Data from: A novel growth model evaluating age-size effect on long-term trends in tree growth.

1.One of the major problems in understanding growth trends in long-lived trees is the difficulty of separately quantifying the effects of tree size and age. Careful statistical control of the axiomatic age×size covariation is therefore required to identify long-term trends in tree growth and their drivers, and to predict forests' responses to environmental changes reliably. 2.To address this issue, we present a novel tree growth model: a 'two-dimensional lognormal growth model'. This is an extension of the one-dimensional lognormal growth model, in which tree growth is modelled primarily as a function of size. Our model assesses the trend in tree growth over time by explicitly partitioning the effects of age and size, controlling the covariation. The model is then extended to incorporate the effects of neighbourhood crowding and individual tree variation. 3.To demonstrate our model, we apply it to long-term monitoring data from a mature (104-year- old) plantation of Japanese cedar. Thinning operations of various intensities have been applied to this plantation, and the diameter of each individual tree has been measured repeatedly. 4.We observed a pronounced age-related decline in diameter growth. However, at each age, greater tree size was associated with a higher growth rate. The growth-size curve predicted from the model became flatter with tree age, and the curve's peak shifted rightwards as tree age increased. The model reveals that the sensitivity of a target tree to neighbourhood crowding depends strongly on neighbours' size, and also provides an estimate of among-tree variation in growth performance. 5.Although the relationships between growth, size and age in long-lived trees are very complex, our growth model supports the conclusion that it is possible to predict long-term trends in tree growth reliably with respect to both age and size. In addition, the model's flexibility will facilitate more robust testing of species-specific responses to long-term environmental changes.

1. 解析长寿树木生长趋势面临的核心难题之一，是难以单独量化树体大小与树龄对生长的影响。因此，为精准识别树木生长的长期趋势及其驱动因子，并可靠预测森林对环境变化的响应，需对树龄与树体大小的天然协变关系进行严格的统计控制。
2. 针对该问题，本研究提出一种全新的树木生长模型：二维对数正态生长模型（two-dimensional lognormal growth model）。该模型是一维对数正态生长模型（one-dimensional lognormal growth model）的扩展——后者将树木生长主要建模为树体大小的函数。本模型通过显式拆分树龄与树体大小的效应并控制协变关系，实现对树木生长随时间变化趋势的评估。后续我们进一步扩展该模型，纳入邻体拥挤效应与个体树木生长变异的影响。
3. 为验证该模型的有效性，我们将其应用于一片成熟（树龄104年）的日本柳杉（Japanese cedar）人工林的长期监测数据。该人工林曾接受不同强度的疏伐作业，且对每株林木的树干直径进行了重复测量。
4. 研究观测到直径生长随树龄增长呈现显著的下降趋势。但在同一树龄下，树体越大，生长速率越高。模型预测的生长-大小曲线随树龄增长逐渐趋于平缓，且曲线峰值随树龄增加向右偏移。模型还揭示，目标林木对邻体拥挤的敏感性在很大程度上取决于邻体的树体大小，同时该模型可估算林木间生长性能的差异。
5. 尽管长寿树木生长、大小与树龄间的关系极为复杂，但本研究提出的生长模型验证了一个结论：即可同时针对树龄与树体大小，可靠预测树木生长的长期趋势。此外，该模型具备良好的灵活性，将有助于针对物种特异性的长期环境变化响应开展更稳健的检验。