A further analysis of the quasi-1/2 power law of tree height in stratified forest communities

  • Takuo Yamakura


To clarify a statistical basis of the empirical fact designated as the quasi-1/2 power law of tree height in stratified natural forest communities, a derivative of Pearson's type VII distribution was adopted and used for describing the frequency distribution of individual tree height in a subpopulation extracted from a forest stand by the symmetric type difference diagram already proposed for the stratification of samples. Limited by the quasi-1/2 power law of tree height, all the coefficients of Pearson's type VII distribution were expressed as empirical equations of tree density in a subpopulation obtained from the stratification of samples. These empirical equations led to the normalized density function of tree height and gave a statistical basis for the quasi-1/2 power law of tree height. In addition to tree height data, the stem diameter at breast height and tree weight data for a forest stand were also stratified into subpopulations by using symmetric type difference diagrams. In conclusion, a new system was proposed for describing the dependence of mean tree height, mean stem diameter at breast height, and mean tree weight on tree density in a subpopulation.

Key words

Derivative of Pearson's type VII distribution Forest stratification Subpopulation The quasi-1/2 power law of tree height The quasi-3/2 power law system 



hectare (=10,000 m2)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ando, T. 1962. Growth on the natural stands of Japanese red pine (Pinus densiflora Sieb. et Zucc.). II. Analysis of stand density and growth. Bull. Govt. For. Expt. Stan., Tokyo147: 45–773Google Scholar
  2. — 1968. Ecological studies on the stand density control in even-aged pure stand. Bull. Govt. For. Expt. Stan., Tokyo210: 1–153.Google Scholar
  3. Forestry and forest Products Research Institute. 1983. Studies on the treatment of artificial multistoried forests. Bull. For. & For. Prod. Res. Inst., Japan323: 1–218.Google Scholar
  4. Glass, N.R. 1967. A technique for fitting models with nonlinear parameters to biological data. Ecology48: 1010–1013.CrossRefGoogle Scholar
  5. Golley, F.E., J.T. Mcginnis, R.G. Clements, G.I. Child andM.J. Duever. 1975. Mineral Cycling in a Moist Forest Ecosystem. Univ. of Georgia Press, Athens.Google Scholar
  6. Grubb, P.J., J.R. Lloyd andT.C. Whitmore. 1963. A comparison of montane and lowland rain forest in Ecuador 1. The forest structure, physiognomy, and floristics. J. Ecol.51: 567–601.CrossRefGoogle Scholar
  7. Hallé, F., R.A.A. Oldeman andP.B. Tomlinson. 1978. Tropical Trees and Forests. Springer-Verlag, Berlin.Google Scholar
  8. Harper, J.L. 1977. Population Biology of Plants. Academic Press, London.Google Scholar
  9. Hozumi, K., H. Koyama andT. Kira. 1955. Intraspecific competition among higher plants. IV. A preliminary account on the interaction between adjacent individuals. J. Inst. Polytech. Osaka City Univ.6, Series D: 12–130.Google Scholar
  10. Meakin, P. 1983. Diffusion-controlled deposition on fibers and surfaces. Phys. Rev.A27: 2616–2623.CrossRefGoogle Scholar
  11. Mithen, R., J.L. Harper andJ. Weiner 1984. Growth and mortality of individual plants as a function of available area. Oecologia62: 57–60.CrossRefGoogle Scholar
  12. Nagano, M. andT. Kira 1978. Aboveground biomass.In T. Kiraet al., ed., Biological Production in a Warm-Temperate Evergreen Oak Forest of Japan, JIBP Synthesis vol. 18, pp. 69–82. Univ. of Tokyo Press, Tokyo.Google Scholar
  13. Ogawa, H. andT. Kira 1977. Methods of estimating forest biomass.In T. Shidei and T. Kira, ed., Primary Productivity of Japanese Forests—Productivity of Terrestrial Communities—, JIBP Synthesis, vol. 16, pp. 15–25. Univ. of Tokyo Press, Tokyo.Google Scholar
  14. —. 1965. Comparative ecological studies on three main types of forest vegetation, in Thailand. II. Plant biomass. Nature and Life in SE Asia4: 49–80.Google Scholar
  15. Reineke, L.H. 1933. Perfecting a stand-density index for even-aged forests. J. Agric. Res.46: 627–638.Google Scholar
  16. Richards, P.W. 1952. The Tropical Rain Forest (Reprinted with corrections 1979). Cambridge Univ. Press, Cambridge.Google Scholar
  17. Shidei, T. 1956. Problems of Stand Density. Japan Forest Technical Society, Tokyo (in Japanese).Google Scholar
  18. — 1967. Forest Tending and Its Ecological Bases. Norin Shuppan, Tokyo (in Japanese).Google Scholar
  19. Tadaki, Y. 1963. The pre-estimating of stem yield based on the competition-density effect. Bull. Gov. For. Exp. Sta., Tokyo154: 1–19.Google Scholar
  20. — 1964. Effect of thinning on stem yield volume studied with competition-density effect; on the case ofPinus densiflora. Bull. Gov. For. Exp. Sta., Tokyo166: 1–22.Google Scholar
  21. —. 1963. The ecological studies on the quantitative thinning. Bull. Kyoto Univ. For.34: 1–31.Google Scholar
  22. Takayasu, H. 1986. Fractal. Asakura Syoten, Tokyo (in Japanese).Google Scholar
  23. White, J. 1981. The allometric interpretation of the self-thinning rule. J. Theor. Biol.89: 475–500.CrossRefGoogle Scholar
  24. Whitmore, T.C. 1984. Tropical Rain Forests of the Far East. Clarendon Press, Oxford.Google Scholar
  25. Yamakura, T. 1985a. Statistical basis for the 3/2 power law system (Frequency distribution of individual weight, stem diameter and height in plant stands. VIII). Jap. J. Ecol.35: 169–182.Google Scholar
  26. — 1985b. Tree height distribution inChamaecyparis obtusa plantations (Frequency distribution of individual weight, stem diameter and height in plant stands. IX). Jap. J. Ecol.35: 345–355.Google Scholar
  27. — 1987. An empirical approach to the analysis of forest stratification. I. Proposed graphical method derived by using an empirical distribution function. Bot. Mag. Tokyo100: 109–128.CrossRefGoogle Scholar
  28. — 1988. An empirical approach to the analysis of forest stratification. II. Quasi-1/2 power law of tree height in stratified forest communities. Bot. Mag. Tokyo101: 153–162.CrossRefGoogle Scholar
  29. — 1980. Frequency distribution of individual weight, stem diameter and height in plant stands. I. Proposed new distribution density functions derived by using the finite difference method. Jap. J. Ecol.30: 307–321.Google Scholar
  30. Yoda, K. 1965. A preliminary survey of the forest vegetation of eastern Nepal. I. Methods of survey and original data.In M. Numata, ed., Ecological Study and Mountaineering of Mt. Nubur in Eastern Nepal, 1963, pp. 45–73. Himalayan Expedition of Chiba Univ., Chiba.Google Scholar
  31. —. 1963. Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants. XI). J. Biol. Osaka City Univ.14: 107–129.Google Scholar

Copyright information

© The Botanical Society of Japan 1989

Authors and Affiliations

  • Takuo Yamakura
    • 1
  1. 1.Department of Biology, Faculty of ScienceOsaka City UniversityOsaka

Personalised recommendations