J Guillemot
email: joannes.guillemot@gmail.com

N K Martin-Stpaul

E Dufrêne

C François

K Soudani

J M Ourcival

N Delpierre

The dynamic of the annual carbon allocation to wood in European tree species is consistent with a combined source-sink limitation of growth: implications for modelling

The extent to which wood growth is limited by carbon (C) supply (i.e. source control) or by cambial activity (i.e. sink control) will strongly determine the responses of trees to global changes. Nevertheless, the physiological processes that are responsible for limiting forest growth are still a matter of debate. The aim of this study was to evaluate the key determinants of the annual C allocation to wood along large soil and climate regional gradients over France. The study was conducted for five tree species representative of the main European forest biomes (Fagus sylvatica, Quercus petraea, Quercus ilex, Quercus robur and Picea abies).

The drivers of stand biomass growth were assessed on both inter-site and inter-annual scales. Our data set comprised field measurements performed at 49 sites (931 siteyears) that included biometric measurements and a variety of stand characteristics (e.g. soil water holding capacity, leaf area index). It was complemented with process-based simulations when possible explanatory variables could not be directly measured (e.g. annual and seasonal tree C balance, bioclimatic water stress indices). Specifically, the relative influences of tree C balance (source control), direct environmental control (water and temperature controls of sink activity) and allocation adjustments related to age, past climate conditions, competition intensity and soil nutrient availability on growth were quantified.

The inter-site variability in the stand C allocation to wood was predominantly driven by age-related decline. The direct effects of temperature and water stress on sink activity (i.e. effects independent from their effects on the C supply) exerted a strong influence on the annual stand wood growth in all of the species considered, including deciduous temperate species. The lagged effect of the past environmental conditions (e.g. the previous year's water stress and low C uptake) significantly affected the annual C allocation to wood. The C supply appeared to strongly limit growth only in temperate deciduous species.

We provide an evaluation of the spatio-temporal dynamics of the annual C allocation to wood in French forests. Our study supports the premise that the growth of European tree species is subject to complex control processes that include both source and sink limitations. The relative influences of the growth drivers strongly vary with time and across spatial ecological gradients. We suggest a straightforward modelling framework with which to implement these combined forest growth limitations into terrestrial biosphere models.

Introduction

Forests play a critical role in the global carbon (C) cycle. Inventory-based estimates indicate that established forests have been a persistent carbon sink for decades, sequestering almost 30 % of the world's total anthropogenic C emissions between 1990 and 2007 [START_REF] Pan | A large and persistent carbon sink in the world's forests[END_REF]. The fate Published by Copernicus Publications on behalf of the European Geosciences Union.

of the sequestered C is highly dependent on the C dynamic in trees, which determines the residence time of C in forest ecosystems. Despite its importance for the future terrestrial C sink [START_REF] Carvalhais | Global covariation of carbon turnover times with climate in terrestrial ecosystems[END_REF][START_REF] Friend | Carbon residence time dominates uncertainty in terrestrial vegetation responses to future climate and atmospheric CO 2[END_REF], the partitioning of C among tree organs and ecosystem respiration remains poorly understood [START_REF] Brüggemann | Carbon allocation and carbon isotope fluxes in the plant-soil-atmosphere continuum: a review[END_REF]. In particular, there has been a considerable amount of debate regarding the physiological mechanisms that drive the increment of the forest woody biomass [START_REF] Palacio | Does carbon storage limit tree growth?[END_REF][START_REF] Wiley | A re-evaluation of carbon storage in trees lends greater support for carbon limitation to growth[END_REF]. The fraction of assimilated C stored in woody biomass can be inferred by combining biometric measurements with estimates of the C exchange between the ecosystem and atmosphere, based on the eddy-covariance (EC) technique [START_REF] Babst | Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites[END_REF][START_REF] Litton | Carbon allocation in forest ecosystems[END_REF][START_REF] Wolf | Allometric growth and allocation in forests: a perspective from FLUXNET[END_REF]. Global meta-analyses (that included data from various biomes and species) have revealed a strong correlation between the observed gross primary production (GPP) and the woody biomass increment [START_REF] Litton | Carbon allocation in forest ecosystems[END_REF][START_REF] Zha | Gross and aboveground net primary production at Canadian forest carbon flux sites[END_REF]. Accordingly, growth has long been thought to be C limited, because of the hypothesized causal link between C supply and growth (i.e. source control; [START_REF] Sala | Carbon dynamics in trees: feast or famine?[END_REF]. The environmental factors that have been reported to affect growth (soil water content, temperature, nutrient content, light and CO 2 ) were therefore supposed to operate through their effects on photosynthesis and respiration fluxes. This C-centric paradigm underlies most of the C allocation rules formalized in the terrestrial biosphere models (TBMs) that are currently used to evaluate the effects of global changes on forests [START_REF] Clark | The Joint UK Land Environment Simulator (JULES), model description -Part 2: Carbon fluxes and vegetation dynamics[END_REF][START_REF] Dufrêne | Modelling carbon and water cycles in a Beech forest -Part I: Model description and uncertainty analysis on modelled NEE[END_REF][START_REF] De Kauwe | Where does the carbon go?, A model-data intercomparison of vegetation carbon allocation and turnover processes at two temperate forest free-air CO 2 enrichment sites[END_REF][START_REF] Krinner | A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system[END_REF][START_REF] Sitch | Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model[END_REF].

Source control of wood growth is a mechanism that has been questioned by several authors, who argue that cambial activity is more sensitive than C assimilation to several environmental stressors [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]. In particular, the decrease in cell turgor that occurs because of water stress strongly affects cell division and expansion [START_REF] Woodruff | Size-dependent changes in biophysical control of tree growth: the role of turgor, in Size-and age-related changes in tree structure and function[END_REF] before there is any strong reduction in the gas exchange [START_REF] Muller | Water deficits uncouple growth from photosynthesis, increase C content, and modify the relationships between C and growth in sink organs[END_REF][START_REF] Tardieu | Water deficit and growth. Co-ordinating processes without an orchestrator?[END_REF]. Similarly, cell division is more sensitive than photosynthesis to low temperatures [START_REF] Körner | Winter crop growth at low temperature may hold the answer for alpine treeline formation[END_REF]. The onset of cambial activity is also known to be highly responsive to temperature [START_REF] Delpierre | Temperate and boreal forest tree phenology: from organ-scale processes to terrestrial ecosystem models[END_REF][START_REF] Kudo | The effects of localized heating and disbudding on cambial reactivation and formation of earlywood vessels in seedlings of the deciduous ring-porous hardwood, Quercus serrata[END_REF][START_REF] Lempereur | Growth duration is a better predictor of stem increment than carbon supply in a Mediterranean oak forest: implications for assessing forest productivity under climate change[END_REF][START_REF] Rossi | Predicting xylem phenology in black spruce under climate warming[END_REF] and, in turn, may partly determine annual cell production and wood growth [START_REF] Lupi | Xylem phenology and wood production: resolving the chicken-or-egg dilemma[END_REF][START_REF] Rossi | A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere[END_REF]. Finally, the quality and quantity of available soil nutrients, particularly nitrogen (N), could affect growth independently of their impacts on C assimilation, because of the relatively constrained stoichiometry of tree biomass [START_REF] Leuzinger | Beyond global change: lessons from 25 years of CO 2 research[END_REF]. These studies suggest that growth is limited by the direct effects of environmental factors (i.e. sink control). However, numerous key environmental factors (e.g. nutrients, temperature and water) affect both sink and source activities, and it is thus difficult to determine whether wood growth is more related to C supply or to the intrinsic environmental sensitivity of cambium functioning [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]. The extent to which wood growth is under source or sink control is of paramount importance for predicting how trees will respond to global changes and specifically how increasing atmospheric CO 2 will affect forest productivity and the future terrestrial C sink. The implementation of the respective roles of source and sink controls on growth in TBMs is therefore a substantial challenge for modellers, because it may determine our ability to project future forest C sink, diebacks and distributions [START_REF] Cheaib | Climate change impacts on tree ranges: model intercomparison facilitates understanding and quantification of uncertainty[END_REF][START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]Leuzinger et al., 2013).

