Lamina shape does not correlate with lamina surface area: An analysis based on the simplified Gielis equation

The simplified Gielis equation (SGE) can approximately describe the leaf shapes of many different broad-leaved plant species by replacing two parameters of the SGE with leaf width and leaf length with a floating ratio (c-value) to adjust for leaf length. In this study, we tested the validity of the SGE in predicting leaf area using 20 bamboo species, 12 species of Rosaceae, 5 species of Lauraceae, and 5 species of Oleaceae. We find that c-values in leaf length for 20 bamboo species are all smaller than zero, whereas, for most tree species, c-values are larger than zero. Using c-values, there was a strong correlation (>0.99 for most of the species investigated) between actual and predicted leaf area. Also, using the SGE to fit the leaf profile data, the predicted leaf width approaches its actual value, whereas the predicted length is larger than or smaller than its actual value (for bamboo species and most tree species, respectively). Although c-values ranged from -15% to zero for bamboo species and from zero to 17% for tree species, the mean percent error in leaf area for most species did not exceed 5%. These findings indicate that leaves exhibit more variation in length than in width, i.e., leaf area is fairly conservative despite considerable variation in leaf shape. Given that the SGE adequately describes the areas of leaves with complex forms (e.g., several species of Rosaceae), our data indicate that the SGE is a useful tool for describing leaf morphometrics and may open a door for the study of leaf shape evolution. (C) 2019 The Authors. Published by Elsevier B.V.