François Lebourgeois
email: francois.lebourgeois@agroparistech.fr

Nicolas Delpierre

Eric Dufrêne

Sébastien Cecchini

Sébastien Macé

Luc Croisé

Manuel Nicolas

Assessing the roles of temperature, carbon inputs and airborne pollen as drivers of fructification in European temperate deciduous forests

Keywords: beech, temperate oaks, fructification, gross primary productivity, pollen, temperature, secondary growth

Quercus petraea, and Fagus sylvatica.

• We analysed the relations of fruit production with airborne pollen, carbon and water resources and meteorological data in 48 French forests over 14 years (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007).

• In oak, acorn production was mainly related to temperature conditions during the pollen emission period, supporting the pollen synchrony hypothesis. In beech, a temperature signal over the two previous years eclipsed the airborne pollen load.

• Fruit production in Quercus and Fagus was related to climate drivers, carbon inputs and airborne pollen through strongly non-linear, genus-specific relations.

• Quercus and Fagus also differed as regards the secondary growth vs. fructification trade-off. While negative relationships were observed between secondary growth and fruit production in beech, more productive years benefited to both secondary growth and reproductive effort in oak.

Introduction

Fruit production is a crucial step in the life cycle of trees [START_REF] Silvertown | The evolutionary ecology of mast seeding in trees[END_REF]. A regular occurrence of fruit production is required for the natural regeneration of forests. Fruit production is also a pre-requisite for species migration whether natural or human-assisted [START_REF] Wall | The evolutionary ecology of nut dispersal[END_REF][START_REF] Benito-Garzon | Testing scenarios for assisted migration of forest trees in Europe[END_REF][START_REF] Koralewski | Plants on the move: Assisted migration of forest trees in the face of climate change[END_REF][START_REF] Aubin | Traits to stay, traits to move: a review of functional traits to assess sensitivity and adaptive capacity of temperate and boreal trees to climate change[END_REF]. In anemophilous perennial plant species such as forest trees, fruit production highly varies across years. The occurrence of a high production event synchronized among individuals from a regional population is known as a "masting" event [START_REF] Kelly | The evolutionary ecology of mast seeding[END_REF][START_REF] Koenig | Patterns of annual seed production by northern hemisphere trees: A global perspective[END_REF]; [START_REF] Kelly | Mast seeding in perennial plants: Why, how, where?[END_REF][START_REF] Wesolowski | Interannual variation in tree seed production in a primeval temperate forest: does masting prevail?[END_REF][START_REF] Fernández-Martínez | The North Atlantic Oscillation synchronises fruit production in western European forests[END_REF][START_REF] Nussbaumer | Patterns of mast fruiting of common beech, sessile and common oak, Norway spruce and Scots pine in Central and Northern Europe[END_REF][START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. The hypotheses of predator satiation and maximization of pollination efficiency (i.e. higher seed/flower ratios in high-flowering years) have been proposed to explain the evolutionary emergence of masting [START_REF] Kelly | Mast seeding in perennial plants: Why, how, where?[END_REF][START_REF] Satake | A resource budget model to explain intraspecific variation in mast reproductive dynamics[END_REF][START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF].

The occurrence of a mast year depends on the successful development of a large mass of viable flowers and fruit [START_REF] Smaill | Climate cues and resources interact to determine seed production by a masting species[END_REF]Fernandez-Martinez et al. 2012;[START_REF] Kasprzyk | Relationships among weather parameters, airborne pollen and seed crops of Fagus and Quercus in Poland[END_REF][START_REF] Pearse | Cues versus proximate drivers: testing the mechanism behind masting behavior[END_REF][START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF][START_REF] Monks | Resource limitation underlying multiple masting models makes mast seeding sensitive to future climate change[END_REF]. The development of flowers highly affects fruit production and, in temperate forest trees, it starts with the floral transition of dormant buds during the growing season that preceeds fructification [START_REF] Miyazaki | Nitrogen as a key regulator of flowering in Fagus crenata: understanding the physiological mechanism of masting by gene expression analysis[END_REF]Delpierre et al. 2016b). It is not perfectly clear which environmental cues or internal resources determine floral transition. Yet, available nitrogen has been demonstrated as a strong signal in Fagus crenata [START_REF] Miyazaki | Nitrogen as a key regulator of flowering in Fagus crenata: understanding the physiological mechanism of masting by gene expression analysis[END_REF], and can be inhibited by too high spring temperatures [START_REF] Kon | Proximate factors causing mast seeding in Fagus crenata: the effects of resource level and weather cues[END_REF]. Both carbon and nitrogen resources are required for bud development and flowering in spring [START_REF] Han | Recent developments in understanding mast seeding in relation to dynamics of carbon and nitrogen resources in temperate trees[END_REF], which occurs close to leaf-out, and they are mostly drawn from the tree reserves. Because pollination is a density-dependent process in selfincompatible plants such as most forest trees, the efficiency of flower production is better in years when a large part of the tree population produces flowers (a process known as pollen coupling; [START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF]. Density-dependence is further relaxed in years with high pollen phenological synchrony among trees [START_REF] Koenig | What drives masting? The phenological synchrony hypothesis[END_REF], which may depend on temperature conditions during bud burst (Bogdziewicz et al. 2017b). Adverse weather conditions (i.e. rain, high humidity, low wind) may affect pollen transport and compromise pollination [START_REF] Kasprzyk | Relationships among weather parameters, airborne pollen and seed crops of Fagus and Quercus in Poland[END_REF], while late frost events may damage flowers [START_REF] Vitasse | Increase in the risk of exposure of forest and fruit trees to spring frosts at higher elevations in Switzerland over the last four decades[END_REF]. When pollination occurs, several hazards may compromise the formation of viable fruit. The least known phase occurs between pollination and fecundation; it lasts one to two months in temperate forest trees and may be compromised by too high temperatures [START_REF] Hedhly | Warm temperatures at bloom reduce fruit set in sweet cherry[END_REF]. Considering these biological facts, a relatively high number of studies have investigated the role of local climate in determining fruit production in temperate forest trees (mostly temperature, [START_REF] Sork | Prediction of acorn crops in three species of North American oaks: Quercus alba, Q rubra and Q velutina[END_REF][START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF][START_REF] Pearse | Cues versus proximate drivers: testing the mechanism behind masting behavior[END_REF], as well as the role of air pollen concentrations [START_REF] Kasprzyk | Relationships among weather parameters, airborne pollen and seed crops of Fagus and Quercus in Poland[END_REF] or climate conditions during pollen emission (Bogdziewicz et al. 2017b). Some studies even considered teleconnections (e.g. NAO, Fernandez-Martinez et al. 2017) as possible drivers of fruit production synchrony across stands at a continental scale [START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. However, the development of viable fruit following fecondation also requires carbon (mostly provided by photosynthesis; [START_REF] Hoch | Fruit production in three masting tree species does not rely on stored carbon reserves[END_REF][START_REF] Ichie | Are stored carbohydrates necessary for seed production in temperate deciduous trees?[END_REF]) and nitrogen resources [START_REF] Han | Nitrogen storage dynamics are affected by masting events in Fagus crenata[END_REF], and non-limiting water [START_REF] Misson | Phenological responses to extreme droughts in a Mediterranean forest[END_REF]. The impact of resource availability has been investigated more rarely on large datasets, albeit indirectly from the autocorrelation of fruit time series.

European beech (Fagus sylvatica) has been described as a "flowering masting" species, i.e.

flowering and the subsequent airborne pollen concentrations are the main limitations to fruit production (Kasprzyck et al. 2014;Bogdziewicz et al. 2017b). Previous-year temperatures, often in the form of temperature differences between year-1 and year-2 growing seasons, have also been invoked as a putative driver of fructification in beech (Bogdziewicz et al. 2017b;[START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]). However, their functional interpretation is still unclear [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF][START_REF] Pearse | Cues versus proximate drivers: testing the mechanism behind masting behavior[END_REF][START_REF] Monks | Resource limitation underlying multiple masting models makes mast seeding sensitive to future climate change[END_REF]. A lower number of studies have addressed European deciduous oaks (Quercus petraea and Quercus robur). These studies reported a lower dependence of fruit production on pollen concentrations per se in oak (Kasprzyck et al. 2014), but evidenced an impact of pollination duration or temperature during the pollen season (Bogdziewicz et al. 2017b).

In mast years, fruit production may represent a substantial amount of tree carbon productivity.

