.494) 70(0.455) 22(0.143) n = 131, 94, 182, 128 for the four samples. ~~ indicates ~~~ Negro Females N=62 No. (freq.) 5(0.081) 43(0.694) g(0.073) 15(0.121) 25(0.202) 2(0.032) 22(0.355) 6(0.048) S(0.081) 93(0.750) 13(0.105) SS(0.452) 56(0.903) 69(0.567) 106(0.855) 3(0.048) S(0.065) 20(0.161) 27(0.218) 32(0.258) 5(0.081) 56(0.452) 6t0.048) lOO(0.807) 21 (0.169) 0(0.000) 18(0.145) 15(0.121) 7(0.113) 27(0.218) 19(0.153) 12(0.097) 4(0.032) 61(0.492) S(0.081) 30(0.242) 56(0.452) 94(0.758) 64(0.681) gg(O.798) 36(0.290) 65(0.524) 4210.339) 24(0.194) 19(0.153) lg(0.153) 13(0.210) 25(0.202) S(0.081) 5(0.040) SS(0.686) 56(0.452) 3(0.024) 3(0.024) 38(0.307) 2210.177) 114(0.919) 16(0.129) 64(0.516) 50(0.403) 17(0.137) Males N=99 No. (freq.) 6(0.061) 88(0.889) 43(0.217) 21 (0.106) 56(0.283) 10(0.101) 1l(O.111) 49(0.248) 13(0.131) 155(0.783) 21(0.106) 21 (0.106) 21(0.212) 103(0.520) 189(0.955) 5(0.051) 22(0.111) 63(0.318) 32(0.161) 45(0.227) 2t0.020) 97(0.490) g(0.046) 167(0.843) 46(0.232) 8(0.040) S(0.025) 17(0.086) 13(0.131) 32(0.162) 26(0.131) 18(0.091) 4(0.020) 1OO(0.505) 29(0.293) 50(0.253) 96(0.485) 182(0.919) 107(0.588) 181(0.914) 53(0.268) 94(0.475) SS(0.283) 14(0.071) 37(0.187) 25(0.126) 2 1(0.212) 32(0.162) 1l(O.111) 12(0.061) 139(0.702) 45(0.227) I(O.005) g(0.046) 43(0.217) 25(0.126) 188(0.950) lO(0.051) 125(0.631) 78(0.394) 23(0.116) Females N=83 No. (freq.) 6(0.072) 73(0.880) 24(0.145) 17(0.102) 45(0.271) 2 (0.024) 17(0.205) 33(0.199) g(O.108) 117(0.705) 15(0.090) 52(0.313) 24(0.289) 85(0.512) 158(0.952) l(0.012) 19(0.115) 38(0.229) 22(0.133) 31(0.187) Z(0.024) 96(0.578) g(0.054) 145(0.874) 38(0.229) 12(0.072) 3(0.018) g(0.054) lO(0.121) 31(0.187) 14(0.084) ll(0.066) 2(0.012) gl(0.548) 8(0.096) 60(0.361) 64(0.386) 128(0.771) 78(0.609) 151(0.910) 48(0.289) gO(0.542) 51(0.307) lO(0.060) 6(0.036) 14(0.084) 26(0.313) 37(0.223) g(0.108) 5(0.030) 114(0.687) 33(0.199) 0(0.000) 4(0.024) 25(0.151) 15(0.090) 155(0.934) 12(0.072) 123(0.741) 88(0.530) 32(0.193) 430 ROBERT S. CORRUCCINI bers of each sex in each sample roughly equal. This is also questionable, since doing so may lessen inter-population distance through inclusion of intra-population heterogeneity. Our inability to determine sex accurately in human skeletons complicates sex variation tests. Accuracy of only about 80% is claimed by even the most experienced physical anthropologists working with complete skulls (Giles and Elliott, ’63; Kajanoja, ’66). Furthermore, Weiss (‘72) detects an additional systematic bias of 12% toward males throughout skeletal studies. This error of over 20% in sex identification lessens statistical precision and would be even greater in material of average archeological preservation. It is of value to test the sex difference assumption with series of known sex. This is done in Caucasian and Negro crania from the Terry Collection. First, univariate differences in each trait are tested using chi-square. Then overall difference between sexes is assessed through the multivariate Theta-square distance. (White male, White female, Black male and Black female) are compared. Again, individual traits are tested by chi-square and overall divergence by Theta-square. If increasing age affects nonmetrics gradually, correlation between age and the ordinally-scored version of traits, in which intermediate gradations are recognized, should measure dependence more sensitively. Spearman’s rank-order correlation coefficient is used to compare ordinal traits with ranked age in the four groups. Intercorrelation between nonmetric variants A major advantage of discrete traits is their apparent lack of correlation, rendering valid the practice of accumulating trait differences on an equally-weighted basis to estimate distance. Truslove (‘61) demonstrated this feature for the mouse, and Berry and Berry (‘67) and Kellock and Parsons (‘70a) did so for human samples. Hertzog (‘68) presented data which seem to confirm the statistical significance of discrete trait correlations, but Benfer (‘70) Age dependence replied that, while formally significant, Berry and Berry (’67) do not test the these correlations are nevertheless too low claim that discrete traits do not vary with to indicate meaningful predictivity between age. Ossenberg (‘69a, ’70) detects age- traits. regression (for hypostotic variants) and The significance of association among age-progression (for hyperostotic variants) binary variants is investigated, as in sevin several cases. Most of this age variation eral of the above studies, through chioccurs between infancy and early adult- square analysis of association contingency hood, few traits changing with age beyond tables. Only those traits are compared maturity. which are common enough to allow for a Age estimation in archeological remains minimum value in any cell of n = 5. is even more prone to error than sex deThe relative level of inter-trait associatermination, especially for adult skeletons. tion, as well as its absolute significance No substantial investigation of advanced as ascertained by chi-square, is also an age effects on nonmetric variants has been important consideration. Neither