Analysis of the hominoid os coxae by Cartesian coordinates

Analysis of the Hominoid 0 s Coxae by Cartesian Coordinates H E N R Y M. MCHENRY AND 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 - Cartesian coordinates . Multivariate analysis

A B S T R A C T 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, SK 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 tha 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 the 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 i ts parts may not adequately represent important features such as the relative positions of mus- cle 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 pro- vide one method. Benfer (’75) and Creel and Preuschoft 1’76) have recently presented ex- amples 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 mea-

AM. J. PIIYS. ANTHROP. 11978) 48: 215-226.

surements taken on the same 0 s coxae and re- ported 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 tha t the reconstruction can be made by comparing one side to 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- tially present on the left side but not on the right. Articulating the entire pelvis as recon- structed by Robinson aids in the process of accurately reconstructing the bone. The other fossils are SK 3155 from Swartkrans (Brain et al., '75; McHenry, '72, '75b,d; McHenry and Corruccini, '75) dated between 1.5 and 2.5 million years ago, and MLD 7 and MLD 25 from Makapansgat (Dart, '49a,b, '57, '58; Zihlman and Hunter, '72) dated at about the same age as Sts 14. The Swartkrans specimen is missing most of the ischium and pubis and requires reconstruction of the anterior superior spine and part of the iliac crest (see McHenry, '75, for a discussion of how this was done). The two Makapansgat specimens consist of only the iliac portion of the 0s coxae. A separate analysis is done on the nine points common to all four fossils.

The comparative sample consists of 42 Homo sapiens from the Peabody Museum, Harvard University, 27 Pun troglodytes, 29 Gorilla gorilla, and 29 Pongo pygmaeus from the Museum of Comparative Zoology, Harvard University, and the Smithsonian Institution. Approximately equal numbers of males and females make up the sample.

The particular method for finding 3-dimensional coordinates involves the use of a diagraph (fig. 1). The bone is suspended over a sheet of graph paper. The points on the bone

the X and Y coordinates. The Z coordinate is taken as the height of the point above the paper, which could be read from the diagraph. The orientation of the coxal bone does not have to be kept constant from one coxal bone to the next. The advantage of this procedure is that the bones do not have to be in the same position over the graph paper each time.

Sixteen points on the 0s coxa are defined for the purpose of finding their coordinates (fig. 2). The points chosen are easily definable and reasonably homologous from one hominoid species to the next. Because of the obvious difference between the morphology and function of the human 0s coxa and the rest of the hominoids, all of these points probably are not functionally analogous (Benton and Gavan, '60). Another criterion for choosing points is to ensure that the various planes of the 0s coxa such as the iliac blade, the acetabulum, the pubis, the ischium, and the sacral articular surface, are represented by at least three points each.

1. Superior border of the pubic symphysis (suppub) : the point where the long axis of the pubic symphysis intersects its superior border.

2. Inferior border of the pubic symphysis (infpub): the point where the long axis of the pubic symphysis intersects its inferior border.

3. Rim of the acetabulum a t the pubis (rimpub): the point on the rim of the acetabulum 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

II

217

i Fig. 2 Position of points desc

axis of the ischium with the inferior border of the ischium on its midline.

5. Ischial tuberosity (tub): the most superi- or 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.

:ribed by Cartesian coordinates.

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 as 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 theo- retically 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 equal- ly 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 con- touring fit) analytical method to assimilate such data. Again, this is complicated and it is difficult to refer the results back to the original data (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 reduc- tion (factor analysis in his case) on X. Y and Z coordinates fixed in some frame of reference. This provides just as much discrimination and


taxonomic or functional information, and makes actual morphological patterns (relative migration of landmarks) more under- standable; finally, i t is much easier to do.

Sneath (’67) however, offers some sugges- tions for data transformation which are un- doubtedly 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 transforma- tions are as 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. 11 is on the X- Y 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 subtract- ing 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 trans- forms 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 tradi- tional 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 sym- metrical structures, but rotation of 3-dimensional unsymmetrical structures (like the cox- a1 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 ex- periments indicated that selection of different standards for rotation did not appreciably af- fect 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 an un- known point.

