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Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We obtained 3D point cloud data of tree shape of Japanese zelkova ( Zelkova serrata ) and Japanese larch ( Larix kaempferi ) using the NavVis Lidar scanner, then applied a cylinder structure extraction from point cloud data with error estimation. We then formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. Subsequently, we constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. The derived theory recapitulates the trade-off among branch growth anisotropy, stress-gravity length, and branch shape, which may open the quantitative way to evaluate mechanical and morphological rationality of tree branches.

Exploring the mechanical and morphological rationality of tree branch structure based on 3D point cloud analysis and the finite element method