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Analysis of the hominoid os coxae by Cartesian coordinates.

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Analysis of the Hominoid 0 s Coxae by Cartesian Coordinates
H E N R Y M. MCHENRY A N D ROBERT S. CORRUCCINI
Department of Anthropology, Uniuersit.y of Californra, Davis, California 95616 and
Diuasion of Physical Anthropology, Smithsonian Institution,
Wushington, LJ C. 20560
K E Y WORDS 0 s coxae . Australopithecus
nates . Multivariate analysis
-
Cartesian coordi-
ABSTRACT
This study is based upon 48 3-dimensional coordinates taken on
4 fossil hominid and 127 extant hominoid coxal bones. The fossils include Sts 14,
S K 3155, MLD 7, and MLD 25. The comparative sample consists of 42 Homo
sapiens, 27 Pan troglodytes, 29 Gorilla gorilla and 29 Pongo pygmaeus. The coordinates improve the metrical represenlation of the bone beyond what can be done
with linear measurements because the shape complexity of the os coxae is SO
great. The coordinates are rotated and translated so t h a t all bones are in a standard position. The coordinates are then standardized for each specimen by dividing all coordinates by the pooled standard deviation of X, Y, and Z coordinates.
These data are treated to standard statistical analyses including analysis of variance, Penrose size and shape statistics, principal coordinates and components,
and canonical variates analysis. The data are then further altered by using some
specimen as a standard and rotating each specimen until t h e total squared distance between its coordinates and those of the standard are minimized. The same
statistics are applied to these “best fit” data. The results show a high degree of
agreement between the methods. The hominid os coxae are fundamentally different from the other hominoids and the fossil hominids share the basic hominid
configuration but with some unique differences.
The shape of the pelvic bone i s so complex
that. i t is difficult to describe hy conventional
techniques. Simple lengths and widths of its
parts may not adequately represent important
features such as the relative positions of muscle attachments in 3-dimensional space or the
angles between planes. To do this requires
some way of rendering the 3-dimensional nature of the bone. Cartesian coordinates provide one method. Benfer (’75) and Creel and
Preuschoft 1’76) have recently presented examples of :&dimensional coordinate analyses
of crania and the results are of undoubted
value. How exactly to treat coordinates as
input data is still a relatively unexplored
question which we address in this paper.
The purpose of this study is to assess the
morphological affinities of fossil and extant
hominoid 0 s coxae using multivariate analysis
of Cartesian coordinates. These 3-dimensional
coordinates supplement a list of linear meaAM. J. PIIYS. ANTHROP. 11978) 48: 215-226.
surements taken on the same 0 s coxae and reported earlier (McHenry, ’72, ’75b; McHenry
and Corruccini, ’75).
MATERIALS A N D METHODS
This study is based upon 48 3-dimensional
coordinates taken on four fossil hominid and
127 extant hominoid 0s coxae. The fossils include Sts 14 from Sterkfontein, South Africa,
classified as Australopithecus africanus by
most authorities but reclassified to Homo
ufricanus by Robinson (’72).The dating of this
specimen i s problematical but most agree i t s
age falls between 2 and 4 million years ago.
Sts 14 is reasonably complete, but some reconstruction is necessary on the pubis, ischial
tuberosity, and anterior superior iliac spine.
Fortunately both right and left specimens are
present so t h a t the reconstruction can be
made by comparing one side t o the other. This
becomes particularly important when recon-
215
216
HENRY M. MCHENRY AND ROBERT S. CORRUCCINI
Fig. 1 Method of obtaining Cartesian coordinates with diagraph
structing the pubic symphysis which is par- the X and Y coordinates. The Z coordinate is
tially present on the left side but not on the taken as the height of the point above the
right. Articulating the entire pelvis as recon- paper, which could be read from the diagraph.
structed by Robinson aids in the process of The orientation of the coxal bone does not
accurately reconstructing the bone. The other have to be kept constant from one coxal bone
fossils are SK 3155 from Swartkrans (Brain et to the next. The advantage of this procedure is
al., '75; McHenry, '72, '75b,d; McHenry and that the bones do not have to be in the same
Corruccini, '75) dated between 1.5 and 2.5 mil- position over the graph paper each time.
lion years ago, and MLD 7 and MLD 25 from
Sixteen points on the 0s coxa are defined for
Makapansgat (Dart, '49a,b, '57, '58; Zihlman the purpose of finding their coordinates (fig.
and Hunter, '72) dated at about the same age 2). The points chosen are easily definable and
as Sts 14. The Swartkrans specimen is missing reasonably homologous from one hominoid
most of the ischium and pubis and requires re- species to the next. Because of the obvious difconstruction of the anterior superior spine and ference between the morphology and function
part of the iliac crest (see McHenry, '75, for a of the human 0s coxa and the rest of the
discussion of how this was done). The two hominoids, all of these points probably are not
Makapansgat specimens consist of only the functionally analogous (Benton and Gavan,
iliac portion of the 0s coxae. A separate analy- '60). Another criterion for choosing points is to
sis is done on the nine points common to all ensure that the various planes of the 0s coxa
four fossils.
such as the iliac blade, the acetabulum, the
The comparative sample consists of 42 pubis, the ischium, and the sacral articular
Homo sapiens from the Peabody Museum, surface, are represented by at least three
Harvard University, 27 Pun troglodytes, 29 points each.
