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Symmetry 2018, 10(4), 118;

A Simple Method for Measuring the Bilateral Symmetry of Leaves

Co-Innovation Centre for Sustainable Forestry in Southern China, College of Biology and the Environment, Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China
Tasmanian Institute of Agriculture, University of Tasmania, Private Bag 98, Hobart, Tasmania 7001, Australia
Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 55812, USA
Authors to whom correspondence should be addressed.
Received: 21 March 2018 / Revised: 14 April 2018 / Accepted: 16 April 2018 / Published: 18 April 2018
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Many plant leaves exhibit bilateral symmetry, but such symmetry has rarely been measured because of the lack of practical methods. We propose a simple method for achieving the above objective. A leaf is divided into left and right sides, and several equally-sized strips are generated to intersect each side of that leaf to generate pairwise left and right sub-regions. A standardized index (SI) for measuring bilateral symmetry is built based on the left–right areal differences of those sub-regions. The leaves of 10 species of plants were sampled for testing the method’s validity. Based on the experimental data, we compared the root-mean-squared error (RMSE), SI, and areal ratio (AR) of the left side to the right side of the leaf. The SI measures the bilateral symmetry of plant leaves well, and it is better than the RMSE and AR for eliminating the effect of leaf size on the goodness of fit. The SI proposed here is the best indicator for evaluating the degree of bilateral symmetry and can be potentially used for comparing the difference in the bilateral symmetry of leaves of different plants. View Full-Text
Keywords: leaf area; leaf size; mirror image; spatstat; standardized index leaf area; leaf size; mirror image; spatstat; standardized index

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Shi, P.; Zheng, X.; Ratkowsky, D.A.; Li, Y.; Wang, P.; Cheng, L. A Simple Method for Measuring the Bilateral Symmetry of Leaves. Symmetry 2018, 10, 118.

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