Abstract In his paper on net primary productivity of terrestrial communities predicted from climatological data, Rosenzweig (1968) argued that variability in productivity is well accounted for by (evapo)-transpiration, and that water from transpiration is, on global scales, the most variable component in the photosynthesis reaction. The goal of this paper is to investigate whether variability in plant growth on local scales and within species is primarily related to transpiration under several scenarios including different terrain curvature, slope aspect, soil characteristics, and climate ranges. We test the hypothesis that this relationship exists because root growth into the surface soil layers (0–2 m) tends to follow paths with minima in resistance, which in turn maximizes water flow and nutrient delivery rates that regulate growth. The set of all connected paths with individual pore-to-pore flow resistances less than a critical, percolating, value forms a cluster with mass fractal dimensionality, df. We propose that roots follow paths through the 2D percolation cluster, defining the set of all optimal flow paths, making the 2D value of df from percolation relevant to root fractal dimensionality. The tortuosity of such optimal paths as defined in percolation theory should then relate root length to root radial extent, linking the parameters of root tortuosity and plant productivity. Our analysis of large data sets across species implies that root radial extent and tree height are both proportional to cumulative transpiration until trees approached maximum height, and their growth rates are proportional to the transpiration rate, not to the moisture content. Local variations in tree height as functions of the variables investigated appear generally consistent with deduced variations in transpiration. Here this correlation is investigated more closely in the context of studies addressing individual tree species.

中文翻译：

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基于渗流理论描述根土相互作用的新现象学模型

摘要 Rosenzweig (1968) 在他关于根据气候数据预测的陆地群落净初级生产力的论文中认为，生产力的变异性很好地由（蒸发）-蒸腾作用来解释，并且蒸腾作用产生的水是全球范围内变化最大的光合作用反应中的成分。本文的目的是研究局部尺度和物种内植物生长的变异性是否主要与几种情景下的蒸腾有关，包括不同的地形曲率、坡度、土壤特征和气候范围。我们检验了这种关系存在的假设，因为进入表层土壤层 (0-2 m) 的根部生长倾向于遵循阻力最小的路径，这反过来又使调节生长的水流量和养分输送速率最大化。具有小于临界渗透值的各个孔间流动阻力的所有连接路径的集合形成具有质量分形维数df的簇。我们建议根沿着路径通过 2D 渗透集群，定义所有最佳流动路径的集合，使来自渗透的 df 的 2D 值与根分形维数相关。渗透理论中定义的这种最佳路径的曲折度应将根长度与根径向范围联系起来，将根曲折度和植物生产力的参数联系起来。我们对跨物种的大数据集的分析表明，根径向范围和树木高度都与累积蒸腾量成正比，直到树木达到最大高度，它们的生长速率与蒸腾速率成正比，而不是与水分含量成正比。作为所研究变量的函数，树高的局部变化似乎与推断的蒸腾变化一致。在这里，在针对单个树种的研究背景下更密切地研究了这种相关性。