Statistical analysis

We applied generalized additive models (GAMs) for each site to assess the temporal dynamics of the differentiation phases and to produce the tracheidograms (Supplementary Data Fig. S1). The assessment of the temporal dynamics was based on Cuny et al. (2014) and Balducci et al. (2016). The raw data provided the number of cells produced at each differentiation phase at the sampling times (Supplementary Data Fig. S1). These data, computed for ten individuals per site, were averaged by year and by site before modelling the temporal dynamics.

We fitted GAMs with splines to the xylogenesis data to obtain three curves that describe the daily sequence of cell production for the three differentiation phases, i.e. (1) enlargement, (2) secondary wall deposition and (3) maturation. The timing (the onset for each phase) was extracted from the three curves as the day when each cell position underwent a differentiation phase. The duration of enlargement and wall formation was defined as the difference between the onset of one phase and the onset of the successive phase (Supplementary Data Fig. S1).

The tracheidograms of lumen area, lumen diameter and cell wall thickness were obtained based on the percentile position of the cells across the tree ring. Using the GAMs, we measured cell traits along multiple radial cell rows. We then averaged the standardized percentiles of their horizontal position to provide average sizes (Supplementary Data Fig. S1). We computed cell diameter as the sum of the lumen diameter and 2× single cell wall thicknesses.

The relationship between dynamics (duration of enlargement and cell wall formation) and cell traits (cell diameter and cell wall thickness) was described as a yearly average by applying a modified von Bertalanffy growth equation according to the formula:

where a, k and b represent the asymptote, growth rate and horizontal intercept, respectively. The fit was validated visually using the distribution of the residuals, and, when required, parameters were adjusted with lower or upper bounds to improve the overall fit. Statistics were performed running the mgcv (Wood, 2017), nls and stats packages in R (R Core Team, 2017).