Title: 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.