The monitoring of seasonal radial growth of woody plants addresses the ultimate question of when, how and why trees grow. Assessing the growth dynamics is important to quantify the effect of environmental drivers and understand how woody species will deal with the ongoing climatic changes. One of the crucial steps in the analyses of seasonal radial growth is to model the dynamics of xylem and phloem formation based on increment measurements on samples taken at relatively short intervals during the growing season. The most common approach is the use of the Gompertz equation, while other approaches, such as general additive models (GAMs) and generalised linear models (GLMs), have also been tested in recent years. For the first time, we explored artificial neural networks with Bayesian regularisation algorithm (BRNNs) and show that this method is easy to use, resistant to overfitting, tends to yield s-shaped curves and is therefore suitable for deriving temporal dynamics of secondary tree growth. We propose two data processing algorithms that allow more flexible fits. The main result of our work is the XPSgrowth() function implemented in the radial Tree Growth (rTG) R package, that can be used to evaluate and compare three modelling approaches: BRNN, GAM and the Gompertz function. The newly developed function, tested on intra-seasonal xylem and phloem formation data, has potential applications in many ecological and environmental disciplines where growth is expressed as a function of time. Different approaches were evaluated in terms of prediction error, while fitted curves were visually compared to derive their main characteristics. Our results suggest that there is no single best fitting method, therefore we recommend testing different fitting methods and selection of the optimal one.

中文翻译：

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在 R 中模拟二次增长的季节性动态

对木本植物季节性径向生长的监测解决了树木何时、如何以及为何生长的终极问题。评估生长动态对于量化环境驱动因素的影响和了解木本物种将如何应对持续的气候变化非常重要。分析季节性径向生长的关键步骤之一是根据生长季节相对较短间隔采集的样品的增量测量来模拟木质部和韧皮部形成的动态。最常见的方法是使用 Gompertz 方程，而其他方法，如通用加法模型 (GAM) 和广义线性模型 (GLM)，近年来也进行了测试。首次，我们用贝叶斯正则化算法 (BRNNs) 探索了人工神经网络，并表明该方法易于使用，抗过拟合，倾向于产生 s 形曲线，因此适用于推导二级树生长的时间动态。我们提出了两种允许更灵活拟合的数据处理算法。我们工作的主要成果是XPSgrowth()函数在径向树生长 (rTG) R 包中实现，可用于评估和比较三种建模方法：BRNN、GAM 和 Gompertz 函数。新开发的函数在季节性木质部和韧皮部形成数据上进行了测试，在许多生态和环境学科中具有潜在的应用，其中增长表示为时间的函数。根据预测误差评估不同的方法，同时对拟合曲线进行视觉比较以得出它们的主要特征。我们的结果表明，没有单一的最佳拟合方法，因此我们建议测试不同的拟合方法并选择最佳拟合方法。