Constructing a Theory for Scaling and More

Abstract

West and Brown reply: The theory we developed with Brian Enquist on the origins, implications, and ramifications of universal scaling laws in biology, and which we reviewed in our article in Physics Today, is predicated on the idea that life at all scales is sustained by optimized, space-filling, hierarchical branching networks whose terminal units are invariant. The theory not only explains quarter-power scaling but leads to detailed quantitative calculations and predictions of many biological phenomena.We suggested that the generic underlying principles of the theory are derived from natural selection. Adrian Bejan suggests, however, that they follow from his constructal theory and that our idea was already implicit in his 1996 paper in which he investigated the special case of traffic flow through a network of streets. Although there are clearly qualitative areas of overlap, particularly concerning modeling trees and his specific version of optimization and space-filling, it is difficult for us to see any explicit connection to our work. He did not consider allometric scaling in biology, nor is there any mathematical derivation of the three major principles underlying our theory.It is true, as Alexandru Morega points out, that in Bejan’s 2000 book, published three years after our original paper, he does consider biological systems and presents a derivation of the 3/4 power law for metabolic rate. The derivation is based on the special case of the role of blood flow in dissipating heat. Even if correct, that derivation is not general and is relevant only for warm-blooded mammals and birds. The vast majority of animals and plants are ectothermic, having body temperatures that mirror their environment, so heat dissipation is unimportant and consequently has not been a major target of natural selection. Nevertheless, ectothermic organisms also exhibit quarter-power scaling, which we claim is because their distribution networks have been selected to optimize the distribution of energy and materials.We agree that there appear to be general principles of flow network and design that have crafted, and are exhibited by, a wide variety of biological and human systems. Bejan’s book is a serious attempt to address this intriguing and very important observation. It remains to be seen, however, whether constructal theory is sufficiently general, detailed, and mechanistic to describe these systems in a quantitative, predictive, and analytic way. A significant contribution would be to have a convincing derivation from more fundamental principles of our assumptions that much of life is sustained by optimized, space-filling, hierarchical branching networks whose terminal units are invariant.© 2005 American Institute of Physics.