Alméras T, Fournier M
INRA, UMR Ecologie des Forêts de Guyane, BP 709, 97310 Kourou, France.
J Theor Biol. 2009 Feb 7;256(3):370-81. doi: 10.1016/j.jtbi.2008.10.011. Epub 2008 Nov 1.
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.
对树木生物力学设计的研究通常集中在树干的刚度、抗折断或抗连根拔起能力以及弹性稳定性上。在此，我们考虑另一种与生长和重力相互作用相关的生物力学限制。由于树干是细长结构且从不完全对称，树木质量的增加总会导致弯曲运动。鉴于树木当前的机械设计，除非发生一些向重力性校正，否则这些运动随时间的累积最终会导致下垂习性。这种校正是通过新木材成熟过程中产生的不对称内力实现的。因此，正在生长的树干的长期稳定性取决于直径生长产生的向重力性校正如何平衡因自身重量增加而产生的干扰。提出了基于梁理论的一般力学公式来模拟这些现象。推导了与生长增量相关的干扰和校正速率，并将其表示为树干形态、横截面解剖结构和木材特性等基本特征的函数。利用先前发表的数据对这些特征进行评估表明，校正与干扰之间的平衡强烈依赖于向重力性校正的效率，而这又取决于木材成熟应变的不对称性、偏心生长以及木材刚度梯度。通过结合干扰和校正速率，向重力性性能表明了生长过程中树干弯曲的动态变化。它取决于树干的生物力学特征和尺寸。通过分析尺寸效应，我们表明从长期来看，向重力性校正的必要性可能会限制树干的异速生长。将这种限制与弹性稳定性的要求进行比较，结果表明向重力性性能限制了倾斜树干和树枝的高度增加。因此，该功能的性能可能会限制树干的细长程度和倾斜度，进而限制树木在异质环境中捕获光线的能力。
