BRIEF COMMUNICATION
Multivariate Analysis of Gigantopithecus Mandibles ROBERT S. CORRUCCINI Division of Physical Anthropology, Smithsoninn Institution, W a s h i n g t o n , D.C. 20560
KEY WORDS Gigantopithecus . Australopithecines ate analysis . Mandible . Teeth.
.
Multivari-
ABSTRACT Multivariate analysis of measurements of the teeth and mandibles of Gigantopithecus species has been conducted, using several methods. Results indicate Gigantopithecus is a n aberrant form, less related to australopithecines and gorillas than the latter are to each other. Gracile and robust australopithecines differ considerably more than do male and female gorillas.
While metrical data are justlfiably used widely in assessing fossils, there is an unresolved problem in how best to analyze and present the data. Commonly, indices are derived from subjectively chosen pairs of variables, and different samples compared through univariate tests. One problem with indices is explaining why certain ones are chosen while other combinations are not. There are (p2-p)/2 possible bivariate combinations for p measurements. Interpreting the cause of variation in indices is difficult; for instance, the divisor could be increasing or the dividend decreasing to produce identical indices in two different fossil lineages. Given a large enough body of data, any hypothesis could presumably be supported through deriving and presenting just the right indides. Frayer ('73) presents the hypothesis that Gigantopithecus was a hominid, ancestral to robust australopithecines. While he gives an excellent array of metrical data, his analysis is based on certain indices which seem to separate Gigantopithecus and australopithecines from gorillas (Simons and Chopra, '69). On a trait-by-trait basis, Frayer shows Gigantopithecus either falls in the upper australopithecine range for molar indices or in the lower range for indices concerning anterior mandibular reduction. As Le Gros Clark ('55) stressed long ago, it can be very misleading to treat a list of individual traits in isolation rather than considering them as a unified morphological pattern. For instance, Ashton and Zuckerman's ('50) odontometrical study showed overlap between australopithecines and pongids AM. J. PHYS.ANTHROP.,42: 167-170.
in every variable, yet the australopithecine dentition taken as a whole is unquestionably hominid. It is desirable to synthesize patterns of univaria t e and bivaria t e variation through the techniques of multivariate analysis. This brief communication concerns the application of several multivariate methods to Frayer's ('73) mandibular measurements. I shall also briefly discuss the relation between my findings and those of Robinson and Steudel ('73) regarding their multivariate analysis of dental measurements. MATERIALS AND METHODS
Several variables and individuals have been deleted from Frayer's data ('73: table 1 and appendix). The M3 lengths and breadths are not used because these are not present in some Gigantopithecus specimens. Australopithecine fossils missing more than half the measurements are excluded. This leaves 17 variables: bicanine breadth, symphyseal height, corpus height and width, Pg- Mz chord, and length and breadth of In through Mz. The samples are of 20 Pan gorilla males, 20 P. gorilla females, 10 robust australopithecines (TM 1517, SK 12, 23, 34, 74, and 858, Omo L7-125, ER 729 and 818, and Natron), 7 gracile australopithecines (MLD 18 and 40, Sts 7, 36 and 52, ER 730 and 992), and 4 specimens of Gigantopithecus (1 G. bilaspurensis from India, 3 G. blachi from China). The data are transformed into allometrically-adjusted shape variables (Corruccini, '72). First, a variable expressing 167
168
ROBERT S. CORRUCCINI
overall size is computed as the average taken over every measurement for an individual. Allometric regression in P. gorilla is performed to provide a model of size-shape dependence. This follows the equation log y = log b a (log x), where the independent variable is the standard size variable. Each variable is exponentiated using the parameter a to render the measurement approximately isometric with respect to the size variable. Then all variables are converted to ratios of the size variable. This is a more standardized and interpretable way than conventional indices to eliminate size from the metrical information. I use three methods to compare samples. The first of these is canonical variates analysis, which scales the Generalized Distance “D2” onto orthogonal axes of discrimination. Some of the assumptions Fig. 1 Three-dimensional stereogram of