Damage and fluctuations induce loops in optimal transport networks

TL;DR

This paper investigates how damage resilience and load fluctuations lead to the formation of loops in optimal biological transport networks, contrasting with the loopless trees optimized solely for efficiency.

Contribution

It introduces models showing that damage and load variability naturally induce loops in optimal transport networks, inspired by leaf venation patterns.

Findings

Damage resilience promotes loop formation in networks.

Load fluctuations also favor the emergence of loops.

Optimal networks under these criteria are not trees, but contain loops.

Abstract

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.