Gorilla gorilla, and 29 Pongo pygmaeus from
1. Superior border of the pubic symphysis
the Museum of Comparative Zoology, Harvard (suppub) : the point where the long axis of the
University, and the Smithsonian Institution. pubic symphysis intersects its superior border.
Approximately equal numbers of males and
2. Inferior border of the pubic symphysis
females make up the sample.
(infpub): the point where the long axis of the
The particular method for finding 3-dimen- pubic symphysis intersects its inferior border.
sional coordinates involves the use of a
3. Rim of the acetabulum a t the pubis (rimdiagraph (fig. 1).The bone is suspended over a pub): the point on the rim of the acetabulum
sheet of graph paper. The points on the bone intersected by the axis of the pubic bone.
are projected down to the paper below, giving
4. Ischium- (isch): the intersection of the
ANALYSIS OF THE HOMINOID OX COXAE
217
II
i
Fig. 2 Position of points desc:ribed by Cartesian coordinates.
axis of the ischium with the inferior border of
the ischium on its midline.
5. Ischial tuberosity (tub): the most superior point on the ischial tuberosity on the midline of its posterior surface.
6. Rim of the acetabulum a t the ischium
(rimisch):the rim of the acetabulum a t the intersection of the axis of the ischium.
7. Center of the acetabulum (acet): the center of the acetabulum found by using a special
plexiglass device with concentric circles with
a marker in the center.
8. Rim of the acetabulum a t the ilium
(rimil): the rim of the acetabulum a t the intersection of the anterolateral border of the
iliac blade (just below the anterior inferior
iliac spine).
9. Anterior inferior iliac spine (antinf): the
center of the anterior inferior iliac spine or
the marking of the attachment of the rectus
femoris.
10. Anterior superior iliac spine (antsup):
the center of the anterior superior iliac spine
or the end of the iliac crest.
11. Center of the crest (crest): the point on
the crest midway between the anterior and
posterior ends of the crest located by the use of
a tape measure.
12. Crest a t the sacral surface (sac): the
point on the iliac crest where the anterior
border of the sacral surface of the ilium intersects.
13. Posterior superior iliac spine (postsup):
the posterior iliac spine or the posteromedial
end of the crest.
14. Posterior inferior iliac spine (postinf):
the posterior inferior iliac spine or the most
posteriorly projecting point on the auricular
surface.
15. Auricular surface a t the iliopectineal
line (iliop): the point on the border of the
auricular surface where the iliopectineal line
intersects.
16. Sciatic notch (sciatic): the center or
deepest point of the sciatic notch.
At least five planes can be defined using
these points. The plane of the pubis is represented by points 1-3. The plane of the ischium
is defined by the next three points (4-6).The
acetabular plane is described by points 3, 6,
and 8. The plane of the ilium can be defined by
several combinations such a s points 8,10, and
15, or 8 , 1 1 , and 14. The plane of the sacral articular surface is defined by points 12, 14,
and 15.
Cartesian coordinates of landmarks theoretically contain all the information that
would be contained in linear measurements
between the same landmarks (Oxnard, '73),
but may be much easier to obtain. Fourier
analysis has been suggested to analyze equally spaced-out points along a morphological
outline (Lestrel, '741, but this technique is
unnecessarily elaborate, hard to interpret,
and time-consuming. Likewise, Sneath ('67),
outlines a trend-surface (polynominal contouring fit) analytical method to assimilate
such data. Again, this is complicated and it is
difficult to refer the results back to the original d a t a (interrelations of morphological
points), although the resulting contour maps
have many uses in comparison and interpretation.
Benfer ('75) suggested the most productive
analytical method of simply doing data reduction (factor analysis in his case) on X. Y and Z
coordinates fixed in some frame of reference.
This provides just as much discrimination and
218
HENRY M. MCHENRY AND ROBERT S. CORRUCCINI
taxonomic or functional information, and
makes actual morphological patterns (relative migration of landmarks) more understandable; finally, i t is much easier to do.
Sneath (’67) however, offers some suggestions for data transformation which are undoubtedly very wise to undertake prior to
analysis when (unlike Benfer’s situation)
large size differences are expected. Like linear
measurements, coordinates will merely measure size difference many times over if there is
much gross size variation, muting more important shape variation. These transformations are a s follows:
1. Rotate and translate each bone (or structure) into a standard position (in this case,
point No. 8 becomes the origin, point No. 13,
lies on the X-axis, and point No. 11is on the XY plane).