RESULTS

Table 1 presents 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 di- rections relative to the iliac blade. In most re- spects 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 1 reflects the amount of difference between means compared to the general within- sample 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

ANALYSIS OF THE HOMINOID OX COXAE 219

TABLE 1

Mean shape variables in standard deviation units of the original coxal coordinates

Homo Pan Gor11Ia Pongo F-ratio 142) Sts 14 (27) (29) (29) ( 5 . 151 d.f.1 Measurement

1. suppubX 2. suppubY 3. suppubZ 4. in fpubX 5. in fpubY 6. in fpubZ 7. r impubX 8. r impubY 9. r impubZ

10. ischX 11. ischY 12. ischZ 13. t u b X 14. t u b Y 15. t u b 2 16. r imischX 17. r imischY 18. r imischZ 19. acetX 20. acetY 21. acetZ 22. r imilX 23. r i m i l Y 24. r i m i l Z 25. a n t i n f X 27. an t i n fZ 28. antsupX 29. antsupY 30. antsupZ 31. crestX 32. crestY 33. crestZ 34. sacX 35. sacY 36. sacZ 37. postsupx 38. postsupY 39. postsup2 40. post in fX 41. post in fY 42. postinfZ 43. i l i opX 44. i l i opY 45. i l iopZ 46. sciatic X 47. sciat icY 48. sciat ic2

-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

-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

-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

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

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 Mahala- nobis D distances given in figure 3. These coefficients represent a preliminary multivariate analysis to assess the overall affinities

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 identi- cal. 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


TABLE 2

Correlation coefficients between principal coordinate projections and variables for the

48-variable analysis

Principal coordinates

I I1 I11 Measurement

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

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

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 that 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

11 I h

HOMO S T S M 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 sep- arateGorilla 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

ANALYSIS OF THE HOMINOID OX COXAE

.

221

0 -

-2 -

HOMO * P A N 0

0 O D 0 0 0 0 .

D O 0 0 . 0 0 0 . . O . . . 0 . . . .

. O . 0 0 0 '7

0 0

0 0

0 0

0 . .

0 0 I]

G O R I I I A O

P O N G O ' S J S 1 4 *

0 0 0

0 0 D O

D O 0 0 0 . .

0 . . . [ I . . 0 .. 0. . . * O r O O 0 0.. 0 . . .*

. . * . ... . .. 0 . . - 0 .

0 . 0 . 0

0 . . . 0 .

0 .

.. * . ... . .. 0 . . - 0 .

0 . 0 . 0

0 . . . 0 .

0 .

I H O M O r)

P A N 0

G O R I L L A * PONGO 0

S T S 14 *

m . . . . 0 . * . . . . .. 0 . .. .

0 . . ... . 0. .

0 . . B ' -4 -2 0 2 4 6

I Fig. 4A

B

Dispersion of the first and second principal components based on 48 size-standardized coordinates.

Dispersion of the first and third principal components based on 48 size-standardized coordinates, All specimens are plotted but many do not show due to overprinting.

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 the total between-group variance and separates Homo from the 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 between- group 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 the other groups a re 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

Homo Pan Gorilla Pongo F-ratio (42) Sts 14 (27) (29) (29) (5, 151 d.f.1 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. pstinfZ 27. iliopX 28. iliopZ 29. sciaticX 30. sciaticZ

- 0.84 - 1.25 - 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

-0.64 - 1.03 -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

-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

- 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

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

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


most coordinate comparisons to establish and fix the coordinates. The coordinates them- selves 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 Z- axis. I t 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 superi- or 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

T a '\.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 14 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 calcula- tion of this analysis, a fourth variable is gen- erated. 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 dis- tinctiveness.

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


TABLE 4

Correlation coefficients between canonical variates and variables for the rotated 30-variable analysis

Canonical variate

I I1 I11 IV Measurement

1. suppubX 2. suppub2 3. infpubX 4. infpub2 5. rimpubX 6. rimpubZ 7. ischX 8. ischZ 9. tubX

10. tubZ 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. postinfZ 27. iliopX 28. iliopZ 29. sciaticX 30. sciatic2

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

-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

-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

- 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

17.0 125.0 1 22.1 I 23.0 21.2 118.7 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 previ- ously (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

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 i t 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.


