| Allometric scaling relationships, including the {dollar}{lcub}3over4{rcub}{dollar}-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 structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks. The model predicts: (i) a fractal-like branching architecture with specific scaling exponents; (ii) allometric exponents which are simple multiples of 1/4; and (iii) values of several invariant quantities.; Extensions of the model to vascular plants provides a quantitative framework for an integrative explanation for plant structure and function. It invokes biomechanical constraints to predict the proportion of conducting to non-conducting tissue. It shows how tapering of vascular tubes permits resistance to be independent of tube length, thereby regulating resource distribution within a plant and allowing the evolution of diverse sizes and architectures, but limiting the maximum height for trees. The model accurately predicts several anatomical and physiological scaling laws in vascular plants. In addition, it shows how the constraints placed on the movement and transformation of energy through fractal-like networks ultimately constrains several ecological and life-history characteristics of vascular plants including population density, mass production, and ecosystem productivity. Results presented here provide theoretical and empirical support for quarter-power allometric scaling in vascular plants. They also suggest that a common mechanistic framework of allometric theory based on principles of resource distribution can explain many attributes of biology diversity. |