2. Center each bone. This means shifting
coordinates so that the mean of the coordinates of each dimension (X, Y, and Z) is zero
for each individual. This is done by subtracting the mean of each individual’s coordinates
for a dimension from all the raw coordinate
values for that dimension (say, XI. Thus the
0, 0 , O point is the center of each individual
rather than a point somewhere outside the
structure, and all specimens are centered on
each other. Specimens are now compared by
differential expansion of their landmarks
around the central point.
3. Standardize the coordinates of each specimen to equal variance. This effectively transforms the specimens to the same size in terms
of the dispersion of points around the center.
This should be equivalent to cancelling out
the area of a 2-dimensional structure. The
standardization is performed by dividing all
coordinates by the pooled standard deviation
of X, Y, and Z coordinates. Steps 2 and 3, thus,
are simply statistical normalization (Sokal
and Sneath, ’63) except for pooling of the standard deviations of separate dimensions. The
data are then treated to a succession of standard statistical analyses including analysis of
variance, Penrose size and shape statistics,
principal coordinates and components, and
canonical variates analysis.
4. Rotate specimens to “best fit.” One specimen is chosen as a standard, and every other
specimen is rotated until the total squared
distance between its coordinates and those of
the standard are minimized. Thus, comparison
is without reference to any fixed points or
planes with the orientation of the structures
depending on all the landmarks. This seems
clearly preferable to depending on some traditional plane (e.g., the Frankfurt Horizontal)
which then itself becomes the major (or only)
source of variation. Sneath gives an elegant
and simple method for 2-dimensional rotation
or rotation of 3-dimensional bilaterally symmetrical structures, but rotation of 3-dimensional unsymmetrical structures (like the coxa1 bone) is impossibly complicated. We use
the most typical (centroidal in non-rotated
analyses) human specimen as the standard
reference for 2-dimensional rotation. Some experiments indicated that selection of different
standards for rotation did not appreciably affect results. We used the X and Z dimensions
which showed the most variance, and which
give a lateral view of the bone. Following
these steps, the coordinates were treated as
independent variables and again entered into
standard statistical programs. Fossils were
included in primary distance calculations as if
they represented sample means except for the
48-variable canonical variable analysis in
which Sts 14 had to be included as a n unknown point.
RESULTS
Table 1presents the means for the size standardized coordinates. The major contrast is
clearly between the hominids and the pongids.
So, for example, the anterior superior iliac
spine is in a completely different position in
the hominids and pongids. Another striking
difference is the orientation of pubis and
ischium which are twisted in opposite directions relative to the iliac blade. In most respects the sts 14 specimen is most like Homo
particularly in traits describing the shape of
the iliac blade. The major difference between
the modern and fossil coxal bones is in the position of the ischium relative to the pubis. In
Sts 14 the ischium and pubis are separated by
both Y and Z coordinates whereas in Homo
there is little Y separation. This reflects the
unique morphology of Sts 14 with its short
ischium and relatively long pubis. Several
other more subtle contrasts between the
hominids are discussed below.
The F ratios presented in the sixth column
of table 1reflects the amount of difference between means compared to the general withinsample variance. They show that there are
very few traits that are homogeneous among
the hominoid coxal bones sampled. Especially
heterogeneous are traits concerned with the
219
ANALYSIS OF THE HOMINOID OX COXAE
TABLE 1
Mean shape variables in standard deviation units of the original coxal coordinates
Measurement
1. suppubX
2. suppubY
3. suppubZ
4. i n f p u b X
5. i n f p u b Y
6. i n f p u b Z
7. r i m p u b X
8. r i m p u b Y
9. r i m p u b Z
10. i s c h X
11. i s c h Y
12. ischZ
13. t u b X
14. t u b Y
15. t u b 2
16. r i m i s c h X
17. r i m i s c h Y
18. r i m i s c h Z
19. a c e t X
20. a c e t Y
21. acetZ
22. rimilX
23. r i m i l Y
24. r i m i l Z
25. a n t i n f X
27. a n t i n f Z
28. a n t s u p X
29. a n t s u p Y
30. antsupZ
31. c r e s t X
32. crestY
33. crestZ
34. sacX
35. sacY
36. sacZ
37. postsupx
38. postsupY
39. postsup2
40. p o s t i n f X
41. p o s t i n f Y
42. postinfZ
43. i l i o p X
44. i l i o p Y
45. i l i o p Z
46. sciatic X
47. sciaticY
48. sciatic2
Homo
142)
Sts 14
-0.54
-0.73
- 0.94
-0.43
- 1.07
-0.68
- 0.60
-0.29
-0.11
-0.21
- 1.09
0.54
-0.12
-0.55
0.51
-0.37
- 0.49
0.37
- 0.17
-0.18
0.03
- 0.57
0.16
0.09
-0.61
-0.05
-0.73
0.91
- 0.08
0.54
1.39
0.09
1.07
0.98
- 0.08
1.18
0.16
0.09
0.90
0.01
0.20
0.38
0.31
- 0.12
0.27
0.10
0.14
-0.43
-1.01
-0.76
-0.57
- 1.26
-0.57
-0.59
-0.24
-0.11
-- 0.43
-0.75
0.65
-0.36
-0.52
0.67
-0.53
-0.32
0.37
-0.16
-0.20
0.05
- 0.45
0.31
-0.02
-0.45
-0.09
-0.53
1.12
-0.04
0.58
1.37
- 0.02
1.21
0.70
-0.16
1.23
0.31
-0.02
0.77
-0.10
0.10
0.47
0.12
-0.11
0.23
0.01
0.08
position of the ischium and the anterior superior iliac spine. The primary source for the
heterogeneity in most traits is the contrast between hominids and pongids. Differences are
greatest in the X direction and in these, Sts 14
is most like Homo.