maninherent in canonical variates computations are not satisfied by these data, and dibular morphometric distances. The three axes are canonical variates one (long horizontal axis), probably cannot be met in any metrical two (short horizontal axis) and three (vertical study involving fossils (Corruccini, ’74). axis). The lines connect points to their position It is necessary to compare statistical re- on the horizontal plane. Symbols: G, Gigantopithecus; RA, Robust australopithecines; GA, sults with a non-parametric methodGracile australopithecines; GM, Gorilla males; one which doesn’t use within-group co- GF, Gorilla females. variance to affect between-group differences, which doesn’t assume normally distributed variables, and which needn’t breadth, I? breadth, canine length and P3 be supplied with arbitrarily grouped sam- length contrasted with relatively small P4 ples of individual fossil specimens. Prin- length and breadth. The second axis repcipal coordinate analysis is used for this resents less than half the variance of the purpose. The technique scales the simple first, as it separates out just one sample: linear distance “d” (Sokal and Sneath, Gigantopithecus. The phenetically isolated ’63) between samples or individuals onto position of this genus resides in its relasuccessive independent axes. The distance tively huge corpus height, P, - Mz chord is the square root of the summed squared and MI length combined with exceptiondifferences between two trait lists, based ally small 12 length. on the Pythagorean theorem for distance Thus both of the first two canonical between two points in a geometric space. variates separate Gigantopithecus out at Weighted pair-group cluster analysis (So- one extreme. The third variate, and last kal and Sneath, ’63) based on “d” is also to represent an appreciable amount of done. variability, affects the greatest separation both between robust and gracile australoRESULTS pithecines and between male and female Figure 1 shows the three-dimensional gorillas. However, the two australopitheconfiguration of canonical variate relation- cine means are four times as far apart as ships. On the first canonical axis, Gigan- gorilla sexes. It is the gracile australotopithecus and P. gorilla fall at opposite pithecines which separate in the direction extremes, and australopithecines are near- of the male gorillas. Robust australopitheer Gigantopithecus. This axis accounts for cines differ from graciles in having relaabout two-thirds of the total discrimi- tively small bicanine breadth and corpus nation. The variables separating gorillas height, and large symphyseal height, P4 from other hominoids are large bicanine length and MI breadth. Sorting of indi-
+
MULTIVARIATE ANALYSIS OF GIGANTOPITHECUS
169
vidual robust and gracile specimens is with the exception of G . blacki I1 on axes absolute, with no overlap, in any pairwise one versus three. plot of variates one, two and three. An interesting byproduct of this GiganResults of principal coordinate analysis topithecus-oriented analysis is the fact are, interestingly, virtually identical to that robust-gracile australopithecine difthe canonical variates. The first principal ferences (D2=35) are so much greater coordinate separates Gigantopithecus from than pongid sexual dimorphism (DZ = 5). P . gorilla, and represents 66.1% variance There is actually less distance between as compared with 64.3% in the first ca- male gorillas and gracile australopithenonical variate. The second principal co- cines than between the two australopitheordinate places Gigantopithecus and Aus- cine forms. This reflects poorly on the tralopithecus at opposite extremes and “single species hypothesis” since advocontains 26.3% variance (28.5% for ca- cates of that philosophy consider australononical variate two). Principal coordinate pithecine variability analogous to gorilla three segregates robust and gracile aus- dimorphism. tralopithecines, accounting for 6.7% variShape analysis of the dental ance (5.6% for canonical variate three). measurements alone The correlation between the simple distance “d” and the Generalized Distance These conclusions also apply substan“D’ is r = 0.98. tially to the data of Robinson and Steudel Cluster analysis produces the following (‘73). They performed multiple discrimisteps. First P. gorilla sexes cluster to- nant analysis on lengths and breadths of gether. A t a considerably lower level of hominoid teeth and conclude, among other similarity, robust and gracile australo- things, that G . bilaspurensis is similar to pithecines cluster. Next, P . gorilla joins robust australopithecines and ancestral Australopithecus. Finally Gigantopithecus to them. Their data is essentially the same joins the cluster at the last step. as Frayer’s (’73) but for the deletion of mandibular corpus measurements and adDISCUSSION dition of samples representing Pongo p y g Frayer’s (‘73) own data reject the hy- maeus, Pan troglodytes, Homo erectus and pothesis of special affinity between Gigan- H . sapiens. Robinson and Steudel’s analysis can be topithecus and Australopithecus. His conclusion that the “mandible and dentition objected to on the basis of their failure to of G . bilaspurensis and Australopithecus, separate considerations of size and shape. then, closely resemble each other” is cor- Thus they analyze raw dental measurerect only in the limited sense that both ments, and the results, expectably, are differ from P. gorilla. True, Gigantopithe- dominated by size. Their plots show robust cus is nearer to Australopithecus (D2= 83) and gracile australopithecines consistently than to P . gorilla (D’= 104) in total mor- closer than are the sexes within P . gorilla phometric pattern. But more importantly, and Pongo. Female Pongo falls closer to Australopithecus is considerably closer to P . troglodytes than to male Pongo. Male gorillas (D’ = 43) than to Gigantopithecus. Pongo and female P . gorilla are nearer Gigantopithecus shows a Generalized Dis- each other than either is to the opposite tance of 75 to robust and 91 to gracile sex of their own species. This extreme disaustralopithecines. Since Australopithecus tortion of results by sex dimorphism neand P . gorilla are not particularly closely gates the validity of drawing taxonomic related taxa, the Australopithecus-Gigan- conclusions, for of what meaning is the topithecus relationship may be very re- position of, say, Gigantopithecus if the mote indeed. This conclusion is not altered technique cannot correctly affiliate sexes by considering G . bilaspurensis in isolation of a single species? I have collected odontometric data comfrom the three G . blacki specimens, for G . bilaspurensis fell in a central position parable to Robinson and Steudel’s (’73) among the Gigantopithecus cluster in all from Garn et al. (’64, ’66, ’67) for Ohio bivariate plots of individuals. The earlier whites, Wolpoff (’71) for H. erectus and Indian species is not closer to Australo- Australopithecus, and Ashton and Zuckerpithecus than are G . blacki specimens, man (’50) for Pongo, P . troglodytes and
170
ROBERT S. CORRUCCINI TABLE 1
Principal coordinate positions f o r hominoid species based on length and breadth of C - M 2 T h e order followed b y cluster analysis is indicated to t h e left Taxon
Coordinate one (60.6%)
:
.
(5.74)
0.75
0.57
0.03
-:--Pongopygmaeus female
0.56
0.37
- 0.08
-:--Pan gorilla male
0.37
0.26
0.23
0.07
0.07
0.38
1.10
- 0.27
0.02
1.05
-0.12
. :... .. _.._ . .. -:--Pan gorilla female . . . . ----Pan . troglodytes male . ____ ____. . _.__ Homo snpiens .. _-._ .. ... .. -:--Homo erectus ... ... ____ .. ____ . : -:--gracile australopithecines
- 0.32
._.___.___ robust australopithecines
- 1.22
- 0.23 - 1.03 - 0.54 - 0.41 - 0.26
__
- 0.45
0.87
__..
..‘
-’--Pan troglodytes female ___.
~
Coordinate three
(29.9%)
-;--Pongo p y g m a e u s male
____ . . ___-
Coordinate two
~
..-__._ .-__-__ _-Gigantopithecus bilaspurensis
P . gorilla. These mean measurements are inferior to Robinson and Steudel’s carefully collected data, but highly similar results were obtained from distance analysis of the raw dimensions. Size differences, especially between the sexes, were the main source of variation. Therefore these data were again analyzed, using the deliberately shape-oriented distance “d” followed by principal coordinate and cluster analysis. Table 1 shows the results. Both of the first two principal coordinates separate hominids from pongids, but in different ways. The first separates robust australopithecines at one pole from small pongids at the other, while the second separates modern man from the larger pongids. Gigantopithecus bilaspurensis is maximally separated from hominids on the second coordinate, and is approached most closely by Pongo. Principal coordinate three shows G. bilaspurensis distinct from every other hominoid. The combination of extraordinarily reduced canine and P3 length with narrow molars in G . bilaspurensis is unique among hominoids. Gigantopithecus is again an extreme outlier in the cluster analysis, while the correct clustering of pongid sexes lends some confidence to taxonomic interpretation of these results.
