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Citation: Bonˇcina, A.; Trifkovi´c, V.;
Ficko, A. 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.
Forests 2023,14, 793. https://
doi.org/10.3390/f14040793
Academic Editor: Xiangdong Lei
Received: 17 February 2023
Revised: 3 April 2023
Accepted: 8 April 2023
Published: 12 April 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
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
Andrej Bonˇcina * , Vasilije Trifkovi´c and Andrej Ficko
Department of Forestry and Renewable Forest Resources, Biotechnical Faculty, University of Ljubljana,
Veˇcna pot 83, 1000 Ljubljana, Slovenia; vasilije.trifkovic@bf.uni-lj.si (V.T.); andrej.ficko@bf.uni-lj.si (A.F.)
*Correspondence: andrej.boncina@bf.uni-lj.si; Tel.: +386-1-3203-500
Abstract:
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, and
environmental factors and (2) test for differences in their growth rate on different soils. Based on
26,291 permanent sampling plots (500 m
2
each), we developed a linear mixed-effects model of
the diameter increment for each of these tree species. The models explained 32%–47% of the total
diameter increment variability. The models differ in the set of predictors. All models suggested a
non-linear effect of tree diameter on diameter increment. Nine predictors were common to all three
models (stand basal area, quadratic mean diameter, basal area of overtopping trees, the proportion of
beech in the stand volume, inclination, elevation, mean annual temperature, mean diurnal range,
and soil unit), and six predictors were specific for one or two models (tree diameter, logarithm of
tree diameter, proportion of other broadleaves, site productivity, rockiness, eastness index). Tree
diameter was the most important variable for fir growth, while climatic variables explained most of
the variability in pine diameter growth. The soil unit contributed from 5.3% to 7.5% to the explained
diameter increment variability. 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.
Keywords:
individual tree diameter increment model; silver fir; Scots pine; black pine; species
mixture; topography; soil unit; seminatural forest
1. 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), to-
pographic 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.
Forests 2023,14, 793. https://doi.org/10.3390/f14040793 https://www.mdpi.com/journal/forests
Forests 2023,14, 793 2 of 16
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
–
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 prop-
erties [
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.
Forests 2023,14, 793 3 of 16
2. Materials and Methods
2.1. 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%).
Forests 2023, 14, 793 3 of 18
2. Materials and Methods
2.1. Study Area
The study was conducted in a 12,000 km2 forest area in Slovenia (Figure 1). The cli-
mate in Slovenia is a combination of a continental climate in the northeast, an alpine cli-
mate 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 inu-
ence 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 litho-
logical 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-na-
ture 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
m3 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 r (7%), sessile oak (Quercus petraea (Ma.) Liebl., 5%) and Scots
pine (4%). The proportion of black pine is much lower (<1%).
Figure 1. The forested area (green) and the grid of permanent sampling plots (PSP) in Slovenia (PSP
= black dots, n = 26,291) were used in the study.
2.2. Data Sources
Forest inventory data [24] served as the primary source of data for analyzing diame-
ter 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 m2) 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 rst meas-
urements 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 (Ta-
ble A1). Topographic variables were derived from a digital elevation model (12.5 m reso-
lution) [25], while climatic variables were derived from long-term climate records in the
period 1971–2000 [26] and downscaled from the original 1 km2 resolution to the sampling
plot grid using the nearest neighbor method.
2.3. Explanatory Variables and Their Selection
Periodic diameter increment (DI), calculated as the dierence between two consecu-
tive measurements of diameter at breast height over a 10-year period, was transformed
Figure 1.
The forested area (green) and the grid of permanent sampling plots (PSP) in Slovenia
(PSP = black dots, n = 26,291) were used in the study.
2.2. 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.
Forests 2023,14, 793 4 of 16
Table 1. List of variables used in modeling with their means and standard deviations.
Variables Code Unit
Fir Scots Pine Black Pine
Note 1
Mean SD Min Max Mean SD Min Max Mean SD Min Max
Periodic diameter increment of trees ID cm 10y−13.5 2.5 0.0 10.0 2.4 1.8 0.0 10.0 2.2 1.7 0.0 10.0 dv
Initial diameter of a tree D cm 31.8 15.2 10.0 105.0 29.2 10.1 10.0 80.0 27.1 11.5 10.0 77.0 in
Basal area BA m2ha−134.5 11.2 1.0 85.4 29.9 11.3 1.5 81.3 33.4 14.3 1.7 76.9 in
Quadratic mean diameter QMD cm 28.9 7.3 10.0 82.0 23.8 5.4 11.0 56.0 23.7 7.1 11.0 49.0 in
Gini index of tree diameter diversity GINI - 0.3 0.1 0.0 0.8 0.3 0.1 0.0 0.7 0.3 0.1 0.0 0.6 in
Shannon index SHAN - 0.8 0.3 0.0 2.3 0.8 0.4 0.0 2.3 0.3 0.4 0.0 1.9 in
Basal area of overtopping trees BAL m2ha−120.1 12.9 0.0 83.5 14.2 10.3 0.0 68.1 17.1 12.9 0.0 67.1 in
Proportion of beech in BA PBEECH - 0.2 0.2 0.0 1.0 0.1 0.2 0.0 1.0 0.0 0.1 0.0 0.9 in
Proportion of conifers in BA PCONIF - 0.7 0.2 0.0 1.0 0.8 0.2 0.0 1.0 0.9 0.2 0.0 1.0 mc
Proportion of other broadleaves in BA PBROAD - 0.1 0.1 0.0 1.0 0.1 0.2 0.0 1.0 0.1 0.2 0.0 1.0 in
Site productivity K m32.1 0.2 1.1 2.8 1.8 0.2 1.1 2.7 1.5 0.3 1.1 2.7 in
Inclination INCL ◦17.1 8.9 0.0 60.0 13.5 10.8 0.0 53.0 13.4 8.4 0.0 43.0 in
Elevation ELEV m 822.5 241.3 107.0 1644.0 474.1 227.2 90.0 1527.0 554.0 220.1 36.0 1210.0 in
Rockiness ROCK % 28.6 23.7 0.0 100.0 5.3 11.3 0.0 100.0 20.8 16.8 0.0 100.0 in
Eastness index (0-1. E; 0-(-1). W) EAST - 0.0 0.4 −0.6 0.5 0.0 0.4 −0.6 0.5 −0.1 0.4 −0.6 0.5 in
Northness index (0-1. N; 0-(-1). S) NORTH - 0.3 0.4 −0.3 1.0 0.2 0.4 −0.3 1.0 0.3 0.4 −0.3 0.8 in
Annual amount of precipitation MAP mm 1729.4 327.1 850.0 3600.0 1532.1 411.6 850.0 2900.0 1379.1 556.7 850.0 2900.0 in
Mean annual temperature MAT ◦C 7.6 1.4 3.0 11.0 8.6 1.7 3.0 13.0 9.4 2.8 3.0 13.0 in
Mean diurnal range (TMAX-TMIN) BIO2 ◦C 10.0 2.1 0.0 16.0 9.2 2.0 2.0 14.0 9.5 2.8 0.0 14.0 in
Max temperature of warmest month BIO5 ◦C 22.8 2.1 16.0 26.0 24.1 2.1 16.0 28.0 24.4 3.0 16.0 28.0 mc
Min temperature of coldest month BIO6 ◦C−4.5 1.2 −9.5 −1.0 −3.8 1.1 −9.5 1.5 −3.1 2.5 −9.5 1.5 mc
Maximum temperature T_MAX ◦C 12.7 1.7 7.0 17.0 13.6 1.8 7.0 18.5 14.5 2.7 7.0 18.5 mc
Minimum temperature T_MIN ◦C 2.7 1.3 −1.0 7.0 4.4 1.2 −1.0 7.0 5.0 1.8 1.0 9.0 mc
Mean temperature of vegetation period T_VEG ◦C 7.2 1.6 1.0 11.3 8.5 2.0 2.3 12.0 9.1 2.7 2.3 12.0 mc
Solar radiation SOLAR kJ m−21890.0 84.3 1580.0 2130.0 1956.2 104.4 1610.0 2395.0 2011.8 174.2 1610.0 2335.0 mc
FAO soil unit * SOIL - - - - - - - - - - - - - in
1dv, dependent variable; in, included in modeling; mc, excluded due to multicollinearity; * categorical variable.
Forests 2023,14, 793 5 of 16
2.3. 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 differ-
ences 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 possi-
ble 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
MAT2in 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 con-
tinuous 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.
Forests 2023,14, 793 6 of 16
2.4. Modeling Approach
The diameter increment of the three tree species was modeled with a linear mixed-
effects 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)).
√ID =b0+b1D+b2D2+b3log D+b4√BA +b5QMD +b6GINI +b7S HAN +b8BAL+
b9PBEECH +b10PBROAD +b11K+b12 INCL +b13 ELEV +b14ROCK +b15EAST+
b16NORTH +b17MAP +b18MAT +b19 MAT2+b20 MAT :MAP +b21 BIO2+b22SOI L+
(1|PSP )+ε
(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 (
τ
00), 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]).
3. Results
3.1. 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, respec-
tively. 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
Forests 2023,14, 793 7 of 16
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.
Table 2.
Results of fitting the linear mixed effect model of periodic diameter increment (stepwise method).
Fir Scots Pine Black Pine
Estimate p-Value VIF Rm% Estimate p-Value VIF Rm% Estimate p-Value VIF Rm%
(Intercept) 1.478 0.000 - - 2.061 0.00 - - 1.812 0.00 - -
D 0.067 0.000 16.19 57.62 - - - - - - - -
D2−0.001 0.000 15.31 - - - - - - - -
log (D) - - - - 0.299 0.00 1.81 8.51 0.326 0.00 1.94 9.02
sqrt (BA) −0.187 0.000 1.73 21.85 −0.130 0.00 1.56 27.66 −0.147 0.00 1.71 42.86
QMD −0.002 0.000 1.62 5.30 −0.024 0.00 1.50 13.83 −0.013 0.00 1.99 <0.01
GINI 0.723 0.000 1.12 1.32 - - - - - - - -
SHAN −0.055 0.000 1.54 <0.01 −0.121 0.00 1.23 5.32 - - - -
BAL −0.006 0.000 3.36 1.32 −0.004 0.00 1.60 2.13 −0.005 0.00 1.73 3.76
PBEECH −0.434 0.000 1.21 4.64 −0.517 0.00 1.17 8.51 −0.456 0.00 1.12 0.75
PBROAD 0.290 0.000 1.60 <0.01 - - - - - - - -
K 0.106 0.000 1.19 <0.01 0.137 0.00 1.14 2.13 - - - -
INCL −0.006 0.000 1.22 1.32 −0.005 0.00 1.54 4.26 −0.007 0.00 1.17 4.51
ELEV −0.000 0.014 2.16 <0.01 −0.000 0.00 2.91 3.19 0.000 0.00 3.42 3.76
ROCK −0.001 0.000 1.49 <0.01 - - - - - - - -
EAST −0.030 0.001 1.01 <0.01 - - - - - - - -
MAT 0.051 0.000 3.07 1.32 −0.079 0.00 3.78 9.57 −0.089 0.00 6.19 16.54
BIO2 −0.010 0.000 2.75 <0.01 0.049 0.00 3.21 8.51 0.058 0.00 4.34 11.28
SOIL * - - 2.76 5.30 - - 2.10 6.38 - - 2.46 7.52
CMc - - - - - - - - −0.010 0.91 - -
CMe −0.133 0.000 - - −0.108 0.00 - - −0.121 0.15 - -
CMx −0.297 0.000 - - −0.022 0.28 - - −0.311 0.00 - -
FLc - - - - −0.399 0.00 - - - - - -
FLe - - - - −0.118 0.11 - - - - - -
GLd - - - - −0.058 0.44 - - - - - -
GLe - - - - −0.010 0.88 - - - - - -
LPd −0.082 0.000 - - 0.029 0.41 - - - - - -
LPk −0.284 0.000 - - −0.111 0.00 - - −0.222 0.00
LPm −0.261 0.000 - - −0.196 0.00 - - −0.074 0.38 - -
LVh −0.035 0.294 - - 0.026 0.32 - - - - - -
PLd 0.026 0.669 - - −0.073 0.00 - - - - - -
PLe - - - - −0.109 0.00 - - - - - -
* CMd served as the reference soil unit.
Table 3. Goodness-of-fit measures for the linear mixed-effect models.
Conditional R2Marginal R2ICC RMSE Sigma τ00
Fir 0.470 0.308 0.234 0.556 0.586 0.105
Scots pine 0.322 0.129 0.222 0.568 0.595 0.101
Black pine 0.316 0.192 0.153 0.567 0.580 0.061
3.2. 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.
Forests 2023,14, 793 8 of 16
Forests 2023, 14, 793 10 of 18
Figure 2. Predictions of the periodic diameter increment of r, Scots pine, and black pine. Only
variables that remained in the nal model for individual tree species (see Table 2) are shown. Vari-
ables: D, tree diameter; BA, basal area; QMD, quadratic mean diameter; GINI, Gini index; SHAN,
Figure 2.
Predictions of the periodic diameter increment of fir, Scots pine, and black pine. Only variables
that remained in the final model for individual tree species (see Table 2) are shown. Variables: D, tree
diameter; BA, basal area; QMD, quadratic mean diameter; GINI, Gini index; SHAN, Shannon index;
BAL; basal area of overtopping trees; PBEECH, the proportion of beech in stand basal area; PBROAD;
the proportion of other broadleaves; K, site productivity; INCL, inclination; ELEV, elevation; ROCK,
rockiness; EAST, eastness index; MAT, mean annual temperature; BIO2, mean diurnal range.
Forests 2023,14, 793 9 of 16
Forests 2023, 14, 793 11 of 18
Shannon index; BAL; basal area of overtopping trees; PBEECH, the proportion of beech in stand
basal area; PBROAD; the proportion of other broadleaves; K, site productivity; INCL, inclination;
ELEV, elevation; ROCK, rockiness; EAST, eastness index; MAT, mean annual temperature; BIO2,
mean diurnal range.
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 r
(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 r (<3%). SOIL explained 5.5 to 7.5% of the DI variability (Table 2). The im-
pact of SOIL on the diameter increment of r was greater than that of climatic or topo-
graphic variables, which was not the case for both pine species.
3.2. Dierences 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 dierent soil units.
Figure 3. Predicted periodic diameter increment of silver r, Scots pine, and black pine on soil units.
Mean values and standard deviations are shown.
Post hoc analysis revealed a limited number of signicant dierences in the growth
of individual tree species between soil units (Table 4).
There were signicant dierences in the diameter growth of r within Cambisols.
Growth on Dystric Cambisols and Dystric Planosols was signicantly 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 signicantly faster on Dystric Cambisols than
that on Eutric Cambisols and Rendzic Leptosols. A similar paern was observed for
growth on Haplic Luvisols, where growth was faster than that on Eutric Cambisols.
Black pine growth on Chromic Cambisols was signicantly slower than that on the
two other Cambisols (CMc and CMd) and Mollic Leptosols. Black pine grew beer on
Calcaric Cambisols than on Rendzic Leptosols.
Figure 3.
Predicted periodic diameter increment of silver fir, Scots pine, and black pine on soil units.
Mean values and standard deviations are shown.
Table 4.
Cohen’s d values for pairs of soil units. Significant differences at p
≤
0.05 are shown in bold.
(a) Fir
CMe CMx LPd LPk LPm LVh PLd
CMd 0.23 0.51 0.14 0.48 0.44 0.06 −0.04
CMe - 0.28 −0.09 0.26 0.22 −0.17 −0.27
CMx - - −0.37 −0.02 −0.06 −0.45 −0.55
LPd - - - 0.34 0.31 −0.08 −0.18
LPk - - - - −0.04 −0.42 −0.53
LPm - - - - - −0.38 −0.49
LVh - - - - - - −0.11
(b) Scots pine
CMe CMx FLc FLe GLd GLe LPd LPk LPm LVh PLd PLe
CMd 0.18 0.04 0.67 0.20 0.10 0.02 −0.05 0.19 0.33 −0.04 0.12 0.18
CMe - −0.14 0.49 0.02 −0.08 −0.16 −0.23 0.01 0.15 −0.23 −0.06 0.00
CMx - - 0.63 0.16 0.06 −0.02 −0.09 0.15 0.29 −0.08 0.09 0.15
FLc - - - −0.47 −0.57 −0.65 −0.72 −0.48 −0.34 −0.71 −0.55 −0.49
FLe - - - - −0.10 −0.18 −0.25 −0.01 0.13 −0.24 −0.07 −0.02
GLd - - - - - −0.08 −0.15 0.09 0.23 −0.14 0.03 0.08
GLe - - - - - - −0.07 0.17 0.31 −0.06 0.11 0.17
LPd - - - - - - - 0.24 0.38 0.01 0.17 0.23
LPk - - - - - - - - 0.14 −0.23 −0.06 0.00
LPm---------−0.37 −0.21 −0.15
LVh - - - - - - - - - - 0.17 0.23
PLd - - - - - - - - - - - 0.06
(c) Black pine
CMd CMe CMx LPk LPm
CMc −0.02 0.19 0.52 0.37 0.11
CMd - 0.02 0.54 0.38 0.13
CMe - - 0.33 0.17 −0.08
CMx - - - −0.15 −0.41
LPk - - - - −0.26
Forests 2023,14, 793 10 of 16
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.
4. Discussion
4.1. 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 condi-
tions [
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
Forests 2023,14, 793 11 of 16
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 hemi-
boreal 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
–
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.
Forests 2023,14, 793 12 of 16
4.2. 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 vari-
ability 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 differ-
ences 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
].
4.3. 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
Forests 2023,14, 793 13 of 16
studies are needed to understand the complex interactions between the variables that
influence the growth of tree species.
5. 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 differ-
ences 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 fir-
and 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.
•
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 man-
agers 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.
Author Contributions:
Conceptualization, A.B.; methodology, A.B.; software, V.T.; validation, V.T.,
A.B. and A.F.; data curation, V.T.; writing—original draft preparation, A.B.; writing—review and
editing, A.B. and A.F. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the research projects V4-2211 Managing Forest Risks in the Era
of Climate Change, V4-2014 The Development of Forest Models for Slovenia and the research program
P4-0059 Forest, Forestry and Renewable Forest Resources, financed by the Slovenian Research Agency.
Data Availability Statement: Not applicable.
Acknowledgments:
We thank the Slovenia Forest Service for providing forest inventory data and
Jan Nagel for proofreading and editing the manuscript.
Conflicts of Interest:
The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in this paper.
Forests 2023,14, 793 14 of 16
Appendix A
Table A1. The number of sampling plots per tree species and soil units used in modeling.
Soil Units Abbrevation Forest Area (%) Number of Plots Number of Trees
Fir Scots Pine Black Pine Fir Scots Pine Black Pine
Dystric Cambisols CMd 30.63 2942 3581 70 11612 15,492 327
Calcaric Cambisols CMc 0.30 - - 46 - - 446
Eutric Cambisols CMe 8.94 970 1014 54 3602 4512 338
Chromic Cambisols CMx 18.43 5462 760 170 28,172 3229 1281
Calcaric Fluvisols FLc 0.07 - 30 - - 168 -
Eutric Fluvisols FLe 0.21 - 43 - - 158 -
Dystric Gleysols GLd 0.20 - 40 - - 180 -
Eutric Gleysols GLe 0.19 - 43 - - 248 -
Dystric Leptosols LPd 4.16 735 214 - 2534 744 -
Rendzic Leptosols LPk 28.17 7194 1054 330 26,515 4902 3154
Mollic Leptosols LPm 1.93 456 193 46 1487 847 555
Haplic Luvisols LVh 2.51 218 409 - 956 1635 -
Dystric Planosols PLd 2.88 56 513 - 171 2567 -
Eutric Planosols PLe 1.39 - 278 - - 1392 -
Total - 100 18,033 8172 716 75,049 36,074 6101
References
1. Pretzsch, H. Forest Dynamics, Growth and Yield, 1st ed.; Springer: Berlin, Germany, 2009; pp. 1–37.
2.
Long, S.; Zeng, S.; Liu, F.; Wang, G. Influence of slope, aspect and competition index on the height-diameter relationship of
Cyclobalanopsis glauca trees for improving prediction of height in mixed forests. Silva Fenn. 2020,54, 10242. [CrossRef]
3.
Vospernik, S. Basal area increment models accounting for climate and mixture for Austrian tree species. For. Ecol. Manag.
2021
,
480, 118725. [CrossRef]
4.
Bonˇcina, A.; Klopˇciˇc, M.; Trifkovi´c, V.; Ficko, A.; Simonˇciˇc, P. Tree and stand growth differ among soil classes in semi-natural
forests in central Europe. Catena 2023,222, 106854. [CrossRef]
5.
Schelhaas, M.-J.; Hengeveld, G.M.; Heidema, N.; Thürig, E.; Rohner, B.; Vacchiano, G.; Vayreda, J.; Redmond, J.; Socha, J.; Fridman, J.; et al.
Species-specific, pan-European diameter increment models based on data of 2.3 million trees. For. Ecosyst.
2018
,5, 21. [CrossRef]
6.
Scharnweber, T.; Manthey, M.; Wilmking, M. Differential radial growth patterns between beech (Fagus sylvatica L.) and oak
(Quercus robur L.) on periodically waterlogged soils. Tree Physiol. 2013,33, 425–437. [CrossRef]
7.
Calvaruso, C.; Kirchen, G.; Saint-André, L.; Redon, P.-O.; Turpault, M.-P. Relationship between soil nutritive resources and the
growth and mineral nutrition of a beech (Fagus sylvatica) stand along a soil sequence. Catena 2017,155, 156–169. [CrossRef]
8.
Kobal, M.; Grˇcman, H.; Zupan, M.; Levaniˇc, T.; Simonˇciˇc, P.; Kadunc, A.; Hladnik, D. Influence of soil properties on silver fir
(Abies alba Mill.) growth in the Dinaric Mountains. For. Ecol. Manag. 2015,337, 77–87. [CrossRef]
9.