productdone. moment correlation nor $-related conAll specimens in the present analysis tingency coefficients, which have been are adult, so there is no basis for testing used in previous binary correlation studies, age-dependence of traits through develop- are appropriate for this purpose (Cox, ’70; ment. Many are known to be age-related Goodman and Kruskal, ’54; Elashoff, Elashuntil adulthood however (Ossenberg, ’69a; off and Goldman, ’67). Edwards (‘63) demBuikstra, ’72). The focus of my analysis onstrates a criterion whereby Yule’s (‘12) is upon post-adolescent changes in non- coefficient “Q” appears more efficient than metric morphology. The simplest way to most others for measuring association. examine this is to separate samples ac- Yule’s coefficient was employed by Sullicording to age and compare individual and van (‘22) to investigate trait dependencies, overall variant frequencies between age with both positive and negative results. groups. “Young” (age 19-39) and “old” This coefficient is computed between all (40 or older) subsamples of each group pairs of dichotomous variants satisfying 431 DISCRETE TRAITS OF HUMAN SKULL the n = 5 minimum criterion within each Terry sample separated by race and sex. The multi-state scoring of nonmetric variation affords another method of analyzing inter-trait correlation. The rank-order coefficient can be applied to these ordinal data, and is a more sensitive test of association than chi-square. To assess the overall significance of the pairwise correlations, Bartlett’s “sphericity” test is applied. The test is based on the magnitude of the determinant or generalized variance of the correlation matrix (Anderson, ’58; Cooley and Lohnes, ’71). If this test indicates significant correlation, it may be worthwhile examining the pattern followed by traits in morphologically integrated complexes or associations (Cooley and Lohnes, ’71). This is done with a principal component analysis of the matrix of Yule association coefficients. The analysis will be done on the pooled average correlation matrix (Imbrie, ’66) to simplify interpretation. Benfer (‘72) indicates that factor analysis of non-parametric coefficients such as Yule’s is as valid as for product-moment correlation coefficients. The correspondence between nonmetric and metric analyses The value of nonmetric variants relative to traditional osteometrics, particularly skull measurements, is an important issue. Berry and Berry (‘67) claim that discrete trait divergence is more genetically meaningful than metrical difference: “There is no doubt that epigenetic variant incidences have considerable advantages over morphological measurements for many anthropological purposes.” To investigate relatedness of nonmetric and metric results among Terry crania, I compute generalized metric (D2) and discrete (Theta-square) distances between eight samples partitioned according to race, age and sex. Comparison of results between different techniques can be accomplished through principal coordinates analysis. This technique reduces matrices of inter-sample distances onto orthogonal axes that successively account for less of the total variance of the matrix. Hopefully, only a few of these axes account for essentially all of the structure of the relationships, and examination of them will yield interpretable patterns among the samples. I similarly compare the measurements with the ordinally-scored version of nonmetric traits. Since two multistate data sets are involved, it is possible to apply the same technique, canonical variates analysis, to both. Comparison can be made with two previous studies (Giles and Elliott, ’62; Howells, ’70a) which established discriminant functions for the identlfication of race and sex from white and Negro skulls. Only 30 of the original 61 nonmetric variants are used in canonical variates analysis due to computer requirements. They are selected on the basis of usage in previous studies. RESULTS Basic statistics Tables 2 and 3 list descriptive statistics for each sample in terms of occurrences and incidences of discrete traits. The data in table 2 were reduced to population divergence measures using the Theta-square statistic (table 4). The divergence between every pairwise combination of White males, White females, Black males and Black females is statistically significant (p< 0.001). Race differences outweigh sex differences. Caucasian sex divergence is greater than for Negroes, and female race divergence is greater than among males. The greatest difference is between Caucasian females and Negro males. Sex differences This was tested within each race by univariate and multivariate methods. Between male and female White crania, 19 out of 61 discrete variants differ significantly at pCO.05 according to chi-square tests. We would expect only three traits to differ through chance variation, given independent traits. The multivariate Thetasquare distance between White sexes of 0.0383 (table 4) is also significant (p< 0 .oooo1). Only nine traits differ significantly between Negro sexes. The multivariate difference is also smaller, but almost as significant as that between White sexes. Caucasians and Negroes differ in pattern of sex differences as well as in extent. Both groups are highly dimorphic with respect to inion salience and sutural infraorbital foramen, but the most significant 4 32 ROBERT S . CORRUCCINI TABLE 3 Occurrences of discrete truits too rare to b e i n c l u d e d i n analysis Number of occurrences for Caucasian Trait Males Females Males Females 3 2 0 0 0 0 0 2 4 1 2 0 2 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 51642 61321 01321 21642 01642 01321 01642 5/32 1 91642 0 0 1 0 0 2 0 1 01642 41642 Coronal ossicle Sagittal ossicle Bregmatic bone Temporal ossicles Ear exos tosis Medio-palatine bones Optic f. anomaly Third occip. condyle Paracondylar or paramastoid process Stylomastoid f. absent Basal bridge 1 I Negro 0 0 0 1 3 TotaliN Lateral to f. ovale and spinous process univariate White sex differences are in frontal grooves, palatine torus and accessory mylohyoid foramen, while among Blacks mastoid foramen and bifaceted condyles provide the greatest difference. This shows the pitfalls inherent in combining different groups for sex comparisons. Different sex variation patterns are also evident in analyses by Jantz ('70) and Humphreys ('71). Age dependence Table 5 shows the relationship between individual traits and age. Genial tubercles, trochlear spurs, inion salience, mastoid foramen, pterygoid foramen and postcondylar canal show the greatest age effects. Generally, patterns of age dependence are erratic over different samples. Over twice as many age dependencies occur as can be explained by random error. TABLE 4 Theta-squared discrete trait distances a n d their standard deviations b e t w e e n race and sex divisions of t h e T e r r y craniul s a m p l e . T h e u p p e r right triungular half gives d i s t u n c e s ; s y m m e t r i c a l counterp a r t s of t h e s e t o t h e lower left a r e stundnrd deuiations of e a c h d i s t a n c e White male White male White female Negro male Negro female White female Negro male Negro female 0.038 0.047 0.079 0.093 0.073 0.008 0.008 0.013 0.011 0.012 0.020 0.005 The left lower part of table 7 presents multivariate nonmetric distances between samples partitioned according to age. Distances between younger and older members of each sex and race group are statistically significant (p < O.Ol), despite the reduced sample sizes. Black females show greater age change than the others. Age distances are comparable to sex distances in magnitude. These results substantiate Akabori's ('33) demonstration of systematic change over age in nonmetric morphology. Intercorrelation between traits Table 6 summarizes results of pairwise correlation analysis between the 61 variants. The average Yule association coefficient per trait pair is fairly constant through each race and sex, falling between the values of 0.208 and 0.290. This average correlation level is not high, but is significantly greater than zero. The claim that nonmetric correlations are considerably lower than metric correlations is not borne out. For male Caucasians, for instance, the average craniometric correlation (product-moment) for 253 pairwise combinations of 23 measurements was r = 0.266 ( 20.03). Table 6 also gives the significance of associations as assessed by chi-square tests. As with Kellock and Parson's ('70a) findings, fewer significant associations occur than expected at p < 0.05. It appears that association, although greater than expected on the average, does not reach a detectable level in individual pairs of binary traits. 433 DISCRETE TRAITS OF HUMAN SKULL TABLE 5 Listing of n o n m e t r i c traits showing significant correlation w i t h age in either of t w o tests. Statistically significcrnt ranh-order correlation b e t w e e n age trnd ordinally-scored ( m u l t i s t a t e ) v a r b e t w e e n binary v a r i a n t s of “old” a n d i a n t s ( + ) and significtrnt chi-square difference “young” partitions of e a c h s a m p l e m e indicnted ( p <0.05) (x) Caucasian Negro Trait Males Mandibular torus Genial tubercles Accessory mental f. Accessory mylohyoid f. Gonial eversion Palatine torus Palatine bridging Maxillary torus Accessory lesser palatine f. Accessory infraorbital f. Anterior ethmoid f. exsutural Posterior ethmoid f. Trochlear spur Frontal f. Metopism Zygo-facial f. Epipteric bone Superior lambdoid ossicle Inferior lambdoid ossicle Ossicle a t asterion Inion salience Marginal meatal f. Mastoid f. Mastoid grooves Postcondylar canal Intermediate condylar c a n a l Bifaceted condyles Jugular f. bridge Pharyngeal fossa L at era1 pterygoid perforation Pterygoid f. f. Vesalium Spino-basal bridge f. ovale spicule f. spinosum-ovale continuous Accessory f. spinosum Females Males Females X +>X X X X + + .x X + X + .X X X X + + .X +>X X + .x + >x + + .X + .X X + + .X X X + ,X + + X + Rank-order correlation of the variants as ordinal attributes decreases with respect to binary associations. The level of statistical significance increases, however, reflecting the greater statistical power of Spearman’s coefficient (table 6, line 6). Significance of overall