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Научни трудове на Съюза на учените в България - Пловдив. Серия В. Техника и технологии. Том XVII, ISSN 1311 -9419 (Print); ISSN 2534-9384 (Online), 2019. Scientific Works of the Union of Scientists in Bulgaria - Plovdiv. Series C. Technics and Technologies. Vol. XVII., ISSN 1311 -9419 (Print); ISSN 2534-9384 (Online), 2019
THICKNESS STRUCTURES OF SEED-TREE HUNGARIAN-OAK, DURMAST AND TURKEY-OAK DENDROCOENOSES
Roumen Petrin and Ivailo Markoff Forest Research Institute of the Bulgarian Academy of Sciences, Sofia
ABSTRACT:
The thickness structures of natural, seed-tree relatively even-aged Hungarian-oak, Durmast and Turkey-oak dendrocoenoses in the Balkan Mountains, namely in the regions of Staro Oryahovo, Sherba, Tsonevo and Aytos Forest Estates, have been studied and presented in this paper. The investigation has been carried out on the basis of 117 sample plots, 56 of these being in Hungarian-oak dendrocoenoses, 58 - in durmast ones, and 3 - in Turkey-oak ones. The ages of all the dendrocoenoses are within the range from 12 to 155 years. Their heights vary from 6 to 28 metres, and their spacing indices are mainly within the range from 70% to 90%.
The purpose of the investigation was to study the curves of the distribution of the numbers of trees according to thickness levels, in terms of the curves' forms, as well as to look for general regularities.
The thickness-level curves of the Hungarian-oak, durmast and Turkey-oak dendrocoenoses were investigated for finding their asymmetries in terms of the average diameter. As a result of the comparative studies of the obtained curves, as to how they correspond to the respective natural indicators, it has been confirmed what was found out during previous investigations, namely: curves of right-hand-side asymmetry and zero natural indicator SNo<0.85; curves of left-hand-side asymmetry and SNo>1.16; and curves of symmetric type - SNo within the range from 0.86 to 1.15. It has been found out that the distribution of the numbers of sample plots, respectively of the thickness-structure curves, according to their symmetry for the three groups investigated in two scenarios - separately and together - is similar. The stands of right-hand-side asymmetry dominate, next followed by the stands of left-hand-side asymmetry.
The average curves of the normal numbers (qxav) have been calculated through the natural indicators method, for the three investigated groups, and these curves have been compared with Tyurin's uniform average curve of normal numbers (This curve pertains to all tree species.). The three average curves of normal numbers qxav - for seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses - are statistically close to Tyurin's curve, which proves the possibilities of studying together the thickness structures of the three tree species and of probable composing of general models of the volumes and the assortment structures.
Key words: Hungarian-oak, durmast and Turkey-oak dendrocoenoses, thickness structure, symmetry of curves according to thickness structure, average curves of normal numbers
Introduction
It is important in terms of every forest that foresters can evaluate the volume and assortment structure of its standing timber as easily, precisely and quickly as possible. For this reason, people need to permanently perfect the normative-and-reference base for forest-evaluation documentation, which is closely related to the improvement of all the respective models and tables. This is why it is always necessary for scientists to improve their knowledge of the regularities of the growth and structures of forest dendrocoenoses.
In 1965, the total area of the coppice dendrocoenoses of Hungarian oak, durmast and Turkey oak in Bulgaria amounted to 489,314 ha, and in 2000 it increased to 623,629 ha (Y. Petrov, 2008), hence, the current importance of studying the thickness structures of these dendrocoenoses in the present investigation.
A number of authors have carried out studies of the structures of forest stands (Tyurin, 1938, Tretyakov, 1952, Sirakov, 1947, Nedyalkov, 1964 and 1967, Mihov, 1991, Mihov et al., 1993, Dimitrov, 2003, and Tonchev, 2007). The more important inferences the above and other authors have made from their studies of stand structures are as follows:
• А. V. Tyurin, 1938, while comparing the tree-number distribution curves for a number of pure, simple, even-aged, normal stands came to the conclusion that the forms of the curves did not depend on the tree species site conditions and spacing index of the stand. The factors found to affect the curves' forms to a certain extent were tree age and the kinds of conducted felling. This gave him the reason for elaborating a uniform curve of the percentage distribution of tree numbers and basal areas according to natural levels of thickness.
