Scaling Mass and Morphology in Leaves: an Extension of the WBE Model

Recent advances in metabolic scaling theory have highlighted the importance of exchange surfaces and vascular network geometry in understanding the integration and scaling of whole-plant form and function. Additional work on leaf form and function has also highlighted general scaling relationships for many leaf traits. However, it is unclear if a common theoretical framework can reveal the general rules underlying much of the variation observed in scaling relationships at the whole-plant and leaf level. Here we present an extension of the general model introduced by G. B. West, J. H. Brown, and B. J. Enquist that has previously been applied to scaling phenomena for whole plants to predict scaling relationships in leaves. Specifically, the model shows how the exponents that describe the scaling of leaf surface area, length, and petiole diameter should change with increasing leaf mass (or with one another) and with variation in leaf dimensionality. The predictions of the model are tested and found to be in general agreement with a large data set of leaves collected from both temperate and arid sites. Our results demonstrate that a general model based on the scaling properties of biological distribution networks can also be successfully applied to understand the diversity of leaf form and function.