Asymmetric Branching in Biological Resource Distribution Networks

Abstract

There is a remarkable relationship between an organism's metabolic rate (resting power consumption) and the organism's mass. It may be a universal law of nature that an organism's resting metabolic rate is proportional to its mass to the power of 3/4. This relationship, known as Kleiber's Law, appears to be valid for both plants and animals. This law is important because it implies that larger organisms are more efficient than smaller organisms, and knowledge regarding metabolic rates are essential to a multitude of other fields in ecology and biology. This includes modeling the interactions of many species across multiple trophic levels, distributions of species abundances across large spatial landscapes, and even medical diagnostics for respiratory and cardiovascular pathologies. Previous models of vascular networks that seek to identify the origin of metabolic scaling have all been based on the unrealistic assumption of perfectly symmetric branching. In this dissertation I will present a theory of asymmetric branching in self-similar vascular networks (published by Brummer et al. in [9]). The theory shows that there can exist a suite of vascular forms that result in the often observed 3/4 metabolic scaling exponent of Kleiber's Law. Furthermore, the theory makes predictions regarding major morphological features related to vascular branching patterns and their relationships to metabolic scaling. These predictions are suggestive of evolutionary convergence in vascular branching. To test these predictions, I will present an analysis of real mammalian and plant vascular data that shows: (i) broad patterns in vascular networks across entire animal kingdoms and (ii) within these patterns, plant and mammalian vascular networks can be uniquely distinguished from one another (publication in preparation by Brummer et al.). I will also present results from a computational study in support of point (i). Namely, that asymmetric branching may be the optimal strategy to balance the simultaneous demands of maximizing the number of nutrient exchange sites (capillaries or leaves) versus hydraulic resistance to resource transport (publication in preparation by Brummer et al.). Finally, I report on improved methods of estimating whole organism metabolism based solely on measurements of vasculature.