University of Washington, Quantitative Ecology and Resource Management, Seattle, WA 98195-2100, USA.
Tree Physiol. 2010 Jan;30(1):3-22. doi: 10.1093/treephys/tpp096. Epub 2009 Nov 27.
Many hypotheses have been advanced about factors that control tree longevity. We use a simulation model with multi-criteria optimization and Pareto optimality to determine branch morphologies in the Pinaceae that minimize the effect of growth limitations due to water stress while simultaneously maximizing carbohydrate gain. Two distinct branch morphologies in the Pareto optimal space resemble Pseudotsuga menziesii (Mirb.) Franco and Abies grandis (Dougl. ex D. Don) Lindl., respectively. These morphologies are distinguished by their performance with respect to two pathways of compensation for hydraulic limitation: minimizing the mean path length to terminal foliage (Pseudotsuga) and minimizing the mean number of junction constrictions to terminal foliage (Abies). Within these two groups, we find trade-offs between the criteria for foliage display and the criteria for hydraulic functioning, which shows that an appropriate framework for considering tree longevity is how trees compensate, simultaneously, for multiple stresses. The diverse morphologies that are found in a typical old-growth conifer forest may achieve compensation in different ways. The method of Pareto optimization that we employ preserves all solutions that are successful in achieving different combinations of criteria. The model for branch development that we use simulates the process of delayed adaptive reiteration (DAR), whereby new foliage grows from suppressed buds within the established branch structure. We propose a theoretical synthesis for the role of morphology in the persistence of old Pseudotsuga based on the characteristics of branch morphogenesis found in branches simulated from the optimal set. (i) The primary constraint on branch growth for Pseudotsuga is the mean path length; (ii) as has been previously noted, DAR is an opportunistic architecture; and (iii) DAR is limited by the number of successive reiterations that can form. We show that Pseudotsuga morphology is not the only solution to old-growth constraints, and we suggest how the model results should be used to guide future empirical investigation based on the two contrasting morphologies and how the morphological contrast may relate to physiological processes. Our results show that multi-criteria optimization with Pareto optimality has promise to advance the use of models in theory development and in exploration of functional-structural trade-offs, particularly in complex biological systems with multiple limiting factors.
许多假说已经提出，以控制树木的寿命。我们使用一个具有多准则优化和帕累托最优的模拟模型来确定松柏科的分支形态，这些形态在最小化因水分胁迫而导致的生长限制的同时，同时最大化碳水化合物的获取。在帕累托最优空间中，有两种截然不同的分支形态分别类似于 Pseudotsuga menziesii (Mirb.) Franco 和 Abies grandis (Dougl. ex D. Don) Lindl.。这些形态的特征是，它们在两种补偿水力限制的途径上的表现不同：最小化到终端叶的平均路径长度（Pseudotsuga）和最小化到终端叶的连接收缩的平均数量（Abies）。在这两个群体中，我们发现叶展示标准和水力功能标准之间存在权衡，这表明考虑树木寿命的适当框架是树木如何同时补偿多种压力。在典型的古老针叶林森林中发现的不同形态可能通过不同的方式实现补偿。我们使用的帕累托优化方法保留了所有成功实现不同标准组合的解决方案。我们使用的分支发育模型模拟了延迟自适应重复（DAR）的过程，即新的叶子从已建立的分支结构内的抑制芽中生长出来。我们基于从最优集合中模拟的分支形态发生的特征，提出了一个关于形态在旧 Pseudotsuga 持续中的作用的理论综合。(i) Pseudotsuga 分支生长的主要限制是平均路径长度；(ii) 如前所述，DAR 是一种机会主义结构；(iii) DAR 受到可以形成的连续重复次数的限制。我们表明，Pseudotsuga 的形态不是适应古老生长限制的唯一解决方案，我们建议如何根据两种对比形态和形态对比可能与生理过程相关的情况，利用模型结果来指导未来的实证研究。我们的结果表明，具有帕累托最优的多准则优化具有推进模型在理论发展和探索功能结构权衡中的应用的潜力，特别是在具有多个限制因素的复杂生物系统中。
