# Cutting tree rings into time slices: how intra-annual dynamics of wood formation help decipher the space-for-time conversion

Gonzalo Pérez-de-lis, Cyrille B K Rathgeber, Laura Fernández-de-uña, Stéphane Ponton

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Gonzalo Pérez-de-lis, Cyrille B K Rathgeber, Laura Fernández-de-uña, Stéphane Ponton. Cutting tree rings into time slices: how intra-annual dynamics of wood formation help decipher the space-for-time conversion. New Phytologist, 2021, 233 (3), pp.1520 - 1534. 10.1111/nph.17869. hal-04219519

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Methods

Cutting tree rings into time slices: how intra-annual dynamics of wood formation help decipher the space-for-time conversion

Gonzalo Pérez-de-Lis<fnref n="1" />,² ID, Cyrille B. K. Rathgeber<fnref n="1" />,³ ID, Laura Fernández-de-Uña<fnref n="1" />,⁴ ID and Stéphane Ponton<fnref n="1" /> ID

Author for correspondence:

Gonzalo Pérez-de-Lis

Email: gonzalo.perezdelis@usc.es

Received: 2 May 2021

Accepted: 11 November 2021

New Phytologist (2021)

doi: 10.1111/nph.17869

**Key words:** cell enlargement, conifer, intra-ring signal, temperate forest, tracheid, tree-ring sectors, wall thickening, xylogenesis.

Summary

* Tree-ring anatomy, microdensity and isotope records provide valuable intra-annual information. However, extracting signals at that scale is challenged by the complexity of xylogenesis, where two major processes – cell enlargement and wall thickening – occur at different times and rates.

* We characterized the space-for-time association in the tree rings of three conifer species by examining the duration, overlapping, inter-tree synchronicity and interannual stability during cell enlargement and wall thickening across regular tree-ring sectors (portions of equal tangential width).

* The number of cells and cell differentiation rates determined the duration of sector formation, which augmented more rapidly throughout the ring for wall thickening than for enlargement. Increasing the number of sectors above c. 15 had a limited effect on improving time resolution because consecutive sector formation overlapped greatly in time, especially in narrow rings and during wall thickening. Increasing the number of sectors also resulted in lower synchronicity and stability of intermediate-sector enlargement, whereas all sectors showed high synchronicity and stability during wall thickening.

* Increasing the number of sectors had a stronger effect on enhancing time-series resolution for enlargement- than for wall-thickening-related traits, which would nevertheless produce more reliable intra-annual chronologies as a result of the more similar calendars across trees and years in wall thickening.

Introduction

In climates with marked seasonality, changing environmental conditions leave anatomically distinguishable boundaries in wood. Thanks to cross-dating, tree rings can be unequivocally assigned to a specific year, which is crucial to correctly interpreting the environmental and functional information imprinted in wood (Fritts, 1976). Although the time resolution of dated tree-ring series is annual, the signal recorded in tree rings is determined by the interaction between physiological responses to environmental conditions and developmental processes occurring at finer timescales. Intra-ring traits could be used to identify seasonal responses of tree growth processes over long time periods. Hence, there is an increasing body of research dealing with intra-ring features, including wood quantitative anatomy (Carrer et al., 2017; Castagneri et al., 2017), microdensity profiles (Pritzkow et al., 2014; Björklund et al., 2017) and stable-isotope composition (Barbour et al., 2002; Helle & Schleser, 2004; Schollaen et al., 2013, 2014).

In order to extract seasonal information, tree rings often have been divided according to tree-ring features, such as earlywood-latewood (Szejner et al., 2018) or intra-annual density fluctuations (De Micco et al., 2012; Belmecheri et al., 2018). Some authors have proposed sampling specific tree-ring zones according to a targeted signal (e.g. carbon (C) and oxygen (O) isotope ratios in the last latewood segment to study fog events in *Sequoia sempervirens* (D.Don) Endl. forests; Roden et al., 2009), abnormal growth features (e.g. bands of unlignified latewood cells; Piermattei et al., 2020), or values of tree-ring profiles such as maximal wood density or maximal lumen area (Pritzkow et al., 2014). Yet, more detailed information on the whole growing season can be obtained by dividing tree rings in cell rows or in regularly spaced sectors (Fig. 1a), and assessing the properties of each of the sectors through *in continuum* measuring techniques (De Micco et al., 2012; Schollaen et al., 2013, 2014). However, although spatial resolution is well-defined in these datasets (i.e. µm or number of cells), the length of the time interval at which

<footnote n="1">¹SILVA, Université de Lorraine, AgroParisTech, INRAE, Nancy 54000, France; ²BIOAPLIC, Departamento de Botánica, EPSE, Universidade de Santiago de Compostela, Campus Terra,</footnote>

<footnote>Lugo 27002, Spain; ³Swiss Federal Research Institute for Forest, Snow and Landscape Research WSL, Birmensdorf CH-8903, Switzerland; ⁴CREAF, Bellaterra (Cerdanyola del Vallés),</footnote>

<footnote>Catalonia E08193, Spain</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1** Tree ring divided into regular sectors and features measured therein (a), and classical theoretical space-for-time assumptions in tree-ring science: (b) basic linear assumption; (c) sigmoidal dendrometer-based assumption; and (d) histological assumption considering xylem cell enlargement (blue bars) and wall-thickening (red bars).</figcaption></figure>

environmental signals are recorded in each spatial unit within the ring (i.e. time resolution) is largely unknown.

Environmental conditions can be imprinted in tree rings in a particular time window during cell differentiation (Rathgeber *et al.*, 2016). Before becoming functional, xylem mother cells follow a succession of differentiation phases: cell enlargement, wall thickening and lignification, and, finally, programmed cell death. The timing of cell differentiation has been assessed through repeated observation of anatomical sections, particularly in conifers thanks to their homogeneous wood structure (composed mainly of tracheids). However, intra-annual growth processes cannot be assessed retrospectively from mature rings. Long intra-ring records thus must be dated through a retroactive space-for-time conversion based on the radial position of the measures. In some cases, it is assumed that xylem cells are formed one after the other following a linear pattern (Fig. 1b), whereby the growing season is divided into discrete time intervals whose duration is proportional to the number of cells (Popkova *et al.*, 2018) or the

sector width (Schollaan *et al.*, 2013, 2014; Szymczak *et al.*, 2019). Other authors have inferred the timing of sector formation through correlative analyses between a chronology of intra-ring parameters and monthly climate records (Carrer *et al.*, 2016, 2017; Castagneri *et al.*, 2017; Belokopytova *et al.*, 2019). However, dating intra-ring chronologies would require that equivalent sectors (i.e. sectors of the same rank) produced in different trees and years were formed during a similar time window, but whether this correspondence exists is largely unknown despite the increasing interest in synchronic interannual growth patterns across populations (Shestakova *et al.*, 2016).

