Figure 1

Mean fraction of the network disconnected from the petiole vs. the fraction of the vein segments removed across all leaves (see Methods ) for both full reticulate networks (red line) and MSTs (blue). Shading represents one standard deviation above and below each curve. These curves demonstrate how in reticulate networks a significantly larger fraction remains connected to the source/sink as network vein segments are sequentially removed. For example when 10% of the vein segments are removed in a hierarchical tree, essentially all nodes are disconnected from the petiole, while approximately 50% of the nodes in a reticulate network remain connected. Robustness is defined as the difference between the two curves (as defined by the difference in the Riemann sums for each curve). Figure 1 Inset: The vein network in this Quercus grisea Liebm. leaf (chosen for clarity), demonstrates that a series of small breaks (red segments) in the network skeleton can yield a maximally spanning hierarchical tree (MST) without loops (blue segment). The MST largely preserves the vein hierarchy and bulk flow properties. The MST in this image was maximized for conductance.