In a mature beech forest, nut production averages 42% (10-79%) of annual wood production, and 12% (3-20%) of net primary productivity [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]. In sessile oak, acorn production can reach 52% of annual wood production (Delpierre et al. 2016a). In beech, as opposed to oak that has small female flowers, the resource investment of non-fertilized female inflorescences is high from the start [START_REF] Abe | Parameterisation and validation of a resource budget model for masting using spatiotemporal flowering data of individual trees[END_REF]. This high resource cost of reproduction prompted researchers to formulate hypothetical resource-investment scenarios (Crone and Rapp 2014; [START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF]. Broadly, these scenarios can be categorized into (i) those involving differential allocation of current-year acquired resources (termed resource-matching, resourceswitching in [START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF], and (ii) those involving accumulation of resources over years (termed resource-storage and veto in [START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF]. Recent studies demonstrated that the carbon needed for fruit formation was mostly derived from current-year photosynthesis [START_REF] Hoch | Fruit production in three masting tree species does not rely on stored carbon reserves[END_REF][START_REF] Ichie | Are stored carbohydrates necessary for seed production in temperate deciduous trees?[END_REF]. This finding reinforces the idea that fruit act as a competing resource sink interacting with other organs in the resource economy of trees. Several studies tracing carbon allocation to different organs suggest that beech allocates less carbon to wood growth during mast years [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] Mueller-Haubold | Climate Responses of Aboveground Productivity and Allocation in Fagus sylvatica: A Transect Study in Mature Forests[END_REF][START_REF] Mueller-Haubold | Climatic Drivers of Mast Fruiting in European Beech and Resulting C and N Allocation Shifts[END_REF], whereas no reduced allocation to wood is observed in beech or oak in other reports [START_REF] Alla | Acorn production is linked to secondary growth but not to declining carbohydrate concentrations in current-year shoots of two oak species[END_REF][START_REF] Hoch | Fruit production in three masting tree species does not rely on stored carbon reserves[END_REF][START_REF] Ichie | Are stored carbohydrates necessary for seed production in temperate deciduous trees?[END_REF]. Similarly, studies linking fruit production and diameter growth yielded contrasting results, with a frequent negative link between these two variables in beech [START_REF] Monks | Testing the resource-matching hypothesis in the mast seeding tree Nothofagus truncata (Fagaceae)[END_REF]Drobyshev et al. 2010;[START_REF] Hacket-Pain | The influence of masting phenomenon on growth-climate relationships in trees: explaining the influence of previous summers' climate on ring width[END_REF] and a positive one in oak [START_REF] Askeyev | The effect of climate on the phenology, acorn crop and radial increment of pedunculate oak (Quercus robur) in the middle Volga region, Tatarstan, Russia[END_REF]Perez-Ramos et al. 2010;[START_REF] Martin | Trade-off between stem growth and acorn production in holm oak[END_REF].

Fewer data are currently available as regards other resources such as nitrogen. Studies on Fagus crenata showed that nitrogen reserve formation was lower in mast years [START_REF] Han | Nitrogen storage dynamics are affected by masting events in Fagus crenata[END_REF], and possibly compromised flowering in the following year [START_REF] Miyazaki | Nitrogen as a key regulator of flowering in Fagus crenata: understanding the physiological mechanism of masting by gene expression analysis[END_REF]. This mechanism may at least partly explain the repeatedly reported negative one-year autocorrelation of fruiting time series in temperate trees.

Previous papers established that beech and oak showed contrasting behaviours in terms of fructification, its proximate drivers (i.e. pollen vs. weather conditions), or the trade-off between reproductive effort and growth. However, they lack a clear ranking of the role of weather determinants, pollen limitation, and current-and previous-year resource availability in determining fruit production variability. These studies rarely addressed interactions among variables, thresholds, non-linear responses or resource availability, apart from indirectly including lag-1 autocorrelation of the fruit production time series. In this paper, we aim at filling this gap studying the influences of weather determinants, carbon resource availability, the airborne pollen load, and pollen-related meteorology on the spatio-temporal variability of fruit production over 14 years (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) in 48 European temperate beech (Fagus sylvatica L.) and oak (Quercus petraea and Q. robur) stands. We also assessed the link between fruit production and wood growth in these species to test for a growth versus fructification trade-off.

Materials and Methods

Sampling design

Data were collected from 48 broadleaved stands of the French Permanent Plot Network for the Monitoring of Forest Ecosystems (RENECOFOR) [START_REF] Ulrich | Le réseau RENECOFOR : objectifs et réalisation[END_REF]. The stands covered a wide range of environmental conditions (Fig. 1 and Online Resource 1). Each stand had a surface of approximately two ha, with a central 0.5-ha fenced zone. The slope was less than 5 % in most stands, and elevation ranged from 20 to 1,400 m asl (mean: 350 m). The maximum soil water holding capacity (SWHCm, in mm) was estimated according to textural properties, soil depth, and coarse element percentages from two trenches per plot [START_REF] Brêthes | Caractéristiques pédologiques des 102 peuplements du réseau. Office National des Forêts Crone EE, Rapp JM[END_REF][START_REF] Piedallu | Mapping soil water holding capacity over large areas to predict potential production of forest stands[END_REF]. SWHCm ranged from 45 to 200 mm, with an average value of 120 mm (Online Resource 1).

Climate data

Mean monthly temperatures and rainfall data were obtained from the 81 closest available stations of the French Climate Network (Météo-France) (Fig. 1). To estimate water supply over the 1994-2007 period, we first computed a monthly climatic water balance (CWB) by calculating the difference between rainfall (R) and potential evapotranspiration (PET, calculated with Turc's formula) [START_REF] Lebourgeois | Appréhender le niveau de sécheresse dans le cadre des études stationnelles et de la gestion forestière à partir d'indices bioclimatiques[END_REF]. Secondly, we calculated a monthly soil water balance using SWHCm values and climatic data. The Thornthwaite formula (Online Resource 2) was chosen to compute soil water balance [START_REF] Thornthwaite | The water balance[END_REF] because this method gives accurate estimations of monthly water content fluctuations from a limited number of parameters and has been successfully used in previous ecological studies [START_REF] Lebourgeois | Mixed stands reduce Abies alba tree-ring sensitivity to summer drought in the Vosges mountains, western Europe[END_REF][START_REF] Trouvé | Stand density, tree social status and water stress influence allocation in height and diameter growth of Quercus petraea (Liebl.)[END_REF][START_REF] Piedallu | Soil aeration, water deficit, nitrogen availability, acidity and temperature all contribute to shaping tree species distribution in temperate forests[END_REF]. A complementary dataset of meteorological variables at the hourly temporal scale was obtained from SAFRAN atmospheric reanalysis (with 8-km spatial resolution, [START_REF] Vidal | A 50-year high-resolution atmospheric reanalysis over France with the Safran system[END_REF]. It included global radiation, rainfall, wind speed, air humidity, and air temperature. We used these variables for climate forcing in the CASTANEA model (see "Process-based simulation data" section).

The NAO (North Atlantic Oscillation) refers to a meridional oscillation of atmospheric masses, with centers of action near the Icelandic low and the Azores high [START_REF] Hurrell | An Overview of the North Atlantic Oscillation. The North Atlantic Oscillation: Climatic Significance and Environmental Impact[END_REF]. Studies have already shown that NAO anomalies correlate with weather conditions at the continental scale [START_REF] Mares | NAO impact on the summer moisture variability across Europe[END_REF][START_REF] Hurrell | North Atlantic climate variability: The role of the North Atlantic Oscillation[END_REF] and with local ecosystem functioning [START_REF] Ottersen | Ecological effects of the North Atlantic Oscillation[END_REF][START_REF] Stenseth | Studying climate effects on ecology through the use of climate indices: the North Atlantic Oscillation, El Nino Southern Oscillation and beyond[END_REF][START_REF] Menzel | SSW to NNE' -North Atlantic Oscillation affects the progress of seasons across Europe[END_REF][START_REF] George | An overview of tree-ring width records across the Northern Hemisphere[END_REF]). Previous studies highlighted that NAO indices may be correlated with fruit production [START_REF] Wright | The El Nino Southern Oscillation variable fruit production, and famine in a tropical forest[END_REF][START_REF] Fernández-Martínez | The North Atlantic Oscillation synchronises fruit production in western European forests[END_REF]), so we also considered monthly NAO indices as candidate variables in our statistical modeling. The NAO index time series were downloaded from the Climate Prediction Center of the National Weather Service (NOAA, < www.cpc.ncep.noaa.gov/ >).

Annual fruit production

Litterfall was collected seasonally from 1994 to 2007 [START_REF] Peaucelle | Time trends in forest litterfall production and relationships with environmental changes: An exploratory approach on data collected from 1995 to 2007 in the RENECOFOR monitoring network[END_REF]. Ten collectors were distributed in the 0.5-ha fenced central part of each plot. Litter collectors were 0.5-m² square traps treated against U.V. radiation and designed with a water drainage system. A sifter (2x2 mm) was placed at the bottom of the trap to retain litter. Trap distribution was regular, with 3

(2) lines throughout the 0.5-ha squared (rectangular) plot. Depending on the stand, 3 to 5 samplings were performed annually. The litter samples were separated according to organs: leaves, small branches (< 2cm diameter), and fruit (acorns and nuts) (Online Resource 3). All compartments were air-dried at 105° C for 24 hours before weighing. Seasonal data were aggregated over biological years from April 1 (i.e. the estimate of the start of the growing season, Peaucelle 2011) to March 31 of the following year. Litterfall mass values from sampling periods overlapping two consecutive biological years were split proportionally to the number of days belonging to each year. To ensure the robustness of the dataset, a given collection was considered as valid only if at least 8 out of 10 collectors were available on the plot. A biological year of collection was considered as valid only if less than 10 % of the days of the year and no autumn day (from September 1 to December 31) were missing. Finally, litterfall production was calculated by dividing the collected data by the total surface area of all the traps, and was then reported to one hectare. Forty-one stands were monitored for at least 10 years, and 12 stands over the whole study period (1994 to 2007). Finally, totals of 347 and 219 annual fruit production data were made available for oak and beech, respectively (Online Resource 3). These data were calculated both as annual fruit biomass (kg ha -1 y -1 ) and fruit number (number of fruit ha -1 y -1 ).

