Modelling seasonal dynamics of secondary growth in R

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.