Pongo t III

1 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; Ox- nard, '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 con- sidering 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 ofdustralo- pithecus 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. Stan- dardization of the coordinates clearly improves the discrimination. In this case the multivariate within-to-between group vari-

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 con- trasted with a view perpendicular to the iliac blade. Despite superficial aspects of resem- blance 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.

LITERATURE CITED

Benfer, R. A. 1975 Morphometric analysis of Cartesian coordinates of the human skull. Am. J. Phys. Anthrop., 42: 371-382.

Benton, R. S., and J. A. Gavan 1960 The concept of homol- ogy applied to the anterior superior iliac spine. Am. J. Phys. Anthrop., 18: 273-279.

Brain, C. K., E. S. Vrba and J. T. Robinson 1974 A new hominid innominate bone from Swartkrans. Ann. Trans- vaal Mu., 29: 55-63.

Chopra, S. R. K. 1958 A "pelvimeter" for orientation and measurement of the innominate bone. Man, 58: 126.

The angle of pelvic torsion in the primates. Z. Morph. Anthrop., 51: 268-274.

The innominate bone of the Australopithe- cinae and the problem of erect posture. Bibl. Primat., 1: 93-102.

Clark, W. E. LeGros 1955 The 0s innominatum of recent pongidae with special reference to that of the Australo- pithecinae. Am. J. Phys. Anthrop., 13: 19-28.

Creel, N., and H. Preuschoft 1976 Cranial morphology of the lesser apes. A multivariate statistical study. Gibbon and Siamang, 4: 219-303. Karger. Basel.

1961

1962


Dart, R. A. 1949a Innominate fragments of Australo- pithecus prometheus. Am. J. Phys. Anthrop., 7: 301-333.

1949b The first pelvic bones ofAustralopithecus prometheus: preliminary note. Am. J. Phys. Anthrop., 7: 255-258.

1957 The second adolescent (female) ilium of Australopithecus prometheus. J. Palaeont. Soc., India, 2: 73-82.

1958 A further adolescent australopithecine ilium from Makapansgat. Am. J. Phys. Anthrop., 16: 473-479.

Day, M. H. 1969 Femoral fragment of a robust australopithecine from Olduvai Gorge, Tanzania. Nature, 221: 230-233.

Locomotor features of the lower limb in hominids. Symp. 2001. SOC. Lond., 33: 29-51.

Hominid postcranial remains from the East Rudolf succession. In: Earliest Man and Environ- ments in the Lake Rudolf Basin. Y. Coppens, F. C. Howell, G. L. Isaac and R. E. F. Leakey, eds. University of Chicago Press, pp. 507-521.

Hominid postcranial material from Bed I, Olduvai Gorge. In: Human Origins: Louis Leakey and the East African Evidence. G. L. Isaac and E. R. McCown, eds. W. A. Benjamin, Menlo Park, California, pp. 363-374.

Howell, F. C. 1955 The pelvic remains of Australopithe- cus. Am. J. Phys. Anthrop., 13: 396.

Jenkins, F. A,, Jr. 1972 Chimpanzee bipedalism. Sci- ence, 178: 877-879.

Lestrel, P. E. 1974 Some problems in assessment of morphological size and shape differences. Yrbk. Phys. An- throp., 18: 140-162.

Lovejoy, C. 0. 1973 The gait of australopithecines. Yrbk. Phys. Anthrop., 17: 147-161.

1978 A biomechanical review of the locomotor diversity of early hominids. In: African Hominidae of the Plio-Pleistocene. C. J. Jolly, ed. Duckworth, London, in press.

Lovejoy, C. O., and K. G. Heiple 1970 A reconstruction of the femur of A. africanus. Am. J. Phys. Anthrop., 32: 33-40.

1972 The proximal femoral anatomy of Aus- tralopithecus. Nature, 235: 175-176.

Lovejoy, C. O., K. G. Heiple and A. H. Burstein 1973 The gait of Australopithecus. Am. J. Phys. Anthrop., 38: 757-700.

&Henry, H. M. 1972 The postcranial anatomy of early Pleistocene hominids. Ph.D. Thesis, Harvard University, Cambridge, Mass.

1975a The ischium and hip extensor mechanism in human evolution. Am. J. Phys. Anthrop., 43: 39-46.

1975b A new pelvic fragment from Swartkrans and the relationship between the robust and gracile australopithecines. Am. J. Phys. Anthrop., 43: 245-262.