- 0.08 -0.70
- 0.02 -0.15
- 0.08 - 0.06 -0.51
LITERATURE CITED Ashton, E. H., and S . Zuckerman 1950 Some quantitative dental characteristics of the chimpanzee, gorilla, and orangoutan. Phil. Trans. B, 234: 471-484. Corruccini, R. S. 1972 Allometry correction in taximetrics. Syst. Zool., 21 : 375-383. 1974 Multivariate analysis in biological anthroaoloev: some considerations. .I. Hum. Evol., 3: (in press). Frayer, D. W. 1973 Gigantopithecus and its relationship to Australopithecus. Am. J. Phys. Anthrop., 39: 413-426. Garn, S. M., A. B. Lewis and R. Kerewsky 1964 Sex difference in tooth size. J. Dent. Res., 43: 306. 1966 Sexual dimorphism in the buccolingual tooth diameter. J. Dent. Res., 45: 1819. Garn, S . M., A. B. Lewis, D. R. Swindler and R. Kerewsky 1967 Genetic control of sexual dimorphism in tooth size. J. Dent. Res., 46: 963972. Le Gros Clark, W. E. 1955 The Fossil Evidence for Human Evolution. Chicago Univ. Press, Chicago. Robinson, J. T., and K. Steudel 1973 Multivariate discriminant analvsis of dental data bearine on early hominid affinities. J. Hum. Evol., 2,
-_
509-528. __-- ~ _
Simons, E. L., and S. R. K. Chopra 1969 Gigantopithecus (Pongidae, Hominoidea) a new species from North India. Postilla, 138; 1-18. Sokal, R. R., and P. H. A. Sneath 1963 Principles of Numerical Taxonomy. Freeman, San Francisco. Wolpoff, M. H. 1971 Metric Trends in Hominid Dental Evolution. Case Western Univ. Stud. Anthrop., 2.
Multivariate Analysis of Gigantopithecus Mandibles ROBERT S. CORRUCCINI Division of Physical Anthropology, Smithsoninn Institution, W a s h i n g t o n , D.C. 20560
KEY WORDS Gigantopithecus . Australopithecines ate analysis . Mandible . Teeth.
.
Multivari-
ABSTRACT Multivariate analysis of measurements of the teeth and mandibles of Gigantopithecus species has been conducted, using several methods. Results indicate Gigantopithecus is a n aberrant form, less related to australopithecines and gorillas than the latter are to each other. Gracile and robust australopithecines differ considerably more than do male and female gorillas.
While metrical data are justlfiably used widely in assessing fossils, there is an unresolved problem in how best to analyze and present the data. Commonly, indices are derived from subjectively chosen pairs of variables, and different samples compared through univariate tests. One problem with indices is explaining why certain ones are chosen while other combinations are not. There are (p2-p)/2 possible bivariate combinations for p measurements. Interpreting the cause of variation in indices is difficult; for instance, the divisor could be increasing or the dividend decreasing to produce identical indices in two different fossil lineages. Given a large enough body of data, any hypothesis could presumably be supported through deriving and presenting just the right indides. Frayer ('73) presents the hypothesis that Gigantopithecus was a hominid, ancestral to robust australopithecines. While he gives an excellent array of metrical data, his analysis is based on certain indices which seem to separate Gigantopithecus and australopithecines from gorillas (Simons and Chopra, '69). On a trait-by-trait basis, Frayer shows Gigantopithecus either falls in the upper australopithecine range for molar indices or in the lower range for indices concerning anterior mandibular reduction. As Le Gros Clark ('55) stressed long ago, it can be very misleading to treat a list of individual traits in isolation rather than considering them as a unified morphological pattern. For instance, Ashton and Zuckerman's ('50) odontometrical study showed overlap between australopithecines and pongids AM. J. PHYS.ANTHROP.,42: 167-170.