The fundamental difference between pongid
and hominid coxal bones is reflected in the
Penrose shape coefficients and the Mahalanobis D distances given in figure 3. These
coefficients represent a preliminary multivariate analysis to assess the overall affinities
Pan
Gor11Ia
(27)
(29)
-0.63
-0.52
-0.66
- 0.94
- 0.76
-0.42
-0.58
-0.03
-0.13
- 1.14
-0.51
0.38
-0.96
-0.34
0.48
-0.69
-0.15
0.19
- 0.44
-0.18
0.02
- 0.38
0.14
0.03
-0.19
- 0.02
0.50
1.02
0.15
1.25
0.88
0.03
1.50
0.39
- 0.04
1.38
0.14
0.03
0.60
-0.19
0.06
0.61
0.03
- 0.15
0.11
-0.11
0.07
-0.49
-0.61
-0.75
-0.80
- 0.83
-0.60
-0.48
- 0.05
-0.15
- 1.07
-0.69
0.19
-0.92
- 0.54
0.38
-0.62
-0.21
0.14
-0.29
- 0.19
0.02
--0.36
0.18
0.08
-0.20
0.08
-0.001
1.17
0.05
1.05
1.17
0.08
1.48
0.43
0.07
1.35
0.18
0.08
0.56
-0.19
0.20
0.65
0.03
-0.03
0.15
-0.12
0.15
Pongo
(29)
-0.63
-0.66
-0.73
- 0.94
-0.91
- 0.48
- 0.58
- 0.07
-0.13
- 1.01
- 0.67
0.34
- 0.80
- 0.50
0.44
-0.67
-0.22
0.19
- 0.38
-0.19
0.02
-0.37
0.15
0.06
- 0.19
0.03
0.31
1.13
0.09
1.14
0.95
0.06
1.40
0.61
-0.04
1.24
0.15
0.06
0.67
-0.11
0.14
0.69
0.15
-0.16
0.11
-0.07
0.10
F-ratio
( 5 . 151 d.f.1
46.4
186.8
111.9
338.1
251.8
59.1
39.1
236.4
10.3
1,416.7
283.2
214.7
1,500.9
45.4
127.6
443.0
386.0
387.4
255.6
2.3
4.7
211.3
181.8
50.0
632.9
69.3
1,140.4
79.9
39.7
930.7
400.9
50.0
417.6
325.8
79.3
93.8
181.8
50.0
156.1
109.0
42.8
251.3
261.5
31.9
68.7
193.8
23.6
of the hominoid coxal bones. The Penrose
shape coefficients are similar in proportion to
the Mahalanobis D distances. Hominids, fossil
or extant, do form a cluster, but this is not to
say the australopithecine specimen is identical. The uniqueness of Sts 14 is reflected by
the Mahalanobis distance of 13.0 between i t
and Homo compared to 23.8 between Homo
and Pun and 15.6 between Pan and Gorilla.
