A Nonlinear Dynamical View of Kleiber’s Law on the Metabolism of Plants and Animals

Author:

Camacho-Vidales Luis Jovanny1,Robledo Alberto1

Affiliation:

1. Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Mexico City 01000, Mexico

Abstract

Kleiber’s empirical law, which describes that metabolism increases as the mass to the power 3/4, has arguably remained life sciences’ enigma since its formal uncovering in 1930. Why is this behavior sustained over many orders of magnitude? There have been quantitative rationalizations put forward for both plants and animals based on realistic mechanisms. However, universality in scaling laws of this kind, like in critical phenomena, has not yet received substantiation. Here, we provide an account, with quantitative reproduction of the available data, of the metabolism for these two biology kingdoms by means of broad arguments based on statistical mechanics and nonlinear dynamics. We consider iterated renormalization group (RG) fixed-point maps that are associated with an extensive generalized (Tsallis) entropy. We find two unique universality classes that satisfy the 3/4 power law. One corresponds to preferential attachment processes—rich gets richer—and the other to critical processes that suppress the effort for motion. We discuss and generalize our findings to other empirical laws that exhibit similar situations, using data based on general but different concepts that form a conjugate pair that gives rise to the same power-law exponents.

Publisher

MDPI AG

Subject

General Physics and Astronomy

Reference44 articles.

1. Kleibers’s Law (2023, December 24). Wikipedia. Available online: https://en.wikipedia.org/wiki/Kleiber%27s_law.

2. Body size and metabolism;Kleiber;Hilgardia,1932

3. Body size and metabolic rate;Kleiber;Physiol. Rev.,1947

4. Kleiber, M. (1961). The Fire of Life. An Introduction to Animal Energetics, John Wiley & Sons, Inc.

5. Quantitative laws in metabolism and growth;Q. Rev. Biol.,1957

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