![An overview of spatial distribution of the sample plots with the range of the investigated relict-endemic forest communities of the Balkan Peninsula [20]. The sample plots of Serbian spruce are located in the Bosnian municipality of Višegrad (Veliki Stolac) and the Macedonian pine in the Serbian municipality of Tutin (Beleg).](https://www.researchgate.net/publication/353947561/figure/fig1/AS:1057801522671616@1629210944014/An-overview-of-spatial-distribution-of-the-sample-plots-with-the-range-of-the_Q320.jpg)
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Article
Impact of Mixing on the Structural Diversity of Serbian Spruce
and Macedonian Pine Endemic to Relict Forest Communities in
the Balkan Peninsula
Aleksandar Popovi´c * , Damjan Panti´c , Milan Medarevi´c, Biljana Šljuki´c and Snežana Obradovi´c
Citation: Popovi´c, A.; Panti´c, D.;
Medarevi´c, M.; Šljuki´c, B.; Obradovi´c,
S. Impact of Mixing on the Structural
Diversity of Serbian Spruce and
Macedonian Pine Endemic to Relict
Forest Communities in the Balkan
Peninsula. Forests 2021,12, 1095.
https://doi.org/10.3390/f12081095
Academic Editor: Dominick
A. DellaSala
Received: 1 July 2021
Accepted: 10 August 2021
Published: 16 August 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 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/).
Department of Forestry, Faculty of Forestry, University of Belgrade, KnezaVišeslava 1, 11000 Belgrade, Serbia;
damjan.pantic@sfb.bg.ac.rs (D.P.); milan.medarevic@sfb.bg.ac.rs (M.M.); biljana.sljukic@sfb.bg.ac.rs (B.Š.);
snezana.obradovic@sfb.bg.ac.rs (S.O.)
*Correspondence: aleksandar.popovic@sfb.bg.ac.rs; Tel.: +381-64-347-37-49
Abstract:
The aim of this paper is to analyze the effect of different degrees of mixing on the diversity
structure in stands left to spontaneous development. The research included two communities of
species endemic to the Balkan Peninsula—the Serbian spruce (Picea omorika Panˇci´c Purk.) and the
Macedonian pine (Pinus peuce Griseb). Data from eight sample plots were used in the research. The
changes in diameter and height structure, spatial arrangement of trees, and diameter differentiation
were analyzed. The analyzed parameters of structural diversity show relatively low to moderate
values. Results showed an increase in mixing was reflected in the width and shape of distributions.
A spatial analysis of stands with a higher degree of mixing showed a tendency towards a random to
regular distribution of individuals, in contrast to stands with a lower degree of mixing which showed
a tendency towards a clump distribution. The pronounced species’ dimensional and spatial diversity
confirms their importance to the condition of modern forest management. Significant differences
in the change of structure are shown by stands with a share of admixed species of above 20% by
volume. The obtained results refer to stands left to spontaneous development, suggesting than an
active research and management approach must be assumed to realize the goal of protecting rare
forest ecosystems.
Keywords: rare forests; biodiversity; stand structure; spatial pattern
1. Introduction
The diversity of vegetation of the Balkan Peninsula, in a broader context, can be
explained by its position where diametrically opposed climatic influences meet and affect
the area [
1
]. The most important relict-endemic forest ecosystems of the Balkan Peninsula
are the communities of Serbian spruce (Picea omorika) and Macedonian pine (Pinus peuce).
Anthropogenic impacts in the past have reduced the range of Serbian spruce to small and
inaccessible habitats along the middle course of the Drina River (Bosnia and Herzegovina,
Serbia) and Macedonian pine to habitats of the highland region (Bulgaria, Serbia, Macedo-
nia, Montenegro, Albania, and Greece) (Figure 1) [
2
]. The character of habitats in which
these communities develop, the passive approach to their protection, as well as the absence
of economic interests, have resulted in poor research of these ecosystems [3,4].
Structural parameters have been assessed as very good indicators of biodiversity and
are recommended as its direct measure [
4
,
5
]. Whittaker [
6
] defines different categories of
biodiversity. The proposed division at the stand level implies a variety of tree positions,
tree species, and their dimensions [
7
–
9
]. The study of these characteristics does not neglect
the significant three-dimensional structure of stands [8,10–13].
Today, unlike in the past when monocultures were of great importance in Europe,
ever more attention is paid to heterogeneous mixed stands [
4
]. The heterogeneity of
natural spontaneously developed stands is higher than in those managed by man [
4
,
14
].
Forests 2021,12, 1095. https://doi.org/10.3390/f12081095 https://www.mdpi.com/journal/forests
Forests 2021,12, 1095 2 of 18
Given their structural complexity, the nature of their research is very complex [
15
,
16
].
Conventional approaches to stand condition analysis based on data such as mean diameter,
dominant height, volume per hectare, etc. ignore the complex nature of the stand and are
predominantly economic in nature. The observing of a stand as a structurally functional
community of individual trees gives us the opportunity to better understand the complex
relationships between individuals in it.
The aim of this research is to evaluate the effect of mixing on the diversity of dimen-
sions and horizontal and vertical structures of stands in relict-endemic communities of
Serbian spruce and Macedonian pine in the area of the Balkan Peninsula. The starting
hypothesis is that an increase in mixing causes an increase in structural differentiation, or
the structural diversity of stands [4,5,17–19].
Forests 2021, 12, x FOR PEER REVIEW 2 of 18
natural spontaneously developed stands is higher than in those managed by man [4,14].
Given their structural complexity, the nature of their research is very complex [15,16].
Conventional approaches to stand condition analysis based on data such as mean diam-
eter, dominant height, volume per hectare, etc. ignore the complex nature of the stand
and are predominantly economic in nature. The observing of a stand as a structurally
functional community of individual trees gives us the opportunity to better understand
the complex relationships between individuals in it.
The aim of this research is to evaluate the effect of mixing on the diversity of di-
mensions and horizontal and vertical structures of stands in relict-endemic communities
of Serbian spruce and Macedonian pine in the area of the Balkan Peninsula. The starting
hypothesis is that an increase in mixing causes an increase in structural differentiation, or
the structural diversity of stands [4,5,17–19].
Figure 1. An overview of spatial distribution of the sample plots with the range of the investigated
relict-endemic forest communities of the Balkan Peninsula [20]. The sample plots of Serbian spruce
are located in the Bosnian municipality of Višegrad (Veliki Stolac) and the Macedonian pine in the
Serbian municipality of Tutin (Beleg).
Figure 1.
An overview of spatial distribution of the sample plots with the range of the investigated
relict-endemic forest communities of the Balkan Peninsula [
20
]. The sample plots of Serbian spruce
are located in the Bosnian municipality of Višegrad (Veliki Stolac) and the Macedonian pine in the
Serbian municipality of Tutin (Beleg).
2. Materials and Methods
2.1. Research Area
During 2019, four sample plots (SP) were established in the stands of Piceaomorika
and another four in the stands of Pinus peuce (Figure 1). The sample plots were located
Forests 2021,12, 1095 3 of 18
in homogeneous, dense and preserved parts of the studied forest community of different
degrees of mixing. The plots are equal in area (0.30 ha) and of regular square shape
(54.8 m ×54.8 m).
The mixed stands of Piceo-OmorikaeAbieti fagetum ˇ
Col.1965 occupy the edges and
lower areas of the investigated locality (Veliki Stolac), where they spatially lean on mixed
communities of spruce, fir, beech, and Austrian pine. The altitude ranges from 1300 m
(SP 2) to 1370 m (SP 3). The exposure is north, and the slope is 30–42
◦
. The parent rock is
limestone with shallowly developed black soils on it [
21
]. The average annual rainfall is
977 mm with an average annual temperature of 5 ◦C.
The Macedonian pine stands at the investigated locality (Beleg) form a vegetation belt
above the forests of spruce and the forests of spruce and Macedonian pine Piceo-Pinetum
peuces Lakš. 1965 [
20
]. They are located at an altitude ranging from 1825 m (SP 5) to
1910 m (SP 6). The exposures are different (SP 5 W-NW; SP 6 N-NW; SP 7 E; SP 8 N), and
the slope of the terrain is 15–30
◦
. The parent rock is limestone, and the soil is shallow
dystric humus-silicate soil. The average annual rainfall is 749 mm, and the average annual
temperature is 5.2 ◦C.
The share of other tree species in the stands of Serbian spruce (SP 1–4) and Macedonian
pine (SP 5–8), expressed as % of volume per hectare (V ×ha−1), is shown in Table 1.
The stands included in this research have the character of strictly protected natural
communities that have not been exposed to direct anthropogenic influences that could have
compromised their natural character. The preservation of these relict-endemic ecosystems
has been contributed to by the difficult-to-access terrain, distance of the locality from
populated areas, and lack of forest roads.
Table 1.
The shares of admixed tree species in the investigated stands expressed in percentage of volume per admixed species.
Species
Picea omorika Pinus peuce
No. of Sample Plot
1 2 3 4 5 6 7 8
Abies alba 5.4 9.7 9.7 7.8 <1 <1 <1 2.4
Picea abies 3.3 6.7 15.7 7.4 12.3 30.8 38.2
Pinus silvestris 1.5 5.4
Pinus nigra 30.3
Pinus mugo <1
Populus tremula 3.5 <1 <1
Acer pseudoplatanus <1 1.4 1.6 1.4
Fagus moesiaca <1 1.8 <1
Sorbus aucuparia <1 <1
Sum 12.5 19.5 29.5 45.8 7.8 12.7 31.2 40.6
2.2. Data Collection
The positions of the sample plots were recorded with a GPS device. The diameters at
breast height (dhb) and the total heights (h) of all trees with a diameter greater than 10 cm
were measured in the sample plots. The trees were marked with numbers at breast height
and their coordinates were recorded. The coordinates were recorded using a WILD T05
theodolite and a laser distance meter from the defined angles of the sample plots.
2.3. Data Processing
Complex structural analysis based on the spatial relationships of neighboring trees
requires the use of the edge-correction method [
22
]. In order to obtain unbiased data, the
plus-sampling method [
23
,
24
] was used. Trees from 44.7 m
×
44.7 m (0.2 ha) subsamples
from sample plots’ centers were used to avoid the edge effect. All parameters of spatial
analysis were calculated on the basis of a defined subsample.
Forests 2021,12, 1095 4 of 18
2.3.1. The Mixing Effect
The mixing effect by the number of trees in the sample plots was defined by the
measure of evenness E[
25
], the percentage ratio of (H) (the species diversity index [
26
]),
and the maximum diversity (H
max
=lnS), where Sis the number of different tree species
in the sample plot. The mixing effect is also defined according to the percentage share
of species by volume (Table 1). Tree volumes were calculated according to the local
models
V=f(dbh,h)
for the analyzed tree species [
27
–
31
]. Volume was calculated for each
individual tree based on input values of diameter and total height according to two-way
volume tables. The volume thus obtained on the sample plots was calculated per hectare.
The measure of spatial segregation of species used is the mingling index M[
32
].
A structural group of four neighboring trees was used to determine this index [
8
,
33
–
35
].
The index of structural groups is calculated according to the following formula:
Mi=1
4
n
∑
j=1
mj(1)
At the level of the sample plot, index Mwas calculated as the arithmetic mean of
the individual values of the M
i
index of structural groups. The designations used in the
function have the following meaning: iis the ordinal number of the reference tree (1
. . .
N),
Nis the number of trees in the plot, jis the number of the neighboring tree (1
. . .
4), nis
the observed number of neighboring trees (4), and m
j
is a parameter (1 if the reference and
neighboring species are different, 0 if they are the same).
2.3.2. Horizontal Structure
The Clark–Evans aggregation index R[
36
] was used to analyze the spatial pattern
of trees in the sample plots. The index was used according to the adjusted calculation
method [
37
] of real (rA) and expected average distance between individuals (rE), as follows:
R=rA
rE =
1
N
N
∑
i=1ri
0.5 ·A
N1/2 +0.0514 ·P
N+0.041 ·P
N3/2
(2)
Letters in the formula have the following meaning: Ais the area (m
2
), Nis the number
of trees, Pis the perimeter (m), and r
i
is the distance from the i-th tree to the nearest neighbor.
The spatial pattern of trees was determined based on the Ripley’s K(r) function [
38
]. The
edge-correction effect [23,39–41] implies an unbiased way of calculating the K(r) function:
K(r) = N−2|A|∑
i6=j
∑w−1
ij Ir(uij)(3)
Interpretation of the results was performed using the L(r) function, in a form that in
the simplest way shows the change in the Lvalue with an increasing distance r. In the
graphical representation of the spatial pattern of trees, we used the adapted form of the L
(r) function [40,42].
L(r) = rK(r)
π−r(4)
The letters in the previous two functions have the following meanings: Ais the area
(m
2
), Nis the number of trees, u
ij
is the distance between the i-th tree and the j-th tree,
I
r
(u
ij
) is the indicator of the function that equals 1 if u
ij ≤
r(or 0 vice versa), w
ij
is the
edge-correction factor for the i-th tree and its neighboring j-th tree, and ris the analyzed
reference distance.
Forests 2021,12, 1095 5 of 18
2.3.3. Vertical Structure
The height structure by sample plots is shown graphically based on the percentage of
trees (N%) by height classes of 3.0 m width. In order to simplify the comparative analysis of
the height structure of individual sample plots, statistical measures of central tendency (av-
erage height), dispersion (standard deviation, variation width), and distribution (skewness,
kurtosis) were used.
Species profile index A[
43
] was used as a unique measure of the height structure of
the sample plots, based on the adapted method of calculating diversity index H[
26
]. The
comparatively significant relative value of the species profile index A
rel
was obtained from
the ratio of absolute Aand maximum Amax value, as follows:
Arel =A
Amax ·100 =
−S
∑
i=1
Z
∑
j=1pij ·ln pij
ln(S·Z)·100 (5)
The letters used have the following meanings: Sis the number of tree species, Zis the
number of vertical layers (3), p
ij
is the share of species in vertical layers (n
ij
/N), n
ij
is the
number of trees of a certain species in the vertical layer, and Nis the total number of trees.
