Diameter Growth of Silver Fir ( Abies alba Mill.), Scots Pine ( Pinus sylvestris L.) , and Black Pine ( Pinus nigra Arnold) in Central European Forests: Findings from Slovenia

: The main objectives of the study were to (1) determine the response of the diameter growth of silver ﬁr, Scots pine, and black pine in Central European seminatural forests to tree, stand


Introduction
Tree species differ in their production rate and growth response to various factors. A complex of environmental, stand, and tree factors results in high variability in tree growth [1]. Most studies on tree growth have focused on the effects of tree variables, such as tree diameter or tree age, and stand variables, such as stand density, mixture, and heterogeneity. Among environmental factors, site productivity (e.g., site index), topographic factors (e.g., slope, aspect, and elevation), and especially climatic factors have often been studied (e.g., [2]), while soil variables have received less attention in tree growth modeling [3,4].
Different approaches are used to study the influence of trees, stand, and environmental factors on tree growth. These generally fall into two categories [4]. The first approach involves precise field measurements of tree growth and the independent variables observed at the research site, such as crown size, distance to neighboring trees, and microsite variables related to climatic and soil conditions. Dendrochronological methods are commonly used to analyze tree growth patterns. However, due to the demanding nature of field measurements, studies are typically conducted at a small spatial scale with a relatively small number of observed trees.
The second approach, adopted in this study, involves a larger spatial scale and a larger sample of trees. This approach often uses data from national forest inventories (e.g., [3,5]). Measurements of trees are less precise than in the first approach, but the larger spatial scale allows the growth of individual trees to be studied under different stand and environmental conditions. Tree growth variables are defined based on successive measurements of trees; therefore, periodic increments are often used as dependent variables. Several proxy variables are used to describe the growth conditions of trees. Instead of distance-dependent competition variables, the stand basal area or the stand basal area of trees larger than the observed tree can serve as a proxy for competition conditions. Tree classes (e.g., in regard to social position, crown size, vigor, status), stand classes (e.g., developmental stages), and site classes (e.g., forest types, soil classes) are used to explain variability in tree growth patterns. Instead of annual or monthly values of climatic variables, their long-term average values were used to characterize differences in climatic conditions between sites.
Soil variables have occasionally been considered in growth modeling (e.g., [6][7][8]). In the growth studies of the second approach, soil units, representing a typical complex of soil properties according to morphological, genetic, chemical, physical, and biological properties [9], can be used as dummy variables (e.g., [3,4]). Soil units characterize differences in soil conditions between sites at a larger spatial scale. However, studies on the growth of tree species, even dominant ones, with respect to differences between soil units are quite rare.
Among conifers, the growth of Norway spruce has probably been the most thoroughly studied among tree species in Europe. Slightly less attention has been paid to Scots pine (Pinus sylvestris L.) and even less to silver fir (Abies alba Mill.; from hereafter fir) and black pine (Pinus nigra Arnold). In Europe, a decline in Norway spruce due to climate change has been observed [10]; therefore, knowledge of other conifers such as fir, Scots pine, and black pine in a different tree, stand, and environmental conditions are becoming increasingly important. Studies on Scots pine growth are more prevalent in Fennoscandia (e.g., [11]) and the Iberian Peninsula (e.g., [12,13]) than in Central Europe. Similarly, growth studies on black pine have mainly been carried out in Southern Europe, whereas they are quite rare in Central Europe. Many studies on Scots pine and black pine have focused on plantations (e.g., [14]), monospecific even-aged stands [11], or stands with two codominant conifers (e.g., [15]) or specific forest types (e.g., [16,17]). Natural and seminatural pine forests have been studied less frequently (e.g., [18,19]). Mixed stands with a significant proportion of broadleaves have not been considered in pine growth studies but have been taken into account in a few fir growth studies (e.g., [3,20,21]). Slovenia is one of the few European countries where clearcutting is prohibited by law. In the last seventy years, mainly the irregular shelterwood system has been used, resulting in relatively well-preserved forests. Well-preserved forests and the availability of growth measurements from very diverse sites provide an opportunity to study the growth of fir, black pine, and Scots pine with respect to different stand and environmental conditions.
The main objectives of this study are to (1) determine the response of the diameter growth of silver fir, Scots pine, and black pine in Central European seminatural forests to tree, stand, and environmental factors and (2) test for differences in their growth rate on different soils. The selected tree species are, besides Norway spruce, the main native conifer tree species in Central European forests. Other native conifers (e.g., Swiss pine, European larch, European yew) are much less common, especially in Slovenian forests. We hypothesize the following: (1) some tree, stand, and environmental predictors in the models of diameter growth are species-dependent, (2) the importance of common predictors for explaining diameter growth differs between the tree species, and (3) there are significant differences in the diameter growth of individual tree species between soil classes.