Since all of the coxal bones are standardized
for size i t cannot be argued that the Sts 14
specimen is different from Homo solely on the
220
HENRY M. MCHENRY AND ROBERT S. CORRUCCINI
TABLE 2
Correlation coefficients between principal coordinate
projections and variables for the
48-variable analysis
I
Principal coordinates
11
h
Measurement
I
1. suppubX
2. suppubY
3. suppubZ
4. infpubX
5. infpubY
6. infpubZ
7. rimpubX
8. rimpubY
9. rimpubZ
10. ischX
11. ischY
12. ischZ
13. tubX
14. tub Y
15. tub Z
16. rimischX
17. rimischY
18. rimisch Z
19. acetX
20. acetY
21. acetZ
22. rimil X
23. rimilY
24. rimil Z
25. antinfX
26. antinfY
27. antinfZ
28. antsupX
29. antsupY
30. antsupZ
31. crestX
32. crestY
33. crestZ
34. sacX
35. sacY
36. sacZ
37. postsupx
38. postsupY
39. postsupz
40. postinfX
41. postinfY
42. postinfZ
43. iliopX
44. iliopY
45. iliopZ
46. sciaticX
47. sciaticY
48. sciaticZ
0.26
-0.66
-0.86
0.94
-0.85
-0.66
-0.34
-0.95
0.47
0.99
- 0.94
0.72
0.98
-0.47
0.50
0.96
-0.97
0.93
0.87
0.13
0.20
- 0.91
0.06
0.33
-0.97
0.88
-0.55
- 0.95
- 0.66
- 0.69
- 0.95
0.89
0.33
-0.96
0.95
- 0.48
- 0.78
0.06
0.33
0.87
0.86
0.45
-0.87
0.91
- 0.02
0.80
0.93
0.39
I1
0.59
0.17
-0.35
0.15
0.15
-0.62
0.54
0.09
-0.26
-0.06
-0.22
-0.63
- 0.08
-0.64
- 0.69
0.04
- 0.08
- 0.29
0.27
-0.07
-0.01
0.07
0.31
0.73
0.04
0.18
0.65
-0.20
0.38
0.05
-0.04
0.30
0.73
0.04
-0.07
0.71
-0.01
0.31
0.73
-0.20
-0.17
0.55
0.11
-0.13
0.72
-0.01
-0.14
0.49
I11
0.42
-0.51
0.19
0.09
- 0.32
0.16
0.47
- 0.06
- 0.24
- 0.04
0.10
0.03
-0.06
0.17
0.12
-0.02
0.10
-0.05
0.17
0.11
0.46
0.12
0.59
-0.51
0.04
0.18
-0.16
-0.12
0.18
- 0.35
-0.11
0.18
-0.51
0.11
-0.11
- 0.08
0.20
0.59
-0.51
-0.15
-0.01
0.33
- 0.02
- 0.20
0.29
0.003
-0.06
0.41
basis of size although allometric factors could
play a role in the differentiation.
Further proof t h a t the primary contrast between hominoid 0s coxae lies between pongids
and hominids is provided by a principal component analysis of the 48 coordinates. The first
principal component explains 54.5% of the
total variance and widely separates hominids
HOMO
STSM
PAN
GORILLA PONGO
GORILLA
PONGO
Fig. 3 Lower left are the Penrose shape coefficients and
upper right are the Mahalonobis D distances based on the
48 size-standardized coordinates with corresponding dendrograms.
from pongids (figs. 4A,B). Sts 14 is close to the
human range and is far removed from the
apes. Traits with high correlations with this
axis (table 2) include numerous variables
which describe the uniqueness of the human
0s coxa. The highest positive correlations are
with isch X, tub X, and rimisch X and rimisch
Y which reflect the unique positioning of the
ischium in Homo relative to the iliac blade
(table 2). Traits describing the orientation of
the acetabulum are also highly correlated
with the first principal coordinate corresponding to the distinctively human positioning of the hip joint relative to the ilium.
All of the X coordinates on the iliac blade have
high correlations which relates to the unique
shape of the blade in human 0s coxae. In most
of these diagnostically human traits Sts 14 is
most similar to Homo.
The second principal component accounts
for 14.7%of the total variance and acts to separateGorilla from other hominoids. Sts 14 and
Homo are close together on this axis. The
traits with high correlations with the second
principal coordinate are those that describe
the distinctive features of the gorilla pelvic
bone such as its relatively broad and high iliac
blade (rimil Z, crest Z, sac Z, postsup Z and
iliop Z have the highest correlations).
Sts 14 is separated by the third principal
component which accounts for 7.3% of the
total variance. Traits with high correlations
include those describing the relative position
of the pubis (suppub X and Y), the acetabulum
(rimpub X, acet Z, rimil Y and Z), and the iliac
blade (crest Z, postsup Y and Z). The fourth
221
ANALYSIS OF THE HOMINOID OX COXAE
0
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HOMO
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*
..
.
.
0
0
.
- 0 .
0
.
0.
0
.
0
.
0
.
I
HOMO
PAN
0
GORILLA *
PONGO
0
S T S 14
r)
*
m
0
O D
O
0-
0
0
0
-2
-
0 0
0
7
'
. O
0
0
0 0
0
0
0
B '
-4
.
0
.
.
.
.
.
. ..
.
.
.
0 0 0 0
D
O
00
... .. ..
.........
.
.
.
0
0 .
.
-2
* .
.
0 . .
0
.
0.
2
0
4
6
I
Fig. 4A Dispersion of the first and second principal components based on 48 size-standardized coordinates.
All specimens are plotted but many do not show due to overprinting.
B Dispersion of the first and third principal components based on 48 size-standardized coordinates,
and higher principal coordinates account for a
diminishingly small part of the total variance
and are of little interest.
