Am J Bot. 1998 Aug;85(8):1082.
The allometric relationship of stem length L with respect to mean stem diameter D was determined for 80 shoots of each of three columnar cactus species (Stenocereus thurberi, Lophocereus schottii, and S. gummosus) to determine whether this relationship accords with that predicted by each of three contending models purporting to describe the mechanical architecture of vertical shoots (i.e., geometric, stress, and elastic similitude, which predict L proportional to D(alpha), with alpha = 1/1, 1/2, and 2/3, respectively). In addition, anatomical, physical, and biomechanical stem properties were measured to determine how the stems of these three species maintain their elastic stability as they increase in size. Reduced major axis regression of L with respect to D showed that alpha = 2.82 ± 0.14 for S. thurberi, 2.32 ± 0.19 for L. schottii, and 4.21 ± 0.31 for S. gummosus. Thus, the scaling exponents for the allometry of L differed significantly from that predicted by each of the three biomechanical models. In contrast, these exponents were similar to that for the allometry previously reported for saguaro. Analyses of biomechanical data derived from bending tests performed on 30 stems selected from each of the three species indicated that the bulk stem tissue stiffness was roughly proportional to L2, while stem flexural rigidity (i.e., the ability to resist a bending force) scaled roughly as L3. Stem length was significantly and positively correlated with the volume fraction of wood, while regression analysis of the pooled data from the three species (i.e., 90 stems) indicated that bulk tissue stiffness scaled roughly as the 5/3-power of the volume fraction of wood in stems. These data were interpreted to indicate that wood served as the major stiffening agent in stems and that this tissue accumulates at a sufficient rate to afford unusually high scaling exponents tot stem length with respect to stem diameter (i.e., disproportionately large increments of stem length with respect to increments in stem diameter). Nevertheless, the safety factor against the elastic failure of stems (computed on the basis of the critical buckling height divided by actual stem length) decreased with increasing stem size tot each species, even though each species maintained an average safety factor equal to two. We speculate that the apparent upper limit to plant height calculated for each species may serve as a biomechanical mechanism for vegetative propagation and the establishment of dense plant colonies by means of extreme stem flexure and ultimate breakage, especially for S. gummosus.
为了确定三个柱状仙人掌物种（钝叶仙人柱、多棱仙人柱和仙人球）的 80 个枝条的茎长 L 与平均茎直径 D 的比例关系，以确定该关系是否符合三个有争议的模型中的每一个，这些模型旨在描述垂直枝条的机械结构（即几何、应力和弹性相似性，分别预测 L 与 D(alpha)成正比，其中 alpha = 1/1、1/2 和 2/3）。此外，还测量了解剖学、物理和生物力学的茎特性，以确定这三个物种的茎如何在增大尺寸的同时保持其弹性稳定性。用 L 对 D 的简化主要轴回归表明，对于钝叶仙人柱，alpha = 2.82 ± 0.14；对于多棱仙人柱，alpha = 2.32 ± 0.19；对于仙人球，alpha = 4.21 ± 0.31。因此，L 的比例关系的标度指数与三个生物力学模型中的每一个都有显著差异。相比之下，这些指数与以前报道的关于 saguaro 的比例关系相似。对从每个物种中选择的 30 个枝条进行弯曲试验得出的生物力学数据分析表明，大部分茎组织的硬度大致与 L2 成正比，而茎的弯曲刚性（即抵抗弯曲力的能力）大致与 L3 成正比。茎长与木质部体积分数呈显著正相关，而对三个物种的汇总数据（即 90 个枝条）的回归分析表明，大部分组织的硬度大致与木质部体积分数的 5/3 次幂成正比。这些数据表明，木质部是茎的主要加固剂，而且这种组织以足够的速度积累，从而提供了与茎直径相比异常高的比例关系（即与茎直径相比，茎长度的增加不成比例）。尽管每个物种的平均安全系数等于 2，但安全系数（根据临界失稳高度除以实际茎长计算）仍然随着每个物种的茎尺寸的增加而减小。我们推测，为每个物种计算的植物高度上限可能是通过极端的茎弯曲和最终断裂来进行营养繁殖和建立密集植物群落的生物力学机制，特别是对于仙人球。
