, Volume 19, Issue 1, pp 1–14 | Cite as

How to measure stand density

  • Boris ZeideEmail author
Original Article


Foresters have produced many measures of stand density. Yet, none of these is entirely satisfactory. A majority of the measures (stand density index, basal area, and leaf area) present number of trees per unit area as a function of one factor: average tree size. This paper identifies the second factor driving self-thinning: the accumulation of gaps between tree crowns inevitable even in dense stands with a sizeable overlap of crowns. A model accounting for both factors allows us to quantify stand density and find a single number characterizing the density of undisturbed stands. The number changes with species, being higher for more shade tolerant ones. It is found that the second factor affects survival of trees but not their growth. This means that there are two kinds of stand density.


Canopy closure Competition Diameter increment Growth equations Self-tolerance 



I appreciate many useful comments by Jayaraman Kadiroo, Ralph Meeker, Mike Shelton, and two anonymous referees. My thanks to Dan Leduc for reviewing the manuscript and digitizing Reineke’s data. Support from the Arkansas Agricultural Experiment Station is appreciated.


  1. Alban DH, Laidly PR (1982) Generalized biomass equations for jack and red pine in the Lake States. Can J For Res 12:913–921Google Scholar
  2. Assmann E (1970) The principles of forest yield study. Pergamon, New York, p 506Google Scholar
  3. Avery TE, Burkhart HE (2002) Forest measurements, 5th edn. McGraw-Hill, New York, p 456Google Scholar
  4. Begon M, Harper JL, Townsend CR (1996) Ecology, 3rd edn. Blackwell, LondonGoogle Scholar
  5. Bickford CA, Baker FS, Wilson FG (1957) Stocking, normality, and measurement of stand density. J For 55:99–104Google Scholar
  6. Briegleb PA (1952) An approach to density measurement in Douglas-fir. J For 50:529–536Google Scholar
  7. Chapman HH (1953) Effects of thinning on yields of forest-grown longleaf and loblolly pines at Urania, LA. J For 51:16–26Google Scholar
  8. Clason TR (1994) Impact of intraspecific competition on growth and financial development of loblolly pine plantations. New For 8:185–210Google Scholar
  9. Committee on standardization of volume and yield tables (1926) Methods of preparing volume and yield tables. J For 24:653–666Google Scholar
  10. Craib IJ (1947) The silviculture of exotic conifers in South Africa. British Empire Forestry Conference. City Printing Works, PietermaritzburgGoogle Scholar
  11. Gadow K (1986) Observations on self-thinning in pine plantations. S Afr J Sci 82:364–368Google Scholar
  12. Gingrich SF (1967) Measuring and evaluating stocking and stand density in upland hardwood forests in the central states. For Sci 13:38–53Google Scholar
  13. Harding RB, Grigal DF (1985) Individual tree biomass estimation equations for plantation-grown white spruce in northern Minnesota. Can J For Res 15:738–739Google Scholar
  14. Harper JL (1977) Population biology of plants. Academic, New YorkGoogle Scholar
  15. Kays S, Harper JL (1974) The regulation of plant and tiller density in a grass sward. J Ecol 62:97–105 (The key point is reprinted as Figure 10.6 in Gurevitch et al. 2002. Ecology of plants. Sinauer, Sunderland, Mass.)Google Scholar
  16. Kozlowski TT, Kramer PJ, Pallardy SG (1991) The physiological ecology of woody plants. Academic, New YorkGoogle Scholar
  17. Lohrey RE (1985) Aboveground biomass of planted and direct-seeded slash pine in the West Gulf Region. In: Saucier JR (ed) The 1984 southern forest biomass workshop. USDA Forest Service, Southeastern Forest Experiment Station, Fort Collins, pp 75–82Google Scholar
  18. MacKinney AL, Chaiken LE (1935) A method of determining density of loblolly pine stands. Technical Note No. 15. USDA Forest Service, Appalachian Forest Experiment Station, West VirginiaGoogle Scholar
