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Yes, West, Brown and Enquist"s model of allometric scaling is both mathematically correct and biologically relevant
Author(s) -
BROWN J. H.,
WEST GEOFFREY B.,
ENQUIST B. J.
Publication year - 2005
Publication title -
functional ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.272
H-Index - 154
eISSN - 1365-2435
pISSN - 0269-8463
DOI - 10.1111/j.1365-2435.2005.01022.x
Subject(s) - scaling , allometry , statistical physics , invariant (physics) , biology , branching (polymer chemistry) , exponent , metabolic rate , biological system , mathematics , computer science , physics , ecology , geometry , mathematical physics , materials science , linguistics , philosophy , composite material , endocrinology
The WBE theory shows how the quarter-power scalings of metabolic rate and many other biological attributes have their origin in the fractal-like designs of resource distribution networks. These designs are based on three simple principles: (1) a space-filling network that branches hierarchically to supply all parts of the three-dimensional body; (2) body-size invariant terminal units, such as capillaries or leaf petioles; and (3) mini- mization of the energy and time required to distribute resources. The WBE model of the mammalian cardio- vascular systems additionally shows quantitatively and realistically how the scalings of the structure and hydrodynamics solve the problem of distributing blood from a beating heart through elastic hierarchic- ally branching arteries to body-size invariant capillaries. The model correctly predicts not only the scaling para- meters and absolute values of many characteristics of mammalian cardiovascular systems that have been measured by biomedical researchers (see Table 1 in WBE), but also the values in the hypothetical numerical example proposed by K & K (see Table 1, below). By applying the fundamental principles listed above to other resource supply networks in different taxa of organisms, the WBE model explains the origin of the ubiquitous quarter-power scaling exponents that have puzzled biologists since the 1930s (e.g. Kleiber 1932; Peters 1983; McMahon & Bonner 1983; Calder 1984: Schmidt-Nielsen 1984).