IUSS Working Group WRB. World Reference Base for Soil Resources 2014, Update 2015, International Soil Classification System for
Naming Soils and Creating Legends for Soil Maps; World Soil Resources Reports No. 106; FAO: Rome, Italy, 2015.
10.
Bosela, M.; Tumajer, J.; Cienciala, E.; Dobor, L.; Kulla, L.; Marˇciš, P.; Popa, I.; Sedmák, R.; Sedmáková, D.; Sitko, R.; et al. Climate
warming induced synchronous growth decline in Norway spruce populations across biogeographical gradients since 2000. Sci.
Total. Environ. 2021,752, 141794. [CrossRef]
11.
Pukkala, T. Predicting diameter growth in even-aged Scots pine stands with a spatial and non-spatial model. Silva Fenn.
1989
,23,
101–116. [CrossRef]
12.
Palahí, M.; Pukkala, T.; Miina, J.; Montero, G. Individual-Tree Growth and Mortality Models for Scots Pine (Pinus sylvestris L.) in
North-East Spain. Ann. For. Sci.
2003
,60, 1–10. Available online: https://hal.archives-ouvertes.fr/hal-00883671 (accessed on 15
March 2023). [CrossRef]
13.
Crecente-Campo, F.; Soares, P.; Tomé, M.; Diéguez-Aranda, U. Modelling annual individual-tree growth and mortality of Scots
pine with data obtained at irregular measurement intervals and containing missing observations. For. Ecol. Manag.
2010
,260,
1965–1974. [CrossRef]
14.
Tavankar, F.; Rafie, H.; Latterini, F.; Nikooy, M.; Senfett, M.; Behjou, F.K.; Maleki, M. Growth parameters of Pinus nigra J.F. Arnold
and Picea abies (L.) H. Karst. plantations and their impact on understory woody plants in above-timberline mountain areas in the
north of Iran. J. For. Sci. 2018,64, 416–426. [CrossRef]
15.
Houtmeyers, S.; Brunner, A. Individual tree growth responses to coinciding thinning and drought events in mixed stands of
Norway spruce and Scots pine. For. Ecol. Manag. 2022,522, 120447. [CrossRef]
16.
Hökkä, H.; Repola, J.; Moilanen, M. Modelling volume growth response of young Scots pine (Pinus sylvetris) stands to N, P, and K
fertilization in drained peatland sites in Finland. Can. J. For. Res. 2012,42, 1359–1370. [CrossRef]
17.
Repola, J.; Hökkä, H.; Salminen, H. Models for diameter and height growth of Scots pine, Norway spruce and pubescent birch in
drained peatland sites in Finland. Silva Fenn. 2018,52, 10055. [CrossRef]
18.
Pretzsch, H.; del Río, M.; Ammer, C.; Avdagic, A.; Barbeito, I.; Bielak, K.; Brazaitis, G.; Coll, L.; Dirnberger, G.; Drössler, L.; et al.
Growth and yield of mixed versus pure stands of Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) analysed
along a productivity gradient through Europe. Eur. J. For. Res. 2015,134, 927–947. [CrossRef]
Forests 2023,14, 793 15 of 16
19.
Ruiz-Peinado, R.; Pretzsch, H.; Löf, M.; Heym, M.; Bielak, K.; Aldea, J.; Barbeito, I.; Brazaitis, G.; Drössler, L.; Godvod, K.; et al.
Mixing effects on Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) productivity along a climatic gradient
across Europe. For. Ecol. Manag. 2020,482, 118834. [CrossRef]
20.
Monserud, R.A.; Sterba, H. A basal area increment model for individual trees growing in even- and uneven-aged forest stands in
Austria. For. Ecol. Manag. 1996,80, 57–80. [CrossRef]
21. Myung, I.J. Tutorial on maximum likelihood estimation. J. Math. Psychol. 2003,47, 90–100. [CrossRef]
22. Buser, S.; Komac, M. Geologic map of Slovenia 1:250.000. Geologija 2002,45, 335–340. [CrossRef]
23.
Vidic, N.J.; Prus, T.; Grˇcman, H.; Zupan, M.; Lisec, A.; Kralj, T.; Vršˇcaj, B.; Rupreht, J.; Šporar, M.; Suhadolc, M.; et al. Soils of
Slovenia with Soil Map 1:250000; Publications Office of the European Union: Luxembourg, 2015. [CrossRef]
24. SFS. Forestry Data Collection; Slovenia Forest Service (SFS): Ljubljana, Slovenia, 2014.
25. GURS. Digital Relief Model; Surveying and Mapping Authority of the Republic of Slovenia: Ljubljana, Slovenia, 2021.
26.
SEA. Databases and Maps of the Slovenian Environment Agency (ARSO); Slovenian Environment Agency: Ljubljana, Slovenia, 2022.
27.
Trifkovi´c, V.; Bonˇcina, A.; Ficko, A. Analyzing asymmetries in the response of European beech to precipitation anomalies in
various stand and site conditions using decadal diameter censuses. Agric. For. Meteorol. 2022,327, 109195. [CrossRef]
28.
Bonˇcina, A.; Rozman, A.; Dakskobler, I.; Klopˇciˇc, M.; Babij, V.; Poljanec, A. Gozdni Rastišˇcni Tipi Slovenije: Vegetacijske, Sestojne
in Upravljavske Znaˇcilnosti, 1st ed.; Oddelek za gozdarstvo in obnovljive gozdne vire Biotehniške fakultete, Zavod za gozdove
Slovenije: Ljubljana, Slovenia, 2021; p. 575.
29.
MAFF. Pedological Map of Slovenia; Ministry of Agriculture, Forestry and Food: Ljubljana, Slovenia, 2007. Available online:
https://rkg.gov.si/vstop/ (accessed on 22 March 2023).
30.
FAO. Soil Map of the World, Revised Legend, with Corrections; World Resources Report No. 60; FAO: Rome, Italy, 1988; pp. 119–137.
31.
Wang, W.; Chen, X.; Zeng, W.; Wang, J.; Meng, J. Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for
Oaks (Quercus spp.) Considering Forest Structural Diversity. Forests 2019,10, 474. [CrossRef]
32.
Uzoh, F.C.C.; Oliver, W.W. Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout
the western United States using a multilevel linear mixed effects model. For. Ecol. Manag. 2008,256, 438–445. [CrossRef]
33.
Bates, D.; Mächler, M.; Bolker, B.; Walker, S. Fitting Linear Mixed-Effects Models Using lme4. J. Stat. Softw.
2015
,67, 48. [CrossRef]
34.
Lüdecke, D.; Ben-Shachar, M.S.; Patil, I.; Waggoner, P.; Makowski, D. performance: An R Package for Assessment, Comparison
and Testing of Statistical Models. J. Open Source Softw. 2021,6, 3139. [CrossRef]
35.
Length, R.V. emmeans: Estimated Marginal Means, aka Least-Squares Means. R Package Version 1.7.3. 2022. Available online:
https://CRAN.R-project.org/package=emmeans (accessed on 26 February 2023).
36.
Bueno, S.; Bevilacqua, E. Modeling Stem Diameter Increment in Individual Pinus occidentalis Sw. trees in La Sierra, Dominican
Republic. For. Syst. 2010,19, 170. [CrossRef]
37.
Hu, X.; Duan, G.; Zhang, H. Modelling Individual Tree Diameter Growth of Quercus mongolica Secondary Forest in the Northeast
of China. Sustainability 2021,13, 4533. [CrossRef]
38.
Klopciˇc, M.; Boncina, A. Patterns of tree growth in a single tree selection silver fir–European beech forest. J. For. Res.
2010
,15,
21–30. [CrossRef]
39.
Dobrowolska, D.; Bonˇcina, A.; Klumpp, R. Ecology and silviculture of silver fir (Abies alba Mill.): A review. J. For. Res.
2017
,22,
326–335. [CrossRef]
40.
Moreno, P.C.; Palmas, S.; Escobedo, F.J.; Cropper, W.P.; Gezan, S.A. Individual-Tree Diameter Growth Models for Mixed
Nothofagus Second Growth Forests in Southern Chile. Forests 2017,8, 506. [CrossRef]
41.
Lhotka, J.M.; Loewenstein, E.F. An individual-tree diameter growth model for managed uneven-aged oak-shortleaf pine stands
in the Ozark Highlands of Missouri, USA. For. Ecol. Manag. 2011,261, 770–778. [CrossRef]
42.
Mina, M.; Huber, M.O.; Forrester, D.I.; Thürig, E.; Rohner, B. Multiple factors modulate tree growth complementarity in Central
European mixed forests. J. Ecol. 2017,106, 1106–1119. [CrossRef]
43.
Mikalajunas, M.; Pretzsch, H.; Mozgeris, G.; Linkeviˇcius, E.; Augustaitiene, I.; Augustaitis, A. Scots pine’s capacity to adapt to
climate change in hemi-boreal forests in relation to dominating tree increment and site condition. Iforest—Biogeosciences For.