Pollen count data

To assess the influence of pollen limitation, we used pollen count data from the "Réseau National de Surveillance Aérobiologique" (RNSA). The data consist of bi-hourly counts (aggregated to the daily time scale in the present case) expressed as the number of pollen grains per m 3 of air, affiliated to a particular taxon (determined at the genus level, i.e. oak and beech) by microscopy analysis. The RNSA network consists of ca. 90 stations spread across continental France. For each forest stand, we estimated the daily pollen aerial concentration as the inverse-distance-weighted average concentration measured in all RNSA stations in a 100km radius (corresponding to 3.2 RNSA stations on average, 65 km away from a given stand).

For each site-year, we defined the start / peak / end of the pollen season as the day of year when 5% / 50% / 95% of the cumulative annual pollen emissions were reached.

Process-based simulation data

We used the ecophysiological process-based model CASTANEA (Dufrêne et al. 2005;Davi et al. 2009;Delpierre et al. 2012) to simulate tree carbon (C) resource availability [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional -structural model[END_REF], in the form of gross primary productivity (GPP), net primary productivity (NPP), and tree internal C reserve concentrations. CASTANEA simulates the stand-atmosphere CO2 exchanges at the half-hourly scale by combining photosynthesis, autotrophic respiration, carbon allocation, soil organic carbon, and soil hydrology sub-models. The model proved able to reproduce the interannual fluctuations of CO2 fluxes in European forests (Delpierre et al. 2012) as well as spatial [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional -structural model[END_REF]) and interannual variability of aerial growth [START_REF] Guillemot | Environmental control of carbon allocation matters for modelling forest growth[END_REF] in oak and beech. In this work, we used the CASTANEA parameterization developed in a previous work over the RENECOFOR network [START_REF] Guillemot | Assessing the effects of management on forest growth across France: insights from a new functional -structural model[END_REF]. Every year from 1994 to 2007, the hourly-to-daily simulated GPP, NPP, and C reserves were aggregated over different time periods (gC m -2 month -1 or season -1 or year -1 ). The C balance was simulated for all 20 beech stands, but only for 23 oak stands out of 28 because model input parameters were not available for all stands.

Tree-ring chronologies

Stands were mature (mean age: 104 years in 2007), with typical basal areas (means: 19 -23 m - 2 ha) and dominant heights (means: 25 -29 m) for broadleaved trees in managed high forests (Online Resource 4). To study the relationship between fruit production and growth, trees were cored in 2009. Unfortunately, it was not possible to core all the stands and all the trees as we did in 1997 (Lebourgeois et al. 2005;[START_REF] Mérian | Spatial variation and temporal instability in climate-growth relationships of sessile oak (Quercus petraea [Matt.] Liebl.) under temperate conditions[END_REF]. Thus, among the 48 stands, a subsample of 30 stands was cored (25 oak stands and 5 beech stands) (Online Resource 4). In each plot, 10 dominant trees were cored (two cores per tree, 500 cores for oak, 100 cores for beech, 8,400 ring measurements) and cross-dated using pointer years [START_REF] Mérian | Spatial variation and temporal instability in climate-growth relationships of sessile oak (Quercus petraea [Matt.] Liebl.) under temperate conditions[END_REF]. Raw treering widths were standardized to remove the well-known strong signal linked to cambial age, stand characteristics and other resource variables (soil chemistry, soil water balance…) (Online Resource 5). To this aim, tree-ring widths predicted by the RandomForest model (see Statistical Modeling section) were subtracted from the observed values to define residual tree-ring widths (i.e. standardized values, ResRW). ResRW data were then used as an explanatory variable to test for the growth vs. fructification trade-off.

Statistical Modelling

We used the non-parametric statistical method RandomForest (RF) to model the spatiotemporal variability of fruit production. RF is a machine-learning algorithm based on bootstrapped decision trees. Unlike classical regression techniques for which the relationship between the response and predictors is pre-specified (for example, straight line, quadratic) and the test is performed to prove or disprove the relationship, RF assumes no such relationship.

Since no assumptions are made about the nature of the relationships among the response and predictor variables, RF allows for the possibility of interactions and nonlinearities among variables. Consequently, RF is effective in uncovering structure in data with hierarchical or non-additive variables. For all these reasons, there has been increasing interest in the use of RandomForest techniques in ecological studies within the last 10 years [START_REF] Breiman | RandomForests[END_REF][START_REF] Liaw | Classification and regression by randomForest[END_REF][START_REF] Lin | Random forests and adaptive nearest neighbors[END_REF][START_REF] Prasad | Newer classification and regression tree techniques: Bagging and random forests for ecological prediction[END_REF][START_REF] Strobl | An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests[END_REF]. Briefly, RF classifies a dependent variable (fruit production in the present case) among groups defined as a combination of intervals of multiple predictors, resulting in a so-called "decision tree". RF builds each decision tree with both randomly chosen dependent variables and predictors (mtry).

In fact, mtry is the randomly chosen subset of the total number of initial predictors used to find the best split at each branching node. By fitting a high number (ntree) of training individual decision trees (i.e. a "forest" of decision trees), RF captures the variance of several predictors concomitantly, so that a high number of variables can participate in the prediction. This optimizes predictive accuracy in the final tree [START_REF] Breiman | RandomForests[END_REF], which is selected on the basis of its predictive ability quantified from data unused during the training phase ("out-of-bag" (OOB) data). Here, the optimized values for mtry and ntree were 4 and 2,000, respectively [START_REF] Oshiro | How Many Trees in a Random Forest ? Machine Learning and Data Mining in Pattern Recognition[END_REF]. RF gives two complementary variable accuracy values [START_REF] Ishwaran | Variable importance in binary regression trees and forests[END_REF]Ehrlinger 2015): variable importance (vimp) and minimal depth (depth). If a predictor is important in the model, then randomly assigning values for that predictor should worsen predictions. vimp expresses this effect, with a higher vimp value indicating a more important predictor. Depth assumes that the most discriminant main predictors are those that most frequently split nodes nearest to the trunks of the trees where they partition large groups in the dataset. Lower values of depth indicate predictors important in splitting large groups of data.

RF returns the RMSE of adjusted values calculated on the training data. It also returns the RMSE of predicted values (OOB error). It is a valid estimate of the test error for the model, since the response for each observation is predicted using only the trees that were not fit using that observation (OOB predictions). RF gives also the percentage of explained variance (i.e. the measure of how well OOB predictions explain the target variance of the training set). For the best predictors, we drew partial dependence plots (PdP), which display the predicted response (Y) as a function of one of the predictors (X). PdP gives a graphical depiction of the effect of X, highlighting both the form and, if any, the threshold of the predicted response (Ehrlinger 2015). We also drew conditioning plots (coplots) to highlight how (Y) depended on two variables (X1, X2). Y was examined as a function of X1 conditional on X2 within n groups of X2 intervals. These methods were applied using the RandomForests [START_REF] Breiman | RandomForests[END_REF]) and ggRandomForests packages (Ehrlinger 2015) within R 3.4.3 statistical software.

Putative candidate variables of fruit production

To apply RF modelling, we selected stands and years with a complete dataset of potential predictors. Thus, among the initial 48 stands and 566 fruit biomass site-years, analyses were performed on 43 stands (20 beech stands and 23 oak stands) accounting for 460 site-years ( 204and 256, respectively). For climate data, we studied a pool of 285 candidate variables combining values or differences from current and previous years [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF][START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]) at an annual, seasonal, or monthly scale for rainfall, temperature, wind speed, global radiation, PET, CWB… (See Climate Data section). We also included monthly NAO values (12 values per year). C resource availability was assessed from a pool of 122 simulated GPP, NPP and C reserves (gC m -2 month -1 or season -1 or year -1 ). For pollination, we studied seven variables: total annual pollen counts (gr m -3 y -1 ), mean daily number of pollen grain (over the whole year or over the period of pollen emission), dates of the (i) onset, (ii) peak, and (iii) end of pollen emission, and duration (number of days) of emission. Atmospheric pollen concentrations do not provide any direct information on pollination success, so we used the pollen concentration time series and climate data to define a set of "pollen meteorology indexes". We hypothesized that warm and dry conditions during the period of pollen flight would generally increase pollination success, allowing for longer pollen residence time in the atmosphere (Kasprzyck et al. 2014). Hence the 108 pollen meteorology indexes were computed as the average temperature (daily min, max, or average), relative humidity and average rainfall, or number of days in 1-to 60-day windows from (i) the start date of pollen emission, and (ii) the observed peak date of pollen emission. Finally, for oak, current and previous-year detrended tree-ring width (ResRW) was also considered as an explanatory variable for acorn production.

We further tested the importance of stand characteristics, phenological variables (leaf unfolding, leaf colouring, growing season length [START_REF] Lebourgeois | Simulating phenological shifts in French temperate forests under two climatic change scenarios and four driving GCMs[END_REF], and soil nutritional values (pH, carbon-nitrogen ratio, saturation rate, nitrogen and phosphorus contents in the first two soil horizons) [START_REF] Brêthes | Caractéristiques pédologiques des 102 peuplements du réseau. Office National des Forêts Crone EE, Rapp JM[END_REF]. As those variables never entered as discriminant predictors of fruit production in the RF models, we excluded them from the rest of the analysis.

