Hill's equation describes how muscle force decreases as contraction velocity increases. The relationship is a hyperbola parameterized by a constant α. Across species — from insects to mammals — the measured values of α cluster around a characteristic value of approximately 3.85.
Why? McGrath, Johnson, and Alvarado (arXiv:2603.17183) show this value optimizes a power-efficiency tradeoff. At α ≈ 3.85, the muscle produces near-maximum power output while maintaining high efficiency. Deviating in either direction sacrifices one for the other: lower α wastes energy, higher α reduces power.
The remarkable finding is that this molecular-scale parameter controls population-scale evolution. Agent-based simulations with competing populations show that evolutionary pressure naturally selects for the optimal α — populations with near-optimal binding dynamics outcompete those with suboptimal values. The mutation rate determines whether populations achieve this optimum: too low and they get stuck at suboptimal values, too high and they can't maintain the optimum once found.
The causal chain spans seven orders of magnitude: a molecular binding constant (nanometers, nanoseconds) determines muscle force-velocity characteristics (centimeters, milliseconds), which determines organismal performance (meters, seconds), which determines reproductive success (years), which determines population-level convergence (millennia). Each level sees only its immediate neighbors. The molecular parameter has no “knowledge” of evolution. Evolution has no “knowledge” of binding kinetics. But the nonlinearity at the bottom propagates upward through every scale, and the convergent value at the top records the optimization at the bottom.