The allocation of assimilated C within forest ecosystems is a complex, integrative process that can be described by several non-exclusive principles [START_REF] Franklin | Modeling carbon allocation in trees: a search for principles[END_REF] that include (i) allometric scaling, (ii) functional balance and (iii) evolution-based optimal responses. (i) The allometric scaling principle is based on the assumption that biophysical laws, such as the mechanical constraints associated with plant hydraulic architecture and the construction of watertransport system [START_REF] Magnani | Age-related decline in stand productivity: the role of structural acclimation under hydraulic constraints[END_REF], determine C partitioning among the different tree compartments. (ii) The functional balance principle suggests that the organ responsible for acquiring the limiting resource is preferentially allocated C. Consistent with this principle, higher C allocation to fine roots at the expense of C allocation to wood growth has been reported for poor or dry soils [START_REF] Chen | Allocation of gross primary production in forest ecosystems: allometric constraints and environmental responses[END_REF][START_REF] Keyes | Above-and below-ground net production in 40-year-old Douglas-fir stands on low and high productivity sites[END_REF]. In addition, a possibly greater allocation to root symbionts and exudates at the expense of biomass production has also been reported [START_REF] Vicca | Fertile forests produce biomass more efficiently[END_REF]. (iii) Finally, the optimal response principle postulates that allocation maximizes fitness in a fixed environment. This hypothesis agrees with the idea that a dynamic reserve pool acts as temporary storage, possibly at the expense of growth, to promote longterm tree survival [START_REF] Chapin | The ecology and economics of storage in plants[END_REF][START_REF] Sala | Carbon dynamics in trees: feast or famine?[END_REF]. Indeed, time lags between C uptake and growth have been reported [START_REF] Gough | Whole-ecosystem labile carbon production in a north temperate deciduous forest[END_REF][START_REF] Richardson | Seasonal dynamics and age of stemwood nonstructural carbohydrates in temperate forest trees[END_REF]. The optimal response principle is consistent with several wellknown life-history traits, such as preferential allocation to reproduction in ageing plants, which could lead to age-related declines in woody biomass allocation [START_REF] Genet | Age-related variation in carbon allocation at tree and stand scales in beech (Fagus sylvatica L.) and sessile oak (Quercus petraea (Matt.) Liebl.) using a chronosequence approach[END_REF][START_REF] Thomas | Age-related changes in tree growth and functional biology: the role of reproduction, in Size-and age-related changes in tree structure and function[END_REF]. The woody biomass increment therefore appears to be under the control of multiple factors. The effects of these drivers are expected to strongly vary in space and time. Consequently, studies have reported conflicting relationships between the C supply and wood growth [START_REF] Gielen | Biometric and eddy covariance-based assessment of decadal carbon sequestration of a temperate Scots pine forest[END_REF][START_REF] Richardson | Seasonal dynamics and age of stemwood nonstructural carbohydrates in temperate forest trees[END_REF], ranging from no significant relationships [START_REF] Mund | The influence of climate and fructification on the inter-annual variability of stem growth and net primary productivity in an old-growth, mixed beech forest[END_REF][START_REF] Rocha | On linking interannual tree ring variability with observations of whole-forest CO 2 flux[END_REF] to close relationships on seasonal [START_REF] Babst | Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites[END_REF][START_REF] Granier | Ten years of fluxes and stand growth in a young beech forest at Hesse, North-eastern France[END_REF][START_REF] Zweifel | Link between continuous stem radius changes and net ecosystem productivity of a subalpine Norway spruce forest in the Swiss Alps[END_REF] or annual [START_REF] Ohtsuka | On linking multiyear biometric measurements of tree growth with eddy covariancebased net ecosystem production[END_REF][START_REF] Peichl | Biometric and eddy-covariance based estimates of carbon fluxes in an agesequence of temperate pine forests[END_REF][START_REF] Zweifel | Link between continuous stem radius changes and net ecosystem productivity of a subalpine Norway spruce forest in the Swiss Alps[END_REF] timescales. Determining the key processes that affect wood growth on different spatio-temporal scales is necessary in order to explain these apparently contradictory results using a common framework. Moreover, investigations should be conducted at the species level, because phylogeny may strongly constrain forest functioning [START_REF] Carnicer | Contrasting trait syndromes in angiosperms and conifers are associated with different responses of tree growth to temperature on a large scale[END_REF][START_REF] Drobyshev | Species specific growth responses of black spruce and trembling aspen may enhance resilience of boreal forest to climate change[END_REF]

2013

) and induce different growth determinants among taxa [START_REF] Genet | Age-related variation in carbon allocation at tree and stand scales in beech (Fagus sylvatica L.) and sessile oak (Quercus petraea (Matt.) Liebl.) using a chronosequence approach[END_REF].

There is a gap between the knowledge obtained from global studies of universal C allocation rules in forests and our understanding of the cell processes that underlie cambial activity; currently, this gap appears to be the primary obstacle to a more complete understanding of wood growth drivers. In this regard, species-specific studies that evaluate the dynamic of C partitioning to annual wood growth along soil and climate gradients would be highly useful but are lacking. Unfortunately, there is a scarcity of data sets that combine EC and growth measurements at the same sites [START_REF] Luyssaert | CO 2 balance of boreal, temperate, and tropical forests derived from a global database[END_REF]. Here, we circumvented this limitation by complementing stand and soil measurements at a French permanent plot network of 49 forest sites with process-based simulations of annual and seasonal tree C balance (Fig. 1). Simulations were performed using a process-based model (CASTANEA, [START_REF] Dufrêne | Modelling carbon and water cycles in a Beech forest -Part I: Model description and uncertainty analysis on modelled NEE[END_REF] that was thoroughly validated using EC data from throughout Europe [START_REF] Davi | Modelling carbon and water cycles in a beech forest[END_REF][START_REF] Delpierre | Exceptional carbon uptake in European forests during the warm spring of 2007: a data-model analysis[END_REF][START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF] and was applied using site-specific parameters. By relating biometric measurements to variables that explain the C source and sink activity, we evaluated the key drivers of the annual C allocation to stand wood growth in five species that are representative of the main European forest biomes: Fagus sylvatica, Quercus petraea and Quercus robur for temperate deciduous broadleaf forests; Picea abies, for high-latitude and high-altitude evergreen needleleaf forests; and Quercus ilex, an evergreen broadleaf species from Mediterranean forests. Specifically, the relative influence of annual and seasonal (from 1 month to 1 year) tree C balance (source control), direct environmental control (water and temperature effects on sink activity) and allocation adjustments related to age, past climate conditions, competition intensity and soil nutrient availability on tree growth were considered (Fig. 1). We aimed to (1) quantify the relative contributions of source and sink controls to the spatio-temporal dynamic of forest wood growth across a wide range of environmental contexts and (2) provide information that can be used to refine the representation of forest growth causalities in TBMs.

Materials and methods

We based our analyses on three complementary data sources: field measurements, climatic variables from atmospheric reanalysis [START_REF] Vidal | A 50-year high-resolution atmospheric reanalysis over France with the Safran system[END_REF] and process-based simulation data. This hybrid approach allowed us to assess and disentangle the effects of previously reported environmental and endogenous drivers of C allocation to wood growth (Fig. 1).

Study sites and field data

We gathered field measurements from 48 plots from the French Permanent Plot Network for the Monitoring of Forest Ecosystems (RENECOFOR; [START_REF] Ulrich | Organization of forest system monitoring in France-the RENECOFOR network[END_REF] and the Puéchabon tower flux site [START_REF] Martin-Stpaul | The temporal response to drought in a Mediterranean evergreen tree: comparing a regional precipitation gradient and a throughfall exclusion experiment[END_REF]. The location and general climatic features of these plots are shown in Fig. 2 and Table 1. Complete site description is available in Supplement S1.

Growth measurements and historical stand growth reconstruction

Growth measurements were obtained via two methods. The first method was dendrochronological sampling, in which 12 to 30 overstorey trees per plot were cored to the pith at breast height with an incremental borer. Cores were collected in 1994 at the RENECOFOR sites and in 2008 at the Puéchabon site [START_REF] Lebourgeois | RENECOFOR -Etude dendrochronologique des 102 peuplements du réseau[END_REF]J. M. Ourcival, unpublished data). Tree circumferences at breast height (CBHs) and total heights were also measured. The average stand age was inferred from the tree ring series. The second method was forest inventories, in which extensive CBH surveys were conducted in a 0.5 ha area of every plot [START_REF] Cluzeau | RENECOFOR -Interprétation des mesures dendrométriques de 1991 à 1995 des 102 peuplements du réseau[END_REF][START_REF] Gaucherel | Changes of the potential distribution area of French Mediterranean forests under global warming[END_REF]J. M. Ourcival, unpublished data). Tree ring series were combined with the CBH surveys to reconstruct the historical CBHs of every tree on the plots (over 8 to 43 years, Supplement S1). The entire stand tree CBH distribution was reconstructed from the CBHs of the sampled trees using an empirical tree competition model [START_REF] Deleuze | A flexible radial increment model for individual trees in pure even-aged stands[END_REF]. This model stipulates that only trees with a CBH above a given threshold (σ , the minimum circumference needed to gain direct access to sunlight) have a significant level of growth. Overstorey trees then have an annual basal area growth rate that is proportional to their size, according to a slope coefficient, γ . Following the work of [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional-structural model[END_REF], the model was calibrated annually, beginning at year (n) of the core sampling and used iteratively to reconstruct the past stand CBH growth. The σ parameter was first defined using an empirical relationship with the maximum CBH of the stand tree distribution from year (n). The γ parameter was then adjusted using the tree rings measured on the sampled trees in year (n -1). The parameterized model was finally used to predict the basal area increments of all the trees in the distribution, and consequently the tree CBH distribution in the year (n -1). A detailed description of the iterative process can be found in Supplement S2 and in [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional-structural model[END_REF].

The inferred past trajectory of the stand CBH distribution was used to calculate the historical number of stems (numstem, Table 2) and stand basal area, which we considered to be a proxy for within-stand competition intensity (SBA, Table 2; [START_REF] Kunstler | Effects of competition on tree radial-growth vary in importance but not in intensity along climatic gradients[END_REF]. The historical total woody stand biomass was also calculated (Supplement S3) using species-specific tree-level allometric functions [START_REF] Bontemps | Long-term changes in forest productivity: a consistent assessment in even-aged stands[END_REF][START_REF] Bontemps | Shifts in the height-related competitiveness of tree species following recent climate warming and implications for tree community composition: the case of common beech and sessile oak as predominant broadleaved species in Europe[END_REF][START_REF] Dhôte | Un modèle hyperbolique pour l'ajustement de faisceaux de courbes hauteur-diamètre[END_REF][START_REF] Seynave | Picea abies site index prediction by environmental factors and understorey vegetation?: a two-scale approach based on survey databases[END_REF][START_REF] Vallet | Development of total aboveground volume equations for seven important forest tree species in France[END_REF] and wood density models [START_REF] Bouriaud | Modelling variability of wood density in beech as affected by ring age, radial growth and climate[END_REF][START_REF] Wilhelmsson | Models for Predicting Wood Properties in Stems of Picea abies and Pinus sylvestris in Sweden[END_REF][START_REF] Zhang | Modelling wood density in European oak (Quercuspetraea and Quercusrobur) and simulating the silvicultural influence[END_REF]. For Q. ilex, we used the appropriate function from [START_REF] Rambal | The growth respiration component in eddy CO 2 flux from a Quercus ilex mediterranean forest[END_REF] to calculate the stand woody biomass from CBHs.

Past annual woody biomass increments (AWBIs) were then inferred (Supplement S4).

Measurements of stand characteristics

The stand measurements included the soil water holding capacity (SWHC), leaf area index (LAI), leaf N content (LNC) and soil nutrient availability (SNA). The SWHC was estimated via the soil depth and texture measured at two soil pits per plot [START_REF] Brêthes | RENECOFOR -Caractéristiques pédologiques des 102 peuplements du réseau[END_REF]. The LAI was estimated from litter collection [START_REF] Pasquet | Determination des chuttes de littières sur le réseau RENECOFOR de 1995 à 2002[END_REF], and the sunlit LNC was determined annually for eight trees between 1993 and 1997 [START_REF] Croisé | RENECOFOR -Interprétation des analyses foliaires réalisées dans les 102 peuplements du réseau de 1993 a 1997 et premières évaluations interdisciplinaires[END_REF].

SNA was assessed as the soil's C : N biomass ratio, the absolute value of the cation-exchange capacity and the per cent base saturation [START_REF] Ponette | Chimie des sols dans les 102 peuplements du réseau[END_REF]. These soil indices were measured at three depths (0 to 10 cm, 10 to 20 cm, 20 to 40 cm) and were used to categorize the soil plots into three nutrient classes, from low to high nutrient availability (Supplement S5). The SNA, SWHC and LNC were used to characterize plot fertility in the statistical analyses (Table 2). Gross primary production of the previous (y -1) year g C m -2 S T frost Sum of the average daily temperatures below -2 • C during the last winter (year y -1 and y) Water stress intensity index of the previous (y -1) year unitless S T

• C C ST LNC Leaf nitrogen content g N g D M -1 M S NPP

Climate data

The following meteorological variables at the hourly temporal scale (with 8 km spatial resolution) were obtained from the SAFRAN atmospheric reanalysis [START_REF] Vidal | A 50-year high-resolution atmospheric reanalysis over France with the Safran system[END_REF]: global radiation, rainfall, wind speed, air humidity and air temperature. Temperature, which was related to the average altitudes of the SAFRAN cells, was corrected using plotspecific elevation measurements (assuming a lapse rate of 0.6 • K per 100 m, Supplement S1). These variables were used for climate forcing in the CASTANEA model [START_REF] Dufrêne | Modelling carbon and water cycles in a Beech forest -Part I: Model description and uncertainty analysis on modelled NEE[END_REF]; see the following section). In addition, two annual temperature indices were used as proxies of winter frost damage and low temperature stress during the growing period (frost and templim gp , respectively, Table 2).

Process-based simulation data

We used the CASTANEA model to simulate an ensemble of diagnostic variables that are related to the C source and sink activity of forest stands: the elementary components of the tree C balance, bioclimatic water stress indices and the onset of the biomass growth. The eco-physiological process-based CASTANEA model aims to simulate C and water fluxes and stocks of a monospecific, same-aged forest stand on a rota-tion timescale. The hourly stand-atmosphere C fluxes predicted by the CASTANEA model have been thoroughly validated using EC data from throughout Europe [START_REF] Davi | Modelling carbon and water cycles in a beech forest[END_REF][START_REF] Delpierre | Exceptional carbon uptake in European forests during the warm spring of 2007: a data-model analysis[END_REF][START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF]. Importantly, the biophysical hypotheses that were formalized in this model are able to reproduce the interplay of the complex mechanisms that leads to inter-annual variability in the stand C balance [START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF]; modelling this interplay has been recognized as a substantial challenge for TBMs [START_REF] Keenan | Terrestrial biosphere model performance for inter-annual variability of land-atmosphere CO 2 exchange[END_REF]. A complete description of CASTANEA is provided in [START_REF] Dufrêne | Modelling carbon and water cycles in a Beech forest -Part I: Model description and uncertainty analysis on modelled NEE[END_REF], and subsequent modifications are described in [START_REF] Davi | The fundamental role of reserves and hydraulic constraints in predicting LAI and carbon allocation in forests[END_REF] and [START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF].

For the purpose of the present study, CASTANEA was parameterized with site-specific SWHC and LNC values. The measured LAI and total woody biomass were used to initialize the model simulations. The model's ability to reproduce the annual variability in LAI and the forest growth has been recently validated [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional-structural model[END_REF]. Nevertheless, the annual standing woody biomass was forced to conform to the observed values, because the model was used for diagnostic purposes in this study. Several groups of variables were simulated and aggregated on an annual basis (Table 2): 1. The elementary components of the tree C balance. These components included the GPP, autotrophic respiration (Ra) and net balance (i.e. net primary productivity, NPP = GPP -Ra). For a given year y, we aggregated the hourly simulated C fluxes over different seasonal time periods, with starting days that ranged from 30 to 190 and ending days that ranged from 190 to 350, at a 2-day resolution. The C fluxes were also summed (i) for the species-specific biomass growth periods reported in the literature (GPP gp , Ra gp and NPP gp ; Supplement S6) and (ii) for the entire preceding year (y -1) as a proxy of the forest C status induced by past climate conditions (lagged effect, GPP y-1 , Ra y-1 and NPP y-1 ).

2. Bioclimatic water stress indices. These indices included the intensity and duration of water stress (WS_int gp and WS_per gp , respectively; Supplement S7) during species-specific growing periods that have been reported in the literature (Supplement S6). The CAS-TANEA model simulated the daily soil water balance, based on a bucket soil sub-model with two layers (a top soil layer and a total soil layer that includes the top soil layer; [START_REF] Dufrêne | Modelling carbon and water cycles in a Beech forest -Part I: Model description and uncertainty analysis on modelled NEE[END_REF]. WS_int gp was then used to quantify the intensity of water stress by summing the reduc index on a daily basis [START_REF] Granier | A lumped water balance model to evaluate duration and intensity of drought constraints in forest stands[END_REF].

reduc t = max 0, min 1, SWC t -SWC wilt 0.4 × (SWC fc -SWC wilt ) ,
where SWC t is the soil water content on day t (mm), SWC wilt is the soil water content at the wilting point (mm) and SWC fc is the soil water content at field capacity (mm).

WS_per gp is the number of days of the current growth period during which the soil water content was less than 60 % of the soil water holding capacity (Table 2, modified from [START_REF] Mund | The influence of climate and fructification on the inter-annual variability of stem growth and net primary productivity in an old-growth, mixed beech forest[END_REF]. Water stress indices were also calculated for the entire preceding year (lagged effect of water stress, WS_int y-1 and WS_per y-1 ).

3. The onset of the biomass growth (camb_onset). We used a new growth-onset module [START_REF] David | Modélisation de la croissance ligneuse chez le Hêtre et le Chêne sessile[END_REF]; N. Delpierre and N. K. Martin-StPaul, unpublished results) based on a temperature sum trigger (Supplement S8).

Statistical analyses

General overview

Statistical analyses were conducted in three complementary steps for each studied species. (1) We calculated the correlation of the AWBIs and the C fluxes (GPP, NPP and Ra) aggregated seasonally (from 1 month to 1 year) to evaluate the relationship between the C supply and annual biomass growth changes.

(2) The dependences of the AWBIs on the C source and the sink activity were evaluated on an inter-site spatial scale to determine the influence of the site characteristics on biomass growth. The relationship between the age and C allocation to woody biomass was also evaluated in this step. By using the age differences among sites, our chronosequence included a large range of ages (including stands that ranged in age from approximately 30 to 150 years old, Table S1 in Supplement).

(3) Finally, the drivers of AWBI were assessed temporally to determine the factors that were responsible for variability in the inter-annual biomass growth. Because many environmental factors affect both forest sink and source activities, there may be strong covariance among the tree C balance and proxies of environmental stress [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF] that could hamper the inferential power of classical statistical tests [START_REF] Graham | Confronting multicollinearity in ecological multiple regression[END_REF]. However, the explanatory variables used in this study generally had correlation coefficients of less than 0.7, the level above which collinearity begins to severely affect model performance [START_REF] Dormann | Collinearity: a review of methods to deal with it and a simulation study evaluating their performance[END_REF]. One exception was the correlation of components of the tree C balance (because NPP = GPP -Ra). Consequently, the tree C balance components were introduced one at a time into the models. In addition, temporal growth dependencies were evaluated using the random forest (RF) learning method [START_REF] Breiman | Random forests[END_REF]. A number of studies have empirically demonstrated the effectiveness of RF at identifying the "true" predictors among a large number of correlated candidate predictors (e.g. [START_REF] Archer | Empirical characterization of random forest variable importance measures[END_REF][START_REF] Cutler | Random forests for classification in ecology[END_REF][START_REF] Genuer | Variable selection using random forests[END_REF]. The explanatory variables considered in our spatial and temporal analyses are presented in Table 2 andFig Team 2013) using the packages lme4 [START_REF] Bates | The lme4 package, R Packag[END_REF], randomForest [START_REF] Liaw | The randomforest package[END_REF] and MuMIn [START_REF] Barton | Package "MuMIn[END_REF]. Because Quercus petraea and Quercus robur are difficult to distinguish in the field and have a high hybridization rate [START_REF] Abadie | Strength, diversity and plasticity of postmating reproductive barriers between two hybridizing oak species (Quercus robur L. and Quercus petraea (Matt) Liebl.)[END_REF], these two species were grouped in the analyses and are hereafter collectively referred to as "temperate oaks".

Correlations between growth and C fluxes

Pearson correlations between the AWBIs and simulated C fluxes in different seasonal time periods were calculated separately for each site. The highest median correlation value for each species was retained and tested against zero using Wilcoxon signed-rank tests. Critical correlations (i.e. the threshold values for a significant difference with the retained maximum correlation) were determined to evaluate the sensitivity of the correlation values to changes in the C flux aggregation periods.

Drivers of spatial variations in biomass growth

The drivers of spatial variations in biomass growth were evaluated using multiple-regression models using an information-theoretic approach [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF]. The AWBIs and the considered explanatory variables were averaged for each plot. The variables introduced into the linear models were centred and scaled such that their normalized coefficient estimates indicated the relative influence of the predictors on the AWBI. The elementary components of tree C balance (NPP, GPP and Ra) were introduced one at a time into the models. For each species, multiple-regression models that contained all possible combinations of the explanatory variables were fitted. The models were compared using the second-order Akaike information criterion (AIC), and all models with an Akaike weight of at least 1 % of the best approximating (lowest AIC) model were considered to be plausible [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF]. Ultimately, we retained the variables that appeared in at least 95 % of the selected models. Models fitted using P. abies data were restricted to a maximum of three explanatory variables because of the small sample size (n = 6, Table 1). Q. ilex (n = 1) was not considered in the spatial analyses. The uncertainty of the simulated C fluxes was assessed in the analyses using a bootstrap procedure [START_REF] Chernick | Bootstrap methods: A guide for practitioners and researchers[END_REF]): all linear models were fitted 1000 times, and at each iteration, the C flux values were randomly sampled within the root-mean-square error of the CASTANEA simulations (Supplement S9) to obtain a parameter estimate distribution for each variable. We finally retained the explanatory variables with parameter estimate distributions that excluded the zero value at a two-tailed probability level of 5 %.

Drivers of temporal variations in biomass growth

A temporal analysis was conducted on the standardized AWBI series: a double-detrending process was applied to each series based on an initial linear regression model, followed by fitting a cubic smoothing spline with a 50 % frequency response cut-off [START_REF] Mérian | Spatial variation and temporal instability in climate-growth relationships of sessile oak (Quercus petraea [Matt.] Liebl.) under temperate conditions[END_REF]. For analysing the temporal variations in biomass growth we used an RF learning method [START_REF] Breiman | Random forests[END_REF], which was possible because of the large sample size (n = 931 site-years). The RF learning method is a non-parametric method that is used to rank the contribution of different explanatory variables and evaluate their marginal effects on a variable of interest without assuming an a priori dependence. The RF method combined 500 binary decision trees that were built using bootstrap samples from the initial data set. The decision trees aimed to reduce the heterogeneity of the explained variable in the resulting branches. For each of the 500 trees, the data that were not involved in the tree construction were used for validation. The tree predictions and errors were then averaged to provide the final RF results. The RF method does not overfit or require cross-validation [START_REF] Cutler | Random forests for classification in ecology[END_REF]. A subset of explanatory variables was randomly chosen at each node, thus reducing the effect of collinear variables on the output. The RF method was used to select variables that explained the temporal variability in biomass growth [START_REF] Genuer | Variable selection using random forests[END_REF]. Variable selection relied on permutation importance, i.e. the existence of an increase in the global mean square error when a given variable was randomized in the validation subsamples. The forms of the dependences were illustrated by partial dependence plots (graphical depiction of the marginal effect of a given variable; [START_REF] Cutler | Random forests for classification in ecology[END_REF].

