Skip to main content
Log in

Phase diagrammatic approach to the analysis of growth curve using theu-w diagram —Basic aspects

  • Published:
The botanical magazine = Shokubutsu-gaku-zasshi Aims and scope Submit manuscript

Abstract

To analyze growth curve quantitatively theu-w diagram is proposed. Herew is defined as any growth quantity at a given time of observation andu is defined as the ratio of relative growth rate ofw tow. Theu-w diagram can be obtained by plotting a series of observed values ofu andw on log-log coordinates.

Theu-w relationship constructed to lead a generalized form of the logistic and Mitscherlich curve results in the growth curve almost equivalent to the curve expected from the Bertalanffy differential equation and thus includes the Richards growth function as a special case. These results show that the approach using theu-w diagram appears to give a useful tool for the growth analysis in general and to be flexible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bertalanffy, L. von. 1949. Problems of organic growth. Nature163: 156–158.

    Google Scholar 

  • Causton, D.R. andJ.C. Venus. 1981. The Biometry of Plant Growth. Edward Arnold, London.

    Google Scholar 

  • Nishiwaki, Y. andK. Shinozaki. 1952. A new method of representing the population growth. J. Osaka City Med. Center1: 150–156 (in Japanese).

    Google Scholar 

  • Oberhettinger, F. 1970. Hypergeometric functions.In: M. Abramowitz and I.A. Stegun, ed., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables p. 555–565. Dover Publications, New York.

    Google Scholar 

  • Osumi, S. andY. Ishikawa. 1983. Applicability of the Richards' growth function to analysis of growth of tree. Sci. Rep. Kyoto Pref. Univ. Agr. No.35: 49–76 (in Japanese with English summary).

    Google Scholar 

  • Richards, F.J. 1959. A flexible growth function for empirical use. J. Exp. Bot.10: 290–300.

    Google Scholar 

  • Shidei, T. ed. 1963. Productivity of forest ecosystem in terms of cycling of matter. Material1: 104 (in Japanese).

    Google Scholar 

  • Shinozaki, K. 1962. Logistic theory of plant growth. D. Sc. thesis, Kyoto Univ. (in Japanese).

  • — 1976. Effects of removal on a growing system. Physiol. Ecol. Jap.17: 101–107 (in Japanese with English summary).

    Google Scholar 

  • — andT. Kira. 1961. TheC-D rule, its theory and practical uses. J. Biol. Osaka City Univ.12: 69–82.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hozumi, K. Phase diagrammatic approach to the analysis of growth curve using theu-w diagram —Basic aspects. Bot Mag Tokyo 98, 239–250 (1985). https://doi.org/10.1007/BF02488774

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02488774

Key words

Navigation