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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Biomechanical design and long-term stability of trees:Morphological and wood traits involved in the balance between weight increase and the gravitropic reaction This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A c c e p t e d m a n u s c r i p t A c c e p t e d m a n u s c r i p t 2 AbstractStudies on tree biomechanical design usually focus on stem stiffness, resistance to breakage or uprooting, and elastic stability. Here we consider another biomechanical constraint related to the interaction between growth and gravity. Because stems are slender structures and are never perfectly symmetric, the increase in tree mass always causes bending movements. Given the current mechanical design of trees, integration of these movements over time would ultimately lead to a weeping habit unless some gravitropic correction occurs. This correction is achieved by asymmetric internal forces induced during the maturation of new wood.The long-term stability of a growing stem therefore depends on how the gravitropic correction that is generated by diameter growth balances the disturbance due to increasing self weight.General mechanical formulations based on beam theory are proposed to model these phenomena. The rates of disturbance and correction associated with a growth increment are deduced and expressed as a function of elementary traits of stem morphology, cross-section anatomy and wood properties. Evaluation of these traits using previously published data shows that the balance between the correction and the disturbance strongly depends on the efficiency of the gravitropic correction, which depends on the asymmetry of wood maturation strain, eccentric growth, and gradients in wood stiffness. By combining disturbance and correction rates, the gravitropic performance indicates the dynamics of stem bending during growth. It depends on stem biomechanical traits and dimensions. By analyzing dimensional effects, weshow that the necessity for gravitropic correction might constrain stem allometric growth in the long-term. This constraint is compared to the requirement for elastic ...

Functional ecology has long considered the support function as important, but its biomechanical complexity is only just being elucidated. We show here that it can be described on the basis of four biomechanical traits, two safety traits against winds and self-buckling, and two motricity traits involved in sustaining an upright position, tropic motion velocity (MV) and posture control (PC). All these traits are integrated at the tree scale, combining tree size and shape together with wood properties. The assumption of trait constancy has been used to derive allometric scaling laws, but it was more recently found that observing their variations among environments and functional groups, or during ontogeny, provides more insights into adaptive syndromes of tree shape and wood properties. However, oversimplified expressions have often been used, possibly concealing key adaptive drivers. An extreme case of oversimplification is the use of wood basic density as a proxy for safety. Actually, as wood density is involved in stiffness, loads, and construction costs, the impact of its variations on safety is non-trivial. Moreover, other wood features, especially the microfibril angle (MFA), are also involved. Furthermore, wood is not only stiff and strong, but it also acts as a motor for MV and PC. The relevant wood trait for this is maturation strain asymmetry. Maturation strains vary with cell-wall characteristics such as MFA, rather than with wood density. Finally, the need for further studies about the ecological relevance of branching patterns, motricity traits, and growth responses to mechanical loads is discussed.