Testing the packing rule across the twig–petiole interface of temperate woody species
2012
Chen, Hong | Niklas, Karl J. | Sun, Shucun
Theories that incorporate the area-preserving rule of Leonardo da Vinci predict that the sum of the cross-sectional lumen area of xylem conduits (vessels or tracheids) is constant across different levels of branching. If true, this rule obtains the packing rule, according to which (1) vessel cross-sectional lumen area (A) will negatively and isometrically scale to vessel number per unit area (N) and (2) the distal to proximal vessel diameter ratio (DR = D ₙ₊₁/D ₙ ) should scale as the −1/2 power of the distal to proximal vessel number ratio (NR = N ₙ₊₁/N ₙ ), i.e., DR = NR⁻¹/². Using data collected from the terminal twigs and the petioles of 60 temperate (27 evergreen and 33 deciduous) woody species from southwestern China, we determined the scaling relationships for A versus N and for DR versus NR. Analyses of the data revealed contrasting scaling exponents and normalization constants for A versus N and for DR versus NR and no consistent trend across the two species groupings or between the two organ types (as predicted by the area-preserving and packing rules). These results caution against applying these rules ubiquitously to all species or to different organ types (even on the same plant).
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