Short-term dendrometer surveys also have been used to date intra-ring isotope (Barbour *et al.*, 2002), wood anatomy (Pacheco *et al.*, 2018) and wood microdensity (Bouriaud *et al.*, 2005) records, by inferring intra-annual changes in cell division rates and the time required for intra-ring sectors to enlarge (Ogée *et al.*, 2009; Schollaan *et al.*, 2014; Soudant *et al.*, 2016). Although this approach accounts for the fact that environmental
information is integrated in wood in a nonlinear way (Fig. 1c), some concerns have been raised regarding its use to date tree-ring isotope records (Monson *et al.*, 2018). Growth in volume and in biomass have been shown to be decoupled (Cuny *et al.*, 2015), which places two alternative timescales on intra-annual series of tree-ring features (Fig. 1d). In addition, differentiation phases frequently comprise several cell rows simultaneously, suggesting that tree-ring cells are not formed in separate time windows but instead in overlapping time intervals. For these reasons, xylogenesis data increasingly have been used to date intra-ring isotope records (Treydte *et al.*, 2014; Belmecheri *et al.*, 2018; Fonti *et al.*, 2018). However, temporally unstable tree phenology and wood formation rates could undermine the use of short-term xylogenesis data to interpret long intra-ring series. A detailed study of the association between space and time within tree rings therefore is required to better understand the information obtained at the intra-annual scale in tree-ring science (Pritzkow *et al.*, 2014; Schollaen *et al.*, 2014; Monson *et al.*, 2018).

In conifers, cell counts obtained weekly from wood microsec-
tions can be used to compute wood formation kinetics at the site
level, encompassing the timing, rate, and duration of enlarge-
ment and wall thickening for each tracheid within a tree ring
(Cuny et al., 2013, 2014). Here, this approach is developed fur-
ther to investigate the association between space and time within
tree rings using data from three sites located in the Vosges Moun-
tains (northeastern France), where three coexisting conifer species
(silver fir (Abies alba Mill.), Norway spruce (Picea abies (L.) H.
Karst.) and Scots pine (Pinus sylvestris L.)) were monitored over a
3-yr period (Cuny et al., 2014). For this purpose, we combined
quantitative wood anatomy data with estimations of timings of
tracheid differentiation based on an empirical model of wood for-
mation dynamics in order to date the formation of different
intra-ring sectors. Three main scientific questions were addressed
for the enlargement and wall-thickening phases: (1) Are regular
sectors formed in separate time windows of the same duration?
(2) How does the number of sectors (sector frequency) affect time
resolution in tree rings? and (3) Can individual intra-ring series
based on regular sectors from different trees and years be pooled
together to build representative chronologies?

Materials and Methods

Dataset characteristics

We used xylogenesis data from three sites located between 350
and 700 m above sea level in the Vosges mountains (northeastern
France) (Cuny et al., 2014). The climate of the study area is tem-
perate with continental influence. The mean temperature for the
period 1961–1990 was 8.3°C with a mean annual precipitation
of 1315 mm. The 2007–2009 period was slightly warmer than
average, and the amount of precipitation ranged from 1508 mm
in 2007 to < 1200 mm during the two following years. Mean
temperature in 2007–2009 was higher at the low-elevation site
(P3: 10.3°C) than at the intermediate (P2: 9.2°C) and high-
elevation (P1: 8.6°C) sites (F = 18.423, P < 0.001), whereas
mean annual precipitation was 1741 mm at P1, 1149 mm at P2

and 998 mm at P3 (F = 37.435, P < 0.001; Supporting Information Fig. S1).

For each stand, 15 individuals belonging to the three study
species (five per species) were monitored between 2007 and 2009.
Each week, from April to November, a microcore was taken from
the stem of each tree at c. 1.3 m aboveground using a Trephor®
tool (Vitzani, Belluno, Italy). Microcores were dehydrated and
embedded in paraffin before 5–10-µm-thick transverse sections
were cut and stained with cresyl violet acetate. See Cuny et al.
(2012) for further details about sample collection and processing.

A transmitted light microscope equipped with a polarizing fil-
ter (AxioImager.M2; Zeiss) was used to count the number of
enlarging, wall-thickening and mature tracheids along at least
three radial files in each cross-section. Tracheid lumen diameter
and shape were used to distinguish enlarging cells from the nar-
rower cambial cells, whereas birefringence of secondary walls
under polarized light was used to identify wall-thickening and
lignifying cells (hereafter referred as wall-thickening cells solely).
Mature tracheids were determined by their empty lumens and
their lignified walls, which appear uniformly blue (Cuny et al.,
2012). The number of cells per differentiation phase from the
three radial files were averaged, and then standardized according
to the number of cells in the previous ring using the R package
CAVIAR (Rathgeber et al., 2018). In addition, tracheid dimensions
(i.e. cell radial diameter and cell-wall thickness) were measured
on digital images of mature tree rings (samples taken at the end
of the growing season) on at least three radial files per tree and
year using the software WINCELL (Regent Instruments, Québec,
QC, Canada) (see Cuny et al., 2014, for details).

Assessment of the timing of sector formation

Generalized additive models (GAMs) were used to fit the weekly cell counts per differentiation zone for each tree and growing season (Fig. 2a). Enlarging and wall-thickening cell counts were fitted using GAMs with a quasi-Poisson distribution (Wood, 2006). However, because mature cells accumulate along the growing season until reaching a plateau once the ring is completed, the accumulation of mature cells was fitted using shape-constrained additive models (SCAMs) with a quasi-Poisson distribution (Pya & Wood, 2014). In a similar way to the approach described by Cuny *et al.* (2013) for stand-level calculations, tree-level GAMs and SCAMs were used to predict the counts of enlarging (EZ), wall-thickening and lignifying (WZ), and mature (MZ) cells for each day of the year (DOY). The cumulative sums of differentiating and mature cells (EWMZ, WMZ and MZ) then were calculated, and new SCAMs were fitted to the obtained curves. The EWMZ curve was used to derive the cell entry rates (eR) into the enlargement zone (i.e. cell division rates) in each date by using the equation from Cuny *et al.* (2013). The inverse functions of these models were used in turn to compute the timings of tracheid differentiation phases. Hence, using this approach we estimated the dates for the beginning and cessation of enlargement (bEᵢ and cEᵢ, respectively) and wall thickening (bWᵢ and cWᵢ, respectively) for each ‘virtual cell’ *i* in the ring (Fig. 2b). For a given cell *i*, cEᵢ was assumed to be concurrent
<figure><img src="image_5.png" /><figcaption>**Fig. 2** Illustration of the methodology used to date xylem cell residence times in differentiation phases (a, b) and tree-ring sectors formation (c, d). (a) Example of fitting of generalized additive model (GAM) and shape-constrained additive model (SCAM) on series of weekly cell counts for EZ (cell enlargement), WZ (wall thickening), MZ (mature), WMZ (wall-thickening + mature), and EWMZ (cell enlargement + wall-thickening + mature) zones for one individual and year. Cell timings are computed using the cumulative curves MZ, WMZ and EWMZ, and dates of cessation of tree-ring enlargement (blue dashed line) and maturation (red dashed line). (b) Resulting durations of cell enlargement (blue bars, dE) and wall thickening (red bars, dW) according to cell position along the ring. bE, date of the beginning of cell enlargement; cE, date of cessation of cell enlargement; bW, date of the beginning of cell-wall thickening; cW, date of cessation of cell-wall thickening. (c) Illustration of the data used to compute the duration of enlargement (dSE), wall thickening (dSW) and both processes (dSX) of a sector (background shadow). bEfirst, date of the beginning of enlargement of the first-born cell in a sector; bWfirst, date of the beginning of wall thickening of the first-born cell in a sector; cElast, date of cessation of enlargement of the last-born cell in a sector; cWlast, date of cessation of wall thickening of the last-born cell in a sector; %TRW, percentage of the final tree-ring width. (d) Illustration of the overlapping between the different periods of differentiation within a sector.</figcaption></figure>

with bWᵢ, whereas cWᵢ was equivalent to full tracheid maturation (Table S1). The residence time of a cell *i* in enlargement was defined as dEᵢ = cEᵢ - bEᵢ, whereas that of wall thickening was given by dWᵢ = cWᵢ - bWᵢ (Fig. 2b). Models were developed using the packages R/MGCV (Wood, 2006) and R/SCAM (Pya & Wood, 2014) for GAM and SCAM calculations.