Finally, we studied 524 variables as predictors of the fruit produced annually throughout all site-years. We performed RF modelling at the genus scale (i.e. considering F. sylvatica on the one hand and grouping Q. petraea and Q. robur on the other hand). For oak, we mixed data from the two species because (i) pollen data were only available at the genus level, (ii) too few data were available for Quercus robur to compute an accurate specific model, and (iii) similar fruiting patterns were observed between Q. petraea and Q. robur stands growing under similar ecological conditions (data not shown). We designed five nested RF models for oak and beech according to the nature of the candidate predictors (Table 1) width data in addition to model CGPCP. All these models included previous-year fruit production to account for a possible lag-1 effect (i.e. a negative auto-correlation). Following previous works [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF][START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]) that evidenced a strong influence of a temperature difference signal, all models included the ∆T(Jun to Jul)-1-2 variable (that is, the difference in average June-July temperatures between the last-but-one year (year-1) and the last-but-two year (year-2) preceding the current year; [START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. The functional interpretation of ∆T is still unclear and possibly related to resource availability [START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]) and to resource-limited floral induction [START_REF] Monks | Resource limitation underlying multiple masting models makes mast seeding sensitive to future climate change[END_REF]), so we further included the year-1 and year-2 simulated components of the carbon balance in all models but the C model, which only included climate data (see above). As parsimony is an underlying As RF models gave qualitatively similar results for fruit biomass and fruit number (i.e. similar environmental drivers, data not shown), we chose to only present fruit biomass models.

Results

Fruit production and airborne pollen concentrations

Oak stands produced an annual mean of 251 kg of acorns per ha (Fig. 2a), with an average amount of ca. 250,000 acorns ha -1 y -1 (Online Resource 3). Beech stands produced a mean of 174 kg of nuts ha -1 y -1 (Fig. 2b), i.e. an average number of more than one million nuts per ha (Online Resource 3). For all three species, fruit represented only around 5 % of the total amount of litterfall (Online Resource 3), and no link emerged between stand dendrometric characteristics and fruit production.

Although the total amounts of nuts was highly variable among stands, a fruit-bearing cycle with a two-year return period appeared in beech (Fig. 2b and3b). A high-production year was followed by a reduced production year (lag-1 autocorrelation = -0.54, p<10 -9 , Online Resource 6), with high synchronization among populations (Online Resource 7). The highest acrosspopulation median value was observed in 2004 (573 kg ha -1 ) and the lowest in 2005 (2.9 kg ha - 1 ).

Oak fruit production appeared highly variable over the years for a given stand as well as across stands. The oak fruit-bearing cycle appeared quite different with (i) a less pronounced bisannuality of fruit production as compared to beech (but still on average a significant lag-1 autocorrelation = -0.14, p<0.03, Online Resource 6), and (ii) no clear synchronization among populations (Fig. 2a and3a) (Online Resource 7). Some stands produced acorns relatively regularly, whereas others produced acorns at very irregular intervals. For these stands, a long period (5 to 10 years) with no or very low acorn production was followed by a very high production year. The highest median fruit production values were observed in 2007 (438 kg ha - 1 ). That year was also the most "synchronized" year: high production (up to 125 % of the mean value) was observed for more than 60 % of the stands.

The airborne pollen concentration time series reconstructed for oak (Fig. 2c) and beech (Fig. 2d) displayed contrasted patterns. Whether considering daily means or annual sums, airborne pollen concentrations were one order of magnitude higher in oak than in beech. In beech, air pollen concentrations were clearly biennial (Fig. 2d and3d) (lag-1 autocorrelation = -0.41, p<10 -7 , Online Resource 6); that behaviour was not so marked in oak (lag-1 autocorrelation = -0.23, p<0.01, Online Resource 6). In beech, pollen emission was synchronized across stands (Fig. 2c and3c).

Ecological determinism of fruit production

Oak stands

The best RF models (CGPCP and CGPW) explained around 16% of the spatio-temporal variance of acorn biomass (Table 1 andFig. 4). The mean temperature in the 16-day period following the onset of pollen emission (Tpol16) and spring (April) temperature were the most important predictors, followed by previous September temperature, summer and spring water balance, and August GPP. In the CGPW model, RF also linked current-year wood growth and fruit crop. Whatever the model, neither the airborne pollen concentration nor previous-year resources (under the form of simulated components of the carbon balance or previous-year acorn crop) were identified as discriminant predictors of acorn production.

Partial dependence plots showed strong nonlinearity of the acorn production response, with a sharp shift in predicted biomass for air temperature thresholds of 13°C for the onset of pollen emission, 11°C in April, and 16.5°C in previous September (Fig. 4). Warm temperatures during these periods were associated with increased acorn biomass. The highest marginal effect was observed during pollen emission, when a 13°C to 17°C rise more than tripled acorn biomass (Fig. 4). In April, a 2.5-increase in predicted biomass was observed when the temperature rose from 11°C to 15°C. Given the major role of these drivers, the partial dependence of the remaining variables looked flat (Fig. 4). Lastly, predicted fruit biomass was all the higher as annual radial growth increased (ResRW > 0) (Fig. 4). Conditioning plots showed that the interaction of increasing temperatures in the 16-day period following the onset of pollen emission (Tpol16) with increasing April temperatures, summer GPP or summer CWB (less negative, i.e. wetter, values) favored a high fruit biomass production (Fig. 5a, c-d). Similarly, the co-occurrence of both high spring temperatures and high radial growth was observed at siteyears of high acorn production (Fig. 5b). Overall, the RF models overestimated observed low values and underestimated observed high fruit production values (Online Resource 8).

Beech stands

The proportion of variance explained by the RF models was higher for beech (~ 45%) than for oak (~ 16%) (Table 1 and Fig. 6). The RF models highlighted a high dependency of fruit production on temperature, followed by pollen and GPP. Fruit production was closely linked to thermal conditions, (i) during the previous years through ∆T(Jun to Jul)-1-2 (i.e. the difference in average June-July temperatures between year -1 and -2) and T(Jun-Jul)-2 (i.e. the average June-July temperature (in °C) in year -2), and (ii) in February and October of the current year.

Unlike for oak, the airborne pollen concentration and NAO variables appeared relevant to predict fruit biomass, but no pollen meteorology indexes were selected by the RF models (Table 1 and Fig. 6). Lastly, RF models identified late-season GPP (November) as a marginal predictor of fruit production.

Among the predictors selected to explain the variance in beech fruit production, ∆T(Jun-Jul)-1-2 was clearly dominant, and made the partial dependence of the remaining variables look rather flat (Fig. 6). A positive difference in summer temperatures between the two previous years (i.e. the summer of year -1 warmer than the summer of year -2) led to a ~ 3-fold fruit biomass increase (Fig. 6). Warmer conditions in current February and October also promoted annual fruit production. The respective thresholds were 6°C and 11°C, corresponding to rises in biomass values of 45% and 67%. In contrast, a warm summer two years before fruit production (~17°C threshold) decreased annual production by 40% (Fig. 6). Finally, daily values of airborne pollen concentrations above 5 gr m -3 led to a 30% increase of biomass. Increasing November GPP also promoted biomass, with a threshold value of 5 gC m -2 (+20%, Fig. 6).

Conditioning plots showed that when summer temperature differences (∆T) were negative (i.e.

when the summer of year-1 was colder than the summer of year-2), the fruit biomass remained low whatever the values of the other parameters (Fig. 7a-c). Thus, pollen and autumn environmental drivers (temperature in October or GPP in November) promoted biomass more efficiently in the case of positive differences in summer temperatures between the two previous years. Similarly to oak, the RF models overestimated observed low values and underestimated observed high fruit production values (Online Resource 9).

Discussion

Contrasting determinants of fruit production in oak and beech

In oak, fruit production in year y increased with current spring temperatures (Fig. 4), as already observed across the Quercus genus under both warm temperate (Fearer et al. 2008) and Mediterranean climates [START_REF] Koenig | Acorn production by oaks in central coastal California: Influence of weather at three levels[END_REF][START_REF] Pearse | Cues versus proximate drivers: testing the mechanism behind masting behavior[END_REF]. More precisely, we evidenced that temperatures during the 16-day window following the start of pollen emission was a key predictor of fruit production in oak. These results support the pollen synchrony hypothesis already reported in oak (Bogdziewicz et al. 2017a, b for Q. petraea, Q. robur and Q. ilex and [START_REF] Koenig | What drives masting? The phenological synchrony hypothesis[END_REF] for Californian oaks). Moreover, they are reinforced by the negative correlation observed in our data between pollen emission duration and temperature (Spearman ρ=-0.53, p<10 -9 , Online Resource 10). Interestingly, we did not identify pollen count data as a predictor of fruit production in oak; this suggests that the measured regional air pollen concentration was not a critical determinant of fruit production in our dataset. Similar observations were made on oaks in Eastern [START_REF] Kasprzyk | Relationships among weather parameters, airborne pollen and seed crops of Fagus and Quercus in Poland[END_REF]Bogdziewicz et al. 2017b) and Mediterranean Europe (Fernandez-Martinez et al. 2012), in line with the decoupling of flower and fruit production (Ducousso et al. 1993;Bogdziewicz et al. 2017b) in these species.