• Simeon Nedyalkov, 1955, found that the forms of the variation curves of the distribution of beech trees in seed-tree stands in percentages according to thickness levels depended on average diameter and, respectively, age. About growing stocks of uneven-aged spruce trees, this same author (1967) established different curves of distribution for the particular generations. For the generations at different ages, the distribution curves have bell-shaped or parabolic aspects, and the general curve, for all of them, is of an exponential aspect.
• Е. P. Dimitrov, 1978, has found for mature beech dendrocoenoses that age and spacing index do not affect the aspect and nature of the variation curve of tree distribution according to thickness levels.
• Е. ^ Dimitrov, 2003, having investigated different functions of tree-number distribution according to thickness levels, has found out the availability of three typical distributions: symmetric (or normal), right asymmetric and left asymmetric. He has cited investigations by Tishenko, 1926, where the latter, while simultaneously investigating in detail the tree-number distributions in Scots-pine, spruce, aspen and birch dendrocoenoses, found out that these distributions did not depend on spacing index, age, site index (stand-quality level) but only on the average diameter and the tree species.
• Tretya kov, 1927, while using data obtained by himself, and other ones taken from Weise, Kunze and others, carried out a detailed study of the regularities of the structures and variation of some dendrobiometric characteristics in even-aged pure stands and in uneven-aged mixed ones of complex sylvicultural systems. He established that forest structure always had a constant nature regardless of spacing index, age, tree species, growth conditions, and stands - as normal so complex, mixed ones. This gave him the reason to formulate the Law about the Uniformity of Stand Structure.
1. PURPOSE
The purpose of the present investigation is the studying of the thickness structures of seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses with a view to solving the following problems:
1. Establishing the different types of thickness structures of coppice Hungarian-oak, durmast and Turkey-oak dendrocoenoses and investigating the symmetry (or asymmetry) of each thickness-level curve.
2. Comparing the parametric average curves of the normal numbers for the investigated dendrocoenoses of the three groups with A. V. Tyurin's average curve developed for all tree species with a view to finding out proximities of values, which would give a reason for drawing important inferences.
3. OBJECTS OF THE INVESTIGATION
The present investigation pertains to seed-tree, relatively even-aged Hungarian-oak, durmast and Turkey-oak dendrocoenoses in the Balkan Mountains, namely in the regions of Staro Oryahovo, Sherba, Tsonevo and Aytos Forest Estates. It has been carried out in 117 sample plots, 56 of these being in Hungarian-oak dendrocoenoses, 58 - in durmast ones, and 3 - in Turkey-oak ones. The ages of all the dendrocoenoses are within the range from 12 to 155 years. Their heights vary from 6 to 28 metres, and their spacing indices are mainly within the range from 70% to 90%.
4. METHODS
For each sample plot have been calculated the natural levels of thickness (NLT) after Tyurin, 1938, which are obtained by dividing the absolute levels of thickness by the average diameter; this is a mathematical approach that makes it possible to unify the abscissa points of thickness-structure curves. Besides, it was also necessary to make equal the variation range, which has been realised by dividing the variation range into 10 relative lengths, 0.05, 0.15, 0.25 and so on to 0.95, which correspond to particular natural levels of thickness, and this has been realised through the methods assumed (Mihov, 2005) for investigating the thickness structure by means of the natural indicators method (Douhovnikov, 1966). The number of the trees for each particular relative length has been calculated as a percentage. The curves of the percentage distribution of the trees, after their unification as a total of 100%, have been transformed into curves of the total distributions, where the number of the trees for each thickness level is calculated as a percentage with accrual. Further on, the curves of the normal numbers have been obtained by dividing the percentages for the particular levels of thickness by the percentage for the last level, i.e. by 100. Obtaining the normal numbers', also called 'quality indicators', curves is a stage of the calculations done through the natural indicators method (Douhovnikov, 1966; Mihov, 2005). This method makes it possible to indicate the aspect of a given investigated curve by means of a single number - the zero coefficient of a straight line. Using the normal numbers' curves, an average curve of the normal numbers (qxav) has been calculated for the particular aggregates of curves. Then, each curve of normal numbers (qxi) is divided by the average one (qxav) thus obtaining the straight line of the natural numbers, whose coefficients are called natural indicators. The natural indicators have been calculated through the least squares method while solving a system of two equations with two unknown values. For the investigated dendrocoenoses have been calculated particular average curves of normal numbers (qxav), as well as an average one among them, i.e. a general average curve of the normal numbers. The zero natural indicators (ZNIs) - SNo have been calculated while using (1) a separate average curve of the normal numbers for each of the three tree species and (2) the curve situated among these three ones, i.e. the one that is general for the Hungarian oak, durmast and Turkey oak, i.e. two variants or scenarios of investigating the asymmetry of the curves. The data about the zero natural indicators obtained through the above-mentioned methods, i.e. calculated on the basis of the particular average curves of the normal numbers, have been presented in Table 1.