Morphological measurements of individual xylem cells were used to associate the time of development of each sector with its location into the ring. As the total number of cells measured on the anatomical sections did not always coincide exactly with that estimated by the SCAMs, we used the relative position of the measured tracheids to match both datasets (Fig. 2b). Because the intra-ring resolution more frequently used in dendro-isotopic and dendro-anatomical studies is the sector, not individual cells, tree rings were divided into evenly spaced sectors. Each cell row then was assigned to a sector according to its position. For a ring divided into, for example, 10 sectors, the first consecutive cells whose cumulative length was

within the 10th percentile of the total tree-ring width were assigned to the first sector, whereas those between the 10th and 20th percentiles were assigned to the second sector, and so on (Fig. 2c). Tracheids at the boundary between two sectors were assigned to the sector containing their geometric centre.

## Computation of the duration of sector formation

The periods of enlargement and wall thickening were computed for each sector according to the onset and cessation of each phase (Fig. 2d). The time taken by all of the cells within a sector to complete their enlargement (dSE) then was assessed as:

$$dSE_s = cE_{last,s} - bE_{first,s} \qquad \text{Eqn 1}$$

(bEfirst,s, date of the beginning of the enlargement of the first-born cell of the sector s; cElast,s, date of the end of the enlargement

<figure><img src="image_6.png" /></figure>
of the last-born cell in s). A similar approach was used to compute the duration of wall thickening for a sector (dSW):

$$dSW_s = cW_{\text{last},s} - bW_{\text{first},s} \qquad \text{Eqn 2}$$

(bW<sub>first,s</sub>, date of the beginning of the wall thickening of the first-born cell in s; cW<sub>last,s</sub>, date of the end of the wall-thickening of the last-born cell in s). The total duration of sector formation (dSX) was calculated as:

$$dSX_s = cW_{\text{last},s} - bE_{\text{first},s} \qquad \text{Eqn 3}$$

At the time of formation, sectors can contain both enlarging and wall-thickening cells. Hence, unlike at the cell level, bW<sub>first</sub> is not concurrent with cE<sub>last</sub>. In addition, we assessed the average residence times in number of days for enlarging (dE) and wall-thickening (dW) cells for all of the sectors, along with the number of cells per sector (nC), mean cell entry rates into the enlargement phase (eR), mean cell diameter (CD), mean cell-wall thickness (CWT) and total ring cell number (RCN). The first predicted date of the first-sector enlargement (bE<sub>1</sub>) was identified as the beginning of xylem enlargement (Table S1).

## Sector overlapping, inter-tree synchronicity and interannual stability calculation

In order to evaluate whether successive tree-ring sectors overlapped in time, we analyzed the daily variation on the number of sectors simultaneously containing either enlarging or wall-thickening cells, being counted and expressed as the percentage of overlapping sectors per DOY. The maximum number of time-overlapped sectors then was extracted for each tree.

We calculated inter-tree synchronicity of equivalent sectors among trees within a year (i.e. common sector formation period of each tree and the mean of all the trees of the same species across sites), as well as interannual timing stability across years in each tree (i.e. common sector formation period of each year and the mean of the 3 yr within a tree).

The respective periods of enlargement (SE) and wall thickening (SW) in a given sector s, year y and tree i were intervals denoted by S<sub>syzi</sub> = [b<sub>first,syi</sub> a<sub>last,syi</sub>], where b<sub>first,syi</sub> represents the beginning of a phase (bE<sub>first,syi</sub> for enlargement, bW<sub>first,syi</sub> for wall thickening) in the first-born cell, whereas a<sub>last,syi</sub> is the cessation (cE<sub>last,syi</sub> for enlargement, cW<sub>last,syi</sub> for wall thickening) in the last-born cell. In the same manner, the mean period for a given sector s and year y in all the trees for each species was given by:

$$S_{\text{mean,syz}} = \left[ \frac{1}{t} \sum_{i=1}^{t} b_{\text{first,syzi}}, \frac{1}{t} \sum_{i=1}^{t} c_{\text{last,syzi}} \right] \qquad \text{Eqn 4}$$

(t, total number of trees per species (t = 15)). The common interval (CI) for either enlargement or wall thickening was defined as CI<sub>syi</sub> = S<sub>syi</sub> ∩ S<sub>mean,syi</sub>, which is the intersection between the period in each tree i and the corresponding mean period at the species level. Finally, synchronicity (Syn) of either enlargement

or wall thickening of a given sector s, year y and tree i was calculated as follows:

$$\text{Syn}_{syi} = \frac{\text{CI}_{syi}}{S_{syi}} \times 100 \qquad \text{Eqn 5}$$

(CI<sub>syi</sub>, duration of the common interval for sector s; S<sub>syi</sub>, duration of sector s (Fig. S2)). The same approach was used to evaluate the stability in timing over n yr (n = 3), which was called, by extension, interannual stability. The average for each tree i over n yr was used as the corresponding mean period (S<sub>mean,i</sub>) to calculate the interannual stability index (Fig. S2).

Sector overlapping, inter-tree synchronicity and interannual stability were simulated for a ring divided into 5, 10, 16 (instead of 15 to avoid irrational numbers in sector relative width) and 20 regular sectors. Sector overlapping also was examined at the cell and tree-ring width levels.

## Data analysis

In order to ascertain the drivers of sector formation timespan (dSE, dSW and dSX), we compared the effects of individual cell residence times (dE, dW), cell division rates (eR), number of cells (nC), species and site along a ring divided into 10 regular sectors through generalized linear mixed models with a Gamma error distribution. We used a log-link function for the dSE model, whereas an identity link function was applied in the dSW and dSX models. Up to eight narrow rings that could not be divided into 10 regular sectors containing at least one tracheid in radial direction were discarded from sector duration analyses (n = 127 rings).

Generalized linear mixed models were used to test the effect of variable sector frequency, RCN, mean ring CD and CWT on maximum overlapping. We included CD as a predictor in the sector enlargement model because it is acquired through enlargement (Cuny et al., 2014), whereas the wall-thickening model included both CD and CWT, following findings by Björklund et al. (2017). Linear mixed-effects models were used to assess the relative effect of the first-sector enlargement onset (bE<sub>1</sub>), cell residence times (dE, dW), cell division rates (eR), number of cells (nC) and variable sector frequency on inter-tree synchronicity and interannual stability across the ring. In order to ensure proper pairwise comparisons, 27 rings that could not be divided into 20 regular sectors containing at least one cell were discarded for sector overlapping and inter-tree synchronicity analyses (n = 108 rings), whereas an additional six trees with data available for only 1 yr were not considered in the interannual stability analysis (n = 102 rings).