Oaks are highly self-incompatible (Ducousso et al. 1993). Therefore we hypothesize that years of high synchronization of pollen emission among trees is characterised by high competition among pollen grains emitted by genetically (hence phenologically) distant individuals, favouring pollination success (Almeida-Neto and Lewinsohn 2004; [START_REF] Savolainen | Gene flow and local adaptation in trees[END_REF]). On the other hand, in years of low synchronization, female flowers would more frequently be pollinated by pollen emitted by genetically similar trees, belonging to their phenological class (e.g. "early" or "late" tree), yielding a lower pollination success due to higher genetic resemblance. More generally, we should point out that most of the discussions about pollination success [START_REF] Pearse | Pollen limitation and flower abortion in a wind-pollinated, masting tree[END_REF], Bogdziewicz et al. 2017a, b) take into account pollen emissions, but rarely take into account female flower responsiveness [START_REF] Rapp | Sex allocation, pollen limitation and masting in whitebark pine[END_REF]). Yet this latter point deserves attention because the development of male and female flowers is asynchronous (protandry) in oak, and the time window of pistillate flower responsiveness is rather short (Ducousso et al. 1993). Thermal dependence of flower formation can be hypothesized to interpret the positive dependence of fruit production of year y September temperatures on year -1 (y-1) September temperatures (Fig. 4), but finds no direct support in the literature.

Aside from the prominent influence of temperature, our results show that oak fruit production may be limited by resource (carbon and water) availability. We evidenced a positive dependence of acorn production on the August carbon (GPP) and water availability of the current year, when the phenological synchrony limitation is released (Fig. 5). This result is coherent with data showing that the mass development of acorns occurs mostly in August-September in northern temperate oaks [START_REF] Sharp | Flowering and fruiting in white oaks, pistillate flowering acorn development weather and yields[END_REF][START_REF] Bonnet-Masimbert | Biologie florale et cycle de reproduction de quelques arbres forestiers. Douglas, pin sylvestre, chêne[END_REF]N. Delpierre, unpublished results on sessile oak). With respect to carbon, these results confirm the role of current-year photosynthesis [START_REF] Hoch | Fruit production in three masting tree species does not rely on stored carbon reserves[END_REF][START_REF] Ichie | Are stored carbohydrates necessary for seed production in temperate deciduous trees?[END_REF][START_REF] Han | Recent developments in understanding mast seeding in relation to dynamics of carbon and nitrogen resources in temperate trees[END_REF], as opposed to dependence on carbon reserves accumulated during previous years. RF analysis indeed did not retain simulated carbon reserves or previous-year GPP or previous-year acorn crop as influent predictors of current-year acorn production. The small but positive influence of the August water balance was not particularly expected in these mesic forests (as opposed to its usual mention under Mediterranean climates, e.g. Perez-Ramos et al. 2010, Bogdziewicz et al. 2017a), and will deserve further investigations. It may echo the higher sensitivity of organ growth to water limitation, as compared to the sensitivity of photosynthesis, [START_REF] Hsiao | Plant responses to water deficits, water-use efficiency and drought resistance[END_REF][START_REF] Körner | Paradigm shift in plant growth control[END_REF], reported for wood growth in mesic conditions (Delpierre et al.

2016a).

In beech, our results confirm a prominent relationship with the temperature differential index (∆T) of the two previous years, as initially proposed by [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF] and reported in [START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. The functional interpretation of temperature differential indexes has been discussed by [START_REF] Pearse | Cues versus proximate drivers: testing the mechanism behind masting behavior[END_REF]. These authors showed that the success of ∆T to explain interannual variability of Quercus lobata fruit production was "not as a cue but rather explained by its close relationship to the proximate drivers that have a direct, mechanistic relationship with acorn crop size". The proximate drivers in question were temperature during previous April (related to the pollen coupling hypothesis) and the previous-year acorn crop (related to the resource-limitation hypothesis). Our RF modelling approach included putative predictors related to both sets of hypotheses (i.e. pollen weather conditions for pollen coupling, and simulated C resources in the previous years for resource-limitation). The fact that these variables were not included in the final RF models (Table 1) suggests a low impact of these drivers on fruit production in beech, leaving open the question of the functional meaning of ∆T [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF]. We further noticed that removing ∆T or T from the set of putative drivers over the previous years did not allow for previous-year resource variables to enter the RF model, whether simulated from CASTANEA or measured on the previous year crop. This did not support the resource-limitation or resource-signalling hypothesis (postulated e.g. in [START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]). However, we highlighted that a large part of our C-resource variables were simulated, not measured (except on previous year crops). Although the model we used for simulations fitted well with measured C flux (Delpierre et al. 2012), wood growth [START_REF] Guillemot | Environmental control of carbon allocation matters for modelling forest growth[END_REF]) and C reserve (Davi et al. 2009) data, its evaluation in the RENECOFOR stands remained partial. Therefore we cannot be fully sure about the validity of the C-resource data used in the RF approach. We did not include simulated N resources [START_REF] Han | Nitrogen storage dynamics are affected by masting events in Fagus crenata[END_REF] Besides the influence of ∆T, we evidenced positive relationships between fruit production in beech and current-year February and October temperatures, as well as with November GPP (Fig. 6). The latter was not particularly expected because (i) only a small part of fruit production is shed in November in beech [START_REF] Lebret | Litter production in an Atlantic beech (Fagus sylvatica L.) time sequence[END_REF], and (ii) fruit maturation (i.e. fruit mass increase) is reported to occur much earlier, in July and August [START_REF] Oswald | Floraison, pollinisation et fructification chez le Hêtre (Fagus sylvatica L.)[END_REF]. Interestingly, the ∆T variable fully eclipsed the role of the airborne pollen load, which appeared as the most important predictor of fruit production in beech [START_REF] Kasprzyk | Relationships among weather parameters, airborne pollen and seed crops of Fagus and Quercus in Poland[END_REF]Bogdziewicz et al. 2017b) when ∆T was not taken into account (data not shown, but in this "no-∆T" model, the R²=0.28 was much lower than in the present model R²>0.40, Table 1). In both cases (i.e. considering ∆T or not in the RF model), we observed a clear threshold-type dependence of fruit production on the airborne pollen load (Fig. 6). The average beech airborne pollen concentration in the RNSA data (7 grains m -3 of air) was one order of magnitude lower than for oak (41 grains m -3 of air), consistent with other datasets accounting for the relative abundances of tree species [START_REF] Geburek | Temporal pollen pattern in temperate trees: expedience or fate?[END_REF]. We hypothesized that these low pollen loads reduced the probability of pollination [START_REF] Lyles | Plant reproduction and environmental noise: How do plants do it?[END_REF] and in turn fructification in beech. Beech airborne pollen loads showed a distinct biennial pattern (Fig. 2d and3d), which echoed the bienniality of floral initiation already reported in this species [START_REF] Bonnet-Masimbert | Biologie florale et cycle de reproduction de quelques arbres forestiers. Douglas, pin sylvestre, chêne[END_REF]. Bienniality is possibly caused by hormonal inhibition of reproductive bud initiation during a year of fruit production, similarly to observations in orchard trees (Mc Laughlin and Greene 1991).

Descriptive power of statistical analyses for fructification time series

We chose to work on quantitative, continuous fructification data, contrary to other approaches based on semi-quantitative categorical tree crop data (Drobyshev et al. 2010;[START_REF] Hacket-Pain | The influence of masting phenomenon on growth-climate relationships in trees: explaining the influence of previous summers' climate on ring width[END_REF][START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. Whichever the data type (quantitative or categorical), analyses of long-term forest tree fructification time series are characterised by their low descriptive power.

A review of the literature showed that the percentage of variance in the fructification time series explained by statistical models steeply decreases with the number of site-years (Online Resources 11 and 12). This pattern probably arose from the progressive reduction ability of statistical models to describe datasets of increasing variance related to environmental conditions and/or population ontogeny or genetic differentiation. As we aimed to describe spatio-temporal variation of fruit production across temperate forests, we gave the opportunity to our machinelearning approach to include both spatial (stand age, dendrometric measurements, soil nutrient and water reserve characteristics) and spatio-temporal (pollen, weather-related and simulated carbon fluxes) predictors. Since spatial predictors were systematically excluded by the RF algorithm, we can conclude that populations cannot be differentiated based on the site characteristics we tested.

Another source of variance that possibly affected the descriptive ability of our approach is the presence of noise in both the dependent variables (fructification time series) and predictors. The average amount of fruit produced per stand area unit was difficult to measure in forests1 (Online Resource 13), notably in tree species presenting pulsed intermittent fruit production characterised by a very large amplitude. Contrary to most published studies, we worked with natural quantitative biomass data (not log-transformed or categorical data, Online Resource 11).

We believe that an accurate description of the spatio-temporal variability of fruit production (which is by essence highly variable, hence heteroscedastic, in temperate forests) will be best approached using quantitative biomass data because they preserve the natural variability of the signal. This natural variability needs to be described if we are to extrapolate the results in a quantitative mechanistic framework aimed at understanding the impact of fructification on ecosystem functioning. The RF framework we used for our analysis was a non-parametric method, therefore free of any assumption about data distribution [START_REF] Breiman | RandomForests[END_REF].

The pollen count data used as predictors were not measured in forests, but in urban areas located 4 to 101 (mean 65) km from the RENECOFOR stands. For beech, the overall cross-site synchronicity of the pollen time series (54% of site pair combinations yielded significant correlations of their pollen rank time series) gave us confidence in the use of distant pollen data as a proxy for local forest pollen concentrations. Pollen time series were much less synchronous across oak stands (23% of stand pair combinations yielded significant correlations of their pollen rank time series). Such spatial heterogeneity may have compromised the use of distant pollen measurements as representative estimates of local pollen concentrations.