Study Area
The study was conducted in a 12,000 km 2 forest area in Slovenia ( Figure 1). The climate in Slovenia is a combination of a continental climate in the northeast, an alpine climate in the high mountain regions, and a sub-Mediterranean climate in the coastal region, with geographical variations mainly due to diverse topographic conditions and the influence of the Mediterranean Sea, the Alps, and the Pannonian Plain [20]. The average annual temperature is 9.2 • C, and the average annual precipitation is 1426 mm. The main lithological groups are carbonate rocks (54.6%), clastic sediments (36.0%), and metamorphic rocks (4.2%) [22]. The most common soil types in the forest area are Rendzinas and Dystric and Eutric brown soils [23]. Beech forests cover 70% of the total forest area. Close-to-nature forestry based on natural regeneration has been practiced for decades, resulting in smallscale even-aged, and uneven-aged forest stands. The average growing stock is 304 m 3 ha −1 . In total, more than 70 tree species have been recorded in forest inventories, but European beech (Fagus sylvatica, 33%) and Norway spruce (Picea abies (L.) Karst., 30%) dominate, followed by fir (7%), sessile oak (Quercus petraea (Matt.) Liebl., 5%) and Scots pine (4%). The proportion of black pine is much lower (<1%).

Study Area
The study was conducted in a 12,000 km 2 forest area in Slovenia ( Figure 1). The climate in Slovenia is a combination of a continental climate in the northeast, an alpine climate in the high mountain regions, and a sub-Mediterranean climate in the coastal region, with geographical variations mainly due to diverse topographic conditions and the influence of the Mediterranean Sea, the Alps, and the Pannonian Plain [20]. The average annual temperature is 9.2 °C, and the average annual precipitation is 1426 mm. The main lithological groups are carbonate rocks (54.6%), clastic sediments (36.0%), and metamorphic rocks (4.2%) [22]. The most common soil types in the forest area are Rendzinas and Dystric and Eutric brown soils [23]. Beech forests cover 70% of the total forest area. Close-to-nature forestry based on natural regeneration has been practiced for decades, resulting in small-scale even-aged, and uneven-aged forest stands. The average growing stock is 304 m 3 ha −1 . In total, more than 70 tree species have been recorded in forest inventories, but European beech (Fagus sylvatica, 33%) and Norway spruce (Picea abies (L.) Karst., 30%) dominate, followed by fir (7%), sessile oak (Quercus petraea (Matt.) Liebl., 5%) and Scots pine (4%). The proportion of black pine is much lower (<1%).

Data Sources
Forest inventory data [24] served as the primary source of data for analyzing diameter growth and stand variables (Table 1). Trees with a diameter at breast height (D) ≥ 10 cm are measured every ten years on permanent sampling plots (area = 500 m 2 ) distributed on sampling grids of 250 m × 250 m and 250 m × 500 m. Plots were measured twice in rolling inventories in which approx. 10% of plots are measured each year. The first measurements were conducted in the period 1993-2004, and the second in the period 2002-2013 [24]. Sampling plots where at least one of the observed tree species was present were used for the analyses. In total, 26,291 sampling plots and 117,224 trees were analyzed (Table A1). Topographic variables were derived from a digital elevation model (12.5 m resolution) [25], while climatic variables were derived from long-term climate records in the period 1971-2000 [26] and downscaled from the original 1 km 2 resolution to the sampling plot grid using the nearest neighbor method.

