A Metabolic Theory for Everything

By Bob Grant

ARTICLE EXTRAS
Feature: The Powers That Might Be

Audio Slideshow: Discussing Metabolic Theory

Metabolic Theory in Elephants and Mice


Geoffrey West, Jim Brown, and Brian Enquist prefer to call their groundbreaking model "metabolic theory" and not "the metabolic theory of ecology," as some articles have referred to it. 1 "It's unfortunate to associate it only with ecology," says Brown. Indeed, metabolic theory has branched from ecology, and its underlying principles and predictions have the potential to serve in a variety of contexts.


Urban Planning - This past month in the Harvard Business Review's "Breakthrough Ideas for 2007" issue, West wrote about power-law scaling relationships in urban areas. 2 Looking at demographics, infrastructure dimensions, crime rates, intellectual innovation, and rates of disease spread in cities of all sizes around the world, he and his colleagues found that some urban features, including total length of electrical cables, miles of road surface, and number of gas stations, scale with exponents less than one, similar to biological networks such as the vascular and xylem systems. Therefore, as cities' populations double, they should require less than double of these infrastructure features. Some social aspects, however, scale to city size with an exponent greater than one. Measures of wealth and creativity such as GDP, wages, and number of patents filed actually increase more quickly as population increases.


Corporations - West says that some of the patterns true for cities may apply to corporations and industries as well, which would suggest that the larger companies get, the higher their per-employee rate of innovation. But, West writes: "The equations also predict that in the absence of continual major innovations, organizations will stop growing and may even contract, leading to either stagnation or ultimate collapse." 3


Drug Trials - According to West, if pharmaceutical researchers could use the predictions of metabolic theory to reliably scale drug dosage from model organisms to humans, much time and expense might be saved in development.


Tumor Growth - A paper in the Journal of Theoretical Biology reports that the principles of metabolic theory apply to tumor growth. 4 West suspects that tumors co-opt segments of the vascular system while maintaining an attachment to the wider transport network that determines the metabolic characteristics of the whole organism.


Human Fertility - Melanie Moses, a postdoc working with Brown, used metabolic theory to explore the scaling of human fertility with energy consumption. Analyzing more than 25 years of data from 100 countries, they showed that consumption of what they call "extrametabolic energy" strongly influences the number of offspring. This describes the use of resources such as oil, coal, gas, and electricity. Further, they found that human fertility rates decline with a scaling exponent of negative 1/3 as extrametabolic energy increases. This accounts for the reduced birth rates in industrialized nations, possibly due to parents considering potential tradeoffs between child number and the energy investment required.


Computer/Digital Network Design - Stephanie Forest, a computer scientist at the University of New Mexico, will be collaborating with Brown to explore how scaling power laws might inform computer and chip design. If measures such as optimal processing time and chip surface area can be modeled, computers and digital networks might be designed to function more efficiently.

References
1. J.H. Brown et al., "Toward a metabolic theory of ecology," Ecology, 85:1771-89, 2004.
2. G.B. West, "Innovation and growth: size matters," Harvard Business Rev, 85(2):34-5, February 2007.
3. C. Guiot et al., "Does tumor growth follow a 'universal law'?" J Theoret Biol, 225:147-51, 2003.[PubMed]
4. M.E. Moses and J.H. Brown, "Allometry of human fertility and energy use," Ecol Lett, 6:295-300, 2003.

 

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comment:
A Metabolic Theory for Everything
by Gregory C. O'Kelly

[Comment posted 2007-03-05 06:31:29]

I am not familiar with the analysis of West et al. other than what has appeared in this article, and about that I would like to make two observations. The second one is lengthy.

The first one is that the application of the Kleiber's Law to metabolism necessarily includes the term in the exponent for metabolic efficiency (ME), the ratio of the rate at which building/anabolism/the cost of survival and growth takes place, to the rate at which energy, resources, productivity are available. A graph of Kleiber's Law for a wide range of body masses, with one curve for each mass, and the curves on a Cartesian coordinate system with the X axis being ME and the Y axis being metabolic rate, reveals that for things less than one gram metabolic rate skyrockets as ME decreases to 0, while for over one gram metabolic rate plummets.

It was not clear from the article whether West was applying then basal values to society and corporations, or the mathematics for organisms greater than one gram and 25% ME. In his metabolic treatments West does not include ME in the exponent, is tendentious in his fractality, seeming to think that Kleiber's Law applie only to basal considerations and respiratory metabolism dependent upon vascularity. He is at sea yet with regard to neuro-gastric redox coupling and motor activity. And that situation almost certainly overshadows his economic and urban analysis, and grim view of the Darwinian prospects for corporations.

And that leads to observation two. Given a more complete analysis of the mathematics that includes the term for ME in the exponent of mass, we must ask ourselves two questions. First, since we are dealing with social theory, and since that any society must have as its basal unit a couple, then should we place wages and income in the denominator of ME? And for units large than basal shouldn't wages and cost of business be in the numerator of ME, whether for a corporation, a city, or a state? If we did this we could then consider metabolic rate to be market activity in a society based upon the division of labor and using money.

But the trouble is, though West can be thought to correctly suggests that the productivity and innovativeness of the laborer should be in the denominator of ME for social organizations other than basal, he is perhaps misinterpreted when he says the equation predicts collapse for corporations and cities or anything, lacking growth and continuous major innovation. The equation does no such thing. The equation, when applied to either the biology of basal couple organisms or corporate and social organism, to be concordant with the trends revealed in evolution from bacteria to whale, directly demonstrates that the best way to insure the survival of that organism is to decrease basal ME and increase field/corporate ME. And this is done by in human social organisms, whether companies or states or kingdoms or tribes, by increasing wages at the basal level, the denominator of ME; and increasing wages and investment and social spending as the numerator of field/corporate ME.

The equation speaks to the organism's needs for survival and ability to endure scarcity during hard times. That means the numerator of ME for field/corporate mathematics, if it is to reflect how nature does it, should be devoted to equilibrating riches to the basal level and investing in innovations that will further redound to the basal level. That means military Keynesianism, for example, is such an un-biological perversion. But the equation does not say that major growth and innovation is necessary to stave off collapse.

Perhaps an elitist physicist hipped on the libertarian message believes that the 'free' in free market has mathematical relevance beyond the basal level, and that perhaps it is possible to create a social theory based upon the individual. If he does, he is wrong in both cases.