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Leaf area–length allometry and its implications in leaf shape evolution


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Leaf area is proportional to the product of leaf length and width both for herbaceous and woody plants. The coefficient of proportionality falls into the range (1/2, π/4) for the investigated species.


According to Thompson’s principle of similarity, the area of an object should be proportional to its length squared. However, leaf area–length data of some plants have been demonstrated not to follow the principle of similarity. We explore the reasons why the leaf area–length allometry deviates from the principle of similarity and examine whether there is a general model describing the relationship among leaf area, width and length. We sampled more than 11,800 leaves from six classes of woody and herbaceous plants and tested the leaf area–length allometry. We compared six mathematical models based on root-mean-square error as the measure of goodness-of-fit. The best supported model described a proportional relationship between leaf area and the product of leaf width and length (i.e., the Montgomery model). We found that the extent to which the leaf area–length allometry deviates from the principle of similarity depends upon the extent of variation of the ratio of leaf width to length. Estimates of the parameter of the Montgomery model ranged between 1/2, which corresponds to a triangular leaf with leaf length as its height and leaf width as its base, and π/4, which corresponds to an elliptical leaf with leaf length as its major axis and leaf width as its minor axis, for the six classes of plants. The narrow range in practice of the Montgomery parameter implies an evolutionary stability for the leaf area of large-leaved plants despite the fact that leaf shapes of these plants are rather different.

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We are thankful to Robert D. Guy, the Communicating Editor and two anonymous reviewers for their invaluable comments on the earlier version of this manuscript. We thank Liang Cheng, Yanming Fang, Shuyan Lin and Xiao Zheng for their help during the leaf collection. This work was nominally financially supported the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Correspondence to Julian Schrader.

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Shi, P., Liu, M., Ratkowsky, D.A. et al. Leaf area–length allometry and its implications in leaf shape evolution. Trees 33, 1073–1085 (2019).

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  • Allometry
  • Montgomery model
  • Leaf area
  • Leaf dimension
  • Thompson’s principle of similarity