King D, Loucks O L
Radiat Environ Biophys. 1978 Aug 10;15(2):141-65. doi: 10.1007/BF01323263.
Working from the general postulate that natural selection of plant form operates so as to maximize the survival potential of a species, this paper examines the hypothesis that the mechanical support of tree foliage must approach optimality in the use of wood, i.e., that tree stems and branches will have "optimal form" with respect to the amount of support tissue. Mathematical models of bole and branch form are presented, based on the proposition that either wind or gravity are the primary limiting factors for tree size and shape. Predictions of trunk and branch diameter as a function of tree size were tested with dimensional measurements of Populus tremuloides. The individual stems were selected from close-grown stands of differing ages. For small and intermediate trees, trunk diameter is such that stems have only 1.6 times as much wood as the minimum required to keep the tree from buckling under its own weight due to elastic instability. Branch diameters are shown to be close to the minimum required to maintain the spatial position of growing branches, as well as withstand wind forces. This minimal branch cost not only reduces the load which the stem must support against elastic instability, but allows the crown to flex in high winds. The flexing, in turn, reduces the drag force exerted by the wind on the trunk. Thus, the hypothesis that the observed tree form is an optimal design cannot be rejected on the basis of these results. Additional studies are planned with respect to optimal foliage distribution.
基于植物形态的自然选择旨在最大化物种生存潜力这一普遍假设，本文探讨了树木叶片的机械支撑在木材使用方面必须接近最优状态的假说，即相对于支撑组织的数量，树干和树枝将具有“最优形态”。基于风或重力是树木大小和形状的主要限制因素这一命题，给出了树干和树枝形态的数学模型。利用颤杨的尺寸测量对树干和树枝直径作为树木大小函数的预测进行了检验。这些单株树干选自不同年龄的密植林分。对于中小树木，树干直径使得树干的木材量仅为防止树木因弹性失稳而在自身重量下屈曲所需最小值的1.6倍。结果表明，树枝直径接近维持生长中树枝空间位置以及承受风力所需的最小值。这种最小的树枝成本不仅降低了树干为抵抗弹性失稳而必须支撑的负荷，还使树冠在强风中能够弯曲。反过来，这种弯曲减少了风对树干施加的阻力。因此，基于这些结果，不能拒绝观察到的树木形态是一种最优设计这一假说。计划针对最优叶分布开展进一步研究。
