The origin of how variation in biological rates and times scale with body size have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. While the model predicts numerous scaling relationships in biology, it is based on a core assumption that vascular networks are symmetric respect to their geometric properties. Here we test new theory that incorporates asymmetric branching patterns in self-similar vascular networks to account for the broad range of branching morphology observed in nature. To examine these ideas we compared variation in vascular branching traits across multiple datasets for both plant and mammalian vasculatures. These consist of destructively dissected whole-trees, partial canopy branches, and roots that span a broad range of plant architecture and functionality, as well as the cardiovascular networks of the human head and torso and mouse lungs digitally reconstructed from magnetic resonance imaging.
Variation in metabolism, physiology, life history, and ecological attributes of an organism is largely determined by variation in body size. Our study provides a quantitative basis for how the direct inclusion of asymmetric branching patterns into the WBE model can help to differentiate between intra- and interspecific variation in body size through vascular form. Our analysis of each species' vascular traits reveals that branching geometry is clearly asymmetrical, violating a key assumption of the WBE model, and demonstrating the vast array of branching morphology that vascular networks exhibit across phylogenies. Further, we show how generational variation of branching traits within individual networks can be related to various selective pressures on network function. Examples include transitioning in blood flow from pulsing to laminar in cardiovascular networks, and shifting from structural support to light-capturing strategies in plant networks. Finally, we point to ways that measuring branching traits can inform the processes underlying similarity and variation in allometric scaling in biology. We show how network asymmetry can be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.