Abstract

For trees in forests, striving for light is matter of life and death, either by growing taller toward brighter conditions or by expanding the crown to capture more of the available light. Here, we present a mechanistic model for the development path of stem height and crown size, accounting for light capture and growth, as well as mortality risk. We determine the optimal growth path among all possible trajectories using dynamic programming. The optimal growth path follows a sequence of distinct phases: (i) initial crown size expansion, (ii) stem height growth toward the canopy, (iii) final expansion of the crown in the canopy and (iv) seed production without further increase in size. The transition points between these phases can be optimized by maximizing fitness, defined as expected lifetime reproductive production. The results imply that to reach the canopy in an optimal way, trees must consider the full profile of expected increasing light levels toward the canopy. A shortsighted maximization of growth based on initial light conditions can result in arrested height growth, preventing the tree from reaching the canopy. The previous result can explain canopy stratification, and why canopy species often get stuck at a certain size under a shading canopy. The model explains why trees with lower wood density have a larger diameter at a given tree height and grow taller than trees with higher wood density. The model can be used to implement plasticity in height versus diameter growth in individual-based vegetation and forestry models.

中文翻译：

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树木对光照的追求——在遮荫树冠下实现最佳的高度和直径生长。

 抽象的

对于森林中的树木来说，争取光线是生死攸关的问题，要么通过向更明亮的条件长高，要么通过扩大树冠以捕获更多可用的光线。在这里，我们提出了茎高和冠尺寸发育路径的机械模型，考虑了光捕获和生长以及死亡风险。我们使用动态规划确定所有可能轨迹中的最佳增长路径。最佳生长路径遵循一系列不同的阶段：(i) 初始树冠尺寸扩张，(ii) 茎高向冠层生长，(iii) 树冠在冠层中的最终扩张，以及 (iv) 种子产量不进一步增加尺寸。这些阶段之间的过渡点可以通过最大化适应度来优化，适应度定义为预期的终生繁殖产量。结果表明，为了以最佳方式到达树冠，树木必须考虑朝向树冠的预期增加的光照水平的完整轮廓。基于初始光照条件的短视生长最大化可能会导致高度生长受阻，从而阻止树木到达树冠。之前的结果可以解释冠层分层，以及为什么冠层物种经常在遮荫冠层下停留在一定大小。该模型解释了为什么木材密度较低的树木在给定树高下直径较大，并且比木材密度较高的树木长得更高。该模型可用于在基于个体的植被和林业模型中实现高度与直径增长的可塑性。