Explanatory Variables and Their Selection
Periodic diameter increment (DI), calculated as the difference between two consecutive measurements of diameter at breast height over a 10-year period, was transformed

Data Sources
Forest inventory data [24] served as the primary source of data for analyzing diameter growth and stand variables (Table 1). Trees with a diameter at breast height (D) ≥10 cm are measured every ten years on permanent sampling plots (area = 500 m 2 ) distributed on sampling grids of 250 m × 250 m and 250 m × 500 m. Plots were measured twice in rolling inventories in which approx. 10% of plots are measured each year. The first measurements were conducted in the period 1993-2004, and the second in the period 2002-2013 [24]. Sampling plots where at least one of the observed tree species was present were used for the analyses. In total, 26,291 sampling plots and 117,224 trees were analyzed (Table A1). Topographic variables were derived from a digital elevation model (12.5 m resolution) [25], while climatic variables were derived from long-term climate records in the period 1971-2000 [26] and downscaled from the original 1 km 2 resolution to the sampling plot grid using the nearest neighbor method.

Explanatory Variables and Their Selection
Periodic diameter increment (DI), calculated as the difference between two consecutive measurements of diameter at breast height over a 10-year period, was transformed with square root transformation to make DI less skewed and the variation more uniform and used as the dependent variable.
Tree, stand, site, and climatic variables were included in the analyses (Table 1). Among the tree explanatory variables, the diameter of a tree at the first measurement (D) was used as a proxy for tree size. Additionally, its square (D 2 ) or natural logarithm (log (D)) was tested to account for the possible non-linear relationship between DI and D. The basal area (BA) and quadratic mean diameter (QMD) of the stand were calculated using the data from the first measurement of trees. Basal area per hectare was used to describe stand density. It was square root transformed to account for the non-linear effect of BA on DI.
The structural diversity of forest stands was quantified by the Gini coefficient (GINI), which was calculated at the plot level considering all trees from the first measurement, taking into account the number and basal area of single trees with D ≥10 cm. A higher value of GINI, which ranges from 0 to 1, indicates an uneven-sized stand structure, while values near 0 indicate an even-sized stand structure. The tree species mixture was estimated using the Shannon index (SHAN), which was calculated based on the proportion of single tree species in the total stand basal area for each plot. Additionally, the proportion of beech in the total stand basal area (PBEECH), the proportion of other broadleaves (PBROAD), and the proportion of conifers (PCONIF) were included in the analyses to test for differences in the diameter growth of the three tree species between stands with different tree species composition.
Site productivity was estimated by the volume of a tree with a reference diameter of 45 cm (K), which was available for all tree species and forest sites. K ranged from 1.1 to 2.9 m 3 , indicating differences between sites with regard to tree heights for trees of the same diameter [27]. Five topographic variables were included as candidate variables in the analyses. Elevation (ELEV), inclination (INCL), and rockiness (ROCK) indicate topographic conditions and the severity of the site conditions. ROCK was visually assessed in forest inventories as the proportion of the area covered by stones and rocks [24]. Rockiness has often been used to describe the harshness of growth conditions and forest vulnerability [28]. Eastness (EAST) and northness (NORTH) coefficients describe the aspect.
Finally, nine climatic variables [26] representing the long-term climatic averages (i.e., for the period 1971-2000) were included in the analyses (Table 1). To account for possible interactions between precipitation and temperature, the model included MAT:MAP. We also tested for a non-linear relationship between MAT and diameter growth by including MAT 2 in the analyses.
Soil units (SOIL) were derived from the vector layer of soils on a scale of 1:25,000 [29], where the average size of a mapping unit was 117.95 ha. These mapping units were aggregated into 25 FAO soil units [9,23,30]. Cambisols and Leptosols predominate. The soil units are described by the predominant pedocartographic units with their typical horizons, textures, and parent materials [4]. The criterion for including a soil unit in the analyses was at least 20 plots in the soil unit (Table A1); thus, 8, 13, and 6 soil units were included in the analyses for fir, Scots pine, and black pine, respectively. Dystric Cambisol (CMd) was used as the reference soil unit.
Pearson's correlation coefficients were calculated to assess collinearity among the continuous independent variables. If two variables had a correlation coefficient of r ≥ 0.65, only one of the variables was included in the modeling procedure. Among the stand variables, PCONIF was excluded from the procedure due to its high correlation with PBEECH. Most of the climatic variables were highly correlated with MAT and were therefore excluded (Table 1). Despite the high correlation (r ≥ 0.65) between MAT and MAP, both variables were retained in the analyses due to the particular interest in their effect on diameter growth. Additionally, multicollinearity within the model was checked using the variance inflation factor (VIF); if VIF > 10, the explanatory variable was excluded from the model.