  19. Mandelbrot BB (1983) The fractal geometry of nature. Freeman, New YorkGoogle Scholar
  20. Meyer WH (1938) Yield of even-aged stands of ponderosa pine. Technical Bulletin 630. USDA, WashingtonGoogle Scholar
  21. Meyer WH (1942) Yield of even-aged stands of loblolly pine in northern Louisiana. Bulletin 51. Yale University, School of Forestry, Yale, New HavenGoogle Scholar
  22. Oliver CD, Larson BC (1996) Forest stand dynamics. Wiley, New YorkGoogle Scholar
  23. Pfeifer P, Avnir D (1983) Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J Chem Phys 79:3558–3564CrossRefGoogle Scholar
  24. Reineke LH (1933) Perfecting a stand-density index for even-aged forests. J Agric Res 46:627–638Google Scholar
  25. Schmitt MDC, Grigal DF (1981) Generalized biomass estimations for Betula papyrifera Marsh. Can J For Res 11:837–840Google Scholar
  26. Spurr SH (1952) Forest inventory. Ronald, New YorkGoogle Scholar
  27. Stahelin R (1949) Thinning even-aged loblolly and slash pine stands to specified densities. J For 47:538–540Google Scholar
  28. Toumey JW, Korstian CF (1947) Foundations of silviculture upon an ecological basis, 2nd edn. Wiley, New YorkGoogle Scholar
  29. Tursky MK (2000) Silviculture, 9th edn (in Russian). Moscow University of Forestry, MoscowGoogle Scholar
  30. Vose JM, Allen HL (1988) Leaf area, stemwood growth, and nutrition relationships in loblolly pine. For Sci 34:547–563Google Scholar
  31. Wahlenberg WG (1960) Loblolly pine. The School of Forestry, Duke University, DurhamGoogle Scholar
  32. Weller DE (1987) A reevaluation of the −3/2 power rule of self-thinning. Ecol Monogr 57:23–43Google Scholar
  33. Wenger KF (ed) (1984) Forestry handbook, 2nd edn. Wiley, New YorkGoogle Scholar
  34. West PW (1982) Comparison of stand density measures in even-aged regrowth eucalypt forest of southern Tasmania. Can J For Res 13:22–31Google Scholar
  35. Williams RA (1994) Stand density management diagram for loblolly pine plantations in north Louisiana. South J Appl For 18:40–45Google Scholar
  36. Williams RA (1996) Stand density index for loblolly pine plantations in north Louisiana. South J Appl For 20:110–113Google Scholar
  37. Woodruff DR, Bond BJ, Ritchie GA, Scott W (2002) Effects of stand density on the growth of young Douglas-fir trees. Can J For Res 32:420–427CrossRefGoogle Scholar
  38. Yoda K, Kira T, Ogawa H, Hozumi K (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. J Biol Osaka City Univ 14:107–129Google Scholar
  39. Zeide B (1985) Tolerance and self-tolerance of trees. For Ecol Manage 13:149–166CrossRefGoogle Scholar
  40. Zeide B (1987) Analysis of the 3/2 power law of self-thinning. For Sci 33:517–537Google Scholar
  41. Zeide B (1991) Self-thinning and stand density. For Sci 37:517–523Google Scholar
  42. Zeide B (1993) Analysis of growth equations. For Sci 39:591–616Google Scholar
  43. Zeide B (1995) A relationship between size of trees and their number. For Ecol Manage 72:265–272CrossRefGoogle Scholar
  44. Zeide B (1998) Fractal analysis of foliage distribution in loblolly pine crowns. Can J For Res 28:106–114CrossRefGoogle Scholar
  45. Zeide B (2000) Fractal geometry: addressing the intrinsic spatial uncertainty. In: Heuvelink GBM, Lemmens MJPM (eds) Proceedings of the Fourth International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, July 2000, Amsterdam, pp 755–768Google Scholar
  46. Zeide B (2004) Intrinsic units in growth modeling. Ecol Model (in press)Google Scholar
  47. Zeide B, Pfeifer P (1991) A method for estimation of fractal dimension of tree crowns. For Sci 37:1253–1265Google Scholar
  48. Zhang S, Burkhart HE, Amateis RL (1996) Modeling individual tree growth for juvenile loblolly pine plantations. For Ecol Manage 89:157–172CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.School of Forest ResourcesUniversity of Arkansas at MonticelloMonticelloUSA

Personalised recommendations