Self-Thinning of Plant Populations Dictated by Packing Density and Individual Growth Geometry and Relationships Between Animal Population Density and Body Mass Governed by Metabolic Rate

  • R. Å. Norberg


When individual plants grow in an uncrowded population there is little or no mortality from competition. In a diagram displaying the logarithm of the volume of an average plant against the logarithm of population density, growth trajectories therefore are nearly vertical. But as plants begin to fill up the available space, crowding commences, and the ensuing mortality reduces population density and causes the growth trajectories to bend off towards the ordinate (Figs. 1, 2). As plants grow, the data points representing consecutive growth stages of survivors in a log-log diagram lie along this thinning line, from a high population density and small average volume per plant at lower right, upward and leftward toward the ordinate (Figs. 1, 2).


Plant Population Growth Mode Spatial Volume Ground Area Trunk Diameter 
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  1. Begon M, Firbank L, Wall, R (1986) Is there a self-thinning rule for animal populations? Oikos 46:122–124.CrossRefGoogle Scholar
  2. Calder WA III (1984) Size, function and life history. Harvard Univ Press, Cambridge.Google Scholar
  3. Damuth J (1987) Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy-use. Biol J Linnean Soc 31:193–246.CrossRefGoogle Scholar
  4. Gorham E (1979) Shoot height, weight and standing crop in relation to density of monospecific plant stands. Nature (London) 279:148–150.CrossRefGoogle Scholar
  5. Greenhill AG (1881) Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and of the greatest height to which a tree of given proportions can grow. Proc Cambridge Philos Soc 4:65–73.Google Scholar
  6. Hokkanen JEI (1986) Notes concerning elastic similarity. J Theor Biol 120:499–501.CrossRefGoogle Scholar
  7. Hutchings M (1983) Ecology’s law in search of a theory. New Sci 98:765–767.Google Scholar
  8. Kays S, Harper JL (1974) The regulation of plant and tiller density in a grass sward. J Ecol 62:97–106.CrossRefGoogle Scholar
  9. Lonsdale WM, Watkinson AR (1983) Plant geometry and self-thinning. J Ecol 71:285–297.CrossRefGoogle Scholar
  10. McMahon TA, Bonner JT (1983) On size and life. Sci Am Libr, New York.Google Scholar
  11. McMahon TA, Kronauer RE (1976) Tree structure: deducing the principle of mechanical design. J Theor Biol 59:443–466.PubMedCrossRefGoogle Scholar
  12. Miyanishi K, Hoy AR, Cavers PB (1979) A generalized law of self-thinning in plant populations (Self-thinning in plant populations). J Theor Biol 78:439–442.PubMedCrossRefGoogle Scholar
  13. Norberg RÅ (1988) 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.CrossRefGoogle Scholar
  14. Peters RH, Wassenberg K (1983) The effect of body size on animal abundance. Oecologia (Berlin) 60:89–96.CrossRefGoogle Scholar
  15. Weller DE (1987) A reevaluation of the-3/2 power rule of plant self-thinning. Ecol Monogr 57:23–43.CrossRefGoogle Scholar
  16. Westoby M (1976) Self-thinning in Trifolium subterraneum not affected by cultivar shape. Aust J Ecol 1:245–247.CrossRefGoogle Scholar
  17. Westoby M (1977) Self-thinning driven by leaf area not by weight. Nature (London) 265:330–331.CrossRefGoogle Scholar
  18. Westoby M (1981) The place of the self-thinning rule in population dynamics. Am Nat 118:581–587.CrossRefGoogle Scholar
  19. Westoby M (1984) The self-thinning rule. Adv Ecol Res 14:167–225.CrossRefGoogle Scholar
  20. White J (1977) Generalization of self-thinning of plant populations. Nature (London) 268:373.CrossRefGoogle Scholar
  21. White J (1980) Demographic factors in populations of plants. In: Solbrig OT (ed) Demography and evolution in plant populations. Blackwell, Oxford, pp 21–48.Google Scholar
  22. White J (1981) The allometric interpretation of the self-thinning rule. J Theor Biol 89:475–500.CrossRefGoogle Scholar
  23. White J, Harper JL (1970) Correlated changes in plant size and number in plant populations. J Ecol 58:467–485.CrossRefGoogle Scholar
  24. Whittington R (1984) Laying down the-3/2 power law. Nature (London) 311:217.CrossRefGoogle Scholar
  25. Yoda K, Kira T, Ogawa H, Hozumi H (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. J Biol Osaka City Univ 14:107–129.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • R. Å. Norberg
    • 1
  1. 1.Department of ZoologyUniversity of GothenburgGothenburgSweden

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