A Sceptics View: “Kleiber’s Law” or the “3/4 Rule” is neither a Law nor a Rule but Rather an Empirical Approximation

A Hulbert

doi:10.3390/systems2020186

Abstract

Early studies showed the metabolic rate (MR) of different-sized animals was not directly related to body mass. The initial explanation of this difference, the law, was replaced by the suggestion that MR be expressed relative to mass , where the scaling exponent n be empirically determined. Basal metabolic rate (BMR) conditions were developed and BMR became important clinically, especially concerning thyroid diseases. Allometry, the technique previously used to empirically analyse relative growth, showed BMR of endotherms varied with 0.73-0.74 power of body mass. Kleiber suggested that mass 3/4 be used, partly because of its easy calculation with a slide rule. Later studies have produced a range of BMR scaling exponents, depending on species measured. Measurement of maximal metabolism produced scaling exponents ranging from 0.80 to 0.97, while scaling of mammalian MR during growth display multi-phasic allometric relationships with scaling exponents >3/4 initially, followed by scaling exponents <3/4. There is no universal metabolic scaling exponent. The fact that is an empirical technique to analyse relative change and not a biological law is discussed. Relative tissue size is an important determinant of MR. There is also a need to avoid simplistic assumptions regarding the allometry of surface area.

Highlights

The subject of allometry concerns relative change in structure or function with change in body size.It has a long history stemming from detailed studies of relative growth and is defined as “the growth of body parts at different rates, resulting in a change of body proportions”
For example in one study of a specific mixture of mammal species, where Basal metabolic rate (BMR) varied with the 0.62 power of body mass, mitochondrial membrane surface area per cm3 of brain, liver, kidney and heart all significantly decreased with increased body size
There is no single allometric “law” that describes the relationship between body size and metabolism

Summary

Introduction

The subject of allometry concerns relative change in structure or function with change in body size. (Teissier’s previous term), and coalesce the field of relative growth studies [1,2] They proposed the term isometry (to replace “isogony” and “harmony”) and agreed on the symbolic formulation for allometric growth of y = b·xa, where y is some biological variable, x is body mass, a is the scaling exponent, and b is a constant (the value of y at unity body size, i.e., when x = 1). Following its original use for the study of relative growth, the techniques of allometry have been used to analyse the relationships between a wide range of body functions and body size In this contribution, I intend to apply a historical perspective to the analysis of the relationship between metabolic rate and body size of animals, and I will return to this fundamental surface area/size relationship

Metabolic Rate and Body Size

Findings

Synthesis and Conclusions