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 language | English (US) |
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Pages (from-to) | 3-11 |
Number of pages | 9 |
Journal | Growth, Development and Aging |
Volume | 63 |
Issue number | 1-2 |
State | Published - Mar 1999 |
Keywords
- Allometry
- Functional equations
- Gompertz formula
- Growth
- Self-similarity
- Tumor growth
ASJC Scopus subject areas
- General Agricultural and Biological Sciences