We used this information (variable selection and dependence forms) to test for the significance of the temporal AWBI dependences within the linear model. The uncertainty in the simulated C fluxes was considered in the linear models, following the procedure described in the spatial analysis section.

Results

Relationship between woody biomass growth and C fluxes

The elementary components of the simulated seasonal tree C balance differed in terms of their relationships with the inter-annual variability of the annual woody biomass increments (AWBI, Table 3). The simulated seasonal GPP and NPP were linked to AWBIs with a comparable agreement between species. However, the simulated Ra had weak and often non-significant relationships with the AWBIs across the 49 studied plots. The strongest correlations were obtained for flux aggregation periods that (i) were generally consistent within a species for GPP and NPP but different for Ra and (ii) strongly differed among species (Table 3). The coefficients of variation of the simulated annual NPP, GPP and Ra across the 49 studied sites were 10.8 ± 3, 7.4 ± 2 and 6.8 ± 3 %, respectively. GPP and NPP were summed from the beginning of May to the beginning of August and September, in temperate oaks and F. sylvatica, respectively. The longest GPP and NPP aggregation periods were obtained for P. abies (from the beginning of February to mid-September), and the shortest period were found for Q. ilex (from the beginning of July to mid-August). Minor (less than 20 days) changes in the flux aggregation period associated with the maximum simulated flux-AWBI correlation usually marginally affected the correlation values (Supplement S10). Consequently, aggregation periods that were less than 13 days different (either in terms of their starting or ending dates) from the values reported in Table 3 were generally not significantly lower than the maximum values (see the critical values presented in Supplement S10).

Spatial dynamic of C allocation to woody biomass growth

The inter-site variability in biomass growth was well explained by the selected multiple-regression models (R 2 0.6). We highlighted that species varied in terms of their inter-site dependences (Table 4). The simulated C supply during the growth period (GPP gp , Table 2) was positively correlated with biomass growth in F. sylvatica and P. abies, whereas there was no significant relationship between the average AWBI and photosynthesis among sites for temperate oaks (Fig. 3a). Notably, the final models did not include NPP gp or Ra gp for any species. The stand age was an important driver of biomass growth in temperate oaks and F. sylvatica. The stand age explained a substantial portion of the AWBI : C supply ratio in all species, although the relationship was not significant for P. abies (Fig. 3b). The fraction of C sequestered in woody biomass decreased with stand age (Table 4, Fig. 3b) and was reduced by half in temperate oaks and F. sylvatica stands that were between 50 and 150 years of age (from 0.3 to 0.13 and from 0.25 to 0.1, respectively). Additionally, we identified a significant and positive effect of stand basal area on both AWBI (Table 4) and the AWBI : GPP gp ratio (data not shown) in temperate oaks.

Temporal dynamic of carbon allocation to woody biomass growth

The ranking of the drivers of biomass growth obtained using the RF algorithm indicated that the temporal AWBI dependences varied among species (Fig. 4). The growth of temperate deciduous species was under a more complex environmental control than the growth of P. abies and Q. ilex, with several variables explaining a substantial portion of the annual variability in AWBI (Fig. 4a,b). Simulated C supply (GPP gp ) was strongly related to the AWBI of temperate oaks and F. sylvatica and, to a lesser extent, P. abies (Fig. 4a, b, c), with positive marginal effects (Fig. 5a,e,h). The duration of water stress during the growth period (WS_per gp ) Table 5. Temporal dependences of the annual woody growth: multiple-regression estimates. Data have been centred and scaled. GPP gp is the gross primary production of the growth period, WS_per gp is a water stress index of the growth period, WS_int y-1 is a water stress index of the previous year, templim is a low temperature index of the growth period (Table 2). D1 and D2 are dummy variables (D1 = 0 if GPP gp < 1400 g C m -2 , D1 = 1 otherwise; D2 = 0 if GPP y-1 < 1550 g C m -2 , D2 = 1 otherwise; see Fig. 5). ρ is the parameter of the first-order autoregressive process used to model the temporal autocorrelation of within-stand errors. Values: estimates [F values]. Estimate values differing from 0 are indicated ( * P < 0.05, * * P < 0.01, * * * P < 0.001). The estimate with a index indicates variable not retained in the bootstrap procedure (see main text).

Estimates Species

Q. petraea/ F. sylvatica P. abies Q. ilex Q. robur was the predominant driver of the AWBI variability of Q. ilex, and was also strongly related to growth in temperate deciduous species. Low temperatures during the growth period (templim gp ) most substantially affected P. abies and also explained a portion of the variability in AWBI of temperate oaks. The simulated water and temperature stress indices had negative and quasi-linear marginal effects on the AWBI (Fig. 5). Finally, environmental lagged effects contributed substantially to the AWBI variability in all species: the water stress intensity of the previous year (WS_int y-1 ) affected the growth of F. sylvatica and Q. ilex, whereas the simulated C supply of the previous year (GPP fect on AWBI only under high water stress or low C supply (Fig. 5). The effects of the retained variables (Fig. 4) were evaluated via multiple-regression models that used dummy variables to test for the significance of slope changes when thresholds appeared on partial plots (Fig. 5). The models explained approximately 20 % of the variability in the AWBI for temperate oaks and P. abies, and approximately 40 % of the variability for F. sylvatica and Q. ilex (Table 5). All of the explanatory variables had significant effects, but templim was not retained in the models for temperate oaks after the bootstrap procedure that accounted for the uncertainty of the C flux simulations. We observed significant changes in the slopes of the effect of GPP y-1 on temperate oaks and the effect of GPP gp on P. abies (Table 5). The models with NPP gp and NPP y-1 variables revealed the same AWBI dependences as the models described above, but with reduced explanatory power. The models with Ra gp and Ra y-1 variables were not significant (data not shown).

GPP gp 3.26 × 10 -1 * * * 4.87 × 10 -1 * * * 2.4 × 10 -1 * [3.5] WS_per gp -1.09 × 10 -1 * * -2.04 × 10 -1 * * * -5.8 × 10 -1 * * * WS_int y-1 -2.37 × 10 -1 * * * -2.2 × 10 -1 * [6.3] GPP y-1 3.82 × 10 -1 * [3.3] -4 × 10 -1 * * [3.2] templim -9.60 × 10 -2 * * -1.26 * * * [3.5] D1 -2.4 × 10 -1 * * * D2 -3.9 × 10 -1 * * [0.8] D1 • GPP gp 1.33 * * [8.2] D2 • GPP y-1 -4 × 10 -1 *

Discussion

This study quantified the C that is allocated annually to the woody biomass increment for five species that are representative of the main European forest biomes. By complementing field measurements from a permanent plot network with process-based modelling, our approach circumvented the limitation of EC data scarcity and characterized the annual partitioning of C into woody biomass at 49 sites over France (931 site-years). We were thus able to identify the species-specific drivers of the spatio-temporal dynamics of the allocation of C to wood growth along ecological gradients.

