Generalized additive models reveal the intrinsic complexity of wood formation dynamics

Abstract

The intra-annual dynamics of wood formation, which involves the passage of newly produced cells through three successive differentiation phases (division, enlargement, and wall thickening) to reach the final functional mature state, has traditionally been described in conifers as three delayed bell-shaped curves followed by an S-shaped curve. Here the classical view represented by the ‘Gompertz function (GF) approach’ was challenged using two novel approaches based on parametric generalized linear models (GLMs) and ‘data-driven’ generalized additive models (GAMs). These three approaches (GFs, GLMs, and GAMs) were used to describe seasonal changes in cell numbers in each of the xylem differentiation phases and to calculate the timing of cell development in three conifer species [Picea abies (L.), Pinus sylvestris L., and Abies alba Mill.]. GAMs outperformed GFs and GLMs in describing intra-annual wood formation dynamics, showing two left-skewed bell-shaped curves for division and enlargement, and a right-skewed bimodal curve for thickening. Cell residence times progressively decreased through the season for enlargement, whilst increasing late but rapidly for thickening. These patterns match changes in cell anatomical features within a tree ring, which allows the separation of earlywood and latewood into two distinct cell populations. A novel statistical approach is presented which renews our understanding of xylogenesis, a dynamic biological process in which the rate of cell production interplays with cell residence times in each developmental phase to create complex seasonal patterns.

How does climate influence xylem morphogenesis over the growing season? Insights from long-term intra-ring anatomy inPicea abies

“…8) was evident in two distinct periods: a moderate positive temperature effect at the beginning of the season, and a second one at the end of the summer for the last three or four sectors, lasting for up to 2 months. The latter, much stronger at high elevation, overlaps with the wall-thickening phase in the last part of the ring observed in P. abies at high elevation (Gindl et al, 2001;Rossi et al, 2008), and its duration is in line with current knowledge on the duration of wall formation, which can last from 30 d (mild conditions) to 70 d (cold conditions) in latewood cells (Kirdyanov et al, 2003;Rossi et al, 2008Rossi et al, , 2013Cuny et al, 2013).…”

Couplings in cell differentiation kinetics mitigate air temperature influence on conifer wood anatomy

“…Moreover, for each species, we used the average cell numbers predicted by generalized additive models to calculate the date of entrance of each cell in each differentiation zone (enlargement, wall thickening, and mature) of xylem formation along the developing tree ring, following the method described in Cuny et al (; Figure S2). From these dates, the duration of stay of each cell i in the enlargement ( d E,i ) and wall thickening ( d W,i ) zones were computed.…”

Xylogenesis: Coniferous Trees of Temperate Forests Are Listening to the Climate Tale during the Growing Season But Only Remember the Last Words!

“…In order to accurately characterize wood formation dynamics, generalized additive models were fitted on the standardized numbers of cells for each phase of xylem development, each year, and each individual tree (Cuny et al, 2013), using the R package mgcv (Wood, 2006;R Core Team, 2014). The values of the fitted models were then averaged in order to calculate the mean wood formation dynamics of each species during each year and at each site.…”

“…For each species, we used the average cell numbers predicted by generalized additive models to calculate the date of entrance of each cell into each zone (cambial, enlargement, wall thickening, and mature) of xylem cell production and differentiation along the developing tree ring, based on the method described by Cuny et al (2013). From these dates, the residence durations of each cell i in the cambial (d C,i ), enlargement (d E,i ), and wall thickening (d W,i ) zones and the total duration of its formation (d F,i ) were computed.…”