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An examination of the meaning of cranial discrete traits for human skeletal biological studies.

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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.
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