Biology of Business

Systems

Scaling Law

By Alex Denne

A mathematical relationship describing how a quantity changes as the size of a system changes. Often expressed as power laws where one quantity scales as another raised to some exponent.

Used in the Books

This term appears in 6 chapters:

Foundations Metabolism and Burn Rate

"(1932). Body size and metabolism. Hilgardia, 6(11), 315-353. - Foundational paper establishing the 3/4 power scaling law (Kleiber's Law) for metabolic rate, demonstrating that metabolic rate scales with body mass to the 0.75 power rather than linearly West, G.B., Brown..."

Resource Dynamics Foraging Optimization

"Humphries, Graeme C. Hays, Corey J. A. Bradshaw, Jonathan W. Pitchford, Alex James, Mohammed Z. Ahmed, Andrew S. Brierley, Mark A. Hindell, et al. "Scaling Laws of Marine Predator Search Behaviour." Nature 451, no. 7182 (2008): 1098-1102. > Supports: Lévy flight search patterns in marine predators (line..."

Resource Dynamics Nutrient Networks

"...same principles as animal circulatory systems West, Geoffrey B., James H. Brown, and Brian J. Enquist. "A General Model for the Origin of Allometric Scaling Laws in Biology." Science 276, no. 5309 (1997): 122-126. > Supports: Universal scaling laws in biological branching networks; fractal geometry of va..."

Growth Stages Growth Limits

"...overed that metabolism doesn't scale with mass (M^1.0) but with mass to the 3/4 power (M^0.75). This became Kleiber's Law—one of the most fundamental scaling laws in biology. Kleiber's Law: Basal metabolic rate (BMR) scales as mass^0.75. This means: - 1 kg animal: ~10 watts - 10 kg animal (10× mass): ~56 watts..."

Scale and Complexity Scaling Laws

"...nizational failure before it happens. --- Part 1: The Biology of Scaling Laws The Square-Cube Law: Geometry's Tyranny The most fundamental scaling law is geometric. In three-dimensional objects, surface area scales as length squared while volume scales as length cubed."

And 1 more chapter...

Biological Context

Metabolic rate scales with body mass to the 3/4 power. Surface area scales with volume to the 2/3 power. These scaling relationships constrain what's possible at different sizes—elephants can't have the proportions of ants. Scaling laws reveal deep organizing principles.

Related Terms

Tags

mathematicssizeconstraints