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Water transport in plants obeys Murray's law

Abstract

The optimal water transport system in plants should maximize hydraulic conductance (which is proportional to photosynthesis1,2,3,4,5) for a given investment in transport tissue. To investigate how this optimum may be achieved, we have performed computer simulations of the hydraulic conductance of a branched transport system. Here we show that the optimum network is not achieved by the commonly assumed pipe model of plant form6,7,8, or its antecedent, da Vinci's rule9,10. In these representations, the number and area of xylem conduits is constant at every branch rank. Instead, the optimum network has a minimum number of wide conduits at the base that feed an increasing number of narrower conduits distally. This follows from the application of Murray's law, which predicts the optimal taper of blood vessels in the cardiovascular system11. Our measurements of plant xylem indicate that these conduits conform to the Murray's law optimum as long as they do not function additionally as supports for the plant body.

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Figure 1: Transport networks.
Figure 2: Murray's law.
Figure 3: ANOVA P values comparing the sum of the conduit radii raised to the x power (Σrx) between petiolule versus petiole ranks of compound leaves.

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Acknowledgements

We thank A. Collopy and M. McCord for assistance in collecting plants. This work was partly supported by Sigma Xi (K.A.M.) and NSF (J.S.S.).

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Correspondence to Katherine A. McCulloh.

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Supplementary information

41586_2003_BFnature01444_MOESM1_ESM.doc

Supplementary Information: Cecil Murray originally derived Murray’s law for the cardiovascular system of animals. Despite the many differences between plant and animal vasculature, including the thickness of conduit walls and the number of conduits per rank, Murray’s derivation can easily be extended to plant xylem. In the Supplementary Material, we provide a derivation of Murray’s law with respect to plants. (DOC 61 kb)

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McCulloh, K., Sperry, J. & Adler, F. Water transport in plants obeys Murray's law. Nature 421, 939–942 (2003). https://doi.org/10.1038/nature01444

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