The correlation between the tree C balance and woody biomass growth

Relating EC-based estimates of forest C balance and biometric measurements of woody biomass growth has been the focus of an increasing number of studies. These studies can enhance our understanding of ecosystem C dynamics but have so far provided conflicting conclusions. Indeed, the correlation between woody biomass growth and forest C gain has been reported as both non-significant [START_REF] Mund | The influence of climate and fructification on the inter-annual variability of stem growth and net primary productivity in an old-growth, mixed beech forest[END_REF][START_REF] Richardson | Seasonal dynamics and age of stemwood nonstructural carbohydrates in temperate forest trees[END_REF][START_REF] Rocha | On linking interannual tree ring variability with observations of whole-forest CO 2 flux[END_REF] and highly significant [START_REF] Babst | Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites[END_REF][START_REF] Ohtsuka | On linking multiyear biometric measurements of tree growth with eddy covariancebased net ecosystem production[END_REF][START_REF] Peichl | Biometric and eddy-covariance based estimates of carbon fluxes in an agesequence of temperate pine forests[END_REF][START_REF] Zweifel | Link between continuous stem radius changes and net ecosystem productivity of a subalpine Norway spruce forest in the Swiss Alps[END_REF]. Accordingly, the relationships between AWBI and C fluxes reported in this study strongly varied among sites for each of the species studied (Table 3). Nevertheless, the annual woody biomass increment was consistently related to GPP gp and NPP gp , and only marginally to Ra gp for the majority of sites (Table 3). [START_REF] Babst | Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites[END_REF] reported a similar dependence of biomass growth on C fluxes at five sites that spanned a wide range of latitude in Europe. The authors attributed this result to a common sensitivity of C assimilation and biomass growth to the water balance. Our results also support the view that biomass growth and tree C balance are under the control of distinct but partially correlated processes [START_REF] Beer | Mean annual GPP of Europe derived from its water balance[END_REF][START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]; these processes may or may not induce consistent annual changes, depending on the environmental conditions faced by trees. For F. sylvatica and temperate oaks, maximum correlation values corresponded to flux aggregation periods that were consistent with the previously reported phenology of the woody biomass increment (Table 3, Supplement S10; [START_REF] Michelot | Comparing the intra-annual wood formation of three European species (Fagus sylvatica, Quercus petraea and Pinus sylvestris) as related to leaf phenology and non-structural carbohydrate dynamics[END_REF]. [START_REF] Babst | Above-ground woody carbon sequestration measured from tree rings is coherent with net ecosystem productivity at five eddy-covariance sites[END_REF] and [START_REF] Granier | Ten years of fluxes and stand growth in a young beech forest at Hesse, North-eastern France[END_REF] similarly reported close relationships between the AWBI and forest C fluxes that were summed until cessation of growth (August/September). The flux aggregation periods were, however, not related to the timing of wood growth in Q. ilex or P. abies [START_REF] Cuny | Life strategies in intra-annual dynamics of wood formation: example of three conifer species in a temperate forest in north-east France[END_REF][START_REF] Lempereur | Growth duration is a better predictor of stem increment than carbon supply in a Mediterranean oak forest: implications for assessing forest productivity under climate change[END_REF], which indicates that inter-annual variation in the AWBI is not always solely (or even primarily, e.g. Q. ilex and P. abies) dependent on the C derived from photosynthesis. Specifically, the agreement between the observed Water stress intensity index of the previous year [WS_int , unitless] y-1

Quercus robur

Figure 5. Temporal dependences of annual wood growth: marginal effects of each explanatory variable on the annual wood growth. The lines represent smoothing splines with 50 % frequency response cut-offs. The coloured areas indicate the 95 % confidence intervals. The 5 and 95 % data quantiles (grey areas) were not considered in the discussion. The marginal effect of a given variable X was obtained by fixing the value of X and averaging the RF predictions over all the combinations of observed values for the other predictors in the data set [START_REF] Cutler | Random forests for classification in ecology[END_REF]. The marginal predictions were collected over the entire range of X in the training data using a regular grid.

annual growth and a short period of C flux aggregation in early summer that was reported for Q. ilex corresponds to the effect of growth cessation on the annual biomass increment, which has been attributed to a drought-induced limitation of cambial activity at the Puéchabon site [START_REF] Lempereur | Growth duration is a better predictor of stem increment than carbon supply in a Mediterranean oak forest: implications for assessing forest productivity under climate change[END_REF]. The processes that underlie the relationship of the long flux aggregation period and the annual biomass increment of P. abies may include the effect of late winter temperature on cambium phenology [START_REF] Rossi | Predicting xylem phenology in black spruce under climate warming[END_REF]. Overall, our results suggest that using growth-flux correlation coefficients when investigating either source limitation of growth or the seasonality of C allocation to woody biomass can lead to misleading conclusions.

Between-site variability in the C allocation to woody biomass growth is related to ontogeny and competition intensity

We highlighted an age-related decline in the C partitioning to woody biomass in all three species (Fig. 3b). This result had previously been observed in F. sylvatica stands using measurements of the main C compartments along a chronosequence [START_REF] Genet | Age-related variation in carbon allocation at tree and stand scales in beech (Fagus sylvatica L.) and sessile oak (Quercus petraea (Matt.) Liebl.) using a chronosequence approach[END_REF]. Several non-exclusive processes can explain this age-related trend. Increases in tree height are associated with increases in the hydraulic resistance of xylem, which may lead to declines in the turgor of living cells and result in potentially negative consequences on cambial activity [START_REF] Woodruff | Does turgor limit growth in tall trees?[END_REF]. This constraint may result in a height-related sink limitation of growth [START_REF] Woodruff | Size-dependent changes in biophysical control of tree growth: the role of turgor, in Size-and age-related changes in tree structure and function[END_REF], which is consistent with our results. Additionally, life-history traits, such as a greater emphasis on reproduction in older stands, could also be involved. However, the interactions of growth and reproductive mechanisms are still under debate [START_REF] Hoch | Fruit production in three masting tree species does not rely on stored carbon reserves[END_REF][START_REF] Thomas | Age-related changes in tree growth and functional biology: the role of reproduction, in Size-and age-related changes in tree structure and function[END_REF] and have yet to be properly represented in TBMs. Only the GPP component of the simulated tree C balance was retained in the final models (Table 4), thereby indicating that an increase in maintenance respiration with greater stand biomass most likely did not contribute to the age-related decline in biomass growth [START_REF] Drake | Mechanisms of age-related changes in forest production: the influence of physiological and successional changes[END_REF][START_REF] Tang | Steeper declines in forest photosynthesis than respiration explain age-driven decreases in forest growth[END_REF]. Although height-related hydraulic constraints on C assimilation have been suggested to be an important driver [START_REF] Ryan | The hydraulic limitation hypothesis revisited[END_REF][START_REF] Tang | Steeper declines in forest photosynthesis than respiration explain age-driven decreases in forest growth[END_REF], recent studies have suggested that changes in demography and stand structure may primarily explain the age-related decline observed in stand wood growth [START_REF] Binkley | Age-related Decline in Forest Ecosystem Growth: An Individual-Tree, Stand-Structure Hypothesis[END_REF][START_REF] Xu | Age-related decline of stand biomass accumulation is primarily due to mortality and not to reduction in NPP associated with individual tree physiology, tree growth or stand structure in a Quercus-dominated forest[END_REF]. Our results suggest that changes in the C allocation should also be considered, because no mortality occurred in our plots during the measurement period (data not shown). We additionally identified a significantly higher C partitioning to woody biomass in temperate oak stands with greater competition intensity (i.e. high stand basal area, Table 3). To date, reports regarding the effect of competition on C allocation dynamics are conflicting [START_REF] Litton | Carbon allocation in forest ecosystems[END_REF] and suggest no significant or consistent effect. Moreover, we found no significant effect of soil nutrient availability on the C allocation dynamics along the studied ecological gradient, whereas a recent meta-analysis reported that this factor positively affects C partitioning to forest biomass on the global scale [START_REF] Vicca | Fertile forests produce biomass more efficiently[END_REF]. The RENECOFOR network only includes relatively fertile sites (Supplement S5), which could putatively explain the apparent tension between our results and the conclusions of the meta-analysis. Therefore, more studies are required to elucidate the contributions of the various drivers to the variation in C partitioning to woody biomass on scales that range from local to global.

