Skip to main content
Log in

Allometric scaling in palaeontology: A critical survey

  • Published:
Human Evolution

Abstract

Allometric scaling models, used to describe morphological and functional relationships between two sets of observations, are examined both in concept and in application. This paper focuses on the underlying assumptions and statistics of the methods most frequently used: linear regression, principal axis and standard major axis analysis. It is shown that the standard major axis (SMA) is the most appropriate bivariate linear model in palaeonotological research. Differences among the models discussed are illustrated by a morphometric analysis of dental dimensions in australopithecines.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Blumenberg B. &Lloyd A.T., 1983.Australopithecus and the origin of the genus Homo: aspects of biometry and systematics with accompanying catalog of tooth metric data. Bio Systems, 16: 127–167.

    Google Scholar 

  • Calder W.A., 1984.Size, Function and Life History (Cambridge, M.A.: Harvard University Press.

    Google Scholar 

  • Clarke M.R.B., 1980.The reduced major axis of a bivariate sample. Biometrika, 2: 441–446.

    Article  Google Scholar 

  • Gingerich P.D., Smith R.H. &Rosenberg K., 1982.Allometric scaling in the dentition of primates and prediction of body weight from tooth size in fossils. American Journal of Physical Anthropology, 58: 81–100.

    Article  Google Scholar 

  • Gould S.J., 1966.Allometry and size in ontogeny and phylogeny. Biological Review, 41: 587–640.

    Google Scholar 

  • Harvey P.H., 1982.On rethinking allometry. Journal of Theoretical Biology, 95: 37–41.

    Article  Google Scholar 

  • Harvey P.H. &Mace G.M., 1982.Comparisons between taxa and adaptive trends. In: King’s College Sociology Group, eds. Current Problems in Sociology, pp. 343–361. London, Cambridge University Press.

    Google Scholar 

  • Hoaglin D.C. &Welsch R.E., 1978.The hat matrix in regression and ANOVA. American Statistics, 32: 17–22.

    Article  Google Scholar 

  • Hofman M.A., 1983.Encephalization in hominids: evidence for the model of punctuationalism. Brain, Behavior and Evolution, 22: 102–117.

    Article  Google Scholar 

  • Hofman M.A., 1984.On the presumed coevolution of brain size and longevity in hominids. Journal of Human Evolution, 13: 371–376.

    Article  Google Scholar 

  • Hofman M.A., Fliers E., Goudsmit E. & Swaab D.F., 1988.Morphometric analysis of the suprachiasmatic and paraventricular nuclei in the human brain: sex differences and age-dependent changes. Journal of Anatomy (in press).

  • Hofman M.A., Laan A.C. &Uylings H.B.M. 1986.Bivariate linear models in neurobiology: problems of concept and methodology. Journal of Neuroscience Methods, 18: 103–114.

    Article  Google Scholar 

  • Imbrie J., 1956.Biometrical methods in the study of invertebrate fossils. Bulletin of the American Museum of Natural History, 108: 215–252.

    Google Scholar 

  • Jolicoeur P., 1975.Linear regressions in fishery research: some comments. Journal of the Fishery Research Board of Canada, 32: 1491–1494.

    Google Scholar 

  • Jolicoeur P. &Heusner A.A., 1971.The allometry equation in the analysis of the standard oxygen consumption and body weight in the white rat. Biometrics, 27: 841–855.

    Article  Google Scholar 

  • Jolicoeur P. &Mosimann J.E., 1968.Intervalles de confiance pour la pente de l’axe majeur d’une distribution normale bidimensionelle. Biometrie-Praximetrie, 9: 121–140.

    Google Scholar 

  • Kay R.F. &Simons E.L., 1980.The ecology of Oligocene African Anthropoidea. International Journal of Primatology, 1: 21–38.