Modeling Approach
The diameter increment of the three tree species was modeled with a linear mixedeffects model [31,32] in the lmer() function of the lme4 R package (v1.1-31, [33]), where the variation between plots is represented by the random intercept. Model parameters were estimated using maximum likelihood estimation (MLE) [21]. The diameter increment model (Equation (1)) was parametrized separately for each of the three tree species with a stepwise procedure using all 18 independent variables as candidate variables (Table 1; Equation (1)).
The relative importance of each predictor in the model was estimated based on the relative decrease in the marginal R 2 (R 2 m (%)) when the predictor was included in the model compared to a model without the predictor. The fit of all models was evaluated using the marginal R 2 , conditional R 2 , root mean squared error (RMSE), intraclass correlation coefficient (ICC), random intercept variance (τ00), Akaike information criterion (AIC), Bayesian information criterion (BIC) and residual standard deviation (sigma) [34]. The predictive performance of a fitted model was evaluated using the performance() function in the performance R package (v0.10.2, [34]). The Scheffe test was used to test for differences in tree species growth between soil units. The effect size was determined using Cohen's d with the function eff_size () in the emmeans R package (v1.7.3 [35]).

Diameter Growth Models
Sixteen, twelve, and ten of 18 variables remained in the final DI model for fir, Scots pine, and black pine, respectively ( Table 2). The fixed and random parts of the models explained 32%-47% of the total DI variability ( Table 3). The fixed part of the models explained 13%-31% of the total DI variability. The RMSE value of the models ranged from 0.56 to 0.57 cm. The diameter increment models for the tree species showed a non-linear relationship between D and DI ( Figure 2).
The diameter increment of fir decreases with an increase in stand density (BA), the basal area of overtopping trees (BAL), quadratic mean diameter (QMD), tree species diversity, and the proportion of beech in forest stands (PBEECH). DI is lower at higher elevations (ELEV) and on steeper slopes (INCL) with higher rockiness (ROCK) and in areas with higher diurnal range (BIO2). Conversely, DI is greater in more heterogeneous stands (GINI), with a higher proportion of broadleaves other than beech (PBROAD) on more productive (K) and warmer sites (MAT).
Similar responses to tree, stand, and site variables were observed for Scots pine. Compared to the fir model, the effects of some stand (GINI and PBROAD) and topographic (ROCK and EAST) variables were non-significant. In contrast to fir, the diameter growth of both pine tree species showed a negative response to mean annual temperature (MAT). The response of the diameter growth of black pine is similar to that of Scots pine, with some variables (i.e., SHAN, PBROAD, K, ROCK) having a non-significant effect. Increasing diameter growth along an elevation gradient is one of the peculiarities of black pine growth.
The R m % values (Table 2) for the same predictor differ greatly between tree species; e.g., for stand basal area, it amounted to 21.9% and 42.9% for fir and black pine, respectively. Two climatic variables were highly important for the diameter growth of black pine (Rm% > 25) but not for fir (Rm% < 2). Tree diameter accounted for the majority (>50%) of the explained variability of the diameter growth of fir but not for both pine species (<10%).
Stand basal area (BA) contributed 28% and 43% to the explained variability in the diameter growth of Scots pine and black pine, respectively, which is more than for fir (22%). Similarly, topographic and climatic variables contributed more to the explained variability of Scots pine and black pine diameter growth, 25.5% and 36.1%, respectively, compared to fir (<3%). SOIL explained 5.5 to 7.5% of the DI variability ( Table 2). The impact of SOIL on the diameter increment of fir was greater than that of climatic or topographic variables, which was not the case for both pine species.