Table 1
Values of the zero natural indicators according to sample plots
SP No SNo SP No SNo SP No SNo SP No SNo SP No SNo SP No SNo
Hungarian oak 21 0.76 42 1.65 6 0.90 27 0.65 48 0.63
1 0.99 22 0.15 43 1.45 7 2.48 28 0.63 49 1.06
2 2.28 23 0.90 44 1.36 8 0.96 29 0.77 50 0.65
3 5.42 24 0.48 45 1.53 9 0.70 30 0.73 51 0.94
4 1.04 25 0.51 46 0.23 10 1.57 31 0.75 52 1.16
5 1.91 26 0.64 47 0.38 11 0.21 32 1.62 53 2.36
6 0.68 27 0.64 48 1.21 12 2.11 33 0.84 54 0.88
7 1.03 28 0.47 49 0.48 13 1.44 34 0.83 55 0.91
8 0.77 29 2.02 50 0.78 14 0.85 35 1.89 56 1.99
9 1.00 30 0.52 51 1.57 15 1.10 36 2.12 57 1.14
10 1.08 31 0.57 52 0.72 16 1.20 37 1.38 58 0.70
11 0.60 32 1.09 53 0.66 17 0.76 38 1.46 Tur. oak
12 0.92 33 0.72 54 0.61 18 0.61 39 1.10 1 0.46
13 0.72 34 0.96 55 0.25 19 0.33 40 0.82 2 1.63
14 1.24 35 0.31 56 1.08 20 0.48 41 1.55 3 0.91
15 0.45 36 1.38 durmast 21 0.62 42 1.16
16 0.33 37 0.43 1 0.74 22 0.66 43 1.28
17 0.20 38 0.94 2 0.85 23 0.31 44 0.35
18 2.28 39 1.49 3 1.62 24 0.57 45 0.70
19 1.92 40 0.99 4 0.74 25 0.40 46 0.76
20 0.57 41 0.67 5 0.35 26 0.93 47 0.75
The data about SNo obtained on the basis of the general average curve of the normal numbers will not be
published here; we shall only show the results.
4. RESULTS AND DISCUSSION
4.1. Types of thickness structure according to the asymmetries of the curves of the distribution of the numbers of trees according to levels of thickness
As it can be seen in Table 1, the values of the zero natural indicators vary within the range from -0.14 to +3.57 and when a general average curve of the normal numbers is used, these indicators vary from 0.09 to 2.94. We have distributed the zero natural indicators (ZNIs) of thickness structure (SNo) according to their values into three groups, based on the ranges SNo<0.85, 0.86<SNo<1.15 and SNo>1.16 for both scenarios of investigation.
The symmetry of the thickness-structure curves has been found on the basis of the zero natural indicators' values, with which a correspondence in principle has been found (Petrin et al., 2013; Petrin, R. and I. Markov, 2015), which is expressed in the following: to the low zero natural indicators (SNo<0.85) corresponds a right-hand-side asymmetry, which means that the variation curve of the tree numbers' distribution according to thickness levels is higher in the right-hand-side part of the graph than the natural level of thickness 1.0 of the abscissa. In contrast to it, to the high zero natural indicators SNo>1.16 correspond the thickness-structure curves of a left-hand-side asymmetry, and to the ZNIs within the range of 0.86<SNo<1.15 correspond curves of a symmetrical type. This discovery has been illustrated on Figure 1.
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Fig. 1. Three types of thickness structure depending on values of SNo
Left-hand-site asimmetry SP 18, SNo=2.20
Simmetrie type -asimmetry SP 10, SNo=1.04
Right-hand-site asimmetrySP 35, SNo=0.29
0.4 0.6 0.8 1 1.2 1.4
Natural levels of thickness (NLT)
1.6
1.8
4.2. The influence of tree species upon the thickness-structure curves' distribution according to types of asymmetry
The curves' asymmetry investigated through the natural indicators method (NIM) for the three tree species, separately and as an aggregate, and established for each sample plot, as well as the distribution of sample plots according to types of asymmetry depending on the tree species, have been presented in Table 2 and illustrated on Figures 2 and 3.