2021
,
14, 473–482. [CrossRef]
44.
Ficko, A.; Poljanec, A.; Boncina, A. Do changes in spatial distribution, structure and abundance of silver fir (Abies alba Mill.)
indicate its decline? For. Ecol. Manag. 2011,261, 844–854. [CrossRef]
45.
Dănescu, A.; Albrecht, A.T.; Bauhus, J. Structural diversity promotes productivity of mixed, uneven-aged forests in southwestern
Germany. Oecologia 2016,182, 319–333. [CrossRef] [PubMed]
46.
Ha, W. The Relationship between Terrain Factors and Spatial Variability of Soil Nutrients for Pine-Oak Mixed Forest in Qinling
Mountains. J. Nat. Resour. 2015,30, 858–869.
47.
Pyrke, A.F.; Kirkpatrick, J.B. Growth rate and basal area response curves of four Eucalyptus species on Mt. Wellington, Tasmania.
J. Veg. Sci. 1994,5, 13–24. [CrossRef]
48.
Lovynska, V.; Terentiev, A.; Lakyda, P.; Sytnyk, S.; Bala, O.; Gritsan, Y. Comparison of Scots pine growth dynamics in Polissya and
Steppe zone of Ukraine. J. For. Sci. 2021,67, 533–543. [CrossRef]
49.
Hartl-Meier, C.; Dittmar, C.; Zang, C.; Rothe, A. Mountain forest growth response to climate change in the Northern Limestone
Alps. Trees 2014,28, 819–829. [CrossRef]
Forests 2023,14, 793 16 of 16
50.
Domínguez-Delmás, M.; Alejano-Monge, R.; Wazny, T.; González, I.G. Radial growth variations of black pine along an elevation
gradient in the Cazorla Mountains (South of Spain) and their relevance for historical and environmental studies. Eur. J. For. Res.
2013,132, 635–652. [CrossRef]
51.
Lucas-Borja, M.E.; Vacchiano, G. Interactions between climate, growth and seed production in Spanish black pine (Pinus nigra
Arn. ssp. salzmannii) forests in Cuenca Mountains (Spain). New For. 2018,49, 399–414. [CrossRef]
52.
Here¸s, A.-M.; Polanco-Martínez, J.M.; Petritan, I.C.; Petritan, A.M.; Yuste, J.C. The stationary and non-stationary character of the
silver fir, black pine and Scots pine tree-growth-climate relationships. Agric. For. Meteorol. 2022,325, 109146. [CrossRef]
53.
Martín-Benito, D.; del Río, M.; Cañellas, I. Black pine (Pinus nigra Arn.) growth divergence along a latitudinal gradient in Western
Mediterranean mountains. Ann. For. Sci. 2010,67, 401. [CrossRef]
54.
Seho, M.; Kohnle, U.; Albrecht, A.; Lenk, E. Growth Analyses of Four Provenances of European Black Pine (Pinus Nigra) Growing
on Dry Sites in Southwest Germany (Baden-Wuerttemberg). Allg. Forst-Und Jagdztg. 2010,181, 104–116.
55.
Sharma, M. Modelling climate effects on diameter growth of red pine trees in boreal Ontario, Canada. Trees For. People
2021
,
4, 100064. [CrossRef]
56.
Zhang, X.; Yu, P.; Wang, D.; Xu, Z. Density- and age-dependent influences of droughts and intrinsic water use efficiency on
growth in temperate plantations. Agric. For. Meteorol. 2022,325, 109134. [CrossRef]
57.
Dinca, L.; Marin, M.; Radu, V.; Murariu, G.; Drasovean, R.; Cretu, R.; Georgescu, L.; Timi
s
,
-Gânsac, V. Which Are the Best Site and
Stand Conditions for Silver Fir (Abies alba Mill.) Located in the Carpathian Mountains? Diversity 2022,14, 547. [CrossRef]
58.
Walder, D.; Krebs, P.; Bugmann, H.; Manetti, M.C.; Pollastrini, M.; Anzillotti, S.; Conedera, M. Silver fir (Abies alba Mill.) is able
to thrive and prosper under meso-Mediterranean conditions. For. Ecol. Manag. 2021,498, 119537. [CrossRef]
59. Vršˇcaj, B.; Repe, B.; Simonˇciˇc, P. The Soils of Slovenia; Springer: Dordrecht, Netherlands, 2017. [CrossRef]
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