Metabolic Adaptation Without Adaptation: Decelerating Mass Loss as a Geometric Consequence of a Draining Reservoir

The progressive slowing of weight loss during caloric restriction is routinely ascribed to metabolic adaptation. This interpretation treats the deceleration as a biological adjustment whose magnitude must be estimated after the fact. The present analysis shows that the decelerating trajectory is required by geometry. The human body is a mass reservoir. Net mass outflow occurs across surfaces whose aggregate area scales with retained mass. When outflow is an increasing function of surface area, and surface area is an increasing function of mass, the rate of mass loss must decline as mass declines. This relation follows directly from the continuity equation and the geometry of surface-to-volume scaling; it does not require empirical calibration to be true in principle. Once the geometric term is acknowledged, a large fraction of what has been labelled metabolic adaptation ceases to require biological explanation. The phenomenon that has most persistently disordered obesity research is, to first order, the ordinary behaviour of a draining reservoir.