Chi-Square Test of Biological Space Curve Affinities

  • David Dean
  • Leslie F. Marcus
  • Fred L. Bookstein
Part of the NATO ASI Series book series (NSSA, volume 284)


This project attempts a discrimination of craniofacial shape between Pleistocene and recent humans. In this study three-dimensional craniofacial line tracings, referred to here as ridge curves, were surveyed. By means of a chi-square model, ridge curves taken from fossil specimens considered “transitional” were compared with homologous “average” ridge curves generated from Homo erectus and modern humans, H. sapiens sapiens. Results showed that only two of the five ridge curves, the medial brow and the nuchal torus, were useful in discriminating between these forms and determining the transitional specimens’ affinities. For these two ridge curves the Middle Pleistocene forms showed overwhelming similarity with modern humans. The nature of the separation for the two significant ridge curves was studied with a principal coordinates analysis. This study supports the assignment of Middle Pleistocene transitional specimens to “early” H. sapiens rather than to H. erectus (Dean, 1993).


Registration Point Ridge Curve External Occipital Protuberance Craniofacial Shape Superior Nuchal Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ashton, E. H. 1950. The endocranial capacities of the Australopithecinae. Proceedings of the Zoological Society of London 120: 715–721.CrossRefGoogle Scholar
  2. Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: New York.Google Scholar
  3. Bookstein, F. L. and C. B. Cutting. 1988. A proposal for the apprehension of curving craniofacial form in three dimensions. Pages 127–140 in K. Vig, and A. Burdi (eds.), Craniofacial morphogenesis and dysmorphogenesis. Center for Human Growth and Development: Ann Arbor.Google Scholar
  4. Brown, P. 1989. Coobool Creek: A morphological and metrical analysis of the crania, mandibles and dentitions of a prehistoric Australian human population. Terra Australis 13: 1–205.Google Scholar
  5. Clarke, R. 1990. The Ndutu cranium and the origin of Homo sapiens. Journal of Human Evolution 19: 699–736.CrossRefGoogle Scholar
  6. Cutting, C. B., F. L. Bookstein, B. Haddad, D. Dean, and D. Kim. 1993. A spline-based approach for averaging three-dimensional curves and surfaces. Soc. Pages 29–44 in I. N. Wilson, and D. C. Wilson (eds.), Mathematical methods in medical imaging II. Society of Phto-Optical Institute Engineers 2035.CrossRefGoogle Scholar
  7. Cutting, C., D. Dean, F. Bookstein, B. Haddad, D. Khorramabadi, F. Zonnefeld, and J. McCarthy 1995. A three-dimensional smooth surface analysis of untreated Crouzon’s disease in the adult. Journal of Craniofacial Surgery 6: 444–453.PubMedCrossRefGoogle Scholar
  8. Dean, D. 1993. The Middle Pleistocene Homo erectus/Homo sapiens transition: New evidence from space curve statistics. Ph.D. dissertation; The City University of New York.Google Scholar
  9. Gower, J. 1966. Some distance properties of latent root vector methods used in multivariate analysis. Biometrika 53: 325–338.Google Scholar
  10. Hilbert, D., and S. Cohn-Vossen. 1990. Geometry and the imagination. Chelsea: New York.Google Scholar
  11. Hublin, J-J. 1985. Human fossils from the North African Middle Pleistocene and the origin of Homo sapiens. Pages 283–288 in E. Delson (ed.), Ancestors: The hard evidence. Alan R. Liss: New York.Google Scholar
  12. Jacob, T. 1976. Solo Man and Peking Man. Pages 87–104 in B. A. Sigmon, and J. S. Cybulski (eds.), Papers in honor of Davidson Black. University of Toronto Press: Toronto.Google Scholar
  13. Le Gros Clark, W. E. 1955. The fossil evidence for human evolution, 3rd edition, University of Chicago Press: Chicago.Google Scholar
  14. Le Gros Clark, W. E. 1967. Man apes or ape-men. Robert E. Krieger: New York.Google Scholar
  15. Macintosh, N. W. G., and S. L. Larnach. 1972. The persistence of Homo erect us traits in Australian Aboriginal crania. Oceania 7: 1–7.Google Scholar
  16. Mayr, E. 1951. Taxonomic categories in fossil hominids. Cold Spring Harbor Symposia in Quantitative Biology 15: 109–117.CrossRefGoogle Scholar
  17. Rightmire, G. P. 1990. The evolution of Homo erectus. Cambridge University Press: Cambridge, U. K.Google Scholar
  18. Rohlf, F. J. 1990. Rotational fit (Procrustes) methods. Pages 227–236 in F. J. Rohlf, and F. L. Bookstein (eds.), Proceedings of the Michigan morphometrics workshop. University of Michigan Museum of Zoology Special Publication 2.Google Scholar
  19. Rohlf, F. J. 1993. NTSYS-pc. Numerical taxonomy and multivariate analysis system, version 1. 80. Exeter Software: Setauket, New York.Google Scholar
  20. Rohlf, F. J., and D. E. Slice. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology 39: 40–59.CrossRefGoogle Scholar
  21. Rohlf, F. J., and R. R. Sokal. 1981. Statistical tables. W. H. Freeman: New York.Google Scholar
  22. Russell, M. D. 1983. The functional and adaptive significance of the supraorbital torus. Ph.D. dissertation, The University of Michigan.Google Scholar
  23. Santa Luca, A. P. 1980. The Ngandong fossil hominids. Yale University Publications in Anthropology 78: 1–175.Google Scholar
  24. Sokal, R. R., and F. J. Rohlf. 1981. Biometry: The principles and practice of statistics in biological research, 2nd edition, W. H. Freeman: San Francisco.Google Scholar
  25. Stringer, C. B. 1984. The definition of Homo erectus and the existence of the species in Africa and Europe. Cour. Forsch. Inst. Senckenberg 69: 131–143.Google Scholar
  26. Turner, A., and A. Chamberlain. 1989. Speciation, morphological change and the status of African Homo erectus. Journal of Human Evolution 18: 115–130.CrossRefGoogle Scholar
  27. Weidenreich, F. 1943. The skull of Sinanthropus pekinensis; a comparative study on a primitive hominid skull. Palaeontologica Sinica Series D, 10.Google Scholar
  28. Weidenreich, F. 1951. Morphology of Solo man. Anthropological Papers of the American Museum of Natural History 43: 205–288.Google Scholar
  29. Wilk, M. B., and R. Gnanadesikan. 1968. Probability plotting methods for the analysis of data. Biometrika 55: 1–17.PubMedGoogle Scholar
  30. Wood, B. A. 1984. The origin of Homo erectus. Cour. Forsch. Inst. Senckenberg 69: 99–111.Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • David Dean
    • 1
  • Leslie F. Marcus
    • 2
    • 3
  • Fred L. Bookstein
    • 4
  1. 1.Department of AnatomyCase Western Reserve UniversityClevelandUSA
  2. 2.Department of BiologyQueens College of The City University of New YorkNew YorkUSA
  3. 3.Department of InvertebratesAmerican Museum of Natural HistoryNew YorkUSA
  4. 4.Institute of GerontologyUniversity of MichiganAnn ArborUSA

Personalised recommendations