Forestry Inventory Data Set

The FNFI comprises a network of temporary plots established on a grid of c. 500 × 500 m. If a particular grid node falls within a forested area, a plot is established, the soil type is characterized and the growth of trees determined by dendrometry. We focus on a 66 000-km² study area that extends from the Jura Mountains to the south of the Alps (Fig. 1), within which the climate of the lowlands varies from Mediterranean through oceanic to continental. The mean annual temperature over the period 1980–2000 ranges from 3.5 to 15.7 °C and the mean annual precipitation from 480 to 2220 mm year⁻¹. Data were collected over 10 years, with the timing varying between administrative regions (see Table S1 in Supporting Information). Measurements were taken in three concentric circular plots of different radii, based on diameter at breast height (d.b.h.). All trees with d.b.h. > 7.5 cm, > 22.5 cm and > 37.5 cm were measured within a radius of 6 m, 9 m and 15 m, respectively. For each measured tree, stem diameter, species, status (dead or alive), and radial growth over 5 years were recorded. The radial growth was determined from two short cores taken at breast height. Soil properties were analysed using a soil pit of up to 1 m depth located in the centre of the plot. One or two soil horizons were distinguished from the soil pit, and depth, texture (based on eight classes using the soil texture triangle of Jamagne (1967)) and coarse fragment content were recorded for each horizon. Maximum soil water content was computed based on these three variables, using standard values of water retention for each texture class (Baize & Jabiol 1995).

We selected 16 common tree species for analysis (Table 1) after excluding exotic species, species with fewer than 250 live individuals and sub-canopy trees. In addition, if only the genus of some species had been recorded, such groups were discarded if the constituent species had markedly different ecological strategies (i.e. the group with Acer campestre, Acer opalus and Acer monspessulanum). We also excluded plots if any evidence of a recent (< 5 years) logging operation or disturbance such as fire or wind-throw was recorded during the inventory.

Climatic Variables

Our analysis required climatic data with high spatial resolution, because climate is extremely variable over small distances in mountainous areas. We also needed yearly climatic data because different administrative regions had scheduled data collection for different years, so growth data corresponded to different 5-year windows in different regions. We downscaled the climate data AURHELY of Météo France (1 × 1 km grid; Benichou & Le Breton 1987) to a 100 × 100 m grid using the moving-window regression method of Zimmermann et al. (2007) and a 50 × 50 m digital elevation model (DEM) from Institut Géographique National. We then generated the annual variability of monthly temperature and precipitation data by adding monthly anomalies derived from downscaled time series of the CRU TS 1.2 data set (Mitchell et al. 2003). Using the DEM we also computed mean monthly potential radiation with the Northern Hemisphere corrected method of Kumar, Skidmore & Knowles (1997).

Rather than exploring numerous climatic variables using a lengthy model selection procedure we selected two bioclimatic variables that are known to have strong impacts on tree growth: the degree-day sum over the growing season (DD) and water availability over the growing season (WB). Focusing on these variables helps forge links between our phenomenological approach, process-based models (particularly the model FORCLIM, Bugmann (1996)) and the ecophysiological literature. We calculated DD as the sum of daily temperature for days with average temperature > 5.56 °C over each month of the growing season (defined as the months with an average temperature > 5.56 °C). It was computed across the study area using the interpolation method described in Zimmermann & Kienast (1999). We computed the average DD for the 5 years corresponding to each radial growth measurement. We calculated WB from monthly averages of temperature, precipitation and potential radiation, as well as soil properties, using a ‘bucket approach’ (Bugmann & Cramer 1998; see Appendix S1 in Supporting Information). This involved computing the monthly soil water content (SWCm) for each plot over the period 1980–2001, and then taking WB as the average SWCm over all the months of the growing season within the 5 years corresponding to each radial growth measurement. Species distributions along the two abiotic gradients of DD and WB are represented in Fig. 1.

Crowding Index

An index of crowding (CI) was calculated for each target tree. For each tree i, basal area (m² ha⁻¹) of neighbouring trees on the plot was computed (as divided by the area of the plot where D is d.b.h.). The index of crowding was then computed as the neighbourhood basal area divided by the highest neighbourhood basal area recorded on any of the plots in which the species was present (as Canham et al. 2006). Thus, CI varied between 0 (no crowding) and 1 (maximum crowding) for each species, helping in comparison between species.