The R package lme4 was used to adjust all of the mixed models (Bates et al., 2015). The random effects structure of the models included the factors ‘Tree’ and ‘Year’, selecting the simplest among those minimizing Akaike’s Information Criterion scores (tolerance ≤ 2). Relative importance of fixed effects in the mixed models was evaluated by comparing their respective sum of squares (SS), calculated using R/LMERTEST (Kuznetsova et al., 2017), whereas multiple comparisons across factor levels were
performed with R/MULTCOMP (Hothorn *et al.*, 2008). Marginal and conditional R² for mixed-effect models were estimated following the method proposed by Nakagawa & Schielzeth (2013). Potential multicollinearity problems in models were checked through the variance inflation factor. Differences across species, sites and years regarding wood phenology, dynamics of xylogenesis and tree-ring features in the entire population (n = 135 rings) were assessed complementarily through an ANOVA. Standard errors were calculated to show the variance of the results included in text, tables and figures. All analyses were carried in R v.3.5.0 (R Core Team, 2017).

## Results

### Wood phenology and tree-ring features

The period of xylem formation comprised on average 191 ± 4 d in pine and 190 ± 4 d in fir, but only 179 ± 4 d in spruce (F = 3.331, P = 0.04). Trees at the low-elevation site (P3) had an earlier onset of xylem enlargement (bE₁) and a later cessation of xylem maturation than those at higher sites (P1 and P2). The duration of the wood formation period was in tune with the total amount of cells produced (RCN, r = 0.63, P < 0.001). Mean RCN (tree-ring width, TRW) varied from 73.4 ± 6.7 cells (2544.4 ± 238.0 µm) in fir to 60.0 ± 4.8 cells (1922.5 ± 158.4 µm) in spruce and 43.2 ± 4.1 cells (1309.8 ± 120.0 µm) in pine. Mean CD was inversely correlated to the proportion of latewood (r = -0.62, P < 0.001), which was positively correlated with mean CWT within a ring (r = 0.68, P < 0.001). Higher RCN occurred at P3, whereas the highest mean CD and lowest mean CWT were noted at P1 (P < 0.001; Table S2). Differences in TRW, RCN, CD and CWT across years were negligible (Table S2). RCN was highly correlated with mean cell division rates (eR, r = 0.91, P < 0.001), but inversely correlated with cell enlargement residence times (dE, r = -0.69, P < 0.001).

Tracheid morphology varied from earlywood (i.e. thin walls and wide lumen) to latewood (i.e. thick walls and narrow lumen), as shown by the CWT: CD ratio varying from 5.6 ± 0.1% to 30.0 ± 0.8% in a ring divided into 10 regular sectors (Fig. 3a). The number of xylem cells per sector (nC) steadily increased throughout the ring (Fig. 3b), with a sharp increment in the last sector for fir (≤ 14.1 ± 1.0 cells) and spruce (≤ 11.6 ± 0.8 cells), and less markedly for pine (≤ 7.9 ± 0.6 cells). Directly correlated with nC (r = 0.48, P < 0.001), eR dropped in the last sector (0.23 ± 0.02 cells d⁻¹; Fig. 3c), varying across species (fir > spruce > pine) and sites (P3 > P2 > P1) (Table S2). The maximum eR within the ring was strongly correlated with RCN (r = 0.85, P < 0.001).

### Changes in the duration of sector formation along the ring

Although mean cell enlargement residence time decreased by half along a ring divided into 10 regular sectors (dE₁ = 11.9 ± 0.7 d and dE₁₀ = 5.8 ± 0.8 d; Fig. 3d), the duration of sector enlargement peaked in the last sector (on average, dSE₁ = 21.4 ± 1.2 vs dSE₁₀ = 51.4 ± 2.6 d; Fig. 3e). By contrast, the three- to four-fold increase

in cell residence times in the wall-thickening phase along the ring (on average, dW₁ = 13.6 ± 0.7 d and dW₁₀ = 46.9 ± 2.4 d; Fig. 3d) was akin to that for the duration of sector wall thickening (on average, dSW₁ = 26.4 ± 1.4 and dSW₁₀ = 76.3 ± 2.7 d; Fig. 3e), also being comparable to the two- to three-fold increase experienced by total duration of sector formation along a ring (on average, dSX₁ = 36.3 ± 1.4 d and dSX₁₀ = 82.8 ± 2.9 d; Fig. 3e).

Sectors bearing more cells (nC) with longer residence times and lower cell division rates (eR) had longer durations in all the phases. However, whereas variance in dSE was explained mainly by eR and nC (Table 1), that in dSW and dSX was influenced more by the cell wall-thickening residence times (dW; Table 1). Interestingly, pines showed longer dSE than firs and spruces, except in the last sector (Table 1; Fig. S3).

### Evolution of sector overlapping along the growing season

The maximum proportion of xylem cells experiencing simultaneous wall thickening (on average, 32.7 ± 0.6% of cells, 47.5 ± 2.0% of TRW) was higher than the one experiencing enlargement (on average, 12.4 ± 0.5% of cells, 20.2 ± 0.6% of TRW), in accordance with the longer duration of wall thickening (Fig. 3 vs Fig. 4). The daily proportion of enlarging sectors peaked in May, coinciding with the highest proportions of enlarging cells and TRW (Fig. 4a). Despite the proportion of wall-thickening cells and TRW peaking in late September (late August) in fir and pine (spruce), the maximum % of wall-thickening sectors in a ring divided into 5–20 regular sectors had already been attained in June and remained rather constant for 2–3 months (Fig. 4b).

Models showed that trees producing fewer cells over the year (low RCN) had more overlapped sectors regardless of the phase, although its relative importance was higher during enlargement (see SS in Table 2; Fig. S4). At cell enlargement, pines showed more overlapped sectors than the other species. However, although CD was not related to higher sector overlapping, rings with high mean CWT had more overlapped sectors (Table 2). Sector frequency affected the percentage of overlapped sectors throughout the year (Fig. 4). The maximum percentage of overlapped sectors decreased > 19% for both phases as sector frequency increased from 5 to 16 sectors (Table 2; Figs S4, S5). Differences between 16 and 20 regular sectors were negligible for both phases, however.

### Inter-tree synchronicity and interannual stability in sector formation

For 10 sectors, the formation of the first two to four sectors was highly synchronous among trees of the same species for both enlargement and the wall-thickening period (Fig. 5a), despite trees being located across three study sites at different altitudes (Fig. S6). In subsequent sectors, however, synchronicity remained high for wall thickening (on average, 75% in fir, 77% in spruce and 81% in pine; Fig. 5a) but decreased for enlargement, especially in fir (29% for Sector 8). The comparison, within each tree, of equivalent sectors over the three study years (i.e. interannual stability) showed that the timing of wall
<figure><img src="image_7.png" /><figcaption>**Fig. 3** Structural and time characteristics of tree-ring sectors in silver fir, Norway spruce and Scots pine: (a) Ratio between cell wall thickness (CWT) and cell diameter (CD); (b) mean number of cells per sector (nC); (c) mean cell division rates (eR); (d) mean cell residence time for enlargement (dE, blue bar) and wall-thickening (dW, red bar) phases; and (e) duration of enlargement (dSE, blue line), wall thickening (dSW, red line) and entire formation (dSX, black line) per sector. Mean ± SE values are shown for each study species.</figcaption></figure>
<table><caption>**Table 1** Generalized linear mixed models for the sector enlargement (dSE), wall-thickening (dSW) and entire formation (dSX) timespans (n = 127 rings).</caption><thead><tr><th rowspan="2">Fixed effects</th><th rowspan="2">df</th><th colspan="2">Enlargement (dSE)</th><th colspan="2">Wall thickening (dSW)</th><th colspan="2">Entire formation (dSX)</th></tr><tr><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th></tr></thead><tbody><tr><td>Intercept</td><td></td><td>2.931 (0.031)</td><td></td><td>41.142 (0.697)</td><td></td><td>50.868 (0.527)</td><td></td></tr><tr><td>nC</td><td>1</td><td>0.489 (0.012)</td><td>53.869</td><td>7.661 (0.303)</td><td>43.997</td><td>7.434 (0.277)</td><td>13.565</td></tr><tr><td>eR</td><td>1</td><td>-0.384 (0.008)</td><td>169.046</td><td>-3.727 (0.150)</td><td>29.934</td><td>-3.695 (0.139)</td><td>34.407</td></tr><tr><td>dE</td><td>1</td><td>0.198 (0.009)</td><td>28.537</td><td></td><td></td><td>4.974 (0.163)</td><td>4.900</td></tr><tr><td>dW</td><td>1</td><td></td><td></td><td>18.370 (0.193)</td><td>157.722</td><td>18.617 (0.179)</td><td>100.831</td></tr><tr><td>Species</td><td>2</td><td></td><td>1.289</td><td></td><td>0.094</td><td></td><td>0.128</td></tr><tr><td>Spruce</td><td></td><td>0.056 (0.034)</td><td></td><td>0.639 (0.775)</td><td></td><td>0.497 (0.579)</td><td></td></tr><tr><td>Pine</td><td></td><td>0.136 (0.037)</td><td></td><td>1.115 (0.789)</td><td></td><td>1.777 (0.627)</td><td></td></tr><tr><td>Site</td><td>2</td><td></td><td>0.140</td><td></td><td>0.052</td><td></td><td>0.013</td></tr><tr><td>P2</td><td></td><td>-0.017 (0.035)</td><td></td><td>0.402 (0.801)</td><td></td><td>0.470 (0.590)</td><td></td></tr><tr><td>P3</td><td></td><td>-0.042 (0.036)</td><td></td><td>0.870 (0.773)</td><td></td><td>0.399 (0.599)</td><td></td></tr></tbody><thead><tr><th>Random effects</th><th>Year (Tree)</th><th>Year (Tree) + Tree</th><th>Year (Tree)</th></tr></thead><tbody><tr><td>R<sup>2</sup><sub>(marginal)</sub></td><td>0.770</td><td>0.937</td><td>0.949</td></tr><tr><td>R<sup>2</sup><sub>(conditional)</sub></td><td>0.798</td><td>0.941</td><td>0.953</td></tr></tbody></table>

df, degrees of freedom; $R^2_{(marginal)}$, proportion of variance explained by fixed factors; $R^2_{(conditional)}$, proportion of variance explained by both the fixed and random factors.

Fixed effects: number of cells (nC), cell division rates (eR), cell residence times for enlargement (dE), wall thickening (dW), species (silver fir, Norway spruce and Scots pine) and site (P1, P2, P3). Random effect 'Year (Tree)' denotes that Year is nested in Tree. Significant fixed-effect estimates are highlighted in bold. SEs of the estimates are given in parentheses. Intercept estimates correspond to fir at the high-elevation site (P1). Sum-of-squares (SS) relates to the variance explained by each fixed factor.

<figure><img src="image_8.png" /><figcaption>**Fig. 4** Daily variation of the percentage of sectors containing enlarging (a) and wall-thickening (b) cells in silver fir, Norway spruce and Scots pine. Lines of different colours represent simulations for 5–20 regular sectors and at the cell level. The mean ± SE is shown for each species. The grey area represents the mean percentage of the tree-ring width (TRW) containing cells in enlargement (a) and wall thickening (b) for each study species according to the final annual increment.</figcaption></figure>

thickening was stable throughout the growing season across years, being on average 74% in fir, 82% in spruce and 86% in pine. Conversely, the enlargement of sectors 5–9 tended to occur in

different periods each year (Fig. 5b), albeit with noticeable differences among species (Table 3; Fig. 5b). Similar trends were noted for 10, 16 and 20 sector divisions, whereas higher values
<table><caption>**Table 2** Generalized linear mixed models for the maximum percentage of overlapped sectors (n = 108 rings).</caption><thead><tr><th rowspan="2">Fixed effects</th><th rowspan="2">df</th><th colspan="2">Enlargement</th><th colspan="2">Wall thickening</th></tr><tr><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th></tr></thead><tbody><tr><td>Intercept</td><td></td><td>41.274 (1.198)</td><td></td><td>56.819 (2.068)</td><td></td></tr><tr><td>RCN</td><td>1</td><td>-2.502 (0.141)</td><td>44.056</td><td>-2.079 (0.261)</td><td>1.747</td></tr><tr><td>Mean CD</td><td>1</td><td>0.021 (0.229)</td><td>0.105</td><td>-0.397 (0.307)</td><td>0.583</td></tr><tr><td>Mean CWT</td><td>1</td><td></td><td></td><td>2.297 (0.274)</td><td>1.397</td></tr><tr><td>Sector frequency</td><td>4</td><td></td><td>81.638</td><td></td><td>15.877</td></tr><tr><td>10 sectors</td><td></td><td>-14.682 (1.074)</td><td></td><td>-14.094 (0.928)</td><td></td></tr><tr><td>16 sectors</td><td></td><td>-20.448 (1.010)</td><td></td><td>-19.002 (0.890)</td><td></td></tr><tr><td>20 sectors</td><td></td><td>-22.075 (0.993)</td><td></td><td>-20.696 (0.877)</td><td></td></tr><tr><td>Cell</td><td></td><td>-29.539 (0.934)</td><td></td><td>-22.910 (0.862)</td><td></td></tr><tr><td>Species</td><td>2</td><td></td><td>2.788</td><td></td><td>0.259</td></tr><tr><td>Spruce</td><td></td><td>-0.354 (0.432)</td><td></td><td>0.072 (0.608)</td><td></td></tr><tr><td>Pine</td><td></td><td>3.385 (0.583)</td><td></td><td>-1.336 (0.699)</td><td></td></tr><tr><td>Site</td><td>2</td><td></td><td>0.023</td><td></td><td>0.389</td></tr><tr><td>P2</td><td></td><td>-0.210 (0.520)</td><td></td><td>2.000 (0.726)</td><td></td></tr><tr><td>P3</td><td></td><td>0.090 (0.425)</td><td></td><td>-0.811 (0.664)</td><td></td></tr><tr><td>Random effects</td><td></td><td>Year</td><td></td><td>Year</td><td></td></tr><tr><td>R<sup>2</sup><sub>(marginal)</sub></td><td></td><td>0.765</td><td></td><td>0.706</td><td></td></tr><tr><td>R<sup>2</sup><sub>(conditional)</sub></td><td></td><td>0.767</td><td></td><td>0.716</td><td></td></tr></tbody></table>

df, degrees of freedom; R²(marginal), proportion of variance explained by fixed factors; R²(conditional), proportion of variance explained by both the fixed and random factors.

Fixed effects: ring cell number (RCN), mean cell diameter of the ring (CD), mean cell-wall thickness (CWT), wall thickening (dW), sector frequency (5, 10, 16 and 20 sectors, and cell level), species (silver fir, Norway spruce and Scots pine) and site (P1, P2, P3). Random effect: 'Year'. Significant fixed-effect estimates are highlighted in bold. SEs of the estimates are given in parentheses. Intercept estimates correspond to fir at the high-elevation site (P1) with a ring divided into five regular sectors. Sum-of-squares (SS) relates to the variance explained by each fixed factor.

were found for five divisions, especially during enlargement (Figs S7–S9).

Models indicated that the beginning of enlargement (bE₁) had a significant effect on interannual stability (Table 3), but not on inter-tree synchronicity, with lower inter-tree variability for bE₁ than for dSE₁ and dSW₁ (Table S3). High nC per sector implied less synchronous enlargement, but more synchronous and stable sector wall-thickening. During enlargement, eR and dE had, respectively, a negative and positive impact in both inter-tree synchronicity and interannual stability (Table 3). During wall thickening, inter-tree synchronicity was negatively affected by both eR and dW, but inverse relationships were found for interannual stability. The observed decline in synchronicity and stability as sector frequency increased from 5 to 20 sectors was much stronger for enlargement than for wall thickening (Table 3; Fig. 6). Pines showed the most stable enlargement and wall-thickening time intervals (Table 3; Fig. S6), whereas differences across sites were observed only for enlargement. The variance explained by the fixed factors was limited, however, especially for wall thickening (low marginal R², Table 3).

## Discussion

### Variable time resolution, inter-tree synchronicity and interannual stability of sector formation along the tree ring

In a ring divided into 10 regular sectors, the time taken by the last-formed sectors was three-fold that of the first ones (Fig. 3). Variable sector timespans in intra-ring series entails that climate information is integrated in wood in a nonlinear way, as pointed out by observational tree-ring studies (Schollaan et al., 2014; Soudant et al., 2016), and process-based models (Ogée et al., 2009; Eglin et al., 2010; Belmecheri et al., 2018). However, time resolution also depends on the variable time overlapping between consecutive sectors along the growing season (Fig. 4), which additionally confirms that the information contained in different sectors is not recorded in separate time windows. Large time overlapping across sectors accounts for widespread responses of cell diameter and wall thickness to climate across intra-ring sectors, as reported in dendroanatomy studies (Carrer et al., 2016, 2017; Pacheco et al., 2018), and agrees with high correlations between chronologies obtained from adjacent sectors (Castagneri et al., 2017; Belokopytova et al., 2019).

High inter-tree synchronicity and interannual stability of sector formation is desirable to build chronologies of intra-ring traits. The first and last sectors from different trees were formed in coincident time intervals (inter-tree sector synchronicity, Fig. 5a), but this pattern was maintained in intermediate sectors for wall thickening only. Similar results were obtained for equivalent sectors within the same tree across the three study years (interannual sector stability; Fig. 5b). High synchronicity during the last sector enlargement concurred with the high interseries correlation noted in dendroanatomy studies for latewood sectors (Castagneri et al., 2017; Belokopytova et al., 2019). Likewise, the high interannual coefficient of variation in cell lumen area and wall thickness reported by Belokopytova et al. (2019) in transition wood would be compatible with the lower stability for intermediate sectors noted here during enlargement.

### Mechanisms controlling timespan, overlapping, synchronicity and stability of tree-ring sectors

The duration of sector formation was a result of the combination of xylogenesis traits (cell division rates and residence times in enlargement and wall thickening) and the number of cells per sector (nC). The total duration of sector formation (dSX) was determined mainly by the time taken by tracheids to enlarge (dE) and, to a greater extent, build and lignify their walls (dW). The high importance of dW may be attributed to the fact that, except for the first-formed tracheids, wall thickening takes much longer than cell enlargement (Skene, 1972; Cuny et al., 2014; Balducci et al., 2016; Buttò et al., 2019; Vieira et al., 2020). The significant effect of nC on sector timespan suggests that regular sectoring would exacerbate differences in duration across sectors, with more cell formation intervals being accumulated in sectors containing latewood-like cells (Fig. 3b). This would be aggravated by low cell division rates (eR) occurring at the end of the growing
<figure><img src="image_9.png" /><figcaption>**Fig. 5** Mean inter-tree synchronicity (a) and interannual stability (b) ±SE for 10 sectors during cell enlargement (blue) and wall thickening (red) in silver fir, Norway spruce and Scots pine.</figcaption></figure>

<table><caption>**Table 3** Linear mixed-effects models for inter-tree synchronicity and interannual stability in tree-ring sectors during enlargement and wall thickening.</caption><thead><tr><th rowspan="3">Fixed effects</th><th colspan="4">Inter-tree synchronicity (n = 108 rings)</th><th colspan="4">Interannual stability (n = 102 rings)</th></tr><tr><th colspan="2">Enlargement</th><th colspan="2">Wall thickening</th><th colspan="2">Enlargement</th><th colspan="2">Wall thickening</th></tr><tr><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th><th>Est (SE)</th><th>SS</th></tr></thead><tbody><tr><td>Intercept</td><td>70.452 (4.084)</td><td></td><td>76.167 (3.128)</td><td></td><td>58.670 (4.471)</td><td></td><td>69.308 (3.187)</td><td></td></tr><tr><td>bE<sub>1</sub></td><td>2.723 (2.255)</td><td>1082</td><td>1.065 (1.787)</td><td>83</td><td>6.884 (2.487)</td><td>4847</td><td>3.675 (1.810)</td><td>799</td></tr><tr><td>nC</td><td>-2.752 (0.710)</td><td>11 154</td><td>3.712 (0.431)</td><td>17 222</td><td>0.749 (0.672)</td><td>787</td><td>3.832 (0.403)</td><td>17 537</td></tr><tr><td>eR</td><td>-5.655 (0.541)</td><td>81 121</td><td>-2.724 (0.306)</td><td>18 422</td><td>-5.640 (0.506)</td><td>78 746</td><td>0.989 (0.282)</td><td>2386</td></tr><tr><td>dE</td><td>4.814 (0.527)</td><td>62 003</td><td>-1.250 (0.304)</td><td>3935</td><td>5.325 (0.511)</td><td>68 626</td><td>-0.107 (0.291)</td><td>26</td></tr><tr><td>dW</td><td></td><td></td><td>-1.407 (0.250)</td><td>7338</td><td></td><td></td><td>0.756 (0.233)</td><td>2041</td></tr><tr><td>Sector frequency</td><td></td><td>256 548</td><td></td><td>4949</td><td></td><td>126 391</td><td></td><td>3525</td></tr><tr><td>10 sectors</td><td>-19.992 (1.750)</td><td></td><td>-1.072 (1.008)</td><td></td><td>-13.634 (1.677)</td><td></td><td>-0.304 (0.956)</td><td></td></tr><tr><td>16 sectors</td><td>-30.981 (1.923)</td><td></td><td>-3.031 (1.126)</td><td></td><td>-22.011 (1.852)</td><td></td><td>-1.847 (1.072)</td><td></td></tr><tr><td>20 sectors</td><td>-35.065 (1.993)</td><td></td><td>-3.932 (1.172)</td><td></td><td>-25.264 (1.922)</td><td></td><td>-2.873 (1.118)</td><td></td></tr><tr><td>Species</td><td></td><td>2797</td><td></td><td>1356</td><td></td><td>12 763</td><td></td><td>4300</td></tr><tr><td>Spruce</td><td>2.651 (4.866)</td><td></td><td>3.025 (3.855)</td><td></td><td>4.626 (5.458)</td><td></td><td>5.627 (3.972)</td><td></td></tr><tr><td>Pine</td><td>8.738 (4.511)</td><td></td><td>8.601 (3.562)</td><td></td><td>22.507 (5.056)</td><td></td><td>17.295 (3.673)</td><td></td></tr><tr><td>Site</td><td></td><td>3302</td><td></td><td>384</td><td></td><td>6978</td><td></td><td>351</td></tr><tr><td>P2</td><td>-0.023 (4.799)</td><td></td><td>-4.721 (3.802)</td><td></td><td>0.378 (5.514)</td><td></td><td>-3.834 (4.013)</td><td></td></tr><tr><td>P3</td><td>7.865 (4.446)</td><td></td><td>-3.341 (3.514)</td><td></td><td>13.951 (5.037)</td><td></td><td>4.841 (3.662)</td><td></td></tr><tr><td>Random effects</td><td>Year (Tree)</td><td></td><td>Year (Tree)</td><td></td><td>Year (Tree)</td><td></td><td>Year (Tree)</td><td></td></tr><tr><td>R<sup>2</sup><sub>(marginal)</sub></td><td>0.176</td><td></td><td>0.078</td><td></td><td>0.248</td><td></td><td>0.148</td><td></td></tr><tr><td>R<sup>2</sup><sub>(conditional)</sub></td><td>0.423</td><td></td><td>0.508</td><td></td><td>0.531</td><td></td><td>0.586</td><td></td></tr></tbody></table>

$R^2_{(marginal)}$, proportion of variance explained by fixed factors; $R^2_{(conditional)}$, proportion of variance explained by both the fixed and random factors.

Fixed effects: date of the beginning of the first sector enlargement (bE₁), number of cells (nC), cell division rates (eR), cell residence times for enlargement (dE), wall thickening (dW), sector frequency (5, 10, 16 and 20 sectors), species (silver fir, Norway spruce and Scots pine), and site (P1, P2, P3). Random effect 'Year (Tree)' denotes that Year is nested in Tree. Significant fixed-effect estimates are highlighted in bold. SEs of the estimates are given in parentheses. Intercept estimates correspond to fir at the high-elevation site (P1).
<figure><img src="image_10.png" /><figcaption>**Fig. 6** Variation in mean inter-tree synchronicity (a) and interannual stability (b) during cell enlargement (blue) and wall thickening (red) for rings divided into 5, 10, 16 and 20 regular sectors in silver fir, Norway spruce and Scots pine. Horizontal lines within boxes represent median values, lower and upper box limits correspond to the first and third quartiles, vertical lines mark the most extreme values observed within 1.5 times the interquartile range, and grey dots indicate outliers.</figcaption></figure>

season (Fig. 3c), which would contribute to the extension of the last sector duration. Despite their narrower rings and sectors, pines showed relatively longer sector enlargement, which could be attributed to their overall low eR compared to firs and spruces. Therefore, when comparing different species, thinner ring widths do not necessarily entail shorter ring or sector formation periods.

Consecutive sector overlapping varied between phases, with the daily amount of simultaneous wall-thickening wood being ≤ 27.3% higher than that of enlargement. Longer dSW than dSE across sectors would account for the higher overlapping noted for wall thickening (Fig. 4). This is consistent with the positive effect of mean CWT on overlapping, as thicker walls may be associated with longer wall-thickening periods (Cuny & Rathgeber, 2016; Buttò et al., 2019). The observed decline in dSE and dSW with nC also may explain the reduction in maximum sector overlapping after increasing sector frequency from 5 to 16 sectors (Figs S4, S5). In addition, sector overlapping was magnified in narrow rings (Table 2), which is consistent with RCN being inversely associated with dE. It is worth noting that pines showed narrower rings, longer dSE and more overlapped sectors than the other species. However, narrow rings also resulted from low eR, which should limit accumulation of contemporary cells. Indeed, overlapping peaked in early summer (Fig. 4), the time when cell division rates are maximal in temperate conifers (Cuny et al., 2012; Gričar et al., 2014). This suggests that maximum overlapping depends on the duration of sector formation rather than on eR, even though the latter may control seasonal patterns of sector overlapping.

Sector timespans played a major role in shaping inter-tree synchronicity and interannual stability (Table 3). Sectors formed under low eR and long dE had more synchronous and stable enlargement time intervals, whereas sectors having more cells had a more synchronous and stable wall thickening. Pines had a more stable growth than firs and spruces probably because of their longer dSE (Figs 3, 5). This also is consistent with the decline in synchronicity and stability as sector frequency increased (Fig. 6). Moreover, the higher synchronicity and stability for wall thickening than for enlargement in intermediate sectors is consistent with their dSW being longer than dSE (Fig. 5). However, highly synchronic growth in the first-formed sectors is at odds with their low durations, rather reflecting the low inter-tree variability in xylem growth resumption (bE₁). In cold areas, a tight control of the timing of growth reactivation may be critical to avoid exposition of the new tissues to frost damage (Begum et al., 2012), whereby cambial activity may resume within a narrow range of temperatures (Gričar et al., 2014). Under warmer climates, more asynchronous and variable sector formation could be expected, however, with high inter-tree and interannual variation in wood phenology being reported for tropical (De Mil et al., 2019) and Mediterranean sites (Fernández-de-Uña et al., 2018; Vieira et al., 2020). Indeed, we found that interannual changes in bE₁ had a significant impact on stability. Nonetheless, although warming-induced changes in spring phenology could weaken wood formation synchronisms (Yang et al., 2017), more extreme events later in the season could trigger more synchronic interannual growth patterns across populations (Shestakova et al., 2016).
Implications of developmental constraints on tree-ring sectoring and future research applications

Cell-wall material being deposited on sectors over long and highly overlapped time intervals could smoothen intra-annual fluctuations in wood biomass-related traits compared to volume-related ones. This points out the importance of identifying whether a trait is recorded during enlargement or wall thickening. Wood anatomy traits such as cell diameter (CD) are associated with changes in wood volume, which partially supports the use of dendrometers to date dendroanatomy series (Pacheco et al., 2018). Yet, although CD is determined by conditions affecting cell enlargement (Cuny et al., 2014), CWT and wood microdensity are determined by both cell diameter and conditions affecting wall thickening (Cuny et al., 2014, 2019; Wilkinson et al., 2015; Björklund et al., 2017; Castagneri et al., 2017).

Tree-ring isotope ratios are expected to be recorded during wall thickening and lignification (Monson et al., 2018), when most of the woody biomass is incorporated (Cuny et al., 2015; Locosselli & Buckeridge, 2017). Unlike CD, CWT or wood microdensity, C isotope signal originates in the leaf, long before its incorporation into the ring, being also affected by fractionation processes occurring during sugar transport and storage (Barbour et al., 2002; Gessler et al., 2014). Before becoming structural compounds, young sugars are mixed with multi-year C reserves (Hartmann & Trumbore, 2016), the contribution to growth of which varies seasonally (Helle & Schleser, 2004). This probably mitigates the relative importance of wood cell formation time intervals on the tree-ring isotope signature. Although Treydte et al. (2014) dated whole-wood δ¹⁸O series from larch using the timings of cell enlargement, Fonti et al. (2018) considered the entire cell formation to date whole-wood δ¹³C records in Scots pine. Belmecheri et al. (2018), however, found that modelled δ¹⁸O values in cellulose from false rings of ponderosa pine were more accurate when associated with the wall-thickening period. The recording period also may vary between whole wood and cellulose (Shestakova & Martínez-Sancho, 2021). Cellulose and lignin may not have the same deposition times (Donaldson, 1991), especially in sectors formed after abrupt cooling events, which may delay or hamper lignification (Piermattei et al., 2020). Yet, distinction between dates of wall-thickening and lignification is rare in xylogenesis studies, as it was our case, whereby the whole-wood isotope recording time interval probably would correspond better to the wall-thickening timings from xylogenesis datasets than that of cellulose. Hence, the application of advanced microscopy techniques enabling a better distinction between cellulose and lignin deposition might allow the incorporation of the cellulose isotopic signal to be dated more accurately.

