A General Model for the Origin of Allometric Scaling Laws in Biology

Allometric scaling relationships, including the $3/4$-power law for metabolic rates, which are characteristic of all organisms, are derived from a general model that describes how essential materials are transported through space-filling fractal networks of branching tubes. The model assumes that the energy dissipated is minimized and the terminal tubes do not vary with body size. It provides a complete analysis of scaling relationships for mammalian circulatory systems in excellent agreement with data. More generally, the model predicts the structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks.