Study Sites and Design
For this study, a total of 597 plots were selected in European beech Fagus sylvatica forests of the forest districts Stadtwald Lübeck (53°47′ N, 10°37′ E) and Stadtwald Mölln (53°38′ N, 10°42′ E), which are located in the moraine landscapes of Schleswig-Holstein, Northwest Germany. The forest areas are dominated by deciduous trees (Lübeck: 72%; Mölln: 41%) with total area of 4297 ha (Lübeck) and 1150 ha (Mölln). Elevation ranges from 0 to 90 m asl. The study area is characterized by a suboceanic climate with a mean annual precipitation between 580 and 871 mm and a mean annual temperature of 8·3 °C (Gauer & Aldinger 2005).
Forests are managed according to a low-impact approach based on the protection of natural disturbance regimes within managed stands (Sturm 1993; Westpahl et al. 2004) and are certified according to the Forest Stewardship Council (FSC). We included unmanaged, crowded stands in the modelling data set as regional reference areas to ensure that a comprehensive gradient of stand density was used. Structurally, the investigated stands are multi-layered and uneven-aged (see Fig. S1, Supporting Information).
To test large-scale (regional) edaphic effects on tree growth, we stratified the plots according to their geological substrate. The resulting three beech forest types were characterized by a productivity gradient based on nutrient and water availability: (i) ‘GF-till’ meso- to eutrophic beech forests (Galio-Fagetum; EU habitat code: 9130) on moderately moist to moist recent moraine soils originating from the Weichselian glaciation. Soil texture consists of till (clay/sandy loam) with varying carbonate content, providing an optimal nutrient and water supply. The predominant soil types are (pseudogleyic) Luvisols and Cambisols. (ii) ‘GF-clay’ mesotrophic beech forests (Galio-Fagetum; EU habitat code: 9130) on hydromorphic recent moraine soils. The strong stagnant water influence is induced by basin clay deposits which are covered with silt or sand of varying thickness. These soils have a deficit in aeration during periods of excess water, which in turn increases the abiotic stress for tree growth. The prevailing soil types are strongly pseudogleyic Cambisols and Planosols. (iii) ‘DF’ oligotrophic beech forests (Deschampsio-Fagetum; EU habitat code: 9110) on recent moraine soils which consist of glacial sand deposits of the Weichselian glaciation. A low retention capacity for nutrients and water is caused by a high sand content, which increases the risk of trees suffering drought during summer. The soils are rather acidic (pH 3·5–5·0) compared to the recent moraine. The predominant soil types are podsolic Cambisols.
Optimal growing conditions (lowest level of abiotic stress) are associated with GF-till sites, whereas suboptimal situations are characterized by low top soil aeration during wet periods (GF-clay) or additive effects of summer drought and low nutrient availability (DF). The gradient of decreasing productivity is expressed by the significant decline in site index values, which is a proxy for the growth potential at a given site (Table 1). Thus, the abiotic stress level increases within the series GF-till – GF-clay – DF.
Table 1. Mean (±SD) tree and stand characteristics of the investigated forest types and the associated stress gradient. ‘GF-till’ meso- to eutrophic beech forests (Galio-Fagetum) on moderately moist to moist recent moraine soils; ‘GF-clay’ mesotrophic beech forests (Galio-Fagetum) on hydromorphic recent moraine soils; ‘DF’ oligotrophic, acidophytic beech forests (Deschampsio-Fagetum) on sandy recent moraine soils. Data represent initial inventory values of the modelling data set. The soil nutrient status of the study plots was classified according to the German forest site mapping system (Arbeitskreis Standortskartierung 1996). This index ranges from 1 (very low nutrient availability) to 6 (very high nutrient availability)
|Water-based||–||Temporal water excess||Temporal water deficiency|
|Soil nutrient class (n plots)|
|Eutrophic sites (index 5-6)||173||27||–|
|Mesotrophic sites (index 3–4)||139||151||–|
|Oligotrophic sites (index 1–2)||–||–||107|
|Site indexa (m)||33·3a ± 4·4||31·2b ± 3·9||29·6c ± 4·0|
|Tree age (year)||71·1 ± 36·7||74·9 ± 40·2||94·0 ± 46·7|
|Tree diameter (cm) at 1·30 m||28·6 ± 15·0||29·6 ± 17·0||31·7 ± 16·3|
|Tree height (m)||22·7 ± 8·1||21·9 ± 7·6||23·6 ± 7·4|
|Basal area growth (cm2 year−1)||22·4 ± 15·8||20·7 ± 16·8||25·8 ± 19·9|
|Relative radial growth rateb (%)||6·08 ± 8·2||4·61 ± 5·5||4·42 ± 4·1|
|Basal area all trees (m2 ha−1)||27·6 ± 11·8||28·2 ± 10·1||27·3 ± 11·8|
|Basal area larger trees (m2 ha−1)||15·8 ± 10·3||18·7 ± 10·3||12·2 ± 9·9|
|Proportion beech trees (%)||76·6 ± 24·8||64·2 ± 28·6||73·8 ± 28·5|
We used tree and stand data from sample plot inventories, conducted in 1992 and 2003 (Lübeck) as well as in 1999 and 2009 (Mölln). Measurements were taken in a regular spatial resolution of 180 × 130 m (Lübeck) and 100 × 200 m (Mölln), respectively. Within circular plots (Mölln, plot size: 250 m2) or concentric circular plots (Lübeck, total plot size: 500 m2), all living trees > 7 cm diameter at breast height (DBH) were considered. For each tree, the species, social status and DBH were determined. DBH values represent the average tree size derived from 2 cross-measurements at 1·3 m. Tree height was measured for a subset of 2–4 trees of each species and layer. Annual basal area growth (BAI) was calculated as the difference between the tree basal areas (cm2) at the end and beginning of the sample period divided by the number of vegetation periods.
