Murray's law, the 'Yarrum' optimum, and the hydraulic architecture of compound leaves

There are two optima for maximizing hydraulic conductance per vasculature volume in plants. Murray's law (ML) predicts the optimal conduit taper for a fixed change in conduit number across branch ranks. The opposite, the Yarrum optimum (YO), predicts the optimal change in conduit number for a fixed taper. We derived the solution for YO and then evaluated compliance with both optima within the xylem of compound leaves, where conduits should have a minimal mechanical role. We sampled leaves from temperate ferns, and tropical and temperate angiosperms Leaf vasculature exhibited greater agreement with ML than YO. Of the 14 comparisons in 13 species, 12 conformed to ML. The clear tendency towards ML indicates that taper is optimized for a constrained conduit number. Conduit number may be constrained by leaflet number, safety requirements, and the fact that the number of conduits is established before their diameter during development. Within a leaf, ML compliance requires leaf-specific conductivity to decrease from petiole to petiolule with the decrease in leaf area supplied. A similar scaling applied across species, indicating lower leaf-specific petiole conductivity in smaller leaves. Small leaf size should offset lower conductivity, and petiole conductance (conductivity/length) may be independent of leaf size.