Hierarchical Bayesian Modelling

The radial growth of individual trees was modelled as a nonlinear function of bioclimatic variables (DD and WB), local interactions with neighbouring trees (CI) and tree diameter (D) using a hierarchical Bayesian model (Gelman et al. 2004). Separate models were fitted for the 16 selected species. After exploring different forms of the equation for modelling the effects of abiotic variables and crowding on growth, we decided to use eqn 1 as our main model; radial growth of individual i on plot p was modelled as:

(eqn 1)

where α, β₁, β₂, β₃, γ and δ are parameters to be estimated (model M1).

The crowding response curve (CRC) describes the effect of neighbouring trees on the growth of the target tree with a logistic function (see Gómez-Aparicio, Canham & Martin 2008). If δ is positive, the CRC represents a competitive effect and γ represents the value of CI at which growth is reduced by half (see Fig. S1 in Supporting Information). If δ is negative, the CRC represents a facilitative effect (see Fig. S1). A model lacking the crowding effect (i.e. G_pi = α_p × D^β1 × DD^β2 × WB^β3; model M0) was fitted and compared with M1 to test whether CI was an important factor controlling tree growth. Then a series of alternative models were fitted to test the hypothesis that the shape of the CRCs changed with bioclimatic variables DD and WB. We started by fitting models in which δ was a linear function of DD (δ = δ₀ + δ₁ × DD; model M2), WB (δ = δ₀ + δ₁ × WB; model M3), and both bioclimatic variables (δ = δ₀ + δ₁ × DD + δ₂ × WB; model M4). These models allowed us to test whether the process of competition changed along bioclimatic gradients (i.e. more or less growth reduction for a given CI) and whether there was a shift from competition to facilitation (a shift of δ to negative values).

Observations of trees from the same plot p are not independent and the trees share common biotic and abiotic conditions unexplained by our two environmental variables (i.e. soil fertility and pathogen outbreaks). Therefore, we included this unexplained plot-level variability by modelling α_p as a random log-normal variable. The likelihood function for model M1 as well as a detailed description of our priors is given in Appendix S2. We used R.2.7.1 Software (R Development Core Team 2008) for data manipulation and JAGS 1.0.3 (Plummer 2003) for hierarchical Bayesian modelling (the runjags package was used to interface between R and JAGS). We checked for convergence with two Monte Carlo Markov Chains (MCMC) using the potential scale reduction factor Rhat, setting our convergence threshold at Rhat < 1.1 as recommended by Gelman et al. (2004). We ran MCMC for 20 000 iterations with a 5000 burning period and a thinning of 20. The most parsimonious model for each species was selected using the deviance information criterion (DIC; Spiegelhalter et al. 2002). We evaluated the goodness-of-fit of the best model by computing the proportion of deviance explained (1- Deviance of the model/Deviance of model null), the concordance correlation (CC) and the coefficient of determination (R²), as recommended by Huang, Meng & Yang (2009). To evaluate the percentage of variance explained by the CI (i.e. a partial R²) we computed the increase in R² when a crowding effect was added to the model (i.e. M1 vs. M0).

Changes in competition intensity

Index of competition intensity.  Change in the intensity of plant–plant interactions along abiotic gradients is usually analysed using the following index:

(eqn 2)

where G_+N and G_-N are the growth of the target species in the presence (+N) and absence (-N) of neighbours (Brooker & Kikvidze 2008). This index has been used mainly in analyses of short-term removal experiments, but we adapted it for use with observational data by using our models to predict G_+N and G_-N for each point along bioclimatic gradients.

We computed G_+N and G_-N using growth predictions from our most parsimonious models. For each species we used the model to predict the growth rate of ‘non-crowded’ trees (i.e. G_-N) and crowded trees (G_+N) for all points along the bioclimatic gradients. To make these predictions, we used the average diameter of the species in the model and varied one of the abiotic gradients while keeping the other abiotic gradient fixed at its mean. In the case of non-crowded trees, CI was set at 0. In the case of crowded trees, we set CI as its average value at each point along the bioclimatic gradient to take into account the potential effect of these abiotic variables on the crowding condition. We estimated the average CI at each point along the bioclimatic gradients by fitting a smooth curve between CI and the bioclimatic variable (DD or WB) using generalized additive models (gam function in R, with four degrees of freedom). Finally we used these predictions of G_+N and G_-N to compute C_int.