correlation level is also indicated by the multivariate sphericity tests of correlation matrices (table 6). The two most important principal component axes of the matrix of Yule coefficients represent the two most salient complexes of interrelated traits. The first principal component separates generally hypostotic traits (metopism, the wormian complex of sutural ossicles, and pharyngeal fossa) from the most hyperostotic traits (mandibular, maxillary and palatine tori, + >x + .X + .x + ,x + + + X + X X X + inion salience, zygo-maxillary tubercle). Thus a general gradient of osseous development simultaneously influences many nonmetric variants, although the common effect is rather slight (10% of total variance). The second component axis associates many emissary and bridged foramina together, contrasting them with wormian bones (again forming a unified complex) and orbital traits. Subsequent components did not follow easily interpretable patterns. Correspondence between metric and nonmetric analyses Table 7 compares metric and nonmetric distances between eight Terry samples partitioned by race, sex and age. The first 4 34 ROBERT S. CORRUCCINI TABLE 6 Association and correlation b e t w e e n all pairwise c o m b i n a t i o n s of 61 n o n m e t r i c morphological traits White males Binary scoring 1 . Average Yule coefficient 0.287 (absolute value) 2. Standard error of 0.007 average 3. Number and percent of 50(3.5%) significant x2 associations (p<O.O5) Multistate scoring 4. Average rank-order 0.095 correlation 5. Standard error of 0.002 average 42(2.3%) 6. Number and percent of significant correlations (P <0.01) 7. Significance of Bartlett's p=O.160 sphericity test 1 White females Black males Black females 0.259 0.290 0.208 0.007 0.007 0.007 29(2.4%) 44(3.1% 31(2.9%) 0.101 0.084 0.091 0.002 0.001 0.002 34(1.94) 34(1.9%) 40(2.2%) p=O.O16 p=O.OOO -1 Determinant of this correlatlon m a u i x not calculable. TABLE 7 Craniometric (D2) and n o n m e t r i c ( T h e t a - s q u a r e ) distances b e t w e e n race, sex a n d age subdivisions of Terry Collection crania. Statistical significance of distances at p <0.01 i s indicated. T h e u p p e r right triangular half of t h e m a t r i x gives Dz f o r metrical traits; t h e lower left lists Theta-square based on discrete traits Young white male 0 Id white inale Young white female Young white male Old white male Young white female Old white female Young black male Old black male Young black female Old black female principal coordinate of D2 (metric) relationships is clearly a racial difference factor, accounting for 67.6% of total betweensample variance. The second coordinate, representing 31.2% variance, discriminates the sexes. The third coordinate is relatively minor and reveals age separation (table 8). The first coordinate of discrete trait distance is also one of racial difference, while subsequent axes separate sexes and age groups. As with metric 0 Id white feinale Young black inale 0Id black inale Young black feinale 0 Id black feinale 15.45':' 18.94:' 23,933:' 21.64::' 12.31* 14.73':: 23.59::' 20.26:: 21.96::; 24.53::' 14.62':' 13.64" 21.09':' 21.91': 12.94;' 10.54':' 9.51::' 8.64::' 9. 1 7 !'. 8.62::' 1.35 0.024:' 0,031:: 0,049::: 0.048::' 0.063': 1.19 0.056:' distances, genetic difference seems to be the major determinant of discrete divergence. The same metrical data were analyzed using canonical variates. The first canonical axis for cranial measurements again discriminates races. Coefficients of the variate indicate it is primarily determined by cranial base, superior facial and mandible length, nasal, palatal and interorbital breadth and ramus height. The sec- DISCRETE TRAITS O F HUMAN SKULL TABLE 8 435 other analyses (Akabori, '33), it is justifiPercent variance explained b y latent roots (eigen- able to assume significant sex differences in discrete traits for human populations. u u l i ~ e sfor ) prznciptrl coordinate ( P C ) a n d ccinonicnl unrinte (CV) analyses of discrete and metricnt uar- The pattern of differences will vary from iation group to group, as does sexual dimorphism of metric traits, but overall nonmetric sex Discrete Discrete Metric Metric cv PC cv PC difference is probably significant for all human populations if it is this great in 59.0 72.5 54.5 Race 67.6 Caucasians and Negroes. As in customary variance 15.7 18.2 37.5 Sex 31.2 with metrical analysis, discontinuous varivariance ant studies hereafter should separate sexes 20.5 4.1 4.0 Total age 1.1 (Anderson, '68a). variance Likewise, the hypothesis of age inde4.8 5.2 4.0 Uninter0.1 pretable pendence of discrete traits fails when tested on Terry skulls of known age. The multivariate divergence test (table 7) inond and third axes again identify sex and dicates that cumulative age divergence age variation. While Howells ('70a) found over many traits is more important than 79% race variation and 21 % sex variation marked divergence in a few. It is wellin a similar analysis, my results indicate known that craniometric characters less race and more sex variation (table 8). change with age (Israel, '73), but statisThe canonical axes