2.3.4. Diameter Structure
The diameter structure of trees in the sample plots is graphically shown on the basis
of the percentage of trees (N%) by diameter classes of 5 cm width. In order to facilitate
the comparative analysis of diameter distributions in the sample plots, the statistical
parameters listed for the vertical structure were used.
The diameter differentiation index Td [
32
] was used to analyze diameter diversity.
The index quantifies the diversity of reference tree diameters and their nearest neighbor-
ing trees [
5
,
32
,
44
]. A structural group of four neighboring trees was used to determine
this index [
8
,
32
,
33
,
45
]. Structural group indices were calculated according to the follow-
ing equation:
Tdi=1−1
4
n
∑
j=1
min(dbhi,dbhj)
max(dbhi,dbhj)(6)
At sample plot level, the Td index is calculated as the arithmetic mean of the individual
values of the Td
i
index of structural groups. The letters used in the formula have the
following meaning: iis the number of the reference tree (1
. . .
N), jis the number of the
nearest tree (1
. . .
n), nis the number of nearest trees (4), and Nis the total number of trees
in the plot.
In addition to the above parameters and indices, the Gini coefficient (GC) was used to
estimate the structural unevenness of the sample plots [46,47]:
GC =
n
∑
j=1(2j−1−n)baj
n
∑
j=1baj(n−1)
(7)
The letters used have the following meaning: jis the rank of trees according to the
diameter expressed in ascending order from 1 to n,nis the total number of trees in the
sample plot, bajis the basal area of the j-th tree by rank (m2).
The hyperbolic tangent index S[
48
] was used to define the relationships between the
species in the sample plot. The relationship between the diameters of reference trees of
admixed species and dominant species that are spatially closest to the observed reference
Forests 2021,12, 1095 6 of 18
trees was analyzed. A structural group with four neighboring trees was used [
48
]. The
structural group index Siis calculated as follows:
Si=1
2k
k
∑
j=1
1+tanh(aloge
mi
mj) = 1
k
k
∑
j=1
mi2a
mi2a+mj2a=1
k
k
∑
j=1
1
1+ ( mj
mi)2a(8)
The sample plot index Swas calculated as the arithmetic mean of the structural group
indices S
i
without edge-correction [
22
,
46
]. The letters in the previous formula have the
following meaning: iis the number of the reference tree of the admixed species (1
. . .
N),
jis the number of the nearest dominant tree (1
. . .
k), kis the number of nearest dominant
trees to the reference tree (4), m
i
is the reference tree (observed characteristic-dbh
i
), m
j
is the
neighboring tree (observed characteristic- dbh
j
), factor aranges from 0.0 to 1.5 (the most
appropriate is 1.0), and Nis the total number of trees of admixed species in the sample plot.
2.4. Statistical Analysis
Testing of the distribution of the investigated characteristics of trees in relation to their
normal distribution was performed using the Shapiro–Wilk test of normality. The empirical
data of the distribution and normal distribution were compared. The Levene test was used
to test the homogeneity of variance. A comparison of the empirical distributions of the
analyzed characteristics was done based on the Mann–Whitney U test. The acceptance
(rejection) of the hypotheses about the normality of data distribution, i.e., their mutual
differences, was tested at the significance level of 0.05. The analysis of the relationship
between the used structure parameters was performed using the Spearman’s rank-order
correlation. The testing of the spatial patterns was conducted with 199 Monte Carlo
simulations of the null hypothesis of complete spatial randomness. The parts of the L (r)
function above, below, and within confidence the intervals indicate clumped, regular, and
random spatial patterns.
Different software packages [
49
,
50
] were used in the data processing, analysis, and
testing. The spatial analysis of trees was performed using the “spatstat” [
51
] package in
the R-3.5.1 program [52].
3. Results
3.1. Dendrometric Characteristics of the Investigated Forest Communities
Forest communities of relict-endemic species, according to the basic dendrometric
values (Table 2), have the following characteristics. In the stands of Serbian spruce, the
mean diameter per basal area ranges from 24.7 (SP 2) to 29.9 cm (SP 3), and the mean height
ranges from 25.8 (SP 2) to 27.9 m (SP 3). The number of trees ranges from 810 (SP 3) to
1285 pcs
×
ha
−1
(SP 4). The basal area values range from 52.9 (SP 1) to 65.1 m
2×
ha
−1
(SP 4), and volumes from 649 (SP 1) to 794 m
3×
ha
−1
(SP 4). There is an obvious trend of
increasing volume with an increasing degree of mixing of stands of this community (Va%).
In the Macedonian pine stands, the mean diameter per basal area ranges from 31.8 (SP 5) to
44.2 cm (SP 8) and the height ranges from 17.6 (SP 5) to 20.7 m (SP 8). The number of trees
ranges from 326 (SP 8) to 1015 pcs
×
ha
−1
(SP 5), the basal area ranges from 50.1 (SP 8)
to 80.0 m
2×
ha
−1
(SP 5), and the volume ranges from 511 (SP 8) to 700 m
3×
ha
−1
(SP 5).
There is an evident decrease in the number of trees and volume, as well as an increase in
the mean diameter and height with an increase in the mixing of Macedonian pine stands.
Forests 2021,12, 1095 7 of 18
Table 2. Basic numerical characteristics of the sample plots.
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
No. of Measured Trees 299 368 243 386 305 148 134 98
E (%) 25.7 30.8 45.5 51.7 28.3 32.1 46.7 68.2
Va (%) 12.5 19.5 29.5 45.8 7.8 12.7 31.2 40.6
N (pcs ×ha−1)995 1225 810 1285 1015 493 447 326
BA (m2×ha−1)52.9 58.7 57.1 65.1 80.0 60.7 62.0 50.1
QMD (cm) 26.0 24.7 29.9 25.4 31.8 39.6 41.9 44.2
Do (cm) 34.0 33.4 41.3 38.4 47.7 51.5 59.8 65.0
HQMD (m) 26.4 25.8 27.9 26.1 17.6 19.7 20.3 20.7
HDo (m) 29.2 29.0 30.7 30.2 21.4 22.0 23.1 23.6
HQMD/QMD 101.5 104.4 93.3 102.7 55.3 49.7 48.4 46.8
V(m3×ha−1)649 716 755 794 700 561 596 511
E (%) = evenness of the shares of different species, Va (%) = the percentage of volume of admixed species, N = number of trees, BA = basal
area, QMD = mean diameter per basal area, Do= mean diameter of 20% of the thickest trees, HQMD = mean tree height per basal area,
HDo= mean tree height of 20% of the thickest trees, HQMD/QMD = slenderness, V = volume per ha.
Differences at the community level are expressed in all parameters. The average
values of heights (HQMD; HDo) and slenderness (HQMD/QMD) are higher for 35% (32%)
and 100%, and average value of diameters (QMD; Do) are lower for 48% (52%) in the
community of Serbian spruce. The average number of trees (1079 pcs
×
ha
−1
) and volume
(728 m
3×
ha
−1
) are higher by 82% and 28%, respectively, in the Serbian spruce community
compared to the Macedonian pine community. In contrast, the average value of basal area
in the Macedonian pine community (63.2 m
2×
ha
−1
) is higher by 8% than in the Serbian
spruce community (58.4 m
2×
ha
−1
). The different ratios of volume and basal area in
these two forest communities are a consequence of large differences in slenderness, i.e., the
height structure of the stands.
3.2. Spatial Pattern of Tree Distribution in the Investigated Stands
The average distance between neighboring trees (Table 3) in the community of Serbian
spruce ranges from 1.44 m (SP 2) to 1.84 m (SP 3). The aggregation indices Rhave values
close to the reference random distribution. The test results indicate that only the trees
in the sample plot with the highest degree of mixing (SP 4) have a regular distribution
(p< 0.05). The average distance between neighboring Macedonian pine trees ranges from
1.14 m (SP 1) to 3.41 m (SP 4). The aggregation indices Rdiffer significantly in the sample
plots. The testing indicates that only the trees from sample plot 7 are randomly distributed
in space. In the sample plots with the lowest degree of mixing (SP 5, SP 6), a statistically
significant clumping was found (p< 0.001, p< 0.01), while the trees in the sample plot with
the highest degree of mixing (SP 8) had a regular distribution (p< 0.05).
Table 3. Basic spatial characteristics. Mean distance between individuals (m) and aggregation index (R).
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
Mean distances (m) 1.58 1.44 1.84 1.49 1.14 1.89 2.34 3.41
R1.0003 1.0116 1.0501 1.0724 * 0.7286 *** 0.8426 ** 1.0041 1.1617 *
*p<0.05, ** p<0.01,*** p<0.001.
The spatial pattern of tree distribution in the studied communities was determined
based on the Ripley’s L(r) function (Figure 2). In the community of Serbian spruce in
the first two sample plots with a lower degree of mixing (SP 1, SP 2), the distribution of
trees with a change in distance has different values. Based on the conducted Monte Carlo
simulations of the null hypothesis of complete spatial randomness, at distances of up to
2.0 m (SP 1) the trees are randomly arranged, and at over 2.0 m the arrangement has a
Forests 2021,12, 1095 8 of 18
clump character. In sample plot 2, the random distribution of trees is at distances of up
to 4.0 m, from 4.0 to 8.0 m the distribution is clumped, and at over 8.0 m it is at the upper
limit of statistical randomness. In the other two sample plots (SP 3, SP 4) with a higher
degree of mixing, the distribution of trees is within the limits of statistical significance of
random distribution at all distances.
Forests 2021, 12, x FOR PEER REVIEW 8 of 18
Table 3. Basic spatial characteristics. Mean distance between individuals (m) and aggregation index (R).
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
Mean distances (m) 1.58 1.44 1.84 1.49 1.14 1.89 2.34 3.41
R 1.0003 1.0116 1.0501 1.0724 * 0.7286 *** 0.8426 ** 1.0041 1.1617 *
* p <0.05, ** p <0.01,*** p <0.001.
The spatial pattern of tree distribution in the studied communities was determined
based on the Ripley’s L(r) function (Figure 2). In the community of Serbian spruce in the
first two sample plots with a lower degree of mixing (SP 1, SP 2), the distribution of trees
with a change in distance has different values. Based on the conducted Monte Carlo
simulations of the null hypothesis of complete spatial randomness, at distances of up to
2.0 m (SP 1) the trees are randomly arranged, and at over 2.0 m the arrangement has a
clump character. In sample plot 2, the random distribution of trees is at distances of up to
4.0 m, from 4.0 to 8.0 m the distribution is clumped, and at over 8.0 m it is at the upper
limit of statistical randomness. In the other two sample plots (SP 3, SP 4) with a higher
degree of mixing, the distribution of trees is within the limits of statistical significance of
random distribution at all distances.
In the Macedonian pine community, in sample plots with a lower degree of mixing
(SP 5, SP 6), the distribution of trees has different values with a change in distance. At
distances of up to 3.0 m (SP 5) and 2.5 m (SP 6), the trees are clumped in space. As these
distances increase, the trees have a random arrangement. In the sample plots with a
higher degree of mixing (SP 7, SP 8), the arrangement of trees is within the limits of sta-
tistical significance of random distribution at all distances, with a significantly wider
confidence level.
Figure 2. Ripley’s L(r) function of the spatial pattern of tree locations in the Serbian spruce (a) and Macedonian pine (b)
forest communities. The values of the function higher than expected (positive values) show a tendency towards clump-
ing, values lower than expected (negative values) show a tendency towards a regular distribution at the observed dis-
tance. For simplicity’s sake, lines that indicate a 99% confidence interval based on 199 Monte Carlo simulations of the null
hypothesis of complete spatial randomness were not interpreted in this figure.
In the stands of Serbian spruce the values of Ripley’s L(r) function increase with an
increasing distance, while with increasing mixing they have smaller absolute values at
the observed distances. As the mixing increases, the spatial pattern of trees tends to
change from a clumped to a random distribution. In the stands of Macedonian pine, the
functions have slightly more complex relationships, but it is clear that with increasing
mixing, the arrangement of trees has a trend from a clumped to a regular distribution.
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6 7 8 9 10 11 12
L (r)
Distance r (m)
а.
SP 1
SP 2
SP 3
SP 4
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6 7 8 9 10 11 12
L (r)
Distances r (m)
b.
SP 5
SP 6
SP 7
SP 8
Figure 2.
Ripley’s L(r) function of the spatial pattern of tree locations in the Serbian spruce (
a
) and Macedonian pine (
b
)
forest communities. The values of the function higher than expected (positive values) show a tendency towards clumping,
values lower than expected (negative values) show a tendency towards a regular distribution at the observed distance. For
simplicity’s sake, lines that indicate a 99% confidence interval based on 199 Monte Carlo simulations of the null hypothesis
of complete spatial randomness were not interpreted in this figure.
In the Macedonian pine community, in sample plots with a lower degree of mixing
(SP 5, SP 6), the distribution of trees has different values with a change in distance. At
distances of up to 3.0 m (SP 5) and 2.5 m (SP 6), the trees are clumped in space. As
these distances increase, the trees have a random arrangement. In the sample plots with
a higher degree of mixing (SP 7, SP 8), the arrangement of trees is within the limits of
statistical significance of random distribution at all distances, with a significantly wider
confidence level.
In the stands of Serbian spruce the values of Ripley’s L(r) function increase with an
increasing distance, while with increasing mixing they have smaller absolute values at the
observed distances. As the mixing increases, the spatial pattern of trees tends to change
from a clumped to a random distribution. In the stands of Macedonian pine, the functions
have slightly more complex relationships, but it is clear that with increasing mixing, the
arrangement of trees has a trend from a clumped to a regular distribution.
3.3. Vertical Structure
The distributions of trees by height classes in the sample plots in the investigated
forest communities are graphically presented in Figure 3. Based on the testing of empirical
height distributions (Mann–Whitney U test), a statistically significant difference (p< 0.05)
was found between the distributions in the sample plots.
The arithmetic mean height (hA) in the Serbian spruce stands ranges from 22.4 (SP 4)
to 27.1 m (SP 3). The variation width of heights (hV) is even across the sample plots and
ranges from 29.4 m (SP 1) to 31.7 m (SP 4), with a higher standard deviation in sample plots
with a higher degree of mixing (SP 3, SP 4). The height structure in all sample plots shows
a negative (right) skewness (
α
3 < 0), while the values of the kurtosis coefficient
α
4<3in
SP 1, SP 3, and SP 4 indicate kurtosis from above, and in SP 2 lateral kurtosis (
α4>3
). The
concentration of the number of trees of 30% (SP 1) and 40% (SP 2) in one height class and
lower values of deviation from the arithmetic mean indicate a slightly different structure
compared to the sample plots with a higher degree of mixing (SP 3, SP 4). The height
Forests 2021,12, 1095 9 of 18
structures in these sample plots do not have such clearly expressed maximums and have a
slightly larger variation width.
Forests 2021, 12, x FOR PEER REVIEW 9 of 18
3.3. Vertical Structure
The distributions of trees by height classes in the sample plots in the investigated
forest communities are graphically presented in Figure 3. Based on the testing of empir-
ical height distributions (Mann–Whitney U test), a statistically significant difference (p <
0.05) was found between the distributions in the sample plots.
The arithmetic mean height (hA) in the Serbian spruce stands ranges from 22.4 (SP 4)
to 27.1 m (SP 3). The variation width of heights (hV) is even across the sample plots and
ranges from 29.4 m (SP 1) to 31.7 m (SP 4), with a higher standard deviation in sample
plots with a higher degree of mixing (SP 3, SP 4). The height structure in all sample plots
shows a negative (right) skewness (α3 < 0), while the values of the kurtosis coefficient α4
< 3 in SP 1, SP 3, and SP 4 indicate kurtosis from above, and in SP 2 lateral kurtosis (α4 >
3). The concentration of the number of trees of 30% (SP 1) and 40% (SP 2) in one height
class and lower values of deviation from the arithmetic mean indicate a slightly different
structure compared to the sample plots with a higher degree of mixing (SP 3, SP 4). The
height structures in these sample plots do not have such clearly expressed maximums
and have a slightly larger variation width.
Figure 3. Distribution of trees by height classes in the Serbian spruce (a) and Macedonian pine (b) stands.
In the Macedonian pine stands, hA values are lower than in the stands of Serbian
spruce. They range from 15.5 (SP 5) to 20.5 m (SP 8) and increase with the degree of
mixing in the stand. Thestandard deviation hV also shows higher values with increased
mixing. In all Macedonian pine sample plots, height structures have a negative (right)
skewness (α3 < 0), while in SP 5, SP 6, and SP 8 α4 < 3, and in SP 7 α4 > 3. Like in the
Serbian spruce stands, stands with a lower degree of mixing (SP 5, SP 6) are clearly sep-
arated from stands with a higher degree of mixing (SP 7, SP 8) in terms of height struc-
ture.
The differentiation of the vertical structure is also expressed on the basis of the re-
sults of vertical profile fulfillment Arel (Table 4). In the stands of Serbian spruce, Arel values
range from 43.5% (SP 1) to 58.9% (SP 4), and in the Macedonian pine stands from 45.8%
(SP 5) to 68.6% (SP 8). The growing trend of Arel in stands of both tree species is positively
correlated with the increase in the degree of mixing. The increase in mixing directly af-
fected the complexity of vertical form of the investigated stands.
Table 4. Values of the relative species profile index (Arel).
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
Arel (%) 43.5 46.7 56.8 58.9 45.8 51.8 57.4 68.6
0
10
20
30
40
50
60
4.5
7.5
10.5
13.5
16.5
19.5
22.5
25.5
28.5
31.5
34.5
37.5
40.5
N (%)
Height class (m)
a. SP 1
SP 2
SP 3
SP 4
0
10
20
30
40
50
60
1.5
4.5
7.5
10.5
13.5
16.5
19.5
22.5
25.5
28.5
31.5
34.5
37.5
N (%)
Height class (m)
b. SP 5
SP 6
SP 7
SP 8
Figure 3. Distribution of trees by height classes in the Serbian spruce (a) and Macedonian pine (b) stands.
In the Macedonian pine stands, hA values are lower than in the stands of Serbian
spruce. They range from 15.5 (SP 5) to 20.5 m (SP 8) and increase with the degree of mixing
in the stand. Thestandard deviation hV also shows higher values with increased mixing.
In all Macedonian pine sample plots, height structures have a negative (right) skewness
(
α
3 < 0), while in SP 5, SP 6, and SP 8
α
4 < 3, and in SP 7
α
4 > 3. Like in the Serbian spruce
stands, stands with a lower degree of mixing (SP 5, SP 6) are clearly separated from stands
with a higher degree of mixing (SP 7, SP 8) in terms of height structure.
The differentiation of the vertical structure is also expressed on the basis of the results
of vertical profile fulfillment A
rel
(Table 4). In the stands of Serbian spruce, A
rel
values range
from 43.5% (SP 1) to 58.9% (SP 4), and in the Macedonian pine stands from 45.8% (SP 5) to
68.6% (SP 8). The growing trend of A
rel
in stands of both tree species is positively correlated
with the increase in the degree of mixing. The increase in mixing directly affected the
complexity of vertical form of the investigated stands.
Table 4. Values of the relative species profile index (Arel).
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
Arel (%) 43.5 46.7 56.8 58.9 45.8 51.8 57.4 68.6
3.4. Diameter Structure
Based on the testing of empirical diameter distributions (Mann–Whitney U test),
a statistically significant difference (p< 0.05) was found between the sample plots. In
the Serbian spruce stands, the arithmetic mean diameter (dbhA) ranges from 23.6 (SP 4)
to 28.7 cm (SP 3). A significantly higher variation width (dbhV) and standard deviation
were found in the sample plots with a higher degree of mixing (SP 3, SP 4). The diameter
distribution in the sample plot with the lowest degree of mixing has a negative skewness
(
α
3 =
−
0.16) and kurtosis (
α
4 =
−
0.45), while in other plots the values of
α
3 are positive
at 0.73 (SP 2), 0.42 (SP 3), 1.30 (SP 4), along with
α
4 at 1.69 (SP 2), 0.07 (SP 3), 2.07 (SP 4).
According to the shape of distributions (Figure 4), the sample plots with a lower degree
of mixing (SP 1, SP 2) show a narrower diameter distribution and a more pronounced
concentration of trees within one diameter class. The shapes of distributions focused on
thinner diameter classes indicate pronounced processes of selection and differentiation of
higher diameter classes. Tree differentiation (SP 3, SP 4) becomes more intense with an
increase in mixing in stands (low right part of distribution).
Forests 2021,12, 1095 10 of 18
Forests 2021, 12, x FOR PEER REVIEW 10 of 18
3.4. Diameter Structure
Based on the testing of empirical diameter distributions (Mann–Whitney U test), a
statistically significant difference (p < 0.05) was found between the sample plots. In the
Serbian spruce stands, the arithmetic mean diameter (dbhA) ranges from 23.6 (SP 4) to
28.7 cm (SP 3). A significantly higher variation width (dbhV) and standard deviation
were found in the sample plots with a higher degree of mixing (SP 3, SP 4). The diameter
distribution in the sample plot with the lowest degree of mixing has a negative skewness
(α3 = −0.16) and kurtosis (α4 = −0.45), while in other plots the values of α3 are positive at
0.73 (SP 2), 0.42 (SP 3), 1.30 (SP 4), along withα4 at 1.69 (SP 2), 0.07 (SP 3), 2.07 (SP 4).
According to the shape of distributions (Figure 4), the sample plots with a lower degree
of mixing (SP 1, SP 2) show a narrower diameter distribution and a more pronounced
concentration of trees within one diameter class. The shapes of distributions focused on
thinner diameter classes indicate pronounced processes of selection and differentiation of
higher diameter classes. Tree differentiation (SP 3, SP 4) becomes more intense with an
increase in mixing in stands (low right part of distribution).
Figure 4. Distribution of trees by diameter classes in the stands of Serbian spruce (a) and Macedonian pine (b).
In the stands of Macedonian pine, dbhA grows with an increase in mixing from 29.6
cm (SP 5) to 41.2 cm (SP 8). Like in the case of Serbian spruce, the sample plots with a
higher degree of mixing (SP 7, SP 8) with a significantly higher dbh and standard devia-
tion are clearly differentiated. Diameter distributions in all sample plots have positive α3
values of 0.44 (SP 5), 0.09 (SP 6), 0.58 (SP 7), and 0.48 (SP 8). The value of α4 in the sample
plot with the lowest share of admixed species (SP 5) is negative (−0.39), while the values
in other fields are positive at 0.14 (SP 6), 1.04 (SP 7), and 0.26 (SP 8). Compared to the
normal distribution (SP 6), the forms with the highest concentration of trees in lower
diameter classes (SP 5) and a significantly wider distribution and laid down right part of
the diagram (SP 7, SP 8) reveal more complex relationships in the Macedonian pine
stands (Figure 4). The forms indicate the processes of selection (SP 5), initiated (SP 6), and
pronounced (SP 7, SP 8) tree differentiation. The diameter structure in all sample plots
has a clearly expressed single maximum. The appearance of several less pronounced
peaks along the variation width indicates a more complex structural form of these stands
compared to the classical structure of even-aged stands.
3.5. Parameters of Diameter Diversity
The spatial measure of mixing M clearly distinguishes between two categories of
species segregation in stands (Table 5). The first category with a higher degree of segre-
gation is below 0.20 (SP 1, SP 2, SP 5, SP 6) and the lower one is above 0.20 (SP 3, SP 4, SP
7, SP 8). Mean values of the diameter differentiation index Td in the stands of Serbian
spruce range from 0.24 (SP 2) to 0.31 (SP 4). The index shows a weak (SP 1, SP 2, SP 3) to
0
10
20
30
40
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
N (%)
Diameter class (cm)
а. SP 1
SP 2
SP 3
SP 4
0
10
20
30
40
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
67.5
72.5
77.5
82.5
87.5
N (%)
Diameter class (cm)
b. SP 5
SP 6
SP 7
SP 8
Figure 4. Distribution of trees by diameter classes in the stands of Serbian spruce (a) and Macedonian pine (b).
In the stands of Macedonian pine, dbhA grows with an increase in mixing from
29.6 cm (SP 5) to 41.2 cm (SP 8). Like in the case of Serbian spruce, the sample plots with a
higher degree of mixing (SP 7, SP 8) with a significantly higher dbh and standard deviation
are clearly differentiated. Diameter distributions in all sample plots have positive
α
3 values
of 0.44 (SP 5), 0.09 (SP 6), 0.58 (SP 7), and 0.48 (SP 8). The value of
α
4 in the sample plot
with the lowest share of admixed species (SP 5) is negative (
−
0.39), while the values in
other fields are positive at 0.14 (SP 6), 1.04 (SP 7), and 0.26 (SP 8). Compared to the normal
distribution (SP 6), the forms with the highest concentration of trees in lower diameter
classes (SP 5) and a significantly wider distribution and laid down right part of the diagram
(SP 7, SP 8) reveal more complex relationships in the Macedonian pine stands (Figure 4).
The forms indicate the processes of selection (SP 5), initiated (SP 6), and pronounced (SP 7,
SP 8) tree differentiation. The diameter structure in all sample plots has a clearly expressed
single maximum. The appearance of several less pronounced peaks along the variation
width indicates a more complex structural form of these stands compared to the classical
structure of even-aged stands.
3.5. Parameters of Diameter Diversity
The spatial measure of mixing Mclearly distinguishes between two categories of
species segregation in stands (Table 5). The first category with a higher degree of segrega-
tion is below 0.20 (SP 1, SP 2, SP 5, SP 6) and the lower one is above 0.20 (SP 3, SP 4, SP 7,
SP 8). Mean values of the diameter differentiation index Td in the stands of Serbian spruce
range from 0.24 (SP 2) to 0.31 (SP 4). The index shows a weak (SP 1, SP 2, SP 3) to medium
(SP 4) level of diameter differentiation. In Macedonian pine stands. The index ranges from
0.22 (SP 6) to 0.33 (SP 8) and has a weak (SP 6) to medium (SP 5, SP 7, SP 8) intensity of
diameter differentiation. The differentiation index Td is the highest in the stands with the
highest degree of mixing (SP 4, SP 8), but it does not show a clear correlation with the
change of mixing. Values of the Gini coefficient GC in Serbian spruce range from 0.26 (SP 1)
to 0.41 (SP 4), and Macedonian pine from 0.25 (SP 6) to 0.41 (SP 5).
The Gini coefficient of homogeneity in the stands of Serbian spruce shows a clear
increasing trend with an increasing degree of mixing, while in the stands of Macedonian
pine this trend deviates in the sample plot with the lowest degree of mixing (SP 5). The
hyperbolic tangent index Sof admixed species in the community of Serbian spruce is from
0.41 (SP 1) to 0.78 (SP 4), and has an increasing trend with increasing mixing, while in the
community of Macedonian pine it has values from 0.40 (SP 8) to 0.57 (SP 7) and does not
show a clear correlation with increasing mixing.
Forests 2021,12, 1095 11 of 18
Table 5. Parameters of diameter diversity in the investigated stands.
Stands Picea omorika Pinus peuce
No. of Sample Plot 1 2 3 4 5 6 7 8
M0.16 0.18 0.29 0.39 0.09 0.13 0.30 0.36
Td 0.25 0.24 0.26 0.31 0.32 0.22 0.31 0.33
GC 0.26 0.29 0.31 0.41 0.41 0.25 0.37 0.39
S0.41 0.44 0.65 0.78 0.51 0.50 0.57 0.40
M—spatial mixing index, Td—diameter differentiation index, GC—Gini coefficient of homogeneity, S—hyperbolic tangent index of
admixed species.
3.6. Spearman’s Correlation Coefficient ρ
Based on the established relationship between stand characteristics and mixing, a
correlation analysis was performed using the Spearman’s correlation coefficient
$
(Table 6).
A strong positive correlation was found between the mixing index Mand the aggregation
index R(
$
= 0.87, p< 0.01), the mixing index Mand the relative species profile index
A
rel
(
$
= 0.86, p< 0.05), the aggregation index Rand the relative species profile index
A
rel
(
$
= 0.74, p< 0.05), and the diameter differentiation index Td and the Gini coefficient GC
(
$
= 0.85, p< 0.01). A weak to moderately strong correlation, without statistical significance,
was found among the other parameters of stand structure.
Table 6.
Matrix of Spearman’s correlation coefficient
$
between the species mixing index (M),
aggregation index (R), relative species profile index (A
rel
), diameter differentiation index (Td), Gini
coefficient (GC), and hyperbolic tangent index (S).
M R Arel Td GC S
M—
R0.87 ** —
Arel 0.86 * 0.74 * —
Td 0.32 0.25 0.37 —
GC 0.41 0.23 0.48 0.85 ** —
S0.26 0.01 0.24 0.03 0.42 —
*p<0.05, ** p< 0.01.
4. Discussion
4.1. Differences in the Basic Characteristics between the Researched Stands and Other Stands of the
Same Species
In previous studies of mixed stands of Serbian spruce in Serbia [
53
,
54
], lower values of
all numerical (dendrometric) variables were found at a locality in the immediate vicinity of
the investigated stands except for the number of trees per unit area. The structure of these
stands is much more complex than in the investigated stands and ranges from uneven-aged
stands to structures close to selection stands. The increase in total volume with increasing
mixing was also confirmed by these studies.
Available research on Macedonian pine stands in Macedonia (Pelister) [
27
,
55
] and
Serbia (Šar Mountain) [
56
,
57
], higher values of the mean diameter and height of trees
were found, while the basal area and volumes are smaller than in the investigated stands
resulting from the smaller number of trees. These differences are a consequence of different
ecological conditions of stand development. The stands of Macedonian pine [
27
,
55
–
57
]
are located in optimal conditions of development [
58
], while the investigated stands are
located on the border of the vertical (1825 to 1910 m above sea level) and horizontal (north)
range of the species (Figure 1).
4.2. Effect of Mixing on the Spatial Pattern of Tree Distribution
The spatial distribution of trees in stands is influenced by numerous factors. It
is most influenced by the management system, the origin and structure of stands, the
composition of the species that build them, developmental stages, natural disturbances,
Forests 2021,12, 1095 12 of 18
habitat conditions and abiotic conditions to which they have adapted their development.
In intensively managed stands, the distribution of trees tends towards a regular (random)
distribution [
59
,
60
]. In stands that are not subjected to management treatments, active
selection and differentiation processes influence the regulation of tree distribution with a
tendency toward a regular distribution [
40
,
41
], i.e., random distribution [
60
,
61
], which was
confirmed by this research. These pronounced processes in mixed stands of the studied
species affected the random distribution of trees. The regularity of distribution is especially
pronounced in trees with larger diameters [
40
,
41
], which is also the trend observed in this
research (SP 7, SP 8).
The tendency towards clumping of trees at lower distances in the stands of Serbian
spruce (SP 1, SP 2) can be explained by microhabitat conditions (form of the micro-relief
conditioned by the parent rock, a mosaic shallow initial phase of the soil) and the relative
absence of other species with different bio-ecological characteristics which would contribute
to the process of intensive competition and differentiation. The formed homogeneous
groups in the coves and at the crossings between ridges, which intersect the entire locality,
condition the clumping of trees at relatively larger distances. The clumping of Macedonian
pine trees at lower distances (SP 5, SP 6) can be explained by the specifics of the species
development in high mountain climatic conditions. The relations of the spatial distribution
of the trees can be divided into two groups; I. with a lower degree of mixing (SP 1, SP 2;
SP 5, SP 6), where the trees tend to clump (group) and II. with a higher degree of mixing
(SP 3, SP 4; SP 7, SP 8), where the trees tend to be randomly to regularly distributed.
Wider distributions of dimension (Figures 3and 4) indicate an increasingly pronounced
influence of the separation of ecological niches of different species in mixed stands and
the dimensional unevenness and intensive separation of taller and shorter trees into strata.
This fact also affected the spatial arrangement of the trees.
4.3. Diversity Indices as an Appropriate Measure of Stand Differences (Td, GC)
The diameter differentiation index Td based on the researched references shows
different values in different stand situations. The lowest values are typical of even-aged
stands that are actively managed, 0.11 in taigas [
62
], 0.13–0.21 in pine cultures of different
ages [
41
], 0.21 in an even-aged beech stand [
8
], 0.25 in young Douglas fir culture [
8
],
0.30 [
59
], and 0.34 [
60
] in even-aged stands of different forest types. Slightly higher average
values of Td were found in uneven-aged stands of beech 0.27–0.42 [
63
], 0.36 [
64
], and
0.42 [
8
] in mixed stands of beech. In a series of permanent research plots in the Czech
Republic [
65
–
68
] on a similar sample in protected mixed stands of spruce, fir and beech
values were determined to be from 0.41 to 0.55 [
67
] and in managed mixed stands of beech
of different origin they were from 0.36–0.49 [
68
]. In relict pure stands of Scots pine lower
values (0.20–0.33) were found [
65
]. In research on mixed stands of Scots pine without
management treatment [
66
], a trend of decreasing the degree of diameter differentiation
(from 0.37–0.48 to 0.36–0.42) was determined in the analyzed period of 15 years on all
permanent research plots. The inventory of different forest types in the Austrian Alps
determined the average value of the Td index in stands of 0.37, and values significantly
above this average (0.50) were found in two-story (multi-story) stands [
69
]. In the selected
stands, the determined mean values of the Td index are 0.43 [
64
] and 0.42 [
59
]. The highest
Td values are typical of virgin forests, and they range from 0.47 [70] to 0.76–0.78 [60].
By comparing the presented Td indices, the differentiation of diameters has character-
istic higher or lower values in relation to the developmental and structural type of stands.
These differences indicate, but do not determine, the stand type. In non-managed forests,
the differences are the result of competition between species and within the species during
development, and in forests that are regularly managed, they are a direct consequence of
these relationships and the nature of applied management treatments.
The determined values of the index from 0.24 to 0.33 indicate a simpler type of stand,
which only confirms the previous analysis of the height and diameter structure.
Forests 2021,12, 1095 13 of 18
In the practical use of the Td index, it is important to pay attention to the distribution
of index values of structural groups, as well as the use of appropriate measures of central
tendency. The approximately normal values of the Td index distribution indicate the
possibility of using mean values [
62
] as a representative parameter in the analysis of the
relationship, which is the case here. For significant deviations from the normal distribution,
the use of mode [62] or median [69] is adequate.
The Gini coefficient GC has the lowest values in young even-aged stands of
0.15–0.30 [71]
, 0.22 [
60
], and 0.25 in two-story stands [
69
]. Higher values are typical of
mixed and uneven-aged stands of different compositions (e.g., 0.37–0.54 [
19
], 0.50–0.58 [
71
],
0.49–0.57 [
72
], and 0.35–0.52 [
73
]). Values above 0.60 [
71
] are characteristic of selective
stands and virgin forests. The mean values in the selection stands of the Austrian Alps are
0.63 [
59
]. The highest values of the index were found in beech and spruce reserves and
virgin forests of the southeastern Carpathians 0.69–0.71 [
74
], beech and hornbeam in the
Czech Republic 0.67–0.75 [
60
], beech, fir, spruce in Bosnia and Herzegovina 0.67 [
70
], and
beech in Serbia 0.45–0.52 [
72
]. The values presented in different stands justify the use of GC
as an adequate measure of stand inequality, which also indicates but does not determine
the stand type.
In relation to the distribution of the analyzed dimensions, the indices show certain
regularities. Stands with a normal distribution have lower GC values compared to stands
with the inverse J-shape [
46
,
59
] and regular distributions [
46
]. In this research, two stands
with a statistically significant normal distribution (SP 1, SP 6) have the lowest GC values.
This confirms the assumption that GC values increase with the deviation of the distribution
from the normal shape [
47
,
75
]. The diameter distribution in uneven-aged stands is reflected
in higher and more constant index values compared to even-aged stands [
47
]. In the
research of different forms of pure and mixed stands of spruce, fir, and beech of the Eastern
Carpathians [
75
]GC has been shown to be a useful tool in differentiating different structural
types of stands. Regardless of the established justification and superiority in relation to
other indices [
46
], the possibility of obtaining the same values in different structures (as
with the previous index) limits its application [
76
]. That shortcoming requires the analysis
of the flows of the Lorentz curve on which the index is based or the use of adequate
additional parameters in determining the differences of the analyzed stands [76].
In the practical use of this index, as a useful tool in forest management, it is necessary
to pay attention to the impact of the callipering threshold on its value [
75
], the type and
size of the sample used [
77
], as well as the index value in the structures of transitional
forms in the process of stand regeneration [47].
4.4. Impact of Admixed Species on Stand Structure
In order to determine the causes of changes in structure parameters with an increasing
degree of mixing, the ratio of diameters between admixed and dominant species was
analyzed in the investigated stands. The hyperbolic tangent index Sin the stands of
Serbian spruce has a growing trend in relation to mixing. The parameter shows that,
with an increase in their share, admixed species have larger dimensions compared to the
neighboring (competing) trees of dominant species. This fact can explain the almost regular
changes in the analyzed parameters of the structure of Serbian spruce stands with an
increase in the degree of mixing. The Sindex in Macedonian pine stands does not show a
high dependence on the degree of mixing, but still there are small changes in structural
parameters with its increase. The index determines the cause of the change in diversity
well and determines equally well the competitive status of the relationships among the
species. Serbian spruce in mixed stands can be characterized as extremely endangered by
the competition of admixed tree species. The determined impact of mixing, considering the
priority goal of the survival of this tree species (generally of species diversity), compromises
the justification of establishing the strictest protection regimes of these stands, allowing
them to develop spontaneously.
Forests 2021,12, 1095 14 of 18
4.5. Correlation of the Investigated Parameters of Structural Diversity
There is not much literature data on the impact of mixing on the aggregation index.
Contrary to the obtained results (Table 6), in stands with active management, the established
ratio has a negative character of low intensity [62].
The pronounced link between the vertical fulfillment of the A
rel
profile and the mixing
of stands is based on their mathematical correlation. The obtained values confirm the
advantage of using the index in stands with different numbers of species [
5
], as well as
the impact of deviation of structure from pure single-story stands on the growth of index
values [78].
The impact of mixing on dimensional diversity indices is indirectly expressed through
the impact on stand structure. Differences in the distributions of the investigated stands
with increasing mixing had a positive effect on diameter differentiation indices (Td,GC). A
study of different empirical and theoretical stand situations [
46
] found a strong impact of
mixing on GC values. Significant differences in GC values were found between the pure
and mixed even-aged stands of the most common species of Central Europe [
79
]. Mixed
stands had on average significantly higher GC values (0.46) than pure stands (0.36), with
an established correlation of medium strength.
The moderately strong positive correlation found in studies of the impact of mixing
on the Mand Td differentiation indices in virgin forests [
70
] and actively managed different
forest types [62] was also confirmed by this study.
Prior research in stands of even-aged and almost even-aged structure found a strong
correlation between Td and GC [
80
], which is also confirmed by this study. In contrast, the
weak correlation of these indices in stands of more complex structure, virgin forests [
70
],
diverse stands [
80
], and stands of different types [
71
], emphasizes the impact of structure
on the change in their relationship. The reason for this should be sought in various
mathematical assumptions of the above indices.
Since the hyperbolic tangent index Sis a new index, no research has been performed
on its correlation with other structural parameters. In addition to the tree characteristics
diversity index, it has also been proposed as a useful tool for researching absolute and
relative growth rates [
48
]. Considering the concept of using the index, the relationship
between the Sindex and the mixing index Mdepends on the distribution of the observed
characteristics of the admixed species in stands with different degrees of mixing. In this
research, it has a weak positive correlation with the stand mixing index.
5. Conclusions
The structural diversity of the studied relict-endemic communities confirms their great
importance in terms of biodiversity and reifies their need for protection and conservation
in the Balkans.
Structural indices, whose values clearly vary in different stand situations, have proven
to be useful and reliable indicators for defining stand characteristics, as well as for differen-
tiating stands on the basis of them. Their mutual correlation was observed, as well as their
correlation with the mixing of stands, which implies an increase in structural diversity with
an increase in the degree of mixing in stands.
Compared to pure stands, mixed stands have a more pronounced skewness and
kurtosis of the diameter structure, significantly wider variation widths of diameters and
heights, a more pronounced vertical development, and higher values of structural indices,
which all together result in a greater structural heterogeneity (diversity). These differences
are significantly more pronounced in stands with a higher degree of mixing.
According to the obtained results, a 20% share of admixed species by volume and
the spatial mixing of species Mof 0.20, can be considered the lower limit of the impact of
mixing on the change in structural characteristics of stands, with changes reflected in all
parameters of horizontal and vertical structures.
The past development of the investigated stands without direct anthropogenic in-
fluence caused the formation of the initial phases of virgin stand forms. The established
Forests 2021,12, 1095 15 of 18
experiments contribute to a better understanding of structural relationships in the condi-
tions of spontaneous stand development. The obtained low to medium values of structural
diversity do not justify the existing management concept. In addition, they point to the
need for an active management approach in order to preserve the biodiversity of rare and
endangered forest communities. The dialectical principle of the development of forest
communities, from the initial to the terminal phase, makes the establishment of permanent
and strict protection regimes debatable from the aspect of biodiversity conservation. Finally,
forest communities left to spontaneous development will certainly not go in the direction
of conservation.
Author Contributions:
Conceptualization, A.P. and M.M.; methodology, A.P. and D.P.; software,
A.P.; writing—original draft preparation, A.P., B.Š. and S.O.; writing—review and editing, all authors;
visualization, A.P., B.Š. and S.O.; supervision, M.M. and D.P.; project administration, S.O. All authors
have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the Ministry of Education, Science, and Technological De-
velopment of the Republic of Serbia within the project “Sustainable management of total forest
potentials in the Republic of Serbia”-EVBR 37008.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding authors.
Acknowledgments:
The authors also acknowledge the support of the State Enterprise for Forest
Management “Srbija šume” and State Enterprise National Park “Tara” for providing accommodation
during the field data collection.
Conflicts of Interest: The authors declare no conflict of interest.
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