Purpose

The relationship between root tensile strengths and diameters is often fitted using power law curves. More accurate fitting methodologies were developed, investigating a) the validity of least-squares regression assumptions underlying existing methods, b) how to best quantify intra-diameter variation, and c) whether to fit in terms of tensile strength or tensile force at failure.

Methods

Regression and maximum likelihood estimation were used to fit various power law models. 6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models.

Results

The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution. When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average). Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable; the extra emphasis this method places on the effect of large diameters roots was not appropriate because of the typical abundance of thin roots in the field relative to those tested in tension. Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs.

Conclusion

Power law curves should be fitted in terms of root strength rather than root forces at failure, using the newly developed fitting methods that simultaneously fit both the inter-diameter (power law) and intra-diameter variation and can account for fitting bias. This will increase the reliability of future root reinforcement predictions.

中文翻译：

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改进根系抗拉强度-直径关系的幂律拟合

 目的

根系抗拉强度和直径之间的关系通常使用幂律曲线进行拟合。开发了更准确的拟合方法，调查了 a） 现有方法所依据的最小二乘回归假设的有效性，b） 如何最好地量化直径内变化，以及 c） 是否根据抗拉强度或失效时的拉力进行拟合。

 方法

使用回归和最大似然估计来拟合各种幂律模型。使用来自 153 个现有数据集的 6461 次拉伸强度测量值，涵盖 103 种不同的植物物种，用于比较模型。

 结果

根强度的直径内变化与每个直径的平均强度成正比，最好使用 γ 分布来描述。在对数变换的测量值上使用线性回归时，必须使用数学校正以避免低估实际强度（平均 18%）。与拟合抗拉强度相比，根据失效时的根部力进行拟合不太可靠;该方法对大直径根的影响的额外强调是不合适的，因为相对于在张力下测试的根，田间中通常有大量的细根。提出了阔叶树、针叶树、灌木、草和杂草的平均幂律拟合。

 结论

幂律曲线应根据失效时的根强度而不是根部力进行拟合，使用新开发的拟合方法，同时拟合直径间（幂律）和直径内变化，并且可以考虑拟合偏置。这将提高未来根加固预测的可靠性。