Scaling Law
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 5 chapters:
"(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..."
"M., et al. (1999). "Optimizing the success of random searches." Nature, 401(6756), 911-914. - Sims, D. W., et al. (2008). "Scaling laws of marine predator search behaviour." Nature, 451(7182), 1098-1102. - Stephens, D. W., & Krebs, J. R. (1986). Foraging Theory."
"...ered 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..."
"...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."
"...furcates, and daughter roots explore different soil regions, maximizing exploration per unit root biomass. Empirically, plant root branching follows scaling laws similar to Murray's Law: - Root diameter decreases by ~0.7-0.8× per branching level (similar to 2^(-1/3) ≈ 0.79 in vascular systems) - Root length in..."
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.