Assessing the hypothesis of a growth vs. reproduction trade-off

The hypothesis-testing of a trade-off between traits is often impaired by multiple collinearities among the candidate traits and environmental variables [START_REF] Knops | Negative correlation does not imply a tradeoff between growth and reproduction in California oaks[END_REF][START_REF] Hacket-Pain | The influence of masting phenomenon on growth-climate relationships in trees: explaining the influence of previous summers' climate on ring width[END_REF]. To avoid such a hurdle, we first standardized tree ring width data (TRW, a proxy for tree secondary growth, Online Resource 5) and thereafter used ring width indexes as predictors in the RF model. We observed a positive link between growth and the stand reproductive effort in oak (Fig. 4), so that no trade-off was observed in this dataset between these two carbon sinks.

Such positive relationships have already been observed in both temperate and Mediterranean

Quercus species at the population level [START_REF] Askeyev | The effect of climate on the phenology, acorn crop and radial increment of pedunculate oak (Quercus robur) in the middle Volga region, Tatarstan, Russia[END_REF]Perez-Ramos et al. 2010;[START_REF] Alla | Acorn production is linked to secondary growth but not to declining carbohydrate concentrations in current-year shoots of two oak species[END_REF][START_REF] Martin | Trade-off between stem growth and acorn production in holm oak[END_REF], while negative relationships have also been reported at the individual tree level [START_REF] Martin | Trade-off between stem growth and acorn production in holm oak[END_REF]. Together with the identification of positive links between summer (August) carbon and water availability on fruit production (Fig. 5), these results support the hypothesis that resource availability is an important driver of plant production in Quercus species: "good" production years favour structural C investments in multiple tissues (Perez-Ramos et al. 2010).

Our dataset was more restricted for beech stands, with only 66 site-years' worth of TRW data collected in only 5 stands, so that we did not include this predictor in the main analysis. Yet, the RF analysis conducted on this shorter dataset revealed an opposite pattern in beech as compared to oak (Online Resource 14). In beech, the link between secondary growth and reproductive effort was negative. This confirms a trade-off between these two traits, as already exposed in the literature for this species (Drobyshev et al. 2010;[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] Hacket-Pain | The influence of masting phenomenon on growth-climate relationships in trees: explaining the influence of previous summers' climate on ring width[END_REF], and more generally in the Fagus genus [START_REF] Kon | Proximate factors causing mast seeding in Fagus crenata: the effects of resource level and weather cues[END_REF].

Finally, since previous-year C resources were not selected in the fruit production models, the hypothesis of C-resource accumulation as a necessary condition for fruiting (termed resourcestorage in [START_REF] Pearse | Mechanisms of mast seeding: resources, weather, cues, and selection[END_REF] is not supported by our results.

Conclusions and perspectives

We tested the influence of weather conditions, airborne pollen (under the form of both pollen load and pollen climatology), and carbon and water resources as putative predictors of fruit production. In oak, our results confirmed that fruit production was linked to temperature cues, and further evidenced a marginal positive dependence on current summer carbon and water resources. Temperatures during the pollen emission period were the best predictor of fruit production, supporting the pollen synchrony hypothesis based on an unprecedented large dataset (see Bogdziewicz et al. 2017b for evidence on a smaller dataset). In a previous study conducted on the same tree populations, we identified carbon acquisition as the main ̶ but not sole ̶ driver of wood production in oak [START_REF] Guillemot | 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[END_REF]. Since the role of carbon inputs appeared to be of secondary importance as regards fruit production, our results point to a differential role of resource (carbon) availability in the limitation of organ (wood vs. fruits) growth in oak. In beech, our results confirmed earlier studies reporting a trade-off between secondary growth and reproductive effort. We further confirmed that fructification of beech was primarily related to the differential summer temperature index (∆T, [START_REF] Kelly | Of mast and mean: differentialtemperature cue makes mast seeding insensitive to climate change[END_REF]. Our results add to the discussion relative to the interpretation of the ∆T index since the RF approach did not select variables of previous-year resources, whether under the form of simulated C fluxes from the two preceding years or the form of previous-year fruit crop, considered jointly with ∆T in the same RF model or separately from ∆T in another RF model. Yet, these variables have been found or hypothesized as correlated with the ∆T index [START_REF] Monks | Resource limitation underlying multiple masting models makes mast seeding sensitive to future climate change[END_REF][START_REF] Vacchiano | Spatial patterns and broad-scale weather cues of beech mast seeding in Europe[END_REF]. When ∆T was not taken into account, the RF model pointed to the amount of airborne pollen as the best predictor of fruit production in beech. All processes involving pollen, i.e. initiation and maturation of male flowers, anther dehiscence, pollen flight, and pollination, respond to environmental cues. Internal (carbon and/or nutrient resource) tree limitations also respond to environmental cues, but they remain largely unknown and deserve further investigations.

Our study aimed to understand the sources of variability of fruit production in temperate deciduous trees throughout large spatial and temporal scales. To this aim, we used climate, Cresource and pollen-related variables aggregated from months to years. We believe that further progress could arise from the identification of finer time windows, in relation to flower/fruit development phenophases (e.g. see [START_REF] Sharp | Flowering and fruiting in white oaks, pistillate flowering acorn development weather and yields[END_REF].

Finally, the formulation of a realistic process-based model of fruit production requires further work. This is obvious when considering the low to moderate share of variance explained by the non-parametric RF method across our large dataset (ca. 16% and 45% of variance in the fruit signals explained in oak and beech, respectively). Candidate approaches for investigation will notably imply refining the coarse description of resource availability currently used in resourcebudget models [START_REF] Abe | Parameterisation and validation of a resource budget model for masting using spatiotemporal flowering data of individual trees[END_REF]. For example, these models will have to be coupled with ecophysiological models able to simulate the dynamics of carbon, water (Delpierre et al. 1 for details. Table 1. Summary of the different RandomForest models obtained for the two species and fruit biomass (Biom. in kg ha -1 y -1 ). Each model gives the percentages of explained variance, and the RMSEs on the adjusted and predicted values obtained with the six best predictors. For the retained predictors: 1 or 2 = previous years (-1= one year, -2 = two years); capital letters: parameter type; small letters: month or period (except for PolSeas and ResRW). jas = mean value from July to September; as = mean value from August to September; Tpol16 = mean temperature during the first 16 days of pollen emission (in °C). ∆T(Jun to Jul)-1-2 = Difference (in °C) between mean June to July summer temperatures in year -1 and year -2; T(Jun-Jul)-2 = Difference (in °C) between mean temperatures in June and July in year -2; PolSeas = mean daily number of pollen grains emitted during the pollen emission period (gr. m -3 ). Fruit number results (numbers of fruit ha -1 y -1 ) were similar but with higher percentages of explained variance (18.2 to 26.8 for Quercus,and 41.6 to 48.4

Online Resource 7 Synchrony between stands and changes with distance

To judge the synchrony of fruit production between stands and to see how it changes with distance, we selected stands with a complete data set. Thus, for oak stands, we selected 15 sites with 13 continuous years from 1995-2007 (195 site-years data; 105 different pairs, QR49 vs QP61, QR49 vs QP86,…). For beech, we selected also 15 sites with 12 years from 1995-2006 (180 site-years data; 105 different pairs). We calculated the distance between sites for each pair (Figure 1). For beech, the distance varied from 33 (distance between FS60 and FS02) to 1118 km (FS29 and FS04) with a mean value of 543 (±255) km. For oak, the mean distance was 284 (±127) km with a range from 12 (QR10 and QP10) to 584 km (QP86 and QP57b).

To highlight how the fruit production was correlated between stands, we calculated a correlogram (i.e. correlation matrix) for oak and beech. It allows to analyze the relationship between each pair of numerical variables (here fruit production for each year) of a matrix. The correlation between each pair of variable is visualize through a scatterplot that represents the correlation (corrplot package in R). A synchrony between stands means that fruit production is synchronized (i.e. similar temporal variations) especially for the nearest stands.

Synchrony for oak

The correlogram clearly showed that synchrony between oak stands was weak despite the proximity of the stands (mean distance 284 km) (Figure 2). Thus, the correlation between fruit production was significant (p.value = 0.05) for only 8 pairs (among the 105). QP10-QR59 (dist. 213), QP10-QR70 (139), QP10-QP57a (235), QR70-QR59 (312), QR70-QP57a (112), QP57a-QR71 (230), QP41-QP57b (487 km), QP41-QP86 (119km). No correlation was observed for the nearest stands (QP10-QR10, 12 km; QP21-QR71, 19 km; QP27-QP60, 58 km; QP57a-QP57b, 74 km; QR70-QP01, 88 km…).

Synchrony for beech

The results for beech was quite different with 44 significant correlation confirming the high synchrony between stands despite the distance (mean distance 543 km) (Figure 3). Only one stand (FS29) showed no correlation. The figure 4 shows the change of the frequency of significant correlations between stands according to the distance between the pairs. For example, for the class [0-200] km, the mean distance between the 9 pairs was 134 km. For this class, 6 correlations were significant at the p.value = 0.05 (=66% of significant correlations) and the mean correlation was 0.86. The frequency of significant correlations remained high until the distance of about 500 km and decreased hereafter.

The different clustering tested confirmed the decreasing correlation with increasing distance (Figure 5). The highest synchrony was observed for stands distant from less than 200 km. A sharp decrease was observed for a distance higher than 500 km.

Online Resource 8 Predicted mean fruit biomass of acorns obtained with the CGPW model (Pred.) versus observed values (Obs.) for the 23 oaks stands (n=256 data). The number of over-and underestimations by class of differences (between observations and predictions) and the related means are given. For example, 27 predictions showed a difference between observed and predicted values ≤ 10% : 11 values are overestimated (mean difference: 12 kg ha

  : model C included only climate data; model CG included simulated carbon balance (GPP, NPP, tree C reserves) data in addition to model C; model CGP included pollen data in addition to model CG; model CGPCP included pollen meteorology data in addition to model CGP; model CGPW (for oak) included tree-ring

  requirement in the modeling effort to reduce the risk of overfitting (Evans et al. 2009), only the six best candidate predictors were retained for each final model. Relationships among predictors were also analyzed to avoid collinearity problem (Dormann et al. 2013) (Online Resource 15).

  in our analyses because CASTANEA simulations of the N cycle still need validation against local data.

  Fig. 1 Geographical location of the 48 broadleaved stands of the RENECOFOR network and the 81 climatic stations of the Météo-France network. Black circles: 28 Quercus plots (9 Quercus robur and 19 Quercus petraea plots); Grey triangles: 20 Fagus sylvatica stands; Crosses: 81 climatic stations (36 with rainfall (R) only; 33 with temperatures (T) only; 12 with both R and T (Source: Météo-France)).

Fig. 2

 2 Fig. 2 Interannual variability of fruit biomass production (a, b) and air pollen concentrations (c, d) in the French temperate deciduous forests of the RENECOFOR network. Grey lines depict measured (fruit) or inferred (pollen) data at the individual stand level. The black line depicts interannual variation of the median value, established across stands.

Fig. 3

 3 Fig. 3 Periodograms of fruit biomass production (a, b) and air pollen concentration (c, d) time series in French temperate deciduous forests of the RENECOFOR network. Grey lines depict established periodograms at the individual stand level. The black line depicts interannual variation of the median value, established across stands.

Fig. 4

 4 Fig. 4 Partial dependence plots of the six best significant predictors for predicted acorn biomass in the 23 oak stands (n=256 data) for the CGPW model. Each plot gives a graphical description of the effect of the predictor and highlights threshold response effects. The last graph gives VIMP and DEPTH values for each predictor (sorted from VIMP values). See text andTable 1

Fig. 5

 5 Fig. 5 Conditioning plots of fruit production in the 23 oak stands (n=256 data). Predicted fruit biomass (kg ha -1 y -1 ) as a function of the mean temperature during the first 16 days of pollen emission (Tpol16 in °C) stratified by [a] April temperatures (°C), [b] tree-ring growth (ResRW, no unit), [c] Climatic Water Balance in August (mm) or [d] Gross Primary Productivity in August (gC m -2 ) (see text for details).

Fig. 6

 6 Fig. 6 Partial dependence plots of the six best significant predictors for nut biomass in the 20 beech stands (n=204 data). Each plot gives a graphical depiction of the effect of the predictor and highlights threshold response effects of the CGP* model. The last graph gives VIMP and DEPTH values for each predictor. See text andTable 1 for details.

Fig. 7

 7 Fig. 7 Conditioning plots of fruit production for the 20 beech stands (n=204 data). Predicted fruit biomass (kg ha -1 y -1 ) as a function of summer temperature (mean June and July) differences between years -1 and -2 (∆T in °C) stratified by mean daily air pollen concentrations during the emission period (gr m -3 ) [a], current mean temperature in October (°C) [b], or Gross Primary Productivity in November (gC m -2 ) [c] (see text for details).

Figure 1 .

 1 Figure 1. Distance (in km) between each pair for beech and oak stands. 15 stands for each species and 105 different pairs. The mean distance is 543 km for beech and 284 for oaks.

Figure 2 .

 2 Figure 2. Correlogram for oak stands (15 stands, 105 pairs). A circle indicates a significant correlation (p. value = 0.05) for fruit production between stands. The color and the size of the circle change with the sign of the correlation (from blue o red) and the value (increasing size with increasing value). QR = Quercus robur and QP = Quercus petraea. The number represents the French department.

Figure 3 .

 3 Figure 3. Correlogram for beech stands (15 stands, 105 pairs). A circle indicates a significant correlation (p. value = 0.05) for fruit production between stands. The color and the size of the circle change with the sign of the correlation (from blue o red) and the value (increasing size with increasing value). FS = Fagus sylvatica.The number represents the French department.

Figure 4 .Figure 5 .

 45 Figure 4. Change of the frequency of significant correlations (p. value = 0.05) between beech stands according to the distance between the pairs (n = 15 stands, 105 different pairs). The number above the blue histogram is the

GPP-NPP Pollen Climate Pol groWth

  for Fagus). CGP*: model without NAO values. var. adj. pred.

	Quercus petrae and robur (23 stands and 256 data)
	Type model	% expl. Nb Climate GPP-NPP Pollen Climate Pol groWth var. adj. pred. RMSE Pool of candidate predictors		(sorted by decreasing vimp values) Retained predictors
	C	285 285	x	x	x	x	13.6 173 381	Tapr	CWBaug CWBapr	PETjas -1	Tjas -1	Tas
	CG	407 285	122	x	x	x	14.7 173 379	Tapr	GPPas	CWBaug	Tsep -1	Taug -1 CWBapr
	CGP	414 285	122	7	x	x	idem CG			idem CG
	CGPCP 522 285	122	7	108	x	16.2 169 375	Tpol16	Tapr	Tsep -1	CWBaug	CWBapr GPPaug
	CGPW	524 285	122	7	108	2	16.1 168 373	Tpol16	Tapr	ResRW	Tsep -1	CWBaug GPPaug
	Fagus sylvatica (20 stands and 204 data)
	285 285 Nb Climate C Pool of candidate predictors x x x Type model	x	% expl. 44.2 106 242 ∆T(Jun to Jul) -1-2 RMSE	Toct (sorted by decreasing vimp values) Tfeb T(Jun-Jul) -2 NAOapr PETfeb Retained predictors
	CG	407 285	122	x	x	x	46.3 104 238 ∆T(Jun to Jul) -1-2	Toct	Tfeb	T(Jun-Jul) -2 GPPnov NAOapr
	CGP	414 285	122	7	x	x	43.1 108 246 ∆T(Jun to Jul) -1-2	Toct	PolSeas	T(Jun-Jul) -2	Tfeb	NAOapr
	CGP*	402 273	122	7	x	x	42.9 108 246 ∆T(Jun to Jul) -1-2	Toct	Tfeb	PolSeas T(Jun-Jul) -2 GPPnov
	CGPCP 522 285	122	7	108	x	idem CGP			idem CGP

Short legends for Online Resources (Figures and Tables)