Density dependence effect.  This index contrasts the growth of trees experiencing average levels of competition with the growth of trees unfettered by competition, but to understand competitive interactions more completely it is important to analyse how growth varies with crowding (i.e. density dependence effect of competition). To analyse how the density dependence of competition intensity was affected by the abiotic gradients we directly represented the change of the CRCs between two different levels of stress (for WB or DD). Substitution of eqn 1 into eqn 2 yields the expression of the index of competition intensity as C_int = 1-CRC(CI) [with CRC(CI) the value taken by the CRC at a given level of crowding]. Thus, changes in the C_int are directly related to changes in CRC. To test if there were statistically significant variations in the index C_int or the CRC between low and high levels of stress, we ran Monte-Carlo simulations based on the posterior distributions of model parameters to compute C_int and CRC predictive posterior distributions (Gelman et al. 2004). We then computed the 95% credible interval of the predictive posterior distributions to estimate uncertainties associated with C_int and CRC.

Changes in competition importance

Index of competition importance.  The importance of competition is quantified as:

(eqn 3)

where MaxG_-N is the maximum value of G_-N along the abiotic gradient analysed. C_imp‘expresses the impact of competition as a proportion of the total environment’ (abiotic constraint and competition; Brooker et al. 2005) and follows the definition of Welden & Slauson (1986). We used the same method as for C_int (see above) to predict G_+N and G_-N for all points along the bioclimatic gradients (DD or WB). MaxG_-N was set as the maximum value of G_-N predicted over all points of the bioclimatic gradients (DD or WB). Finally, as for C_int, we used these predictions of G_+N, G_-N and MaxG_-N to compute C_imp.

Density dependence effect.  To understand how density dependence (i.e. the level of crowding) affected the competition importance, we analysed how the importance of competition varies with the CI by computing C_imp for different levels of CI using eqn 3. We did so by simply representing how C_imp changes with CI at a high level of stress (either DD or WB). We used the same Monte-Carlo simulations method as used for competition intensity to compute the 95% credible interval of the predictive posterior distributions, providing us with estimate uncertainties associated with C_imp.

Competition Intensity

The shape of the CRC varied along bioclimatic gradients for 10 of the 16 species (Table 2). It was significantly influenced by water budget for four species, degree-days for four species, and by both variables for the remaining two species (models with lower DIC in Table 2). However, when indices of competition intensity were calculated from the model predictions, they showed rather little variation along these two bioclimatic gradients (Fig. 2); in fact the changes between low and high WB or DD were within the 95% credible intervals for all species except Picea abies (Fig. 2). The changes in mean CI with abiotic stress were of small amplitude and resulted in small variation of the intensity of competition. There was no evidence of a shift to facilitation with increasing abiotic stress for any of the 16 species. We found no link between the intensity of competition experienced by the species and its shade tolerance.

We were able to analyse how intensity of competition varies with crowding at low or at high level of WB and DD simply by plotting the CRCs. This curve hardly varied in shape along bioclimatic gradients (Fig. 3); any variation that was found was generally smaller than the 95% credible intervals. The only significant variations highlighted that the effect of the stress varied with the crowding intensity; for instance the CRC of Fagus sylvatica increased with DD at a CI of 0.15, but decreased at a CI of 0.5, and the CRC of P. abies was unaffected by DD at a CI of 0.15 but increased at a CI of 0.5 (Fig. 3).

Competition Importance

Variation in competition importance along bioclimatic gradients was much stronger. For all species the importance of competition was greater at high values of DD or WB, where tree growth was most rapid (Fig. 4). The amplitude of variation exceeded the 95% credible intervals for most of the species (Fig. 4). However, the importance of competition was high (and the 95% credible intervals large) for some shade-intolerant species growing under xeric conditions (Pinus sylvestris and Quercus robur) and cold environments (P. sylvestris, Pinus cembra, Pinus uncinata and Betula pubescens). Also, the mean index of competition importance (computed over all the FNFI plots where the species was found) was much lower for shade-tolerant than shade-intolerant species (Fig. 5), and there was a significant negative correlation between the shade tolerance index and mean competition importance (ρ = −0.53, P = 0.032). Note that P. cembra is classified as a rather shade-tolerant species by Niinemets & Valladares (2006) but has been considered as an intermediate shade-intolerant species by other authors (Rameau, Mansion & Dume 1993).