A study of the same 48 size-standardized
coordinates using canonical variates analysis
shows similar results (fig. 5).The first canonical variate accounts for 86.8%of t h e total between-group variance and separates Homo
from t h e pongids. Sts 14 is intermediate but is
closest to Homo. The correlations between the
variables and the first canonical variate are
very similar to those in the principal components analysis. The second canonical variate
(accounting for 8.5% of the total betweengroup variance) separates Pan and Gorilla
maximally.Horno andl'ongo fall into a n intermediate position on this axis whereas Sts 14
projects close to Gorilla. The third and last
axis maximizes the projection of Pongo with
Pan minimized and t h e other groups a r e in a n
intermediate position.
A drawback to these 48 variable analyses
222
HENRY M. MCHENRY A N D ROBERT S. CORRUCCINI
Pongo
T
Fig, 5 Centroids of the canonical analysis based on 48 size-standardized coordinates.
TABLE 3
Mean sham Variables in standard deviation units of the rotated coxal coordinates
Measurement
1. subpubX
2. subpubZ
3. infpubX
4. infpubZ
5. rimpubX
6. rimpubZ
7. ischX
8. ischZ
9. tubX
10. tub Z
11. rimischX
12. rimischZ
13. acetX
14. acetZ
15. antinfX
16. antinfZ
17. antsupX
18. antsupZ
19. crestX
20. crestZ
21. sacX
22. sacZ
23. postsupX
24. postsupZ
25. postinfX
26. p st i n f Z
27. iliopX
28. iliopZ
29. sciaticX
30. sciaticZ
Pan
Gorilla
Pongo
F-ratio
(42)
Sts 14
(27)
(29)
(29)
(5,151 d.f.1
- 0.84
- 1.25
-0.64
- 1.03
-0.77
-0.66
- 1.09
- 0.38
- 0.68
- 0.09
- 1.25
0.52
- 1.04
0.61
-0.76
0.27
-0.51
0.06
-0.24
0.005
0.53
0.13
1.34
-0.07
1.62
-0.17
1.48
-0.08
0.64
0.01
0.63
-0.22
0.09
0.07
-0.75
-0.76
- 1.08
-0.52
-0.62
-0.06
- 1.23
0.46
- 1.01
0.65
-0.72
0.31
-0.36
0.10
-0.24
0.14
-0.02
0.07
1.21
-0.11
1.71
- 0.22
1.55
-0.17
0.67
0.13
0.72
-0.16
0.18
0.15
Homo
- 0.68
-0.90
-0.87
-0.11
-0.32
0.76
-0.18
0.72
-0.54
0.54
-0.28
0.06
-0.88
-0.03
- 1.05
-0.06
0.69
0.10
1.41
-0.16
1.56
0.07
1.19
0.24
0.46
-0.17
0.33
0.19
-0.83
-0.76
-0.84
-0.14
-0.61
0.89
-0.51
0.91
-0.76
0.51
- 0.26
0.07
- 0.65
-0.12
-0.77
- 0.04
0.75
-0.04
1.61
-0.25
1.63
- 0.06
1.01
0.12
0.60
-0.16
0.27
0.11
is that the orientation of the coxal bones
depends upon fixed orientations which may
unduly influence differences between human
and ape coxal bones. To remedy this, a second
- 0.83
- 0.78
- 1.16
- 0.45
-0.72
- 0.09
- 1.16
0.51
- 0.92
0.60
-0.79
0.29
-0.47
0.07
-0.24
0.06
0.34
0.08
1.31
- 0.04
1.60
-0.18
1.42
-0.05
0.76
0.10
0.75
-0.25
0.11
0.11
53.9
472.0
333.7
268.9
155.8
13.1
1,100.7
215.9
1,235.5
147.6
222.4
357.5
155.3
4.9
840.9
81.7
1,356.3
18.7
664.5
129.5
111.4
11.5
80.6
114.6
363.3
65.3
162.8
16.2
92.8
33.0
set of multivariate analyses are performed on
30 variables which are rotated to best fit using
X and Z coordinates as described above. This
eliminates the fixed reference plane needed in
223
ANALYSIS OF THE HOMINOID OX COXAE
most coordinate comparisons to establish and
fix the coordinates. The coordinates themselves become the comparative data rather
than just measuring distances from the plane
of comparison; this prevents the landmarks of
that plane from becoming the central and
dominating comparative data. The rotated
coordinates should give a better impression of
overall shape of the structure, rather than
just the comparative orientation of the basic
plane. Table 3 presents the means of these
rotated coordinates. The effect of this rotation
is to line the plane of the iliac blade along the
X axis and the ischio-pubic plane along the Zaxis. It is as if one is looking down a t the crest
of the ilium with the ischium pointing toward
the observer and the pubis pointing away. As
revealed by table 3 the major axis of variation
is again between the hominids and pongids.