  Online Resource 1 Ecological characteristics of the RENECOFOR network stands

	Species	Site code	Name of the forest	Long. Lat. Altitude Slope Aspect (m) (% )	Pr Climate Te	SWHCm Humus (mm) C/N	C/N pH S/T Soil horizon (0-10 cm) N	P	C/N pH S/T Soil horizon (20-40 cm) N	P
		QR 10	de Larivour	4.30 48.34	115	0	/	656 11.2	120	24.0	14.0 4.0 81.8	3	0.025 12.0 4.1 87.2 1.1 0.008
	Quercus robur (n=9)	QR 18 QR 40 QR 49 QR 55 QR 59 QR 65 QR 70	de Verneuil de Gamarde de Monnaie de Haudronville de Mormal d'Azereix d'Anjeux	2.57 46.83 -0.84 43.74 -0.04 47.46 5.77 49.02 3.75 50.17 -0.04 43.20 6.22 47.88	175 20 57 220 149 370 240	0 5 0 0 3 12 0	/ NE / / / SE /	799 11.8 1124 14.4 770 11.6 741 11.0 699 10.6 1423 13.6 1199 10.5	175 140 170 150 200 140 170	32.0 35.0 28.0 35.0 23.0 41.0 25.0	18.0 4.2 86.6 13.0 4.5 79.4 14.0 3.8 62.8 15.0 4.3 84.7 13.0 3.6 27 12.0 4.2 38.6 14.0 4.2 60.8	2.2 1.2 1 2.8 2.3 2.5 1.7	0.013 17.0 4.3 92.2 0.9 0.005 0.015 11.0 4.4 77 0.6 0.006 0.014 5.0 4.2 32.1 0.25 0.005 0.043 12.0 4.3 88.8 1 0.007 0.043 12.0 4.1 57.7 0.8 0.017 0.013 9.0 4.2 22.2 1.4 0.005 0.022 13.0 4.2 46.9 0.8 0.01
		QR 71	de Pourlans	5.24 46.96	190	0	/	818 11.5	180	40.0	15.0 4.0 52.8	1.5	0.026 14.0 4.1 62.1 0.7 0.011
		QP 01	de Seillon	5.24 46.17	260	3	/	1360 12.0	170	22.0	12.0 4.1 18.6	3.5	0.022 13.0 4.1 10.8 0.8 0.008
		QP 03	de Tronçais	2.73 46.67	260	0	/	774 11.7	75	28.0	17.0 3.8	35	1.4	0.02 16.0 4.2 22.1 0.4 0.009
		QP 10	du Temple	4.45 48.30	160	0	/	656 11.2	200	26.0	18.0 3.7 26.5	1.5	0.028 10.0 3.8 26.4 0.7 0.006
		QP 18	de Vierzon	2.13 47.25	176	1	/	772 12.3	130	31.0	18.0 3.7 22.4	1	0.014 20.0 4.1 7.9 0.31 0.005
		QP 21	de Citeaux	5.07 47.07	220	0	/	818 11.5	200	32.0	15.0 4.1 50.1	1.3	0.018 16.0 4.1 38.1 0.5 0.004
	Quercus petraea (n = 19)	QP 27 QP 35 QP 41 QP 51 QP 57a QP 57b QP 58 QP 60 QP 61	de Lyons de Rennes de Blois de Chatrices d'Amelecourt de Mouterhouse de Vincence de Hez-Froidmont de Reno Valdieu	1.50 49.37 -1.54 48.18 1.26 47.56 4.96 49.03 6.48 48.86 7.46 49.02 3.66 46.96 2.29 49.39 0.67 48.52	175 80 127 180 315 320 270 55 220	0 0 0 2 4 15 15 1 5	/ / / S NE NW SW / SE	878 11.3 702 12.4 672 11.8 815 9.9 745 10.4 982 10.0 806 11.2 653 10.9 841 10.4	170 120 175 55 140 80 150 125 110	30.0 22.0 36.0 28.0 31.0 26.0 38.0 25.0 29.0	18.0 3.8 23.8 22.0 3.4 9.2 19.0 3.7 30.5 20.0 3.3 43.5 13.0 4.0 40.5 22.0 3.2 13.9 16.0 4.2 44.7 13.0 3.8 49.5 17.0 3.8 43	1.9 2 2.3 2 1.44 0.035 11.0 3.9 25.9 0.81 0.021 0.025 13.0 3.9 24.4 0.64 0.005 0.019 11.0 4.1 6.8 0.67 0.009 0.023 16.0 3.8 12.9 0.4 0.005 0.036 19.0 3.4 21 0.62 0.014 2 0.014 24.0 4.3 6.2 0.4 0.005 1.7 0.015 14.0 4.1 24.1 0.9 0.007 1.3 0.031 13.0 3.9 34.7 0.3 0.004 2.5 0.013 15.0 3.8 31.7 1 0.004
		QP 68	de la Hardt	7.47 47.69	256	0	/	792 10.9	85	29.0	16.0 4.0 39.3	1.9	0.062 16.0 4.1 18.9 0.6	0.02
		QP 72	de Bercé	0.38 47.79	170	0	/	715 12.3	135	24.0	23.0 3.5 21.4	1.7	0.028 24.0 3.9 9.4	0.2 0.005
		QP 81	de Grésigne	1.75 44.04	300	18	SE	867 12.8	85	38.0	18.0 3.7 28.5	3.1	0.028 14.0 3.9 22	0.7 0.003
		QP 86	de Moulière	0.49 46.62	116	4	NW	713 12.0	80	24.0	23.0 3.2 26.8	1.8	0.02 25.0 4.0 6.4	0.4 0.005
		QP 88	de Darney	6.04 48.02	330	0	/	1427 10.3	185	37.0	17.0 4.0 26.7	2.1	0.026 14.0 4.0 22.4 0.8 0.011
		FS 02	de Retz	3.13 49.19	145	0	/	623 12.0	200	31.0	15.0 3.9 40.9	1.4	0.049 11.0 3.9 40.5 0.6 0.019
		FS 03	des Colettes	3.00 46.19	590	15	N	838 11.0	88	30.0	19.0 3.7 16.9	2.4	0.013 11.0 4.1 7.2	0.7 0.005
		FS 04	du Jabron	5.80 44.13	1300	50	N	708 13.2	120	30.0	16.0 6.0	100	3.3	0.014 12.0 7.4 100	2.2 0.006
		FS 09	de Soulan	1.28 42.93	1250	32	SW	1666 10.4	100	30.0	16.0 3.7 21.6	6.5	0.014 15.0 4.1 9.4	2.9 0.006
		FS 14	de Cerisy	-0.86 49.18	90	4	/	848 11.3	95	22.0	18.0 3.6 14.4	2.5	0.021 14.0 4.1 6.8	0.8 0.007
		FS 21	de Lugny	4.86 47.81	400	3	NE	865 10.6	55	42.0	18.0 6.0	100	5.7	0.037 13.0 7.4 100	3	0.019
	Fagus sylvatica (n=20)	FS 25 FS 26 FS 29 FS 30 FS 52 FS 54a FS 54b FS 55	de la Verrière du Grosbois de Lente de Carnoet de l'Aigoual d'Auberive des Hauts Bois de Haye de Lachalade	6.27 47.18 5.30 44.92 -3.54 47.84 3.55 44.12 5.07 47.80 6.71 48.51 6.07 48.65 5.00 49.17	570 1320 50 1400 440 325 390 250	2 12 0 25 0 5 2 0	W W / SW / E / /	1352 9.0 1712 12.2 942 12.2 2014 5.6 996 10.0 780 10.9 780 10.9 834 11.5	105 50 140 50 45 110 60 80	29.0 28.0 26.0 23.0 40.0 45.0 34.0 30.0	14.0 5.2 14.0 5.9 20.0 4.3 18.1 100 100 22.0 3.7 17.9 15.0 6.4 100 16.0 4.1 39.5 14.0 5.0 100 20.0 3.8 18.5	3.8 7.8 2.4 4.4 3 1.7 4.3 0.9	0.028 11.0 4.8 100 0.04 11.0 6.9 100 0.034 17.0 4.2 15.1 0.8 0.014 1.9 0.009 4.9 0.019 0.024 21.0 4.2 9.5 2.4 0.026 0.009 12.0 7.4 100 1.7 0.004 0.025 14.0 4.1 12.7 0.7 0.009 0.012 11.0 7.2 100 3.4 0.009 0.013 16.0 4.0 8.1 0.3 0.005
		FS 60	de Compiègne	2.87 49.32	138	0	/	738 11.2	88	35.0	16.0 4.9	100	2.2	0.026 12.0 6.2 100	0.6 0.005
		FS 64	d'Ance	-0.66 43.15	400	44	NW	1422 13.5	110	35.0	13.0 4.3 76.8	2.2	0.012 9.0 4.2 63.1 1.1 0.014
		FS 65	de Bize	0.44 43.03	850	25	NW	1058 12.7	88	29.0	16.0 3.7	20	4.7	0.095 9.0 4.1 7.3	1.9 0.032
		FS 76	d'Eawy	1.33 49.72	210	0	/	920 10.5	145	26.0	16.0 3.7 15.3	1.7	0.018 12.0 4.1 6.8	0.5	0.01
		FS 81	de la Montagne Noire	2.18 43.41	700	0	/	1144 11.5	100	27.0	15.0 3.9 19.1	4.8	0.053 14.0 4.3 11	1.7 0.026
		FS 88	du Ban d'Harol	6.24 48.11	400	3	W	1427 10.4	100	32.0	15.0 3.9 14.1	1.4	0.011 16.0 4.0 11.9 0.7 0.005

  Online Resource 8 Mean predicted acorn biomass obtained with the CGPW model versus observed values

		Biomass (kg ha	-1 y -1 )
	Dif. Class	Obs. Pred.	N Mean N Mean Nt Underestim. Overestim.
	≤ 10% 319 315 11 12	16	-20 27
	]10-20%] 370 344 10 33	16	-85 26
	]20-30%] 523 464 8	75	25 -192 33
	]30-40%] 578 453 13 76	16 -325 29
	]40-50%] 503 381 2	96	4	-340 6
	>50%	39 133 135 94	135

e.g. intra-stand spatial variation of fruit production reached an average coefficient of variation of 106% across ten litter traps representing a

2.5-m² sampling area over four years of moderate to good acorn production(2013- 2016) in a temperate sessile oak forest (FR-Fon ICOS research station, www.barbeau.u-psud.fr) (Berveiller D, Delpierre N. and Dufrêne E., unpublished data).

Acknowledgements

This paper builds on data gathered over thousands of hours of field and technical work done by: the Office National des Forêts (ONF) foresters, who collected and classified litterfall data; and collaborators of the RNSA network who prepared and analysed pollen observation data.

We warmly thank them for their work. We thank Hilaire Martin and Baco Said-Allaoui for their work on early related projects, Sebastien Daviller and Raphaël Aussenac for their helpful technical assistance, and Valentin Journé for pointing papers on the seasonality of fruit production in beech. Finally, we thank two anonymous reviewers for constructive comments that helped improving the paper.

Online Resource 12 Percentages of the variance of the fructification datasets explained by statistical models (Table )  Online Resource 13 Spatial variability of fruit crop in a temperate oak forest (FR-Fon, ICOS research station, www.barbeau.u-psud.fr) Online Resource 14 Partial dependence plots of the seven best significant predictors of fruit biomass for the 5 beech stands with tree-ring width data Online Resource 14 Partial dependence plots for the seven best significant predictors for predicted fruit biomass of nuts for the 5 beech stands with tree-ring width data (n=64 data). Each plot gives a graphical depiction of the own effect of the predictor and highlights threshold response effects.VIMP and DEPTH values for each predictor. See Table 1 for the results obtained with the complete dataset (CGP* model).