Study trees showed a high number of sectors being formed simultaneously in early summer (Fig. 4), which is consistent with maximum rates of cell division occurring around the summer solstice (Cuny et al., 2012; Gričar et al., 2014; Balducci et al., 2016). This is in line with TRW series being highly responsive to atmospheric conditions in early summer in temperate and boreal conifers (Carrer et al., 2016, 2017; Belokopytova et al., 2019). Similar relationships were reported for δ¹³C records (Soudant et

al., 2016; Szejner et al., 2016; Fonti et al., 2018), suggesting that the strength of the isotope signal may depend not only on the intensity of the physiological response at the source (e.g. photosynthetic C isotope discrimination), but also on the amount of living tissue at each time. Thus, although early-summer signals are amplified, responses occurring later in the season could be attenuated in annually resolved isotope records, with stressful conditions halting cambial activity remaining likely undetected (Pflug et al., 2015). This is of particular importance in dry Mediterranean sites, where summer drought may lead to a more complex bimodal growth and earlier maximum rates of cell division than in temperate sites (Fernández-de-Uña et al., 2018; Vieira et al., 2020). However, at the intra-annual level, the observed low overlapping in the first- and last-formed sectors could elicit a more distinct signal than in intermediate sectors. This may be the case for redwood rings that show, only at the ring boundary, enriched δ¹⁸O values associated with summer fog (Roden et al., 2009). In addition, the first-formed sector often contains a similar isotope signal as the previous-ring last sector, which has been attributed to the high reliance of growth on internal C and water reserves at the beginning of the growing season (Helle & Schleser, 2004; Gessler et al., 2014; Treydte et al., 2014).

Increasing spatial resolution enables a reduction of sector timespan and thus overlapping (Fig. 4). Nevertheless, high sector frequency may exacerbate asynchrony across trees, particularly during cell enlargement (Fig. 6). In addition, our results convey that the maximum time resolution ultimately is constrained by the number of contemporaneous living cells, rather than by the instrumental capacity to increase spatial measuring resolution. In this regard, we found an optimal sector frequency in temperate conifers of c. 15 regular sectors for rings with 25–200 cells in a radial file (700–6400 µm wide) (Fig. S4). However, the effect of RCN on sector overlapping suggests that the optimal number of sectors would vary for either narrower or wider rings than those observed in our study. Moreover, our observations cannot be generalized to warmer environments, where trees often show complex intra-annual growth patterns and high interannual growth variation (De Mil et al., 2019; Vieira et al., 2020; Ziaco, 2020). Although irregular sectoring based on changes in cell morphology could be appropriate in species with complex intra-ring patterns, equivalence between sectors across trees and years would be uncertain (De Micco et al., 2012). Therefore, irregular sectoring would require previous knowledge of the associations between the timing of wood formation processes and the characteristics of tree rings to minimize subjectivity.

Conclusions

Dendrochronological records are crucial to understand long-term tree functional responses to environmental cues, but their reliability in deciphering intra-annual signals is still unclear because intra-ring sector formation dates cannot be inferred easily in mature rings. Retrospective dating of intra-ring sectors is challenged by the variable time resolution for cell enlargement and wall thickening, but also across successive sectors owing to differences in their formation timespan and variable level of
overlapping. Intra-ring chronologies based on enlargement-
related traits have inherently higher time resolution, whereas
those based on wall-thickening-related traits are more reliable as
a result of their higher level of synchronization among trees and
stability over the years. However, a similar reliability could be
obtained for enlargement-related traits measured near the ring
boundaries. Notwithstanding this, a more mechanistic under-
standing of xylogenesis phases and their structural consequences
across species and environmental conditions is still needed to
properly link wood formation processes (enlargement, wall thick-
ening, lignification), intra-ring traits (isotopic composition, cell
morphology) and the signals that they convey.

Acknowledgments

The authors thank: H. Cuny for collecting, preparing and observ-
ing wood formation and anatomy samples; SILVATECH (Silvat-
ech, INRAE, 2018. Structural and functional analysis of tree and
wood facility, doi: 10.15454/1.5572400113627854E12) from
UMR 1434 SILVA; 1136 IAM, 1138 BEF and 4370 EA
LERMAB from the research center INRAE Grand-Est Nancy for
its contribution to wood sample collection (E. Cornu, E. Farré,
C. Freyburger, P. Gelhaye, and A. Mercanti) and preparation
(M. Harroué); and the editor and two referees for their sugges-
tions. This work was supported by a grant overseen by the French
National Research Agency (ANR) as part of the ‘Investissements
d'Avenir' program (ANR-11-LABX-0002-01, Laboratory of
Excellence ARBRE), and by the program ‘Soutien aux jeunes
chercheurs' (18_GE5_018) funded by the Conseil Régional Grand
Est (France). GPL benefited from a Xunta de Galicia-Fulbright
fellowship (ED481B2019/108) and is grateful to Xunta de Gali-
cia for the recognition of the Research Competitive Reference
Group GI-1809 BIOAPLIC (ED431C 2019/07). LFU was a
recipient of an AgreenSkills+ fellowship funded by the EU's
Seventh Framework Program under grant agreement no. FP7-
609398 (AgreenSkills+ contract).

Author contributions

CBKR, SP and GP-L conceived and designed the research; and
GP-L, CBKR, LF-U and SP participated in analyzing the data
and writing the manuscript.

ORCID

Laura Fernández-de-Uña ID https://orcid.org/0000-0001-8136-2545

Gonzalo Pérez-de-Lis ID https://orcid.org/0000-0002-7913-2190

Stéphane Ponton ID https://orcid.org/0000-0002-4821-2438

Cyrille B. K. Rathgeber ID https://orcid.org/0000-0001-7359-8320

Data availability

Data are available on request from the authors.

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## Supporting Information

Additional Supporting Information may be found online in the Supporting Information section at the end of the article.

**Fig. S1** Temperature and daily precipitation at the study sites.
**Fig. S2** Parameters for inter-tree synchronicity and interannual stability calculation.

**Fig. S3** Duration of sector enlargement, wall thickening and entire formation per site and year.

**Fig. S4** Maximum overlapping against ring cell number.

**Fig. S5** Maximum overlapping across consecutive sectors.

**Fig. S6** Inter-tree synchronicity and interannual stability per site and year.

**Fig. S7** Inter-tree synchronicity and interannual stability for five sectors.

**Fig. S8** Inter-tree synchronicity and interannual stability for 16 sectors.

**Fig. S9** Inter-tree synchronicity and interannual stability for 20 sectors.

**Table S1** List of acronyms, with their definitions and units.

**Table S2** ANOVA of wood phenology and tree-ring structure parameters.

**Table S3** Variability for the beginning of enlargement and first-sector durations.

Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the *New Phytologist* Central Office.