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Testing the packing rule across the twig–petiole interface of temperate woody species

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Abstract

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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Acknowledgments

We thank Xianming Gao, Guoyong Li, Shuang Xiang, Yan Li, Qin Shi, Shuo Wang, and Yanan Li for field assistance, Li Dong and Danrong Wang for laboratory assistance. Thanks are also due to the staff of Gonganshan National Nature Reserve for permitting this study to be conducted. The research was funded by National Science Foundation of China (31170382), Southwest University (SWU110032) and the Fundamental Research Funds for the Central Universities.

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Correspondence to Shucun Sun.

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Communicated by J. Carlson.

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Chen, H., Niklas, K.J. & Sun, S. Testing the packing rule across the twig–petiole interface of temperate woody species. Trees 26, 1737–1745 (2012). https://doi.org/10.1007/s00468-012-0742-3

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