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The influence of branch order on optimal leaf vein geometries: Murray's law and area preserving branching


Price, CA and Knox, S-JC and Brodribb, TJ, The influence of branch order on optimal leaf vein geometries: Murray's law and area preserving branching, PLOS One, 8, (12) Article e85420. ISSN 1932-6203 (2013) [Refereed Article]


Copyright Statement

Copyright 2013 Price et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

DOI: doi:10.1371/journal.pone.0085420


Models that predict the form of hierarchical branching networks typically invoke optimization based on biomechanical similitude, the minimization of impedance to fluid flow, or construction costs. Unfortunately, due to the small size and high number of vein segments found in real biological networks, complete descriptions of networks needed to evaluate such models are rare. To help address this we report results from the analysis of the branching geometry of 349 leaf vein networks comprising over 1.5 million individual vein segments. In addition to measuring the diameters of individual veins before and after vein bifurcations, we also assign vein orders using the Horton-Strahler ordering algorithm adopted from the study of river networks. Our results demonstrate that across all leaves, both radius tapering and the ratio of daughter to parent branch areas for leaf veins are in strong agreement with the expectation from Murray’s law. However, as veins become larger, area ratios shift systematically toward values expected under area-preserving branching. Our work supports the idea that leaf vein networks differentiate roles of leaf support and hydraulic supply between hierarchical orders.

Item Details

Item Type:Refereed Article
Keywords:murrays law, hydraulic network
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Biological mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the environmental sciences
UTAS Author:Brodribb, TJ (Professor Tim Brodribb)
ID Code:88851
Year Published:2013
Funding Support:Australian Research Council (FT100100237)
Web of Science® Times Cited:30
Deposited By:Plant Science
Deposited On:2014-02-18
Last Modified:2017-11-01
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