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 0 HOMO * 0 PAN GOR I I I A P ONGO ' I] O 0 0 0 0 D DO 0 S J S O .. 0 14 0 0 . . .. [ I . * 0 0. Or 0.. O0 O 0 .* . . * . .. ...... . .. . 0 * .. . . 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. 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