Kleiber's Law — Allometric Metabolic Scaling B ∝ M³/⁴

Physics

Kleiber's Law (1932): B = B₀ M^(3/4), holds from bacteria (10⁻¹⁵ g) to whales (10⁸ g). The ¾ exponent emerges from the WBE fractal network model (West, Brown, Enquist 1997): hierarchical branching networks minimize energy dissipation subject to the constraint that terminal units (mitochondria, capillaries) are size-invariant.

Consequences: B/M = B₀ M^(−1/4) — specific metabolic rate decreases with size. Lifespan ∝ M^{1/4}. Heart rate ∝ M^{−1/4}. All biological times scale as M^{1/4}. Life lives at the same "metabolic pace" regardless of size.