Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

A general model for ontogenetic growth


Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism1,2,3,4,5,6. Here, we derive a general quantitative model based on fundamental principles7,8,9 for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties10 and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events2,11,12.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Four typical examples of fits to growth curves (solid lines) using equation (5).
Figure 2: Universal growth curve.

Similar content being viewed by others


  1. Brody, S. Bioenergetics and Growth (Hafner Press, Darien, Connecticut, 1964).

    Google Scholar 

  2. Charnov, E. L. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology (Oxford Univ. Press, Oxford, 1993).

    Google Scholar 

  3. Stearns, S. C. The Evolution of Life Histories (Oxford Univ. Press, Oxford, 1992).

    Google Scholar 

  4. Reiss, M. J. The Allometry of Growth and Reproduction (Cambridge Univ. Press, Cambridge, 1989).

    Book  Google Scholar 

  5. Ricker, W. E. Growth rates and models. Fish Physiol. 8, 677–743 (1979).

    Article  Google Scholar 

  6. von Bertalanffy, L. Quantitative laws in metabolism and growth. Q. Rev. Biol. 32, 217–231 (1957).

    Article  CAS  Google Scholar 

  7. West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997).

    Article  CAS  Google Scholar 

  8. Brown, J. H. & West, G. B. Scaling in Biology (Oxford Univ. Press, Oxford, 2000).

    MATH  Google Scholar 

  9. West, G. B., Brown, J. H. & Enquist, B. J. The fourth dimension of life; fractal geometry and allometric scaling of organisms. Science 284, 1677–1679 (1999).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  10. Alberts, M. Molecular Biology of the Cell (Garland, New York, 1994).

    Google Scholar 

  11. Peters, R. H. The Ecological Implications of Body Size (Cambridge Univ. Press, Cambridge, 1983).

    Book  Google Scholar 

  12. Calder III, W. A. Size, Function and Life History (Harvard Univ. Press, Cambridge, Massachusetts, 1984).

    Google Scholar 

  13. Rogers, D. M., Olson, B. L. & Wilmore, J. H. Scaling for the V ˙ O 2 -to-body size relationship among children and adults. J. Appl. Physiol. 79(3), 958–967 (1995).

    Article  Google Scholar 

  14. Weathers, W. W. & Siegel, R. B. Body size establishes the scaling of avian postnatal metabolic rate: an interspecific analysis using phylogenetically independent contrasts. Ibis 137, 532–542 (1995).

    Article  Google Scholar 

  15. Xiaojun, X. & Ruyung, S. The bioenergetics of the southern catfish (Silurus meridionalis chen). I. Resting metabolic rate as a function of body weight and temperature. Physiol. Zool. 63, 1181–1195 (1990).

    Article  Google Scholar 

  16. Brett, J. R. The relation of size to rate of oxygen consumption and sustained swimming speed of Sockeye Salmon (Oncorhynchus nerka). J. Fish Res. Bd Can. 22, 1491–1501 (1989).

    Article  ADS  Google Scholar 

  17. Hamburger, K. et al. Size, oxygen consumption and growth in the mussel Mytilus edulis. Mar. Biol. 75, 303–306 (1983).

    Article  Google Scholar 

  18. Enquist, B. J., Brown, J. H. & West, G. B. Scaling of plant energetics and population density. Nature 395, 163–165 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Cummins, K. W. & Wuycheck, J. C. Caloric equivalents for investigations in ecological energetics. Mitt. Int. Verein. Theor. Angew. Limnol. 18, 1–158 (1971).

    Google Scholar 

  20. Kohler, A. C. Variations in the growth of Atlantic Cod (Gadus morhua L.). J. Fish. Res. Bd Can. 21(1), 57–100 (1964).

    Article  Google Scholar 

  21. Blueweiss, L. et al. Relationships between body size and some life history parameters. Oecologia 37, 257–272 (1978).

    Article  ADS  CAS  Google Scholar 

  22. Kozlowski, J. Optimal allocations of resources explains interspecific life-history patterns in animals with indeterminate growth. Proc. R. Soc. Lond. B 263, 559–566 (1996).

    Article  ADS  Google Scholar 

  23. Day, T. & Taylor, P. D. von Bertalanffy's growth equation should not be used to model age and size at maturity. Am. Nat. 149, 381–393 (1997).

    Article  Google Scholar 

  24. Enquist, B. J., West, G. B., Charnov, E. L. & Brown, J. H. Allometric scaling of production and life-history variation in vascular plants. Nature 401, 907–911 (1999).

    Article  ADS  CAS  Google Scholar 

Download references


We thank E. Charnov for discussing the role of reproduction in our formalism, L. Thomson for supplying data on salmon and P. Taylor for comments. Support from the National Science Foundation and the National Center for Ecological Analysis and Synthesis are gratefully acknowledged. J.H.B. and G.B.W. also acknowledge the support of the Thaw Charitable Trust and a Packard Interdisciplinary Science Grant.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Geoffrey B. West.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Cite this article

West, G., Brown, J. & Enquist, B. A general model for ontogenetic growth. Nature 413, 628–631 (2001).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing