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Tree diameter, height and stocking in even-aged forests

Diamètre de l’arbre, hauteur et densité dans les forêts équiennes


  • • Empirical observations suggest that in pure even-aged forests, the mean diameter of forest trees (D, diameter at breast height, 1.3 m above ground) tends to remain a constant proportion of stand height (H, average height of the largest trees in a stand) divided by the logarithm of stand density (N, number of trees per hectare): D = β(H − 1.3)/ ln(N).

  • • Thinning causes a relatively small and temporary change in the slope β, the magnitude and duration of which depends on the nature of the thinning.

  • • This relationship may provide a robust predictor of growth in situations where scarce data and resources preclude more sophisticated modelling approaches.


  • • Des observations empiriques suggèrent que dans les forêts équiennes pures, le diamètre moyen des arbres forestiers (D, diamètre à hauteur de poitrine, 1,3 m au-dessus du sol) a tendance à rester une proportion constante de la hauteur du peuplement (H, hauteur moyenne des plus grands arbres dans un peuplement), divisé par le logarithme de la densité (N, nombre d’arbres par hectare) : D = β(H − 1.3)/ ln(N).

  • • L’éclaircie causes un changement relativement faible et temporaire de la pente β, l’ampleur et la durée dépend de la nature de l’éclaircie.

  • • Cette relation peut fournir un solide prédicteur de la croissance dans les situations où peu de données et de ressources excluent des approches plus sophistiquées de modélisation.


  • Bristow M., Vanclay J.K., Brooks L., and Hunt M., 2006. Growth and species interactions of Eucalyptus pellita in a mixed and monoculture plantation in the humid tropics of north Queensland. For. Ecol. Manage. 233: 285–294.

    Article  Google Scholar 

  • Curtis R.O., 1967. Height-diameter and height-diameter-age equations for second-growth Douglas-fir. For. Sci. 13: 365–375.

    Google Scholar 

  • Eichhorn F., 1904. Beziehungen zwischen bestandshohe und bestandsmasse. Allg. Forst-Jagdztg. 80: 45–49.

    Google Scholar 

  • Goulding C.J., 1972. Simulation technique for a stochastic growth model of Douglas-fir. Ph.D. thesis, University of British Columbia, Vancouver, 185 p.

    Google Scholar 

  • Hemery G.E., Savill P.S., and Pryor S.N., 2005. Applications of the crown diameter—stem diameter relationship for different species of broadleaved trees. For. Ecol. Manage. 215: 285–294.

    Article  Google Scholar 

  • Hart H.M.J., 1928. Stamtal en dunning: Een oriënteerend onderzoek naar de beste plantwijdte en dunningswijze voor den djati. Departement van Landbouw, Nijverheid en Handel in Nederlandsch-Indië, Mededeelingen van het Proefstation voor het Boschwezen, No. 21, 219 p.

  • Hasenauer H., 2006. Sustainable Forest Management: Growth Models for Europe, Springer, Berlin, 398 p.

    Book  Google Scholar 

  • Kajimoto T., Osawa A., Matsuura Y., Abaimov A.P., Zyryanova O.A., Kondo K., Tokuchi N., and Hirobe M., 2007. Individual-based measurement and analysis of root system development: case studies for Larix gmelinii trees growing on the permafrost region in Siberia. J. For. Res. 12: 103–112.

    Article  Google Scholar 

  • Kira T.K., Ogawa H., and Sakazaki N., 1953. Intraspecific competition among higher plants. I. Competition-yield-density interrelationship in regularly dispersed populations. Journal of the Institute of Polytechnics, Osaka City University, Series D, 4: 1–16.

    Google Scholar 

  • Lamb D. and Borschmann G., 1998. Agroforestry with High Value Trees. RIRDC Publication No. 98/142, 52 pp. ISBN 0 642 57833 8.

  • Laurie M.V. and Ram B.S., 1939. Yield and stand tables for teak in India and Burma. Indian For. Rec. Silvicult., New Ser., Vol. IV-A, No. 1.

  • Lynch T.B., Wittwer R.F., Stevenson D.J., and Huebschmann M.H., 2007. A maximum size-density relationship between Lorey’s mean height and trees per hectare. For. Sci. 53: 478–485.

    Google Scholar 

  • Mattay J.P. and West P.W., 1994. A collection of growth and yield data from eight eucalypt species growing in even-aged, monoculture forest. CSIRO Forestry and Forest Products, User series 18.

  • Mohler C.L., Marks P.L., and Sprugel D.G., 1978. Stand structure and allometry of trees during self-thinning of pure stands. J. Ecol. 66: 599–614.

    Article  Google Scholar 

  • Nelder J.A., 1962. New kinds of systematic designs for spacing experiments. Biometrics 18: 283–307.