Differences in the Diameter Increment of Fir, Scots Pine, and Black Pine between Soil Units
The growth of tree species varied between soil units (Figure 3). Compared to the growth of trees on the reference soil unit (CMd), growth was 4% higher (see Scots pine on Dystric Leptosols and Haplic Luvisols) and up to 48% lower (see Scots pine on Calcaric Fluvisols). The highest and the lowest diameter increments of tree species were registered on different soil units.
Post hoc analysis revealed a limited number of significant differences in the growth of individual tree species between soil units (Table 4).
There were significant differences in the diameter growth of fir within Cambisols. Growth on Dystric Cambisols and Dystric Planosols was significantly greater than that on most other soil units. Fir grew faster on Dystric Leptosols than on calcareous Leptosols (LPk and LPm). Growth on Chromic Cambisols was lower than that on most other soil units but not less than that on calcareous Leptosols.
The diameter growth of Scots pine was significantly faster on Dystric Cambisols than that on Eutric Cambisols and Rendzic Leptosols. A similar pattern was observed for growth on Haplic Luvisols, where growth was faster than that on Eutric Cambisols.  Table 2) are shown. Variables: D, tree diameter; BA, basal area; QMD, quadratic mean diameter; GINI, Gini index; SHAN,

Differences in the Diameter Increment of Fir, Scots Pine, and Black Pine between Soil Units
The growth of tree species varied between soil units (Figure 3). Compared to the growth of trees on the reference soil unit (CMd), growth was 4% higher (see Scots pine on Dystric Leptosols and Haplic Luvisols) and up to 48% lower (see Scots pine on Calcaric Fluvisols). The highest and the lowest diameter increments of tree species were registered on different soil units. Post hoc analysis revealed a limited number of significant differences in the growth of individual tree species between soil units (Table 4).
There were significant differences in the diameter growth of fir within Cambisols. Growth on Dystric Cambisols and Dystric Planosols was significantly greater than that on most other soil units. Fir grew faster on Dystric Leptosols than on calcareous Leptosols (LPk and LPm). Growth on Chromic Cambisols was lower than that on most other soil units but not less than that on calcareous Leptosols.
The diameter growth of Scots pine was significantly faster on Dystric Cambisols than that on Eutric Cambisols and Rendzic Leptosols. A similar pattern was observed for growth on Haplic Luvisols, where growth was faster than that on Eutric Cambisols.
Black pine growth on Chromic Cambisols was significantly slower than that on the two other Cambisols (CMc and CMd) and Mollic Leptosols. Black pine grew better on Calcaric Cambisols than on Rendzic Leptosols.

