Linking functional traits to multiscale statistics of leaf venation networks.

Leaf venation networks evolved along several functional axes, including resource transport, damage resistance, mechanical strength, and construction cost. Because functions may depend on architectural features at different scales, network architecture may vary across spatial scales to satisfy functional tradeoffs. We develop a framework for quantifying network architecture with multiscale statistics describing elongation ratios, circularity ratios, vein density, and minimum spanning tree ratios. We quantify vein networks for leaves of 260 southeast Asian tree species in samples of up to 2 cm2 , pairing multiscale statistics with traits representing axes of resource transport, damage resistance, mechanical strength, and cost. We show that these multiscale statistics clearly differentiate species' architecture and delineate a phenotype space that shifts at larger scales; functional linkages vary with scale and are weak, with vein density, minimum spanning tree ratio, and circularity ratio linked to mechanical strength (measured by force to punch) and elongation ratio and circularity ratio linked to damage resistance (measured by tannins); and phylogenetic conservatism of network architecture is low but scale-dependent. This work provides tools to quantify the function and evolution of venation networks. Future studies including primary and secondary veins may uncover additional insights.