    Article  Google Scholar 

  • Niklas K.J., Midgley J.J., and Enquist B.J., 2003. A general model for mass-growth-density relations across tree-dominated communities. Evol. Ecol. Res. 5: 459–468.

    Google Scholar 

  • Niklas K.J. and Spatz H.-C., 2006. Allometric theory and the mechanical stability of large trees: Proof and conjecture. Am. J. Bot. 93: 824–828.

    PubMed  Article  Google Scholar 

  • Peichl M. and Arain M.A., 2007. Allometry and partitioning of above- and belowground tree biomass in an age-sequence of white pine forests. For. Ecol. Manage. 253: 68–80.

    Article  Google Scholar 

  • Reineke L.H., 1933. Perfecting a stand density index for even-aged stands. J. Agric. Res. 46: 627–638.

    Google Scholar 

  • Rio M. del, Montero G., and Bravo F., 2001. Analysis of diameter-density relationships and self-thinning in non-thinned even-aged Scots pine stands. For. Ecol. Manage. 142: 79–87.

    Article  Google Scholar 

  • Sharma M., Amateis R.L., and Burkhart H.E., 2002. Top height definition and its effect on site index determination in thinned and unthinned loblolly pine plantations. For. Ecol. Manage. 168: 163–175.

    Article  Google Scholar 

  • Skovsgaard J.P., 1997 Management of Sitka spruce without thinnings. An analysis of stand structure and volume production of unthinned stands of Sitka spruce (Picea sitchensis (Bong.) Carr.) in Denmark. Forskningscentret for Skov and Landskab, Forskningsserien, Vol. 19.

  • Skovsgaard J.P. and Vanclay J.K., 2008. Forest site productivity: Review of the evolution of dendrometric concepts for even-aged stands. Forestry 81: 13–31.

    Article  Google Scholar 

  • Snowdon P. and Benson M.L., 1992. Effects of combinations of irrigation and fertilisation on the growth and above-ground biomass production of Pinus radiata. For. Ecol. Manage. 52: 87–116.

    Article  Google Scholar 

  • Sterba H., 1975 Assmanns Theorie der Grundflächenhaltung und die “competition-density-rule” der Japaner Kira, Ando und Tadaki. Centralblatt für das Gesamte Forstwesen 92: 46–62.

    Google Scholar 

  • Sterba H., 1987 Estimating potential density from thinning experiments and inventory data. For. Sci. 33: 1022–1034.

    Google Scholar 

  • Temesgen H. and Gadow K.V., 2004. Generalized height — diameter models — an application for major tree species in complex stands of interior British Columbia. Eur. J. For. Res. 123: 45–51.

    Google Scholar 

  • Usoltsev V.A. and Vanclay J.K., 1995. Stand biomass dynamics of pine plantations and natural forests on dry steppe in Kazakhstan. Scand. J. For. Res. 10: 305–312.

    Article  Google Scholar 

  • Vanclay J.K., 1994. Modelling Forest Growth and Yield: Applications to Mixed Tropical Forests, CAB International, Wallingford, 312 p.

    Google Scholar 

  • Vanclay J.K., 2006. Experiment designs to evaluate inter- and intraspecific interactions in mixed plantings of forest trees. For. Ecol. Manage. 233: 366–374.

    Article  Google Scholar 

  • Vanclay J.K. and Henry N.B., 1988. Assessing site productivity of indigenous cypress pine forest in southern Queensland. Commonw. For. Rev. 67: 53–64.

    Google Scholar 

  • Vanclay J.K. and Skovsgaard J.P., 1997. Evaluating forest growth models. Ecol. Model. 98: 1–12.

    Article  Google Scholar 

  • Vanclay J.K., Skovsgaard J.P., and Hansen C.P., 1995. Assessing the quality of permanent sample plot databases for growth modelling in forest plantations. For. Ecol. Manage. 71: 177–186.

    Article  Google Scholar 

  • Wilson F.G., 1951. Control of stocking in even-aged stands of conifers. J. For. 49: 692–695.

    Google Scholar 

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

    Google Scholar 

  • Zeide B., 1995. A relationship between size of trees and their number. For. Ecol. Manage. 72: 265–272.

    Article  Google Scholar 

  • Zeide B. and Vanderschaaf C., 2002. The effect of density on the height-diameter relationship. In: Gen. Tech. Rep. SRS-48. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station, pp. 463–466.

    Google Scholar 

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Correspondence to Jerome K. Vanclay.

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Vanclay, J.K. Tree diameter, height and stocking in even-aged forests. Ann. For. Sci. 66, 702 (2009).

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  • monoculture
  • stand density index
  • growth model
  • density management diagram


  • monoculture
  • index de densité de peuplement
  • modèle de croissance
  • diagramme de gestion de la densité