The Phenotypes of Fluctuating Flow: Development of Distribution Networks in Biology and the Trade-off between Efficiency, Cost, and Resilience

Abstract

Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \(Physarum\) \(polycephalum\) as well as mammalian and plant venation. Adaptive rules are believed to guide development of these networks and lead to a reticulate, hierarchically nested topology that is both efficient and resilient against perturbations. However, as of yet no mechanism is known that can generate such networks on all scales. We show how hierarchically organized reticulation can be generated and maintained through spatially collective load fluctuations on a particular length scale. We demonstrate that the resulting network topologies represent a trade-off between optimizing power dissipation, construction cost, and damage robustness and identify the Pareto-efficient front that evolution is expected to favor and select for. We show that the typical fluctuation length scale controls the position of the networks on the Pareto front and thus on the spectrum of venation phenotypes. We compare the Pareto archetypes predicted by our model with examples of real leaf networks.