Predictors of the Diameter Growth of Fir, Scots Pine, and Black Pine
In our study, the models for the three tree species explained 32%-47% of the variation in diameter growth, which is similar to the results from other studies on diverse sites (e.g., [3,5]).
Tree diameter indicates tree age and has often been included in growth models either with a linear (e.g., [36,37]) or non-linear effect (e.g., [32]). Our study showed a non-linear response of diameter increment to tree diameter. Tree diameter accounted for the majority of the explained variability in fir diameter increment. Fir is a shade-tolerant species that often grow in naturally well-preserved stands with high vertical heterogeneity [38,39]. In contrast to the two pine species, it is rarely present in pure even-aged stands and is not present in successional forests. This is probably the main reason for the high importance of tree diameter in the fir model. The competitive status of fir trees is strongly determined by their dimensions. The diameter increment of fir rose up to 49 cm and then dropped, probably also due to the higher age of trees because of the long-term suppression of growth in the understory of uneven-aged stands. Similar results were found in a study of fir diameter growth in Europe [1] and the diameter growth of other tree species [32]. A logarithm of diameter was included in the diameter increment model for both pine species, which is typical for models of several tree species (e.g., [40,41]). The increment of both pines is low and increases monotonically without culmination.
Stand variables explained the majority of the variability in the diameter growth of both pine species, with stand basal area being the strongest individual predictor, especially for black pine diameter growth. The relationship between stand basal area and individual tree growth has been established in several studies, with the effect of stand density on diameter growth being more pronounced for light-demanding tree species. Additionally, the basal area of trees larger than the observed tree (BAL) was included in the model for all tree species, as BAL is a common predictor in models of individual tree diameter growth [3,32].
The proportion of beech in a stand has a negative effect on the diameter growth of the observed tree species. The complementarity of tree species varies strongly with stand, site, and climatic conditions [42]. Our study showed that beech abundance is a more important predictor than the Shannon index, indicating that beech is a highly competitive tree species that slows down the growth of other tree species in a stand. The negative effect of beech mixture on the growth of Scots pine was also reported in a study on the basal area increment of tree species in Austria, while this effect was much weaker for fir [3]. The high negative complementary effect of beech is probably related to the large crown size and crown density of beech compared to other deciduous tree species. On the other hand, the proportion of other broadleaved tree species (e.g., European hornbeam, oaks) has a positive complementary effect on the diameter growth of fir, probably due to their lower height compared to fir. In hemi-boreal forests, the proportion of birch in forest stands also has a positive effect on the diameter growth of Scots pine [43]. This indicates that deciduous tree species may have a contrasting effect on the diameter growth of conifer tree species.
The effect of vertical structural diversity on diameter growth was significant only for fir. Fir is a dominant tree species in many European uneven-aged forests [39,44]. A similar result was reported by [45], who found a non-linear response of fir to stand heterogeneity; the response of large firs to structurally diverse stands is relatively more intense compared to that of smaller firs.
Topographic variables can influence soil properties and, thus, tree growth conditions [46]. Rockiness, slope inclination, and elevation indicate the severity of site conditions. These factors indirectly affect tree growth by influencing moisture, temperature, light, and other chemical and physical site factors [32]. Inclination had a significant negative effect on the diameter growth of all three tree species, while elevation only had a negative impact on fir and Scots pine. Surprisingly, elevation had a positive impact on the diameter growth of black pine, which was also reported from Austria [20], likely due to its correlation with mean annual temperature and mean annual precipitation, and thus also with soil moisture. The effect of rockiness was significant only for fir growth. Rockiness indicates the severity of the site conditions [28]. Rocky soils can hinder root development [47]. The effect of eastness was significant only for fir growth, but this effect was very weak and contributed negligibly to the explained variability in diameter increment.
Our study showed that fir and Scots pine grow better on more productive sites. Several studies (e.g., [32,48]) have reported the strong influence of site productivity, measured by the site index, on tree diameter growth. However, in our study, the impact of site productivity estimated by the volume of a tree with a reference diameter (K) was rather weak and not even significant for black pine growth.
Climatic conditions were also a source of variation in tree diameter growth. Only two climatic variables were significant in the diameter growth models for the three tree species: mean annual temperature and mean diurnal range. Our study showed that both climatic variables were relatively more important predictors of the diameter growth of both pine species, accounting for 18% of the total explained variability. Fir grows better in warmer sites (see [49]), which is common for most tree species, but the opposite was found for both pine species. The negative response of the diameter growth of both pine species to higher mean annual temperatures may be indirectly related to annual precipitation. The latter variable had a strong negative correlation with mean annual temperature (Pearson coefficient > 0.9) and was not included in the model. Therefore, our results indicate an increase in the diameter growth of both pine species as the number of precipitation increases. In hemi-boreal forests, water availability is known as the key parameter of Scots pine productivity [43]. In contrast to our results, the basal area increment of Scots pine in hemiboreal forests increases with higher mean temperature, and the effect of temperature on basal area increment is greater than that of an increased amount of precipitation [43]. Many studies have reported that black pine growth responds to precipitation and temperature in the previous and current years [50][51][52]. Our results on black pine growth are in agreement with the study of [53], who reported the increased growth of black pine in the Mediterranean area during cool summers and cold and wet periods. In Central Europe, however, there is a clear decrease in the diameter growth of black pine for mean growing season temperatures below 10 • C [3]. It is worth noting that there are several subspecies of black pine, such as the Austrian pine and the Corsican pine, whose growth and response to climatic and other variables may be different [54]. The mean diurnal range is rarely used in tree growth modeling (e.g., [55]), although [56] stated that it could become an increasingly important factor for tree growth in the context of climate change. The mean diurnal range had a weakly negative effect on fir growth and a positive effect on Scots pine and black pine growth. It seems to be a very important predictor of the diameter growth of Scots pine and black pine, accounting for 8.5% and 11.3% of the total explained variability in their diameter increment, respectively.
For fir and Scots pine, the diameter growth of dominant trees in the same study area as that used in our study was studied [4]. Our results showed that the response of fir and Scots pine to tree, stand, and environmental variables appear to be slightly different compared to the response of dominant trees of the same tree species only [20]. Differences exist in the set of predictors, e.g., the basal area of trees larger than the observed tree (BAL) was not included in the models for dominant trees. The contribution of some variables to the explained variability of diameter increment is different between models for all trees and dominant trees only. For instance, in the diameter increment model for fir, tree diameter contributed the largest proportion to the explained variability. However, the same variable had a negligible contribution in the model for the dominant firs only. Therefore, it is not appropriate to generalize the diameter growth of dominant trees with respect to stand, site, and climatic variables to all trees of the same tree species.

