Gompertzian growth as a self-similar and allometric process

Ž Bajzer

Research output: Contribution to journalReview article

40 Scopus citations

Abstract

The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.

Original languageEnglish (US)
Pages (from-to)3-11
Number of pages9
JournalGrowth, Development and Aging
Volume63
Issue number1-2
StatePublished - Mar 1 1999

    Fingerprint

Keywords

  • Allometry
  • Functional equations
  • Gompertz formula
  • Growth
  • Self-similarity
  • Tumor growth

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this