West et al. 1997 by K. Sullivan

West et al. 1997 Paper

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

Paper Authors:  Geoffrey B. West, James H. Brown,* Brian J. Enquist

Geoffrey B. West

·       Theoretical Physicist 

·       Distinguished Professor of the Santa Fe Institute

·       Bachelor of  Arts, Cambridge University, 1961

·       Ph.D., Stanford University, 1966

Research Interests:

“Geoffrey West is a theoretical physicist whose primary interests have been in fundamental questions in physics, especially those concerning the elementary particles, their interactions and cosmological implications”.

Santa Fe Institute, https://www.santafe.edu/people/profile/geoffrey-west

James H. Brown                

·       Professor of Biology at the University of New Mexico

·       Bachelor of Arts, Zoology, 1963, Cornell University

·       Ph.D., Zoology, 1967, University of Michigan

Research Interests:

“Community ecology and biogeography, with special projects on granivory in desert ecosystems; biogeography of insular habitats; and structure of dynamics of geographic-scale assemblages of many species”.

Department of Biology at UNM, http://biology.unm.edu/core-faculty/brown.shtml

Brian J. Enquist

·       Professor – Department of Ecology and Evolutionary Biology at the University of Arizona

·       External Professor at the Santa Fe Institute

·       Ph.D. Biology, 1998, University of New Mexico.

·       M.S. Biology, 1994. University of New Mexico,

·       B.A. Biology (With Distinction), 1991. The Colorado College

Research Interests:

“Macroecology, Global Ecology, Comparative Biology, Ecophysiology and Functional Ecology”.  “My collaborative lab group strives to develop a more integrative, quantitative, and predictive framework for biology, community ecology, and large-scale ecology. In particular, we aim to link biological measures across spatial and temporal scales in ecology and evolution”.

University of Arizona, https://brianjenquist.wordpress.com/brian-j-enquist/?wref=tp

Main Points

Allometric scaling relations, including quarter (3/4)-power scaling, refers to the characteristic shared by all organism, and the way in which essential materials are transported through “space-filled fractal networks of branching tubes” that run throughout the body.  The model applies to systems with tree-like structures with terminating ends and include such distribution systems as, plant vascular systems, animal circulatory systems (this was the data they used), and bronchial tubes in animal lungs.   

The paper, which focuses on quarter-power scaling for metabolism and body size in mammals and how these physiological patterns tend to be even multiples of ¼, assumes surface area and volume of the cardiovascular system directly correlate with body size.  However, it isn’t entirely clear why quarter-power scaling is exhibited by nearly all kinds of animals.  This paper attempts to better understand this, by proposing a common mechanism underlying these laws:

“Living things are sustained by the transport of materials through

linear networks that branch to supply all parts of the organism”.

Based on this hypothesis, “a quantitative model that explains the origin and ubiquity of quarter-power scaling” to “predict the essential features of transport systems, such as mammalian blood vessels and bronchial trees, plant vascular systems, and insect tracheal tubes”.   It was developed based on three assumptions:

1.     A fractal-like branching pattern that is space-filling is required.

2.     “The final branch of the network is a size-invariant unit” (i.e. the size (radii, length, & other characteristics) of the minimal elements in the network are the same for all organisms).

3.     “The energy required to distribute resources is minimized” (i.e. fluid resistance is minimized due to the terminating structural nature of the network).

They sought to demonstrate how the quarter-power scaling of metabolic rate, along with other biological traits are the products of fractal-like resource distribution system such as the cardiovascular system in mammals.  By applying the assumption above, West managed to realistically and quantitatively show how the model accurately predicts scaling parameters and absolute values regarding serval traits of the cardiovascular system in mammals.

Questions

1.     Is the quarter-power scaling law supported by allomatric data for classes other than mammals, such as birds and/or reptiles?

2.     Do other types of scaling laws like the quarter-power scaling law exist?  If so, how might they relate to macroecology?

You may be interested in reading a critique published in 2004 by J. Kozlowski and M. Konarzewski entitled “Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant?”  In it, the authors criticize the model, deeming it ‘mathematically incorrect’ and ‘biologically unjustified’.  West et al, countered by publishing the paper “Yes, West, Brown and Enquist’s model of allometric scaling is both mathematically correct and biologically relevant”, in which they, again, justify their findings as being biologically and mathematically sound.