Importance of Soil Units for the Diameter Growth of Fir, Scots Pine, and Black Pine
The soil unit contributed 5.3, 6.4, and 7.5% to the explained diameter increment variability of fir, Scots pine, and black pine, respectively. However, the soil seems to be an even more important predictor when only dominant trees are considered [4]. Our study showed that soil contributes more to the explained diameter variability of fir than topographic or climatic variables. Our results on the influence of soil were similar to those from Austria [3] but with some slight differences for some soil units (e.g., Chromic Cambisols).
The highest growth rate of fir was found in Dystric Planosols, Dystric Cambisols (see [57]), and Haplic Luvisols. Similar findings were reported from Austria [20]. The differences in growth rates on these soil units compared to several other soil units (i.e., calcareous Leptosols and Chromic Cambisols, characterized by shallowness and stoniness and, therefore, lower water-holding capacity) were significant. Fir thrives well in moist sites but is vulnerable to extreme water stress [58]. Our results indicate that fir grows well on acidic soil types with sufficient water-holding capacity [39]. The results for the diameter growth of fir on different soil units were quite similar to those obtained for dominant fir trees only [4]. However, this study found more significant differences between soil units compared to the study that only considered dominant trees.
Both pine species can grow on different sites, but they are often limited to nutrient-poor and dry sites where other tree species (e.g., beech and spruce) are less competitive. They also perform well in early-successional stages, which was partly the case in our study [28]. The fastest growth of Scots pine was recorded on Haplic Luvisols and Dystric Leptosols, which differed slightly from the results for dominant pines only [4] and from the results from Austria [3]. Scots pine grows poorly on Rendzic and Mollic Leptosols and most poorly on Calcaric Fluvisols. However, due to the high variability of diameter increment and the smaller sample of trees on some soil units, the differences were significant only for some pairs of soil units: Dystric Cambisols > Eutric Cambisols and Rendzic Leptosols, and Haplic Luvisols > Eutric Cambisols. It appears that Scots pine reaches maximum growth rates on slightly dystric soils. Similar findings were reported from Austria [20], where the highest diameter growth was found on Dystric Planosols, Dystric Gleysols, and Fluvisols, and the lowest on calcareous Leptosols and Chromic Cambisols. In hemi-boreal forests, Scots pine trees grow better on eutrophic and mesoeutrophic soil than on oligotrophic soil [43].
Black pine grew well on Dystric and Calcaric Cambisols. However, a significant difference between soil units was found between Chromic Cambisols, on which the lowest diameter increment of black pine was registered, and several other soil units (Calcaric and Dystric Cambisols and Mollic Leptosols). A study from Austria reported smaller diameter growth on calcareous Leptosols compared to that on Chromic Cambisols [3], which was not confirmed in our study. However, we found that growth was significantly poorer on Rendzic Leptosols compared to that on Calcaric Cambisols.
Our results generally show that the growth of all three tree species was poor on calcareous Leptosols, which are poor in nutrients and have a low water-holding capacity [3].