The effect of the CI on competition importance differed between species. All species reached an asymptote corresponding to maximum competition importance with increasing level of crowding both at low value off DD and at low value of WB (see Fig. S3). The response of shade-tolerant and shade-intolerant species differed. The shade-tolerant species (defined here as having an index above 2.5) presented much more significant variation of the importance of competition with crowding than shade-intolerant species. These differences were clear in the comparison of the competition importance at a CI of 0.02 and 0.7: for most of the shade-tolerant species these differences were greater than the 95% credible intervals, whereas for shade-intolerant species these differences were not significant (Figs 6 and 7). There were exceptions to this general rule among the shade-tolerant species, such as Quercus ilex, P. cembra and the Acer group for low DD conditions (Fig. 6) and Quercus petraea, Q. ilex and P. cembra for low WB conditions (Fig. 7). However, most of these exceptions were of medium shade tolerance (i.e. close to the threshold of 2.5). Overall, there was a significant correlation between the shade tolerance index and the magnitude of change of competition importance with CI, as indicated by the differences between the upper limits of the credible intervals at a CI of 0.02 and their lower limits at a CI of 0.7 (for WBρ = 0.56, P = 0.021 and for DDρ = 0.59, P = 0.014).

Intensity of Competition Varies Little Along Important Bioclimatic Gradients

The intensity of competition – in terms of its affect on adult growth – varied little in response to water budget (a resource) and degree-day sum (a non-resource). It was small in comparison to model uncertainty, even though growth varied profoundly along these bioclimatic gradients. In addition, none of the 16 species studied demonstrated a shift to facilitation according to the best-fitting model.

Few previous studies have analysed change in plant–plant interaction with abiotic stress for the adult tree stage. One study reported that neighbours facilitated the growth of mature trees in subalpine forest in the northern Rocky Mountains, probably through providing protection against blowing ice and snow (Callaway 1998). Coomes & Allen (2007) found no evidence of a shift to facilitation along an elevation gradient for adult Nothofagus trees in the New Zealand Alps. They even found that competition intensity varied inversely to the prediction of the SGH, with a slightly increased intensity at high elevation. Indirect analysis of adult tree competition based on spatial structure of tree communities also found no evidence in support of the SGH (Welden, Slauson & Ward 1988; Wilson 1991).

Our findings – based on the growth of adult trees – contrast with other research that focussed on herbaceous communities or small regenerating trees. Removal experiments in herbaceous communities often show that plant–plant interactions may shift from competitive to facilitative with increasing abiotic stress (Callaway et al. 2002; Holzapfel et al. 2006 and references in Lortie & Callaway 2006). Competition intensity either increases with increasing productivity (Kadmon 1995; Sammul et al. 2000; Zhang et al. 2008) or does not change detectably (Wilson & Tilman 1993; Cahill 1999; Gaucherand, Liancourt & Lavorel 2006). Experiments involving regenerating trees have produced similar findings (Kitzberger, Steinaker & Veblen 2000; Chambers 2001; Gómez-Aparicio et al. 2004). It may not be surprising to find no evidence of a shift to facilitation for adult trees as facilitation is generally thought to be more frequent at the juvenile stage (Callaway 1995). The patterns of change in intensity and type of plant–plant interaction may thus be different between herbaceous plants, the tree regeneration stage and the tree adult stage. Our results may reflect a lower sensitivity to variations in abiotic conditions and competition of trees at the adult stage than at the juvenile stage.

It is nevertheless important to underline that several limitations of our study may reduce its potential to detect a classic SGH response. Firstly, it is important to note that Goldberg & Novoplansky (1997) proposed that a decrease of competition intensity was most likely in terms of plant survival than plant growth – it could therefore be useful to extend our work to adult tree survival. Secondly, the FNFI data base covers a wide range of climatic conditions, but few plots are established near the tree line (only 34 plots above 2200 m a.s.l.) in the very harsh conditions where Callaway (1998) found a facilitative effect for adult trees. So it is possible that our analyses miss out the extreme part of one of the abiotic gradients where the facilitative processes may be occurring. Nevertheless, our analyses have a large spatial and temporal scope and are thus well suited to detect dominant patterns in tree growth, supporting the idea that there is little variation in intensity and type of plant–plant interaction with increasing abiotic stress for adult tree growth.