in every variable, yet the australopithecine dentition taken as a whole is unquestionably hominid. It is desirable to synthesize patterns of univaria t e and bivaria t e variation through the techniques of multivariate analysis. This brief communication concerns the application of several multivariate methods to Frayer's ('73) mandibular measurements. I shall also briefly discuss the relation between my findings and those of Robinson and Steudel ('73) regarding their multivariate analysis of dental measurements. MATERIALS AND METHODS
Several variables and individuals have been deleted from Frayer's data ('73: table 1 and appendix). The M3 lengths and breadths are not used because these are not present in some Gigantopithecus specimens. Australopithecine fossils missing more than half the measurements are excluded. This leaves 17 variables: bicanine breadth, symphyseal height, corpus height and width, Pg- Mz chord, and length and breadth of In through Mz. The samples are of 20 Pan gorilla males, 20 P. gorilla females, 10 robust australopithecines (TM 1517, SK 12, 23, 34, 74, and 858, Omo L7-125, ER 729 and 818, and Natron), 7 gracile australopithecines (MLD 18 and 40, Sts 7, 36 and 52, ER 730 and 992), and 4 specimens of Gigantopithecus (1 G. bilaspurensis from India, 3 G. blachi from China). The data are transformed into allometrically-adjusted shape variables (Corruccini, '72). First, a variable expressing 167
168
ROBERT S. CORRUCCINI
overall size is computed as the average taken over every measurement for an individual. Allometric regression in P. gorilla is performed to provide a model of size-shape dependence. This follows the equation log y = log b a (log x), where the independent variable is the standard size variable. Each variable is exponentiated using the parameter a to render the measurement approximately isometric with respect to the size variable. Then all variables are converted to ratios of the size variable. This is a more standardized and interpretable way than conventional indices to eliminate size from the metrical information. I use three methods to compare samples. The first of these is canonical variates analysis, which scales the Generalized Distance “D2” onto orthogonal axes of discrimination. Some of the assumptions Fig. 1 Three-dimensional stereogram of maninherent in canonical variates computations are not satisfied by these data, and dibular morphometric distances. The three axes are canonical variates one (long horizontal axis), probably cannot be met in any metrical two (short horizontal axis) and three (vertical study involving fossils (Corruccini, ’74). axis). The lines connect points to their position It is necessary to compare statistical re- on the horizontal plane. Symbols: G, Gigantopithecus; RA, Robust australopithecines; GA, sults with a non-parametric methodGracile australopithecines; GM, Gorilla males; one which doesn’t use within-group co- GF, Gorilla females. variance to affect between-group differences, which doesn’t assume normally distributed variables, and which needn’t breadth, I? breadth, canine length and P3 be supplied with arbitrarily grouped sam- length contrasted with relatively small P4 ples of individual fossil specimens. Prin- length and breadth. The second axis repcipal coordinate analysis is used for this resents less than half the variance of the purpose. The technique scales the simple first, as it separates out just one sample: linear distance “d” (Sokal and Sneath, Gigantopithecus. The phenetically isolated ’63) between samples or individuals onto position of this genus resides in its relasuccessive independent axes. The distance tively huge corpus height, P, - Mz chord is the square root of the summed squared and MI length combined with exceptiondifferences between two trait lists, based ally small 12 length. on the Pythagorean theorem for distance Thus both of the first two canonical between two points in a geometric space. variates separate Gigantopithecus out at Weighted pair-group cluster analysis (So- one extreme. The third variate, and last kal and Sneath, ’63) based on “d” is also to represent an appreciable amount of done. variability, affects the greatest separation both between robust and gracile australoRESULTS pithecines and between male and female Figure 1 shows the three-dimensional gorillas. However, the two australopitheconfiguration of canonical variate relation- cine means are four times as far apart as ships. On the first canonical axis, Gigan- gorilla sexes. It is the gracile australotopithecus and P. gorilla fall at opposite pithecines which separate in the direction extremes, and australopithecines are near- of the male gorillas. Robust australopitheer Gigantopithecus. This axis accounts for cines differ from graciles in having relaabout two-thirds of the total discrimi- tively small bicanine breadth and corpus nation. The variables separating gorillas height, and large symphyseal height, P4 from other hominoids are large bicanine length and MI breadth. Sorting of indi-
