Biomechanical design and long-term stability of trees: morphological and wood traits involved in the balance between weight increase and the gravitropic reaction.

Studies 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, we show that the necessity for gravitropic correction might constrain stem allometric growth in the long-term. This constraint is compared to the requirement for elastic stability, showing that gravitropic performance limits the increase in height of tilted stem and branches. The performance of this function may thus limit the slenderness and lean of stems, and therefore the ability of the tree to capture light in a heterogeneous environment.