A General Model for the Origin of Allometric Scaling Laws in Biology

  title={A General Model for the Origin of Allometric Scaling Laws in Biology},
  author={Geoffrey B. West and James H. Brown and Brian J. Enquist},
Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms and are here derived from a general model that describes how essential materials are transported through space-filling fractal networks of branching tubes. The model assumes that the energy dissipated is minimized and that the terminal tubes do not vary with body size. It provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with… 

Allometric Scaling Laws and the Derivation of the Scaling Exponent

Allometric scaling relations abound in nature. Examples include the power law relating the metabolic rate of organisms to their masses and the power law describing the dependence of the size. In

The origin of allometric scaling laws in biology.

Allometric scaling and central source systems.

  • O. Dreyer
  • Computer Science
    Physical review letters
  • 2001
This work presents a scaling exponent of the form D/D+1, which is simply a consequence of the source distribution of the systems considered and requires no further assumptions.

Scaling Laws in Physiology: Relationships between Size, Function, Metabolism and Life Expectancy

This universal equation, χ M, is applied to study mammals' circulatory network, function, metabolism and life expectancy and it is shown that this power-law scaling is valid even in a class of animals that vary widely in size.

Yes, West, Brown and Enquist"s model of allometric scaling is both mathematically correct and biologically relevant

The WBE model of the mammalian cardiovascular systems shows quantitatively and realistically how the scalings of the structure and hydrodynamics solve the problem of distributing blood from a beating heart through elastic hierarchically branching arteries to body-size invariant capillaries.

A general model for metabolic scaling in self-similar asymmetric networks

A general network model is derived that relaxes the symmetric assumption and defines two classes of asymmetrically bifurcating networks and shows how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume.

Allometric scaling law and ergodicity breaking in the vascular system

Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal



Botanical Scaling. (Book Reviews: Plant Allometry. The Scaling of Form and Process.)

The objective of this book is to show that, in contrast to the empirical approach to the relations between absolute and relative size, and between organic form and process, scaling relations can be analytically derived.

Structural and Functional Determinates of Metabolic Rate

Standard metabolic rates are principally determined by relatively few factors: temperature, mass, and phylogenetic affinities, and the phylogenetic history and relative associations of an animal are important determinates of energy expenditure.

Size and Shape in Biology

The model proposed here promises useful answers in comparisons of living things on both the microscopic and the gross scale, as part of the growing science of form, which asks precisely how organisms are diverse and yet again how they are alike.

The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume.

  • C. D. Murray
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1926
The purpose of these studies is to discuss the possible application of a second principle, the principle of minimum work, to problems concerning the operation of physiological systems.

Comparative cardiovascular dynamics of mammals

Introduction The Mammalian Species The Cardiovascular System Function of the Circulation Book Content Comparative Anatomy and Physiology of the Circulation The Heart Arteries The Veins The

The Ecological Implications of Body Size

A mathematical primer: logarithms, power curves, and correlations, and a mathematical primer for allometric simulation models.

Size‐dependent variations in plant growth rates and the “¾‐power rule”

It is speculated that the anisometric relation between the growth rate and mass of unicellular plants is attributable to a "dilution" of metabolically active cellular constituents with increasing cell size in combination with the scaling of surface area with respect to volume.

The hydraulic architecture of trees and other woody plants

summary In this paper, we have reviewed how the hydraulic design of trees influences the movement of water from roots to leaves. The hydraulic architecture of trees can limit their water relations,