+
MULTIVARIATE ANALYSIS OF GIGANTOPITHECUS
169
vidual robust and gracile specimens is with the exception of G . blacki I1 on axes absolute, with no overlap, in any pairwise one versus three. plot of variates one, two and three. An interesting byproduct of this GiganResults of principal coordinate analysis topithecus-oriented analysis is the fact are, interestingly, virtually identical to that robust-gracile australopithecine difthe canonical variates. The first principal ferences (D2=35) are so much greater coordinate separates Gigantopithecus from than pongid sexual dimorphism (DZ = 5). P . gorilla, and represents 66.1% variance There is actually less distance between as compared with 64.3% in the first ca- male gorillas and gracile australopithenonical variate. The second principal co- cines than between the two australopitheordinate places Gigantopithecus and Aus- cine forms. This reflects poorly on the tralopithecus at opposite extremes and “single species hypothesis” since advocontains 26.3% variance (28.5% for ca- cates of that philosophy consider australononical variate two). Principal coordinate pithecine variability analogous to gorilla three segregates robust and gracile aus- dimorphism. tralopithecines, accounting for 6.7% variShape analysis of the dental ance (5.6% for canonical variate three). measurements alone The correlation between the simple distance “d” and the Generalized Distance These conclusions also apply substan“D’ is r = 0.98. tially to the data of Robinson and Steudel Cluster analysis produces the following (‘73). They performed multiple discrimisteps. First P. gorilla sexes cluster to- nant analysis on lengths and breadths of gether. A t a considerably lower level of hominoid teeth and conclude, among other similarity, robust and gracile australo- things, that G . bilaspurensis is similar to pithecines cluster. Next, P . gorilla joins robust australopithecines and ancestral Australopithecus. Finally Gigantopithecus to them. Their data is essentially the same joins the cluster at the last step. as Frayer’s (’73) but for the deletion of mandibular corpus measurements and adDISCUSSION dition of samples representing Pongo p y g Frayer’s (‘73) own data reject the hy- maeus, Pan troglodytes, Homo erectus and pothesis of special affinity between Gigan- H . sapiens. Robinson and Steudel’s analysis can be topithecus and Australopithecus. His conclusion that the “mandible and dentition objected to on the basis of their failure to of G . bilaspurensis and Australopithecus, separate considerations of size and shape. then, closely resemble each other” is cor- Thus they analyze raw dental measurerect only in the limited sense that both ments, and the results, expectably, are differ from P. gorilla. True, Gigantopithe- dominated by size. Their plots show robust cus is nearer to Australopithecus (D2= 83) and gracile australopithecines consistently than to P . gorilla (D’= 104) in total mor- closer than are the sexes within P . gorilla phometric pattern. But more importantly, and Pongo. Female Pongo falls closer to Australopithecus is considerably closer to P . troglodytes than to male Pongo. Male gorillas (D’ = 43) than to Gigantopithecus. Pongo and female P . gorilla are nearer Gigantopithecus shows a Generalized Dis- each other than either is to the opposite tance of 75 to robust and 91 to gracile sex of their own species. This extreme disaustralopithecines. Since Australopithecus tortion of results by sex dimorphism neand P . gorilla are not particularly closely gates the validity of drawing taxonomic related taxa, the Australopithecus-Gigan- conclusions, for of what meaning is the topithecus relationship may be very re- position of, say, Gigantopithecus if the mote indeed. This conclusion is not altered technique cannot correctly affiliate sexes by considering G . bilaspurensis in isolation of a single species? I have collected odontometric data comfrom the three G . blacki specimens, for G . bilaspurensis fell in a central position parable to Robinson and Steudel’s (’73) among the Gigantopithecus cluster in all from Garn et al. (’64, ’66, ’67) for Ohio bivariate plots of individuals. The earlier whites, Wolpoff (’71) for H. erectus and Indian species is not closer to Australo- Australopithecus, and Ashton and Zuckerpithecus than are G . blacki specimens, man (’50) for Pongo, P . troglodytes and
170
ROBERT S. CORRUCCINI TABLE 1
Principal coordinate positions f o r hominoid species based on length and breadth of C - M 2 T h e order followed b y cluster analysis is indicated to t h e left Taxon
Coordinate one (60.6%)
:
.