of multistate non- tical analysis of the sort that craniometric metric traits again resemble metric pat- characters have been subjected to also terns and separate race, sex and age, re- rejects the supposed age-independence of spectively. Nasal still sharpness, epipteric nonmetric characters. It appears in this bone, pterygo-spinous bridge and parietal regard, as with sex differences, that there notch bone show the highest racial discrim- is no real difference between nonmetric inant coefficients. Sutural infraorbital for- and metric variables. The same concluamen, frontal grooves and inferior lambdoid sion proceeds from a study of the effect ossicle are most useful for discriminating on nonmetric and metric variables of body sexes. The epipteric bone receives the weight (Corruccini, in press). The assumption of lack of correlation highest age discriminatory weight. Totalling variance by factor (table 8) among discrete traits fares a little better. shows similar distance patterns in each While relative association levels, measured analysis. Racial genetic difference always by Yule's coefficient, are almost as high dominates. Discrete traits only produce among nonmetric as among metric traits, about half as much sex difference as met- the statistical significance of those assoric traits. Age (or associated non-genetic ciations is much lower in discrete traits. factors such as illness) influence discrete The reason for this is the greater statistraits several times as much as measure- tical power associated with tests based on normal distribution theory, such as prodments. The significance of multiple-sample dis- uct-moment correlation, as compared with crimination can be measured by Wilk's chi-square. The greater correlation between Lambda statistic (Anderson, '58), which craniometric characters may be an artiis the ratio of within-sample to between- fact of the power of the statistics used on sample generalized variance. Wilks Lamb- the different types of data. Some support da is 0.049 in the metric analysis and for this contention is provided by the rank0.183 in the multistate nonmetric analysis. order correlations based on quantified Thus four times as much overall sample nonmetric variants (table 6), for which separation is afforded by 23 metric traits the frequency of significant correlations as by 30 nonmetric traits in this instance. rises to the extent that it cannot be explained by random fluctuation. This conDISCUSSION clusion is verified by Bartlett's test which The hypothesis of lack of sex difference considers the entire correlation matrix at in discrete traits fails in Terry Collection once. It appears the low correlation becranial samples. A s i t has also failed in tween dichotomous cranial variants is 436 ROBERT S. CORRUCCINI partly a product of the way they are scored, significant, interpretable results. Similar which precludes the use of any but simple population comparisons based on the two statistics. Interaction between nonmetric trait classes have also occurred since nonvariants is low, but significant; this is metric variants were separated by sex, further confirmed by the patterns of non- controlled for age discrepancy and treated metric associations produced by principal by the same numerical techniques as were components analysis. the metrics. That is, when one treats nonThe feeling that nonmetric population metrical and metrical data in the same divergence is more useful than metric dif- way, they apparently behave in much the ference is another questionable allegation. same way. Thus a number of the theoretical bases Jantz (’70) reviews metric-nonmetric comparative studies. He correlates discrete for exclusive reliance upon discrete trait and metrical distances between popula- studies appear poorly grounded in the tions from several studies (Laughlin and case of human populations, regardless of Jorgensen, ’56; Brothwell, ’59; Berry, Ber- their validity for experimental rodents. ry and Ucko, ’67; Berry, Evans and Sen- The key claim of nonmetrical variant adnitt, ’67; Berry and Berry, ’67; Jantz, ’70), vocates, that of highly genetic determinafinding a range of agreement between tion, remains untestable at present in man. r = -0.48 and r=0.66. He concludes Criteria of segregation within families, so there is only a vague relation between the useful in rodent studies, are difficult to two trait classes. Jantz interprets the met- apply to humans since family skeletal rical distances in most of these studies as series are unknown and few discrete osmore genetically meaningful. Rightmire teological traits can be detected in the (‘72) draws the same conclusion using living, either through radiology or palpaAfrican populations. tion. With regard to discrete trait genetics, For eight Terry samples, a total of 28 then, we must resort to examination of pairwise distances result (table 7). The population frequencies to determine anacorrelation between metric (D’) and non- lytic tactics. In relation to the known population metric (Theta-square) distances is r = +0.777 (0.574.89, 95% confidence lim- genetics of extant groups, discrete trait