Limitations of the Study
The study has some limitations that must be noted (see also [4]). First, the influential tree and stand factors, except for long-term averages, were measured at the beginning of the 10-year inventory period. This is a common approach when national forest inventory data are used (e.g., [1,27]). However, stand structure can change considerably over the course of a decade, which was not accounted for in our study. Second, the study used only long-term climate data; extreme weather events and climate anomalies was not addressed. Third, we did not consider some tree variables that may affect diameter growth (e.g., vitality status). The accuracy of the soil map is another limitation [59]. Finally, our study area belongs to the southern part of the Scots pine range, meaning that our estimates of the responses to growth factors cannot be considered average or representative. Some of these weaknesses were partly compensated for by the large data set and diversity of the study site. Further studies are needed to understand the complex interactions between the variables that influence the growth of tree species.

Conclusions
Although the developed models are only locally accurate and cannot be used outside the study area without validation, the model predictions can be compared to those in other stand growth simulators and other geographical regions. The study found differences in the response of the diameter growth of three tree species to tree, stand, site, and climatic variables. The models of the diameter increment for a silver fir, Scots pine, and black pine differ in the set of predictors and their importance. The following key points were identified:

•
The model for fir explained a higher percentage of the variation in diameter growth compared to the models for Scots pine and black pine. • Nine predictors were in common with all three models. Most coefficients in the tree species models for the same predictors were of the same direction. The predictors with contrasting effects were elevation, mean annual temperature, and diurnal range. The diameter growth of black pine positively responded to elevation, while this was not the case for fir and Scots pine. The diameter growth of both pine tree species, in contrast to that of fir, decreased with an increase in mean annual temperature and increased with a higher diurnal range.

•
Tree diameter was the most important variable for fir growth having the inverted U-shaped effect, while the effect of tree diameter on the diameter growth of pines was positive at a decreasing rate. This indicates differences in stand structure between firand pine-dominated stands. • Stand variables were relatively more important predictors for the diameter growth of the pine species compared to fir. • Long-term climatic averages explained most of the variability in pine diameter growth. The growth of Scots and black pine increased with an increase in mean diurnal range and decreased with an increase in mean annual temperature.

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Relatively broad soil classes explained a substantial part of the variability in tree diameter growth. The diameter growth of fir, Scots pine, and black pine differed significantly between 16, 3, and 4 pairs of soil units, respectively, when other factors were set at their mean values. This indicates the importance of local soil conditions. • The findings on the predictors of diameter growth highlight the need for forest managers to pay more attention to those predictors that can be easily measured and controlled by forest management to provide optimal conditions for the growth of the observed tree species.
Appendix A