(5.74)
0.75
0.57
0.03
-:--Pongopygmaeus female
0.56
0.37
- 0.08
-:--Pan gorilla male
0.37
0.26
0.23
0.07
0.07
0.38
1.10
- 0.27
0.02
1.05
-0.12
. :... .. _.._ . .. -:--Pan gorilla female . . . . ----Pan . troglodytes male . ____ ____. . _.__ Homo snpiens .. _-._ .. ... .. -:--Homo erectus ... ... ____ .. ____ . : -:--gracile australopithecines
- 0.32
._.___.___ robust australopithecines
- 1.22
- 0.23 - 1.03 - 0.54 - 0.41 - 0.26
__
- 0.45
0.87
__..
..‘
-’--Pan troglodytes female ___.
~
Coordinate three
(29.9%)
-;--Pongo p y g m a e u s male
____ . . ___-
Coordinate two
~
..-__._ .-__-__ _-Gigantopithecus bilaspurensis
P . gorilla. These mean measurements are inferior to Robinson and Steudel’s carefully collected data, but highly similar results were obtained from distance analysis of the raw dimensions. Size differences, especially between the sexes, were the main source of variation. Therefore these data were again analyzed, using the deliberately shape-oriented distance “d” followed by principal coordinate and cluster analysis. Table 1 shows the results. Both of the first two principal coordinates separate hominids from pongids, but in different ways. The first separates robust australopithecines at one pole from small pongids at the other, while the second separates modern man from the larger pongids. Gigantopithecus bilaspurensis is maximally separated from hominids on the second coordinate, and is approached most closely by Pongo. Principal coordinate three shows G. bilaspurensis distinct from every other hominoid. The combination of extraordinarily reduced canine and P3 length with narrow molars in G . bilaspurensis is unique among hominoids. Gigantopithecus is again an extreme outlier in the cluster analysis, while the correct clustering of pongid sexes lends some confidence to taxonomic interpretation of these results.
- 0.08 -0.70
- 0.02 -0.15
- 0.08 - 0.06 -0.51
LITERATURE CITED Ashton, E. H., and S . Zuckerman 1950 Some quantitative dental characteristics of the chimpanzee, gorilla, and orangoutan. Phil. Trans. B, 234: 471-484. Corruccini, R. S. 1972 Allometry correction in taximetrics. Syst. Zool., 21 : 375-383. 1974 Multivariate analysis in biological anthroaoloev: some considerations. .I. Hum. Evol., 3: (in press). Frayer, D. W. 1973 Gigantopithecus and its relationship to Australopithecus. Am. J. Phys. Anthrop., 39: 413-426. Garn, S. M., A. B. Lewis and R. Kerewsky 1964 Sex difference in tooth size. J. Dent. Res., 43: 306. 1966 Sexual dimorphism in the buccolingual tooth diameter. J. Dent. Res., 45: 1819. Garn, S . M., A. B. Lewis, D. R. Swindler and R. Kerewsky 1967 Genetic control of sexual dimorphism in tooth size. J. Dent. Res., 46: 963972. Le Gros Clark, W. E. 1955 The Fossil Evidence for Human Evolution. Chicago Univ. Press, Chicago. Robinson, J. T., and K. Steudel 1973 Multivariate discriminant analvsis of dental data bearine on early hominid affinities. J. Hum. Evol., 2,
-_
509-528. __-- ~ _
Simons, E. L., and S. R. K. Chopra 1969 Gigantopithecus (Pongidae, Hominoidea) a new species from North India. Postilla, 138; 1-18. Sokal, R. R., and P. H. A. Sneath 1963 Principles of Numerical Taxonomy. Freeman, San Francisco. Wolpoff, M. H. 1971 Metric Trends in Hominid Dental Evolution. Case Western Univ. Stud. Anthrop., 2.