Importance of Competition Falls with Increasing Abiotic Stress

The importance of competition – in terms of its affect on adult growth – increased with productivity along both bioclimatic gradients, i.e. fell with increasing abiotic stress. Previous experimental investigations in relation to the importance of competition have reported that it strongly decreases with increasing stress and that it does not necessarily correlate with competition intensity (Brooker et al. 2005; Gaucherand, Liancourt & Lavorel 2006). As has been the case for competition intensity, these studies have focused on herbaceous communities. The few studies on forest communities have been based on indirect approaches such as analysis of the spatial structure (Welden, Slauson & Ward 1988) or of the distribution of competition-related traits (e.g. maximum height) (Schamp & Aarssen 2009). These studies also reported a decrease of competition importance with increasing stress. Our study thus provides unique and compelling evidence, based on many tree species and over large environmental gradients, that the pattern of decreasing competition importance with increasing stress also holds for tree communities. It seems that this pattern is general and applicable to both herbaceous plants and adult trees.

Clear differences in the mean importance of competition appear between shade-tolerant and shade-intolerant species, with much higher importance values for shade-intolerant species. Given that competition for light is widely recognized as a major driver of forest community assembly and structure (Pacala et al. 1996), it is thus not surprising to see such differences between shade-tolerant and shade-intolerant species. For this reason the further development of a theory of plant–plant interactions along abiotic gradients should include plant strategies (Maestre et al. 2009), with shade tolerance being a trait of primary importance in the case of trees.

Harnessing the Power of Non-Manipulative Approaches for Community-Level Research

Our non-manipulative approach, using recent advances in Bayesian computational statistics, is complementary and not conflicting to traditional manipulative approaches examining plant–plant interactions (see Kikvidze & Brooker 2010 for a discussion about the merging of different approaches of competition importance). It allows us to harness the power of large data bases, such as national forest inventories, to analyse interactions between many species across their entire ranges using long-term response data (5-year growth averages). This sort of analysis is able to capture important processes driving the assembly and dynamics of forest communities. This advance should ultimately contribute to the development of a new theory of plant–plant interactions along bioclimatic stress gradients. One important difference between our approach and the traditional short-term removal experiment is that instead of simply comparing plants grown with and without competition, we can analyse plant–plant interactions through CRCs and how their shapes are affected by bioclimatic variables. These curves enabled us to identify important differences in the responses of different functional groups: for shade-intolerant species the competition importance is high even if they have only few neighbours, whereas for shade-tolerant species competition only becomes important at high crowding indices.

Ultimately the contribution of plant–plant interactions has to be evaluated on the structure and dynamics of communities (Freckleton, Watkinson & Rees 2009). Adult trees contain the majority of biomass of forests, are long-lived and have major influences on all other stages of the life cycle, thus quantifying the effects of competition on their growth is crucial. However, previous studies have concluded that even if competition intensity – in terms of its affect on plant growth – is high, it may not have an important effect on community structure (Lamb & Cahill 2008; Mitchell, Cahill & Hik 2009). Consequently, the effects of plant interactions on the community structure and composition cannot be fully understood simply by focussing on adult tree growth. The effects of these interactions on other components of the life cycle (such as seedling establishment and sapling growth and survival) must be quantified and integrated over the whole life cycle in a plant community dynamics model (Freckleton, Watkinson & Rees 2009) and be put in balance with the other factors important in structuring the community such as abiotic conditions, dispersal limitation, natural enemies, site history, and regional processes of speciation and extinction (Ricklefs 2008).

Our approach brings us a step closer towards community-level analysis of plant–plant interaction impact, because the growth predictions are easily integrated in individual-based models of forest dynamics such as SORTIE (Pacala et al. 1996; Clark et al. 2007; Kunstler, Coomes & Canham 2009). Such models could be used to understand how plant–plant interactions drive plant community structure and dynamics. Nowadays many national forest inventory data sets are available, enabling researchers to test theoretical predictions about plant–plant interactions with non-manipulative estimations over unprecedentedly large spatio-temporal scales and species samples, and link such phenomenological competition models with models of community dynamics.