    Google Scholar 

  • Kendall M.G. &Stuart A., 1979.Functional and structural relationship. In: The Advanced Theory of Statistics. Part 2. Inference and Relationships 4th edn, pp. 399–440. London: Griffin and Co.

    Google Scholar 

  • Kermack K.A. &Haldane J.B.S., 1950.Organic correlation and allometry. Biometrika, 37: 30–41.

    Article  Google Scholar 

  • Kreyszig E., 1970.Introductory Mathematical Statistics: Principles and Methods. New York: Wiley.

    Google Scholar 

  • Kuhry B. &Marcus L.F., 1977.Bivariate linear models in biometry. Systematic Zoology, 26: 201–209.

    Article  Google Scholar 

  • McHenry H.M., 1975.Fossil hominid body weight and brain size. Nature, 254: 686–688.

    Article  Google Scholar 

  • McHenry H.M., 1984.Relative check-tooth size in Australopithecus. American Journal of Anthropology, 56: 297–306.

    Article  Google Scholar 

  • Peters C.R., 1981.Robust vs. gracile early hominid masticatory capabilities: the advantages of the megadonts. Anthropology (UCLA), 7: 161–182.

    Google Scholar 

  • Pilbeam D. &Gould S.J., 1974.Size and scaling in human evolution. Science, 186: 892–901.

    Google Scholar 

  • Pirie P.L., 1978.Allometric scaling in the post-canine dentitions with reference to primate diets. Primates, 19: 583–591.

    Article  Google Scholar 

  • Rayner J.M.V., 1985.Linear relations in biomechanics: the statistics of scaling. Journal of Zoology, 206: 415–439.

    Article  Google Scholar 

  • Ricker W.E., 1984.Computation and uses of central trend lines. Canadian Journal of Zoology, 62: 1897–1905.

    Article  Google Scholar 

  • Sachs L., 1982.Applied Statistics: A Handbook of Techniques. Berlin: Springer.

    Google Scholar 

  • Seim E. &Saether B.-E., 1983.On rethinking allometry: which regression model to use? Journal of Theoretical Biology, 104: 161–168.

    Article  Google Scholar 

  • Smith R.J., 1984.Allometric scaling in comparative biology: problems of concept and method. American Journal of Physiology, 246: 152–160.

    Google Scholar 

  • Sokal R.R. &Rohlf F.J., 1981.Biometry: The Principles and Practice of Statistics in Biological Research, 2nd. edn. San Francisco: Freeman.

    Google Scholar 

  • Sprent P., 1969.Models in Regression and Related Topics. London: Methuen.

    Google Scholar 

  • Sprent P. &Dolby G.R., 1980.The geometric mean functional relationship. Biometrics, 36: 547–550.

    Article  Google Scholar 

  • Theil H., 1971.Principles of Econometrics Amsterdam: Elsevier/North Holland.

    Google Scholar 

  • Uylings H.B.M. Van Eden C.G. &Hofman M.A., 1986.Morphometry of size/volume variables and comparison of their bivariate relations in the nervous system under different conditions. Journal of Neuroscience Methods, 18: 19–37.

    Article  Google Scholar 

  • Wolpoff M.H., 1973.Posterior tooth size, body size, and diet in South African gracile australopithecines. American Journal of Physical Anthropology, 39: 375–394.

    Article  Google Scholar 

  • Wolpoff M.H., 1985.Tooth size-body size scaling in a human population. Theory and practice of an allometric analysis. In: W.L. Jungers Ed. Size and Scaling in Primate Biology, pp. 273–318 (New York, Plenum Press.

    Google Scholar 

  • Wood B.A. &Stack C.G., 1980.Does allometry explain the differences between ‘gracile’ and ‘robust’ australopithecines? American Journal of Physical Anthropology, 52: 55–62.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hofman, M.A. Allometric scaling in palaeontology: A critical survey. Hum. Evol. 3, 177–188 (1988). https://doi.org/10.1007/BF02437441

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02437441

Key words

Navigation