ALONG THE EVOLUTION PROCESS KLEIBER'S 3/4 LAW MAKES WAY FOR RUBNER'S SURFACE LAW: A FRACTAL APPROACH

Author:

LI XIAO-XIA1,HE JI-HUAN1

Affiliation:

1. National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, P. R. China

Abstract

Rubner 1880 surface law reveals that the basal metabolic rate scales with body mass raised to the power of 2/3, which is geometrically correct and biologically relevant. However, Kleiber 1932 scaling law experimentally found that the scaling index was 3/4 instead of 2/3. There is no theory that can explain the Kleiber's data, explanations in Science in 1997 and later in Nature in 2002 for 3/4 scaling law for all life were apparently wrong. Here we show that Rubner's surface law was approximately correct, and it requires modification due to the fact that a cell is porous. Using fractal theory, the scaling index is about 0.7, 0.73, and 0.83, respectively, for inactive, active and motion statuses, and Kleiber's exponent can be fully explained by Rubner's law.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

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