Abstract Understanding the height growth of trees is a fundamental component for scientific knowledge and management of forest ecosystems. The height of dominant trees at a reference-age, commonly known as the site-index, is the most widely used forest productivity indicator globally. Yet, it has been criticized for its restricted applicability to monospecific and even-aged forests, making it unreliable for natural forests or mixed-species where there is not a single meaningful age. Here, I develop a mathematical perspective for using height growth-rate at a reference-height as a new type of site index. I provide the mathematical basis for the proposed index and illustrate its application by fitting a nonlinear mixed-effects differential equation model to tree height growth data of three Nothofagus species in southern Chile. The proposed index allows us to foresee and analyze growth patterns, not only by representing growth-rates as a function of time but also of size. In doing so, the proposed index makes tree growth and productivity analyses accessible to a broader community of researchers.

中文翻译：

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给定高度的高度增长率：森林生产力的数学视角

摘要 了解树木的高度生长是森林生态系统科学知识和管理的基本组成部分。参考年龄的优势树的高度，通常称为立地指数，是全球使用最广泛的森林生产力指标。然而，它因其对单种和偶龄林的适用性有限而受到批评，这使得它对于没有单一有意义年龄的天然林或混种林不可靠。在这里，我开发了一个数学观点，将参考高度的高度增长率用作一种新型的站点索引。我为提议的指数提供了数学基础，并通过将非线性混合效应微分方程模型拟合到智利南部三种 Nothofagus 树种的树高生长数据来说明其应用。提议的指数使我们能够预见和分析增长模式，不仅将增长率表示为时间的函数，而且还表示为规模的函数。这样做时，提议的指数使更广泛的研究人员社区可以进行树木生长和生产力分析。