Many of the same traits that were most
heterogeneous in the unrotated analysis have
the highest F ratios in this rotated analysis
(compare the last column in tables 1 and 3).
Thus the positions of the ischium and ischial
tuberosity are distinctively different in hominids and pongids. The anterior superior iliac
spine is also heterogeneous in the same way as
before. Typically, the F-ratios are increased
for Z coordinates and slightly decreased for X
coordinates as a result of the rotation.
In the canonical variates analysis of the
rotated data (fig. 6) the positions of the centroids are like those in the previous analyses
but the results are more interpretable. The
first variate separates humans from apes and
accounts for 91.6%of the total variance. Sts 14
falls close to the Homo projection. Most of the
variables have high positive or negative correlations (table 4) with this variate reflecting
the fact that the hominid pelvic bone is fundamentally different in shape from the ape
pelvic bone. Hence the 2 (roughly anterior)
projection of the pubis is relatively greater in
Homo than it is in the apes. The ischial tuberosity is much closer to the center of the
bone in humans (tub XI. In apes the plane of
the acetabulum is approximately perpendicular to the plane of the iliac blade but the angle
is more acute in humans. The anterior superior iliac spine is much further from the posterior superior iliac spine in hominids than i t is
in pongids. Sts 14 shares most of these and
many more traits in common with Homo
sapiens.
The second canonical variate resembles the
second axis of the previous analyses with
Pongo
a
'\.T h
Gorilla
P
Pig. 6 Centroids of the canonical analysis based on 30
rotated coordinates.
Gorilla a t one extreme and Pan a t the other.
In this analysis Sts 1 4 is much closer toHomo.
As before variate three maximizes Pongo and
places Sts 14 and Homo close together again.
Since the fossil was entered into the calculation of this analysis, a fourth variable is generated. Although this variate accounts for
only 0.5%of the total variance it is important
for the interpretation of Sts 14 because this
specimen is widely separated from the other
groups on this function. The traits with high
correlations with the fourth variate are those
which describe the uniqueness of the fossil.
These include the X projection of the superior
pubis which is relatively small in the fossil.
The Z projection of the ischial tuberosity is
highly correlated with the fourth variate
which is related to the relatively large distance separating the ischial tuberosity from
the center of the bone in Sts 14.
The overall morphometrical affinities of the
fossil are represented by the Mahalanobis D
distances and the Pythagorean distances between principal coordinate projections (d)
(fig. 7). D and d are proportionately very similar. Although Sts 14 is clearly unique, i t is
about two times nearer to Homo than to the
apes in total distance and it is more than three
times closer to Homo on the first canonical
variate which is the main factor of human distinctiveness.
A final multivariate analysis compares just
the iliac blade (points 8-16 in fig. 2) for the
purpose of including as many of the fossils as
possible. Those specimens from Makapansgat
(MLD 7 and 25) are combined with Sts 14 to
form one group (A. afrzcanus). SK 3155 is used
to represent the robust australopithecine. The
224
HENRY M. MCHENRY AND ROBERT S. CORRUCCINI
TABLE 4
Correlation coefficients between canonical variates and variables for the rotated 30-variable analysis
Canonical variate
Measurement
I
1. suppubX
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
0.12
-0.98
0.98
- 0.99
- 0.93
-0.71
0.99
0.88
0.98
0.72
0.73
0.99
0.88
-0.34
- 0.99
- 0.69
- 0.98
- 0.98
-0.99
0.81
-0.75
- 0.09
0.71
0.73
0.98
0.80
-0.85
0.58
0.97
0.65
suppub2
infpubX
infpub2
rimpubX
rimpubZ
ischX
ischZ
tubX
tubZ
rimischX
rimischZ
acetX
acetZ
antinfX
antinfZ
antsupX
antsupZ
crestX
crestZ
sacX
sacZ
postsupX
postsupZ
postinfX
postinfZ
iliopX
iliopZ
sciaticX
sciatic2
1
17.0 125.0 22.1
21.2 118.7
I 23.0
1
19.0
'+-cc::ApvzJ
ONGO
2.1
1.6
0.5
Fig. 7 Lower left are the Penrose shape coefficients and
upper right are the Mahalanobis D distance based on the 30
rotated coordinates with corresponding dendrograms.
results of the canonical variates analysis (fig.