its). This is apparently the highest con- distances have been questionable in sevcordance to date, but its meaning is ob- eral instances. Brothwell (’59), for examscure since age and sex distances are ple, found Chinese and Peruvian crania included with racial distances, while pre- more closely related than Anglo-Saxon vious studies concentrated on the latter. and London crania. He also found the It may be that this concordance is related Chinese closer to North American Indians to the control exerted over sex variation. than Anglo-Saxons were to Germans or Principal coordinates of these distances, Melanesians to Polynesians. Berry and and canonical variates of the two types of Berry (’67) found South American Indians data, are accordingly similar. The vari- nearer Burmese and Africans than North ance accounted for by race difference is American Indians. Egyptian skulls were virtually identical. There therefore seems closer to South America than to Palestine. to be no basis for judging one type of data As Berry (‘68) admits, some of these values or the other to be more genetic. Sex dif- are “rather odd.” Finnegan (‘72) could ference accounts for considerably less not separate Florida Indians and several variance in discrete than metric distances closely inter-related Northwest Coast (table 8), confirming the claim that minor groups. He suggests that there is a limit variants, though dimorphic, are less so to the heterogeneity of discrete character than measurements. On the other hand, variation that is exceeded when unrelated the age factor in nonmetric traits is sev- groups are compared. On the other hand, it appears that traeral times as large as that in metrics, reflecting poorly on claims that discrete ditional craniometrics have come of age morphology does not respond to non-ge- with the advent of multivariate techniques, netic influences. These differences are and produce expected patterns of variarelatively minor, however. Both nonmetric tion with respect to the known population and craniometric analyses yield genetically genetics of living peoples (Howells, ’69a,b, DISCRETE TRAITS OF HUMAN SKULL '70b, '72). Jantz ('73) and Friedlaender ('70, '71) present evidence of high heritability of anthropo- and osteo-metrics; Nakata, Yu, Davis and Nance ('72) report high heritability of osteometrics through a radiological study. Since discrete traits may not always follow dependable regional patterns, the claim of their superiority over measurements is questionable. There is a considerable amount of speculation on the hereditary nature of human discrete variation, however. Metopism ranks first in historical interest. Various etiological theories were proposed by Papillault (1896), Le Double ('03), Essen-Moller ('28), Remane ('25), Bolk ('17, 'ZO), Schwalbe ('Ol), Fischer ('02), Limson ('24), Correa ('lg), Martin ('14), Calmettes (1878), Ashley-Montagu ('37) and Woo ('49a). Schwalbe ('04) and Schultz ('29) stated the possibility that metopic retardation is a hereditary tendency. AshleyMontagu ('37) suggested single-gene inheritance. Torgerson ('50, '51 a,b, '52) conducted roentgenogram studies indicating single gene determination with 50% penetrance and variable expression. There is also documentation of the genetics of palatine, maxillary and mandibular tori (Drennan, '37; Klatsky, '56; Dorrance, '29; Lasker, '47, '50; Anderson, '68a; Moorrees, Osborne and Wilde, '52; Suzuki and Sakai, '60; Johnson, Gorlin and Anderson, '65). Torgerson ('51a, '52, '54) found sutural traits such as wormian bones possibly resulting from a dominant gene with incomplete penetrance. A variety of other discontinuous variants show evidence of genetic disposition (Selby, Garn and Kanareff, '55; Pepper and Pendergrass, '36; Goldsmith, '22; Collins, '26, '27, '30; Ashley-Montagu, '33; Murphy, '56; Sullivan, '20; Romiti, 1891; Rizzo, '01 ; Perna, '06; Lester and Shapiro, '68). There have been attempts to tie nonmetrical variation to associated metrical variation in skulls (Pittard and Seylan, '36; Woo, '49b, '50; Matiegka, 1899; Hasebe, '13; Schultz, '15; Bennett, '65). Differing versions of the genetic meaning of metrical-nonmetrical associations have been given (Bennett, '65; Ossenberg, '70; Gruneberg, '52, '63). On the other hand, the genetic significance of some discontinuous variants has been disputed. Roche ('64) and Adis-Castro 437 and Neumann ('48) point out that deformation, external stress (wearing of earspools), and disease may cause aural exostoses. Hess ('45, '46) related wormian bones to metabolic disorder of the mesoderm. Bennett ('65) feels all forms of head stress, including pathology and hydrocephaly, may also be involved. Finkel ('71) presents evidence that stress causes wormians. Akabori ('39b) attributed mandibular torus to avitaminosis. Thoma ('37), in distinguishing four varieties of palatine tori, stated that some are due to masticatory buttressing while others are genetic. Hooton ('18), Matthews ('33), Hrdlicka ('40) and Johnson ('59) note the prevalence of oral tori in populations undergoing masticatory stress. Mayhall, Dahlberg and Owen ('70) and Muller and