Inter-annual variability in woody biomass growth is consistent with combined source-sink limitations

Water and temperature stress exerted significant direct control on the inter-annual variation of woody biomass growth (i.e. independent of their effects on C assimilation) for every species and biome (Table 5 and Figs. 4 and5). Cambial growth has been reported to be inhibited at lower water stress levels than photosynthesis [START_REF] Muller | Water deficits uncouple growth from photosynthesis, increase C content, and modify the relationships between C and growth in sink organs[END_REF][START_REF] Tardieu | Water deficit and growth. Co-ordinating processes without an orchestrator?[END_REF]. Indeed, drought-induced decrease in cell turgor strongly affects cell divisions [START_REF] Woodruff | Size-dependent changes in biophysical control of tree growth: the role of turgor, in Size-and age-related changes in tree structure and function[END_REF] and cell wall expansion [START_REF] Cosgrove | Growth of the plant cell wall[END_REF][START_REF] Lockhart | An analysis of irreversible plant cell elongation[END_REF] before gas exchange modulation comes into play. Similarly, there is evidence that cell growth processes, such as cell division, are more sensitive than photosynthesis to low temperatures [START_REF] Körner | Winter crop growth at low temperature may hold the answer for alpine treeline formation[END_REF]. Although these findings documented the plausible mechanisms of sink control of biomass growth at the cellular scale, there is still considerable debate regarding whether the sink or the C source actually limits the growth of the world's forests [START_REF] Palacio | Does carbon storage limit tree growth?[END_REF][START_REF] Wiley | A re-evaluation of carbon storage in trees lends greater support for carbon limitation to growth[END_REF]. The typically observed large C reserve pools [START_REF] Hoch | Non-structural carbon compounds in temperate forest trees[END_REF][START_REF] Würth | Non-structural carbohydrate pools in a tropical forest[END_REF] have been interpreted as a consequence of an overabundant C supply and thus evidence of sink control of tree growth [START_REF] Körner | Carbon limitation in trees[END_REF]. However, recent works have suggested that a source limitation of growth may be compatible with large C reserve pools if part of this mobile C is sequestered rather than stored [START_REF] Millard | Nitrogen storage and remobilization by trees: ecophysiological relevance in a changing world[END_REF] or if C storage is an active tree response to environmental stress [START_REF] Dietze | Nonstructural Carbon in Woody Plants[END_REF][START_REF] Wiley | A re-evaluation of carbon storage in trees lends greater support for carbon limitation to growth[END_REF]. Using an alternative methodology (i.e. a methodology that is not based on C storage measurement) our results suggest that sink limitation has a significant effect on the annual woody biomass growth of five species that are representative of different European biomes, including deciduous temperate forests. Because sink limitation implies that there are periods with significant C supply but no growth, our results also corroborate recent empirical studies that reported a significant role of growth duration in the annual variability of tree radial increment [START_REF] Brzostek | Chronic water stress reduces tree growth and the carbon sink of deciduous hardwood forests[END_REF][START_REF] Cuny | Life strategies in intra-annual dynamics of wood formation: example of three conifer species in a temperate forest in north-east France[END_REF][START_REF] Lempereur | Growth duration is a better predictor of stem increment than carbon supply in a Mediterranean oak forest: implications for assessing forest productivity under climate change[END_REF]. Additionally, we observed that past environmental constraints significantly affected C partitioning to wood growth for each species and biome (Table 5 and Figs. 4 and5). The lagged effect of the previous year's low C supply (GPP y-1 ) possibly indicates a preferential C allocation to storage at the expense of growth in trees that face C reserve pool depletion [START_REF] Bansal | Carbon balance of conifer seedlings at timberline: relative changes in uptake, storage, and utilization[END_REF][START_REF] Wiley | The effects of defoliation on carbon allocation: can carbon limitation reduce growth in favour of storage?[END_REF]. In support of this finding, Richardson et al. (2012) reported a strong relationship between the AWBI and the EC-based estimate of the previous year's C supply in a mature maple stand. The detrimental effect of a previous year's low C supply on temperate oak wood growth (Fig. 4) may be related to growth phenology, because this species relies on C reserves to achieve a large part of its annual biomass growth prior to leaf expansion in the spring [START_REF] Barbaroux | Distribution of aboveground and below-ground carbohydrate reserves in adult trees of two contrasting broad-leaved species (Quercus petraea and Fagus sylvatica)[END_REF]. The lagged effect of high water stress intensity on F. sylvatica and Q. ilex (Fig. 4) may be linked to previous drought-induced mortalities of buds or fine roots [START_REF] Leuschner | Drought responses at leaf, stem and fine root levels of competitive Fagus sylvatica L. and Quercus petraea (Matt.) Liebl. trees in dry and wet years[END_REF][START_REF] López | Thinning effects on carbon allocation to fine roots in a Quercus ilex forest[END_REF]. Indeed, pre-built buds are thought to strongly regulate the following year's cambial activity [START_REF] Delpierre | Temperate and boreal forest tree phenology: from organ-scale processes to terrestrial ecosystem models[END_REF][START_REF] Palacio | Fast replenishment of initial carbon stores after defoliation by the pine processionary moth and its relationship to the re-growth ability of trees[END_REF][START_REF] Zweifel | Intra-annual radial growth and water relations of trees: implications towards a growth mechanism[END_REF] and a recent meta-analysis concluded that C is preferentially allocated to fine roots at the expense of wood growth in stands that face constraining environments [START_REF] Chen | Allocation of gross primary production in forest ecosystems: allometric constraints and environmental responses[END_REF]. Finally, our results suggest that C supply (GPP gp ) is an important driver of the annual woody biomass growth in temperate deciduous forests [START_REF] Daudet | Experimental analysis of the role of water and carbon in tree stem diameter variations[END_REF]. GPP was the component of the simulated tree C balance that was most closely related to the annual variability in growth; this result indicates GPP's important role in explaining the annual variability in the net ecosystem productivity of European forests [START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF]. Overall, our findings support the premise that forest woody biomass growth is subject to complex control processes that include both source and sink limitations, following Liebig's law: although numerous processes potentially influence wood growth, stand growth at a given site and a given year is predominantly limited by the most constraining factor. C (source) limitation of growth can thus only occur when other factors are nonlimiting [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF], a situation that is expected to be rare in strongly constrained environment such as Mediterranean or mountainous areas (Fig. 4).

Toward an integrated modelling framework

Most models that are currently used to project the outcome of global changes on forests represent wood growth as a fraction of the total C uptake (i.e. source control of growth; De [START_REF] De Kauwe | Where does the carbon go?, A model-data intercomparison of vegetation carbon allocation and turnover processes at two temperate forest free-air CO 2 enrichment sites[END_REF]. This C-centric perspective overlooks the possibility of sink control of growth and thus ignores results such as those presented in this study and those of earlier local studies (reviewed by [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]. Consequently, this perspective possibly hampers the ability of TBMs to project future forest productivity [START_REF] Fatichi | Moving beyond photosynthesis: from carbon source to sink-driven vegetation modeling[END_REF]. On the basis of our analysis of the spatio-temporal dynamics of C allocation to wood growth on a regional scale, we suggest a straightforward, combined source-and sink-driven forest growth modelling framework (Fig. 6). In this framework, a potential site-specific allocation coefficient is first defined to represent the effect of soil fertility on the C allocation to wood [START_REF] Vicca | Fertile forests produce biomass more efficiently[END_REF]. In a second step, this coefficient is adjusted to the physiological state of the stand by accounting for the dependences of the C allocation on ontogeny, competition intensity and lagged environmental stressors. Lagged environmental stressors are represented by a negative effect on the previous year's water stress index and low C uptake on the allocation coefficient. The resulting potential allocation coefficient is finally modulated on a daily basis by (i) the phenology of wood growth, which defines the onset and cessation of the growth period [START_REF] Delpierre | Temperate and boreal forest tree phenology: from organ-scale processes to terrestrial ecosystem models[END_REF], and (ii) the sink limitations of wood growth: the coefficient value of a given day is calculated using the potential coefficient value and the water and temperature stresses experienced during that day. The water and temperature stresses induce day-today fluctuations in the allocation coefficient value that represent the sink limitations of wood growth, i.e. the direct effect of water and temperature stresses on growth. The framework presented here is a calibration strategy that requires field data to be implemented in TBMs. Our results can help in defining the forms of the coefficient dependences that will be formalized in the next generation of models (Figs. 3 and5).

