DOI: 10.5061/dryad.fttdz08w4
title: Modelling seasonal dynamics of secondary growth in R

description: 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.
description: Xylem and phloem formation data from
 European beech (<em>Fagus
 sylvatica </em>L.), Norway spruce (<em>Picea
 abies </em>(L.) H. Karst) and pubescent oak
 (<em>Quercus pubescens</em> Willd.)
 from Slovenia. Microcores 2.4 mm in diameter were collected at 7-10 day
 intervals from March to October with the Trephor tool. The microcores,
 containing phloem, cambium and at least the three youngest xylem rings,
 were taken in stems at 0.7–1.7 m above the ground following a helical
 pattern and separated by 3–5 cm to avoid wound effects. The microcores
 were fixed in a solution of ethanol, formalin and acetic acid (FAA) for 1
 week. In the laboratory, anatomical cross sections of developing xylem and
 phloem tissues were prepared and analysed following the protocol described
 by Gričar, et al. (2014) and Prislan, et al. (2013). Dendrometer data collected Sergio Rossi
 from sugar maple and black spruce from Simoncouche site, Canada.
description: Data is provided in three Excel
 spreadsheets. Data_trees are individual measurements of xylem and pholoem
 formation, while parameters have initial values associated with specific
 modelling algorithms to derive temporal secondary tree growth. Data
 dendrometers consist of daily dendrometer values for sugar maple and black
 spurce in Canada.