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Appears in Collections:Biological and Environmental Sciences Journal Articles
Peer Review Status: Refereed
Title: Power scaling, vascular branching patterns, and the golden ratio
Author(s): Frater, Paul
Duthie, A Bradley
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Keywords: Golden Ratio
Vascular Branching
Power Scaling
Issue Date: 2016
Date Deposited: 8-Nov-2016
Citation: Frater P & Duthie AB (2016) Power scaling, vascular branching patterns, and the golden ratio. Ideas in Ecology and Evolution, 9 (1), pp. 15-18.
Abstract: The Golden Ratio (a ratio of ~1.618:1) appears repeatedly in nature including structural and functional traits of organisms (e.g. Fibonacci spirals of snail shells and certain seed heads), the spiraled shape of galaxies and hurricanes, and even in much cultural architecture and art. In the mid-19th century, branching structures in plant and animal vascular systems were found to follow the Golden Ratio; that is, successive branches in the vascular systems of plants and animals tend to follow a length ratio of about 1.618:1. Here we present a model that uses this empirical evidence as a branching ratio in theoretical vascular systems. We then use a defined mass of the model system as a predictor of log-log scaling of terminal units. In this model, log terminal units and log mass scale similarly with that of other models as well as empirical evidence, but with more parsimony and a perspective not yet offered among all available models of allometric scaling. This model invites novel and broad hypotheses on the influence of the Golden Ratio on power scaling in organisms.
DOI Link: 10.4033/iee.2016.9.4.n
Rights: This work is licensed under a Creative Common Attribution 3.0 License. You are free to: Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use
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