1975c Biomechanical interpretation of the early hominid hip. J. Hum. Evol., 4: 343-356.

1975d Fossils and the mosaic nature of human evolution. Science, 190: 425-431.

McHenry, H. M., and R. S. Corruccini 1975 Multivariate analysis of early hominid pelvic bones. Am. J. Phys. An- throp., 43: 263-270.

Mednick, L. W. 1955 The evolution of the human ilium. Am. J. Phys. Anthrop., 13: 203-215.

1973

1976a

1976b

Napier, J. R. 1963 The locomotor functions of hominids. In: Classification and human evolution. S . L. Washburn, ed. Aldine, Chicago, pp. 178-189.

1964 The evolution of bipedal walking in the hominids. Arch. Biol. (Liege), 75 (Suppl.): 673-708.

1967 The antiquity of human walking. Sci. Amer., 216: 56-66.

Oxnard, C. E. 1973 Some problems in the comparative assessment of skeletal form. Symp. SOC. Study Hum. Biol., Vol. 11 (Human Evolution). M. Day, ed. Taylor and Fran- cis, London, pp. 103-125.

1975 Uniqueness and Diversity in Human Evolution. University of Chicago Press, Chicago.

Robinson, J. T. 1972 Early Hominid Posture and Loco- motion. University of Chicago Press, Chicago, Ill.

1978 Evidence for locomotor difference between gracile and robust early hominids from South Africa. In: African Hominidae of the Plio-Pleistocene. C. J. Jolly, ed. Duckworth, London, in press.

Robinson, John T., L. Freeman and B. A. Sigmon 1972 Some aspects of pongid and hominid bipedality. J. Hum. Evol., 1: 361-369.

Sigmon, B. A. 1974 A functional analysis of pongid hip and thigh musculature. J. Hum. Evol., 3: 161-185.

1975 Functions and evolution of hominoid hip and thigh musculature. In: Primate functional morphology and evolution. R. H. Tuttle, ed. Mouton, The Hague, pp. 235-252.

Schultz, A. H. 1969 Observations of the acetabulum of primates. Folia Primat., 11: 181-199.

Sneath, P. H. A. 1967 Trend-surface analysis of transformation grids. J. Zool. (London), 151: 65-122.

Sokal, R. R., and P. H. A. Sneath 1963 Principles of Numer- ical Taxonomy. Freeman, San Francisco.

Straus, W. L., Jr. 1962 Fossil evidence of the evolution of the erect, bipedal posture. Yrbk. of Phys. Anthrop., 10: 334-344.

Washburn, S. L. 1950 The analysis of primate evolution with particular reference to the origin of man. Cold Spr. Harb. Symp. Quant. Biol., 15: 67-78.

Wood, B. A. 1973 Remains attributable to Homo in the East Rudolf succession. In: Earliest Man and Environ- ments in the Lake Rudolf Basin. Y. Coppens, F. Clark Howell, Glynn L. Isaac and R. E. F. Leakey, eds. Univer- sity of Chicago Press, Chicago, pp. 490-506.

1974 Olduvai Bed I post-cranial fossils. A reas- sessment. J. Hum. Evol., 3: 373-378.

Zihlman, A. 1967 Human Locomotion: A Reappraisal of the Functional and Anatomical Evidence. Ph.D. Disserta- tion, University of California Berkeley.

Zihlman, A. 1978 Interpretations of early hominid locomotion. In: African Hominidae of the Plio-Pleisto- cene. C. Jolly, ed. Duckworth, London, in press.

Zihlman, A. L., and W. S. Hunter 1972 A biomechanical interpretation of the pelvis of Australopithecus. Folia Primat., 18: 1-19.

Zuckerman, S., E. H. Ashton, C. E. Oxnard and T. F. Spence 1967 The functional significance of certain features of the innominate bone in living and fossil primates. J. Anat. (London), 101: 608-609.

Zuckerman, S., E. H. Ashton, R. M. Flinn, C. E. Oxnard and T. F. Spence 1973 Some locomotor features of the pelvic girdle in primates. Symp. Zool. SOC. London., 33: 71-165.

Documents

Analysis of the hominoid os coxae by Cartesian coordinates