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A general model for the structure and allometry of plant vascular systems

Abstract

Vascular plants vary in size by about twelve orders of magnitude, and a single individual sequoia spans nearly this entire range as it grows from a seedling to a mature tree. Size influences nearly all of the structural, functional and ecological characteristics of organisms1,2. Here we present an integrated model for the hydrodynamics, biomechanics and branching geometry of plants, based on the application of a general theory of resource distribution through hierarchical branching networks3 to the case of vascular plants. The model successfully predicts a fractal-like architecture and many known scaling laws, both between and within individual plants, including allometric exponents which are simple multiples of 1/4. We show that conducting tubes must taper and, consequently, that the resistance and fluid flow per tube are independent of the total path length and plant size. This resolves the problem of resistance increasing with length, thereby allowing plants to evolve vertical architectures and explaining why the maximum height of trees is about 100 m. It also explains why the energy use of plants in ecosystems is size independent.

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Figure 1: Branching structure.
Figure 2: Effect of sequentially removing branches of increasing radius, r k, on the proportion of total resistance remaining, R k.

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Acknowledgements

We thank K. Niklas and M. Tyree for comments. J.H.B. was supported by the NSF, B.J.E. by the NSF and with an NSF post-doctoral fellowship, and G.B.W. by the US Department of Energy. We also thank the Thaw Charitable Trust for support.

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Correspondence to Brian J. Enquist.

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West, G., Brown, J. & Enquist, B. A general model for the structure and allometry of plant vascular systems . Nature 400, 664–667 (1999). https://doi.org/10.1038/23251

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