For the growth analyses, we randomly selected 1819 beech trees (target trees) from 250-m2 (Lübeck) and 125-m2 (Mölln) circular subplots, placed at the centre of the sample plots to account for edge effects. Only dominant and co-dominant target trees of the upper layer (canopy trees) were considered (classes 1–3 according to Kraft 1884).
Preliminary analyses indicated nonlinear BAI-DBH and BAI-BAL relationships. We therefore applied generalized additive mixed models (GAMMs) with a log link function and gamma distribution to assess growth patterns along the productivity gradient (Wood 2006). Study site and plot were used as random factors, accounting for the intraclass correlation at the site and plot level. To address the skewed response and heteroscedasticity of the BAI data, a gamma probability distribution was preferred, because it retains the structure of the data while accounting for a heteroscedastic error structure and avoiding biased inferences associated with logarithmic transformations (see Gea-Izquierdo & Cañellas 2009).
Basal area increment was modelled as a basic function of tree size (DBH) and tree's competitive status. Basal area of larger trees (BAL) was used as a distance-independent measure of crowding (Wykoff, Crookston & Stage 1982) and calculated as the total basal area of trees larger than the subject tree within a plot. To account for variation in the effect of species composition (inter- versus intraspecific competition), we calculated the proportion of beech trees within a plot (PBT) as the percentage of basal area composed of beech tree individuals. The resulting GAMM is:
where BAIijk is the mean basal area growth, α is the intercept, ƒ1,2 are smoothing functions (thin plate regression splines) of tree size and crowding effects and β is a parametric coefficient of the beech proportion effect. bi + bij denote the random effects of forest sitei and plotj and ε is the residual error of the k-th tree. The optimal amount of smoothing was determined by cross-validation (Wood 2006). To test for size dependency of crowding effects, we additionally considered a two-way interaction term ƒ (DBH, BAL). All models were fitted for each beech forest type separately. Additionally, we compared our semi-parametric model with a log-transformed parametric growth function and normal probability distribution, but the GAMM resulted in a better statistical fit (see Appendix S1, Supporting Information).
Different competing models were evaluated by sequential comparison (backward selection) based on the Akaike Information Criterion (AIC). Only models with an AIC difference (∆AIC) < 4·00 (compared with the best fit model) were considered as models with substantial support (Buhrnham & Anderson 2002). The optimal random effects structure was based on restricted maximum likelihood (REML) estimation, the optimal fixed effects structure was identified by maximum likelihood (ML) method. Parameter estimates of the final model were fitted using the restricted maximum likelihood (REML) method (Zuur et al. 2009). Model accuracy was judged according to the adjusted coefficient of determination (R²adj.) and mean error. The relative influence of the predictors was determined by calculating the percentage change in R²adj. owing to the inclusion of the subject predictor in the model.
To evaluate competition effects, we used two different competition measures: Competition intensity (Cint) and competition importance (Cimp). For each beech forest type, we predicted the radial growth (G) of a focal tree based on our best-fitted models, either in the presence (+) or in the absence (−) of larger competitors. We used the average value of beech proportion along the productivity gradient, while varying tree size and crowding conditions.
Cint was quantified as the response ratio between the growth of a target tree in a low- and a high-density stand (Brooker et al. 2005):
where G− and G+ are the basal area growth of a target tree experiencing a low level of crowding (BAL was set at 0 m2 ha−1) and a high level of crowding (BAL was set at 30 m2 ha−1). Accordingly, higher indices were taken to be those with greater absolute competition impact. As we were interested particularly in management implications, we further analysed changes in Cint with various levels of crowding (BAL varied between 1 and 30 m2 ha−1) by predicting the proportion of growth decline because of crowding. The crowding response (CR) was calculated as:
To determine significant changes in Cint with tree size and stand density, we applied a recursive partitioning approach using the function ctree implemented in the R library party (Hothorn, Hornik & Zeileis 2006). The resulting splits (threshold values) indicate a significant shift in growth reduction in relation to competition intensity. We used the threshold as a management-related indicator for the effectiveness of thinning, because it reflects the balance between maximum growth acceleration and growing stock capacity. The 95% confidence intervals for the thresholds were calculated based on 1000 bootstrap samples.
Cimp can be described as the impact of competition in relation to the total environment (competition and abiotic constraint, Brooker et al. 2005):
where Max G- is the maximum value of G- along the investigated gradient. Accordingly, higher indices were taken to be those with greater competition impact incorporating the role of other processes. Similarly to Cint, we predicted the crowding response (CR) to analyse the density dependence effects on competition importance using eqn 4.
To test tree size-related effects at low and high crowding levels, trees were stratified into three timber tree size classes and competition indices were calculated for each size class separately: (i) small timber trees: DBH 20–35 cm, (ii) medium timber trees: DBH 36–50 cm and (iii) large timber trees: DBH 51–70 cm. Differences in competition indices between forest types were tested by analysis of variance (anova) followed by a post hoc performance (Tukey's HSD test).
Finally, we calculated for each forest type the relationship between the basal area of all trees (BA) and the basal area larger trees (BAL) to facilitate practical management implications.
All statistical analyses were performed using R (R Development Core Team 2009, version 2.10.1). The nonlinear models were fitted using the gamm function from the mgcv library.