Our approach can be seen as an intermediate step toward a more mechanistic representation of C allocation to woody biomass [START_REF] Hölttä | A physiological model of softwood cambial growth[END_REF][START_REF] Schiestl-Aalto | CASSIA-a dynamic model for predicting intraannual sink demand and interannual growth variation in Scots pine[END_REF]. It synthesizes the current knowledge regarding forest growth dependences and has the potential to unify seemingly contradictory observations within a single modelling framework. The simulated growth is indeed subject to the combined controls of C supply and changes in C allocation due to endogenous adjustments and/or modulations of sink activity (Fig. 6). These controls result from distinct processes, which are independently represented in the modelling framework. The relative influences of the various processes, i.e. the simulated growth causalities, are thus likely to vary both spatially and temporally, depending on the environmental conditions faced by trees. Our approach therefore has the potential to shed light on the contrasted results reported by correlative studies. Although the value is comparable to the values of previous studies [START_REF] Lebourgeois | Climatetree-growth relationships of European beech (Fagus sylvatica L.) in the French Permanent Plot Network (RENECOFOR)[END_REF][START_REF] Mérian | Spatial variation and temporal instability in climate-growth relationships of sessile oak (Quercus petraea [Matt.] Liebl.) under temperate conditions[END_REF], the proportion of the annual growth variability that was explained by our approach was moderate (Table 5). Plausible explanations for this result include (i) unreported management interventions that may have skewed the historical stand growth reconstruction and (ii) potentially important growth drivers that were not considered here, such as changes in C partitioning due to mast seeding [START_REF] Mund | The influence of climate and fructification on the inter-annual variability of stem growth and net primary productivity in an old-growth, mixed beech forest[END_REF], genetic differentiation among tree populations [START_REF] Vitasse | Genetic vs. non-genetic responses of leaf morphology and growth to elevation in temperate tree species[END_REF] or allometry-mediated tree acclimation to drought [START_REF] Martin-Stpaul | The temporal response to drought in a Mediterranean evergreen tree: comparing a regional precipitation gradient and a throughfall exclusion experiment[END_REF]. A third factor that hampered the ability of our empirical models to explain the annual growth variability is the potential disagreement between the CAS-TANEA outputs that were used as explanatory variables and the corresponding actual drivers. Although we argued that (i) the CASTANEA model has been thoroughly validated at many EC sites from throughout Europe and (ii) the presented growth dependences demonstrated their robustness against the reported uncertainties of the CASTANEA simulations, the quality of the simulations was limited by the idiosyncrasies of the sites we examined in this study. In particular, a number of past disturbances such as insect outbreaks, windthrow or unreported commercial thinning could have temporarily induced large discrepancies between the actual and simulated C fluxes [START_REF] Grote | Modelling forest carbon balances considering tree mortality and removal[END_REF][START_REF] Hicke | Effects of biotic disturbances on forest carbon cycling in the United States and Canada[END_REF]. The error that is attributable to model performance unfortunately remains unknown because of the absence of EC measurements at our study sites (except for the Puéchabon site; see [START_REF] Delpierre | Quantifying the influence of climate and biological drivers on the interannual variability of carbon exchanges in European forests through process-based modelling[END_REF]. Despite this additional uncertainty, the combined use of field measurements and process-based modelling allowed us to present the first species-specific evaluation of annual C allocation to growth along regional environmental gradients. Our results suggest that implementing the presented C allocation dependences in TBMs will refine the projections of the outcome of global changes on forest growth and have implications for the predicted evolution of forest C sink, forest diebacks and tree species distributions [START_REF] Cheaib | Climate change impacts on tree ranges: model intercomparison facilitates understanding and quantification of uncertainty[END_REF].

The Supplement related to this article is available online at doi:10.5194/bg-12-2773-2015-supplement.

Figure 1 .

 1 Figure 1. The conceptual framework and the three sources of data (field measurements, climate reanalysis and process-based simulations) used in the analyses.

Figure 2 .

 2 Figure 2. Locations of the study sites.

  . 1. Analyses were conducted with R software (R Development Core

Figure 3 .

 3 Figure 3. Spatial dependences of annual wood growth. (a) Relationship of the AWBI and the GPP of the growth period (GPP gp ) averaged over sites. (b) Age-related decline of the C partitioning to AWBI (AWBI / GPP gp ).

Figure 6 .

 6 Figure 6. Modelling framework for a combined source-and sink-driven representation of C allocation to wood growth.

Table 1 .

 1 Climatic features of the studied sites. ETP is annual Penman-Monteith potential evapotranspiration, Precip. is annual precipitation, and Temp. is annual temperature. Values are site averages ± SD among sites.

	Species	Number Number of	Elevation	ETP	Precip.	Temp.	Source
		of plots	site-years	(m)	(mm)	(mm)	( • C)
	F. sylvatica	16	313	565 ± 326	1010 ± 121 1001 ± 133 10.1 ± 0.98 RENECOFOR
	Q. petraea/Q. robur	26	484	193 ± 76	999 ± 71	821 ± 96	10.7 ± 0.63 RENECOFOR
	P. abies	6	101	1056 ± 313	933 ± 44	1559 ± 340	7.1 ± 1.4	RENECOFOR
	Q. ilex	1	43	270	1417	907	13.4	Puéchabon site

RENECOFOR network field measurements Atmosphere fluxes CO2 GPP = NPP + Ra cambium phenology water stress indexes temperature stress indexes

	Radiation
	Precipitation Wind	Temperature
	Vapour pressure deficit
		SAFRAN climate database
		CASTANEA process-based model

Soil water capacity Available soil nutrient Leaf nitrogen content Stand age Competiton intensity Annual Woody Biomass Increments

	CASTANEA input variables
	AWBI dependencies
	evaluated in this study

Table 2 .

 2 Description of the explanatory variables considered in the analyses. The type category indicates the source of the data: measurement (M), SAFRAN climate database (C) or CASTANEA simulations (S). Scale categories indicate the variables considered in spatial (S) and/or temporal (T) analyses.

	IDs	Description

Table 3 .

 3 Relationships of annual wood growth and the components of the seasonal forest carbon balance: NPP, GPP and Ra. The start and end terms (day of the year) indicate the carbon flux period that yielded the maximum value for the median of the growth-flux correlations among sites. The r term is the maximum obtained for the median of the site-specific Pearson correlation coefficients; values that are significantly different from 0 are indicated ( * indicates P < 0.05 and * * indicates P < 0.001). The σ term is the standard deviation of the Pearson correlation values among sites.

	Species			GPP				Ra		NPP
		start end	r	σ	start end	r	σ	start end	r	σ
	F. sylvatica	124 258 0.62 * * 0.18	96	200 -0.29 * 0.33	126 262 0.58 * * 0.24
	Q. petraea/Q. robur 136 214 0.59 * * 0.25	98	192	0.31 * 0.24	130 214 0.50 * * 0.28
	P. abies	32	262 0.52 * * 0.38	78	348	0.11	0.52	32	200 0.49 * * 0.29
	Q. ilex	186 226	0.60		36	256	-0.26		186 226	0.58

Table 4 .

 4 Spatial dependences of the annual woody growth: multiple-regression estimates. Data have been centred and scaled. GPP gp is the gross primary production of the growth period, age is the average age of the stand, and SBA is the stand basal area (Table2). Values: estimates [F values]. All estimate values differed significantly from 0 (P < 0.001). All variables were retained in the bootstrap procedure (see main text).

	Species		Estimates
		GPP gp	age	SBA	P	adj. R 2
	Q. petraea/Q. robur		-8.88 × 10 -1 [39.5] 4.27 × 10 -1 [19.5] < 10 -4	0.69
	F. sylvatica	5.07 × 10 -1 [59.4] -6.96 × 10 -1 [61.6]		< 10 -4	0.88
	P. abies	8.25 × 10 -1 [8.6]			0.04	0.60

Biogeosciences, 12, 2773-2790, 2015 www.biogeosciences.net/12/2773/2015/

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Acknowledgements. We wish to thank the Office National des Forêts and the RENECOFOR network team, particularly Manuel Nicolas and Marc Lanier, for providing the RENECOFOR database. The SAFRAN database was provided by Météo-France as part of the HYMEX project. J. Guillemot received a PhD grant from the French Ministère de l'Enseignement Supérieur et de la Recherche and the University of Paris-Sud. A post-doctoral research grant to N. K. Martin-StPaul was provided by the Humboldt project within GIS Climat. As part of the ICP forests network data (icp-forests.net), the material used in this article is available, free of charge, upon request (please contact M. Nicolas, manuel.nicolas@onf.fr, +00331 60 74 92 28, Office National des Forêts, Fontainebleau, 77300, France).

Edited by: S. Zaehle