8) are very similar to those presented previously (McHenry and Corruccini, '75). The first
axis (accounting for 83.4%of the total variance) separates the hominids from the pongids. Traits with high correlations describe
the unique broad and low shape of the human
I1
-0.38
0.11
-0.08
0.24
-0.19
- 0.25
-0.02
-0.008
-0.007
-0.30
-0.17
-0.16
-0.56
-0.89
0.02
-0.33
0.32
0.25
0.21
0.31
- 0.41
0.67
-0.54
0.49
0.001
- 0.39
- 0.21
- 0.66
- 0.35
-0.49
I11
-0.08
- 0.22
-0.05
-0.15
-0.27
-0.29
0.16
0.19
0.18
0.17
-0.22
0.15
0.15
- 0.006
- 0.08
-0.11
-0.14
-0.25
- 0.12
0.16
-0.12
-0.18
-0.19
0.21
0.26
0.27
0.29
- 0.40
0.08
0.11
IV
- 0.88
0.30
-0.37
0.39
0.49
0.79
-0.38
-0.77
-0.32
- 0.92
0.27
-0.53
-0.57
0.07
0.36
0.76
0.45
0.51
0.54
0.07
-0.11
0.79
-0.70
0.02
-0.35
0.02
0.15
- 0.42
-0.39
0.21
iliac blade. Variate two (accounting for 11.0%
of the total variance) separates the specimens
with exceptionally large iliac fossae (Gorilla
and the australopithecines) from the rest. The
third canonical variate (4.0%of the total variance) minimizes the projection of the robust
australopithecine and separates it from both
Homo and the gracile australopithecine (A.
africanus). Traits with high correlations with
this axis (data not presented) include those
that describe the relative positions of the anterior inferior iliac spine, the posterior part of
the iliac crest, and the anterior border of the
sacral articular surface. Higher axes explain
diminishingly small amounts of the total
variance.
The Pythagorean distance between centroids in this 27 variable canonical variates
analysis shows that the hominids form one
cluster and the pongids another with the fossil
hominids closest to Homo but in a unique position. The distance between Homo and A .
africanus is 9.5 compared with the Homo-A.
ANALYSIS OF THE HOMINOID OX COXAE
Pongo
t
1
III
Gorillo
II
Fig. 8 Centroids of the canonical analysis based on 27
coordinates of the ilium.
robustus distance of 12.0, A. africanus-A.
robustus distance of 12.2, Homo-Pan of 18.1
and Pan-Gorilla of 7.8.
DISCUSSION
The results substantiate earlier conclusions
based upon linear measurements (McHenry,
'72, '75b; McHenry and Corruccini, '75; Oxnard, '73; Zuckerman et al., '73) especially
concerning the hominid nature of the australopithecines. Although unique, Sts 1 4
shows the salient similarities with humans.
The unique features are to be expected considering that an ancestor should not necessarily be just like its descendant and that evolution does not necessarily follow a straight line.
Some have interpreted the unique traits to
mean that the locomotor behavior ofdustralopithecus differed from Homo sapzens (Chopra,
'58, '61, '62; Day, '69, '73, '76a,b; Howell, '55;
Jenkins, '72; Mednick, '55; Napier, '63, '64,
'67; Oxnard, '73, '75; Straus, '62; Washburn,
'50; Wood, '73, '74; Zihlman, '67; Zihlman and
Hunter, '72; Zuckerman e t al., '67, '73). Others
have emphasized the apparent similarity in
locomotor behavior between a t least one form
of early hominid and Homo sapiens (Clark,
'55; Dart, '49a,b, '57, '58; Lovejoy, '73, '74;
Lovejoy and Heiple, '70, "72; Lovejoy et al.,
'73; McHenry, '75a,c; Robinson, '72, '74;
Robinson e t al., '72; Sigmon, '74, '75; Schultz,
'69).
Cartesian coordinates seem to be a good
way to approach the quantification of the total morphological pattern especially when
treated to standardizing procedures. Standardization of the coordinates clearly improves the discrimination. In this case the
multivariate within-to-between group vari-
225
ance ratio (Wilk's lambda) is about 50%
smaller than in the case using techniques of
Benfer ('75) and of Creel and Preuschoft ('76)
which do not standardize. Standardization
by rotation to best fit of a modal human
also improves discrimination although only
slightly.
The results show that even after rotation to
best fit using the X and Z coordinates the overall affinities of Sts 14 are closer to Homo than
to any other hominoid. This is important because the effect of the rotation is to position
the pelvic bone so that the ischio-pubic axis is
parallel to the Z axes, revealing the orientation of the ilium relative to the ischio-pubis as
does plate 3 of Oxnard ('75). Oxnard makes
the point that this manner of viewing the bone
shows i t has significant ape-like traits, as contrasted with a view perpendicular to the iliac
blade. Despite superficial aspects of resemblance between Pan and Australopithecus,
however, the fossil is still closer phenetically
to Homo.
ACKNOWLEDGMENTS
We thank C. K. Brain, P. V. Tobias, M. D.
Leakey, R. E. F. Leakey and M. H. Day for
permission to study the original fossils; R.
Thorington, B. Lawrence, C. Mack, and W. W.
Howells for the use of the comparative primate material in their care; L. C. McHenry for
extensive assistance; and the Wenner Gren
Foundation for Anthropological Research, and
the Committee on Research, University of
California, Davis, for financial support.
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