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.

Allometric scaling of plant energetics and population density


Scaling relationships that describe variation in population density with body size in ecological communities, such as the thinning law in plant ecology1,2,3, can be explained in terms of how individuals use resources as a function of their size. Data for rates of xylem transport as a function of stem diameter show that rates of resource use in individual plants scale as approximately the 3/4 power of body mass, which is the same as metabolic rates of animals4,5,6,7. Here we use this relationship to develop a mechanistic model for relationships between density and mass in resource-limited plants. It predicts that average plant size should scale as the −4/3 power of maximum population density, in agreement with empirical evidence and comparable relationships in animals5,6,8, but significantly less than the −3/2 power predicted by geometric models1. Our model implies that fundamental constraints on metabolic rate are reflected in the scaling of population density and other ecological and evolutionary phenomena, including the finding that resource allocation among species in ecosystems is independent of body size5,6,8.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


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

Figure 1: Relationship between the rate of whole-plant xylem transport and basal stem diameter.
Figure 2: Relationship between average plant mass and maximum population density.
Figure 3: Relationship between total plant biomass (roots, shoots and leaves) and maximal population density30.
Figure 4: Relationship between total xylem flux and average size of the dominant plants in diverse ecosystems.


  1. Yoda, K., Kira, T., Ogawa, H. & Hozumi, K. Self-thinning in overcrowded pure stands under cultivated and natural conditions. J. Biol. Osaka City Univ. 14, 107–129 (1963).

    Google Scholar 

  2. Gorham, E. Shoot height, weight and standing crop in relation to density of monospecific stands. Nature 279, 148–150 (1979).

    Article  ADS  Google Scholar 

  3. White, J. in Studies on Plant Demography: A Festschrift for John L. Harper (ed. White, J.) 291–301 (Academic, New York, (1985)).

    Google Scholar 

  4. Schmidt-Nielsen, K. Scaling: Why is Animal Size so Important? (Cambridge Univ. Press, (1984)).

    Book  Google Scholar 

  5. McMahon, T. A. & Bonner, J. T. On Size and Life (Scientific American Library, New York, (1983)).

    Google Scholar 

  6. Brown, J. H. Macroecology (Univ. Chicago Press, (1995)).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  8. Damuth, J. Population density and body size in mammals. Nature 290, 699–700 (1981).

    Article  ADS  Google Scholar 

  9. Niklas, K. J. Plant Allometry: The Scaling of Form and Process (Univ. Chicago Press, (1994)).

    Google Scholar 

  10. Agusti, S., Duarte, C. M. & Kalf, J. Algal cell size and the maximum density and biomass of phytoplankton. Limnol. Oceanogr. 32, 983–986 (1987).

    Article  ADS  Google Scholar 

  11. White, J. The allometric interpretation of the self-thinning rule. J. Theor. Biol. 89, 475–500 (1981).

    Article  Google Scholar 

  12. Petraitis, P. S. Use of average vs. total biomass in self-thinning relationships. Ecology 76, 656–658 (1995).

    Article  Google Scholar 

  13. Weller, D. E. Areevaluation of the −3/2 power rule of plant self-thinning. Ecol. Monog. 57, 23–43 (1987).

    Article  Google Scholar 

  14. Weller, D. E. The interspecific size-density relationship among crowded plant stands and its implications for the −3/2 power rule of self-thinning. Am. Nat. 133, 20–41 (1989).

    Article  Google Scholar 

  15. Norberg, R. A. Theory of growth geometry of plants and self-thinning of plant populations: geometric similarity, elastic similarity, and different growth modes of plant parts. Am. Nat. 131, 220–256 (1988).

    Article  Google Scholar 

  16. Osawa, A. & Allen, R. B. Allometric theory explains self-thinning relationships of mountain beech and red pine. Ecology 74, 1020–1032 (1993).

    Article  Google Scholar 

  17. Lonsdale, W. M. The self-thinning rule: dead or alive? Ecology 71, 1373–1388 (1990).

    Article  Google Scholar 

  18. Franco, M. & Kelly, C. K. The interspecific mass-density relationship and plant geometry. Proc. Natl Acad. Sci. USA 95, 7830–7835 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Smith, W. B. & Brand, G. J. Allometric Biomass Equations for 98 Species of Herbs, Shrubs, and Small Trees (North Central Forest Experimental Station Research Note NC-299, Forest Service—USDA, (1983)).

    Google Scholar 

  20. Kozlowski, T. T. & Pallardy, S. G. Physiology of Woody Plants (Academic, New York, (1997)).

    Google Scholar 

  21. Chapin, S. F. II in Scaling Physiological Processes: Leaf to Globe (ed. Ehleringer, J. R.) 287–319 (Academic, New York, (1993)).

    Book  Google Scholar 

  22. Grime, J. P. & Hunt, R. Relative growth-rate: its range and adaptive significance in a local flora. J. Ecol. 63, 393–422 (1975).

    Article  Google Scholar 

  23. Tilman, D. Plant Strategies and the Dynamics and Structure of Plant Communities (Princeton Univ. Press, (1988)).

    Google Scholar 

  24. Yoda, K., Shinozaki, K., Ogawa, J., Hozumi, K. & Kira, T. Estimation of the total amount of respiration in woody organs of trees and forest communities. J. Biol. Osaka City Univ. 16, 15–26 (1965).

    Google Scholar 

  25. Whittaker, R. H. & Woodwell, G. M. Dimension and production relations of trees and shrubs in the Brookhaven Forest, New York. Ecology 56, 1–25 (1968).

    Article  Google Scholar 

  26. Huston, M. A. & DeAngelis, D. Competition and coexistence: the effects of resource transport and supply rates. Am. Nat. 144, 954–977 (1994).

    Article  Google Scholar 

  27. Rosenzweig, M. L. Net primary productivity of terrestrial communities: prediction from climatological data. Am. Nat. 102, 67–74 (1968).

    Article  Google Scholar 

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

    Google Scholar 

  29. Shulze, E. al. Canopy transpiration and water fluxes in the xylem of the trunk of Larix and Picea trees—comparison of xylem flow, porometer and cuvette measurements. Oceologia 66, 475–483 (1985).

    Article  ADS  Google Scholar 

  30. Cannell, M. G. R. World Forest Biomass and Primary Production Data (Academic, New York, (1982)).

    Google Scholar 

Download references


We thank G. C. Stevens, C. A. F. Enquist, H. S. Horn, T. K. Lowrey, D. Marshall, K. J. Niklas, J. T. Bonner and J. Damuth for their help. B.J.E. was supported by a Fulbright fellowship and funding by NSF; J.H.B. by NSF; and G.B.W. by the US Department of Energy.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Brian J. Enquist.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


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