Mayhall ('71) note considerable age-dependence in studies of torus mandibularis. Van den Broek ('43) ascribed palatine torus to irritation of the mucous membrane. Mayhall and Mayhall ('71) state that diet may affect the mandibular torus. Kalenscher (1893) thought that the third condyle is only a highly variable muscle attachment. Benfer and McKern ('66) show that olecranon perforation of the humerus is related to bone robusticity and stress on the fossa. Thus while evidence exists of genetic determination of several variants, there is the possibility of other factors. This is not negated by the definition of "epigenetic" variation (Berry and Searle, '63), which implies imposition of phenotypic discontinuity during development rather than at zygote formation, realizing the possibility of environmental action on traits. The question is whether genetic or external influence predominates. There is considerable evidence from laboratory animals of maternal and other non-genetic effects on trait variability (Green, '41; Holt, '48; Searle, '54; Deol and Truslove, '57; Howe and Parsons, '67), but apparently genetic variability is in excess of this. The theoretical mode of inheritance of discrete traits involves a normally distributed additive polygenic variable, epigenetic interaction between developmental processes after inheritance is set, and a discontinuous adult distribution or phenotype after superimposition at some point of a threshold, below which development ceases (Wright, '34; Gruneberg, '51, '52, 4 38 ROBERT S. CORRUCCINI '55, '63; Falconer, '60, '65; Dempster and Lerner, '50; Berry, '63, '68). "The genotype thus determines a probability of the character appearing, or the proportion of environments in which it will actually come to expression" (Dempster and Lerner, '50). Jantz ('70) discusses the significance of the fact that a discrete trait's incidence is a function both of the mean and the variance of the underlying genetic variable, since an individual's genotypic distance from the mean in standard deviation units determines his possession of the trait (Falconer, '65). Genotypic change affects nonmetric and metric traits differently, since a mean or variance change can affect a discrete trait's appearance while only a change in mean would affect most measurements. Furthermore, different modes of selection, drift, and other mechanisms have different effects on the polygenic distributions underlying the phenotype. Some change the mean (directional selection), some change the variance (stabilizing selection), and drift and hybridization may change both. Thus differing agents will cause divergent responses between nonmetrical and metrical phenotypes as a whole. These points are complicated by consideration of nonmetrics as more complex than binary entities. Many nonmetric traits do not conveniently divide into present and absent states, allowing examination of their distributions as multistate traits. For example, the zygo-facial foramen was scored simply by counting the number of well-defined foramina per side. Five categories (zero, 1, 2, 3, and 4 or more foramina) were tabulated and fitted to the binomial distribution (fig. 1). Chisquare shows the fit to be satisfactory, while the fit to a normal distribution failed. This point is made to emphasize the deviation from normal rather than the fit to binomial, but the binomial fits a remarkably wide range of nonmetric trait distributions both in these Terry samples and several Amerind populations (unpublished work in progress) while the normal never does. This indicates random distribution of intermediate states, as opposed to a greater incidence of complete absence or definite presence than can be ascribed to chance. A trait determined by equally additive genes approaches normality of distribution as the number of involved loci increases. The smaller the number of genes involved, the more discontinuously binomial will be the distribution. Alternatively, a binomial distribution can fit a trait resulting from partially additive loci even when many are involved. Discrete variant distributions do not approximate the normal but in many instances fit other curves, although their underlying genetic causes are supposed to be normal. Either reduced number of loci, unequal additivity, or action of key genes may therefore characterize nonmetric variant inheritance, in contrast to additive, highly polygenic inheritance of metrical features (Holt, '45; Fisher, '53; Dempster and Lerner, '50). Heritability differences between continuous traits on the one hand and singlegene, "oligogenic," or non-additive traits on the other cause differences in behavior under varying classes of evolutionary events. Unifactorial and partially additive traits react faster to selection (Boyd and Li, '63). Conginuous traits react more slowly but their variance may change first (Livingstone, '69). Oligogenic traits become more variable through hybridization and heterozygosity, while measurements often do not (Bailit, '66; Hainline, '66). Birdsell ('50) and Livingstone ('72) point out that due to quantitative additive loci, metric characters are randomly increased as much as they are randomly decreased by drift, so that effects tend to cancel out. Discontinuous characters are more susceptible to genetic drift (Angel, '66; Howells, '66a). Benoist ('64) shows that metric variability in isolates can be greater because distributions are flattened by the predominance of two homozygous types, while nonmetric variability is reduced in that the chance of fixation is increased with fewer loci. These facts may help explain some observed differences between metric and nonmetric analyses of human populations. Bennett and Hulse ('66), for example, found little metric difference between Mesa Verde skulls and those of neighboring groups, but the difference in discrete traits was significant. They invoked genetic drift as a possible cause of the variability, a mechanism which would be ex- 439 DISCRETE TRAITS OF HUMAN SKULL 0 0 I 3 2 NUMBER OF FORAMINA Fig. 1 Comparison of observed (solid line) frequency distribution of zygo-facial foramina in male Whites with expected frequencies assuming a binomial distribution (dashed line). The other samples produced similar curves. pected to affect minor variants more than measurements. Likewise, Berry and Smith (cf. Berry, ’68) observe that an isolate of mice was only distinct in terms of discrete variants, which they feel confirms the genetic valence of those variants. Again, genetic isolation would have a lesser effect upon measurements whether or not they are of equal genetic meaning. Longterm directional selection could be expected to affect metric morphology more than nonmetric, since “selection on the all-or-none basis is exceedingly inefficient” (Dempster and Lerner, ’50). This effect has been noted in comparing continental racial samples (Jantz, ’70). T h e meaning of discrete traits for skeletal biological studies Metric and nonmetric characters will behave differently under various mechanisms of genetic change if their hereditary t 440 ROBERT S. CORRUCCINI modes differ. It is in this regard that discrete traits offer their greatest potential contribution - as a control against other data in determining not only genetic affinity but also the processes causing that pattern of affinity. These other data should not be confined to traditional craniometrics or any other single line of inquiry, but should include dental traits, postcranial measurements and morphology, pathology, population dynamics and other parameters of value in skeletal genetic comparisons. The most objectionable aspect of the discrete trait research model is the consideration that skeletal studies can be facilitated by the exclusion of all data but the most easily collected (i.e., discontinuous variants), and that further simplification may be attained through lumping all age, sex, and trait categories as being inherently of equal value and meaning. Even when age and sex subdivisions are not demonstrably different, there is value in analyzing them separately. Angel (’69a,b) has shown how including demographic data with morphology yields interlocking inferences about microevolution, population structure and social biology. Synthesis of this with archeological data can lead to analysis of interconnections between biology, culture and environment. Such data are discarded in considering populations to be structureless aggregates. Comparison of sex differences in morphological distances may also provide a handle on non-random gene flow patterns such as result from matrilocality (Corruccini, ’72). As processes of genetic change in human populations are complex and multifactorial, it is illogical to expect optimal efficiency from a restricted approach emphasizing simplicity. Binary discrete trait analysis is probably the least desirable way to study skeletal population genetics. Metrical analysis may be more reliable, but still not optimal. A battery of trait categories and tests should be employed and compared. Extra weight should initially be given to categories of proven utility, such as metrical morphology and dental traits in conjunction with multivariate analysis. Discrete cranial variants, while desirable as comparative data, have yet to prove themselves equally trustworthy. “It is clear that much more work is needed before non-metric traits can afford a basis for definitive statements about population relationships” (Jantz, ’70). ACKNOWLEDGMENTS This research was accomplished with considerable encouragement and support from Dr. Donald Ortner. I wish to thank Dr. N. Ossenberg, Dr. T. D. Stewart, Dr. Neil Roth, Mr. D. Piacesi and especially Dr. M. Finnegan for profitable discussions. Ms. Lisa Rhudy assisted in measuring and keypunching. Support in the form of my National Science Foundation graduate fellowship and travel funds provided by the Smithsonian Institution are gratefully acknowledged. LITERATURE CITED Adams, J., and R. H. Ward 1973 Admixture studies and the detection of selection. Science, 180: 1137-1143. Adis-Castro, E., and G. K. Neumann 1948 The incidence of ear exostoses in the Hopewell people of the Illinois Valley. Proc. Ind. 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