Abstract:
• 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.