Table 2. Distribution of seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses according to types of asymmetry of thickness-structure curves
Tree species Scenario of investigation
Separate investigation Total SP Aggregate investigation
Type of asymmetry Type of asymmetry
Left-hand-side Symmetric Right-hand-side Left-hand-side Symmetric Right-hand-side
num ber % n % num ber % num ber % n % num ber %
H. oak 18 32.1 10 17.9 28 50.0 56 18 32.1 10 17.9 28 50.0
Durmast 16 27.6 11 19.0 31 53.4 58 13 22.4 8 13.8 37 63.8
T. oak 1 33.3 1 33.3 1 33.3 3 1 33.3 - - 2 66.7
Total 35 29.9 22 18.8 60 51.3 117 (100 %) 32 27.4 18 15.4 67 57.3
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Fig. 2. Distribution of the numbers of sample plots in % according to tree species and types of asimmetry - separate investigation
• 53.4 / 50.0
> Hungarian oak — ■ — durmast
19.0
0 12 3
1 - Left-hand-site asimmetry; 2 - Symmetry; 3 - Right-hand-site
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LO 01 01
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Fig.3. Distribution of the numbers of sample plots in % according to tree species and types of asimmetry - agregate investigation
63.8 / i----1
Hungarian oak — • — durmast
01234
1 - Left-hand-site asimmetry; 2 - Symmetry; 3 - Right-hand-site
asimmetry
The data in Table 2 and the illustrations on Figures 2 and 3 have only been analyzed for the Hungarian oak and the durmast as there are a sufficient number of sample plots for them. One can see from the table and the figures that for these two species, in the separate investigation, there has been found a similar, of too close values, distribution of sample plots according to types of asymmetry: durmast, as compared with Hungarian oak, has a lesser number of sample plots of a left-hand-side asymmetry, the same number of symmetric curves and a larger number of curves, or sample plots, of a right-hand-side asymmetry. Besides, with the aggregate investigation (on the basis of the general average curve of the normal numbers (qxav)), though almost the same proportion of the left-hand-side and right-hand-side asymmetries can be observed, the differences are more substantial, and such a comparison makes it possible to see the places of the two tree species as compared with each other, namely: the left-hand-side asymmetry and the symmetric type are lesser with durmast, whereas the curves of a right-hand-side asymmetry with it are more by 33.3% and this is indicative of a probably better productivity of durmast with all other conditions equal. The separate investigation of the distribution of sample plots reveals precisely the thickness structures of the two tree species, and close is the proximity of the curves of the three types of asymmetry (Fig. 1). This is logical, having in mind their biological relationship: both species belong to the genus Quercus and their natural ranges overlap - from 0 m. alt. to 1,000 m. alt. they grow together. This same pertains also to Turkey oak, though we were not able to reason about it. However, the investigation goes on and in its course the corresponding conclusions about this are drawn.
4.3. The influence of dendrocoenoses' age upon the distribution of the thickness-structure curves
Further on, we have investigated the influence of the sample plots under the trees of the differentiated age groups upon their distribution according to types of asymmetry. The following age groups have been differentiated: up to 80 years; 81-110 years; 111-140 years and over 140 years. The curves outlining the distribution of the sample plots in percentages (%) according to age groups with the three types of asymmetry have been presented on Fig. 4.
On Figure 4, one can see that for all the age groups the curves of the distribution of the sample plots according to types of asymmetry have similar aspects. As age increases, the left-hand-side asymmetry, except for the age group of 81-110 years, increases, whereas the right-hand-side one decreases. With the symmetric type, as an increase so a decrease is noticed. The general inference is that no clear relationship is distinguished between age and dendrocoenoses' distribution according to types of asymmetry; in other words, age slightly influences the asymmetry of the thickness structure, and this confirms earlier investigations of this matter (Dimitrov, 1978).
Фиг. 4. Distribution of the number of Sample plots (SP) in % by Age groups
and type of asimmetry
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up to 80 ; 81-110
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123 Asimmetry: 1 - Left-hand-site ; 2 - Simmetry; 3 - Right-hand-site
4.4. Comparing the average curves of normal numbers (qxav)
We have compared the average curves of the normal numbers for the seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses with Tyurin's uniform average curve of normal numbers, obtained for all tree species (Tyurin, 1938). The results have been presented in Table 3.
As seen in Table 3, the values of the qualitative characteristics of the different tree species with the particular natural levels of thickness (NLT) are close to one another, especially with NLT exceeding 0.9. Wilcoxon's test gives precise data about the proximity of the investigated curves to that of Tyurin. According to him, the curves for Hungarian oak, durmast and Turkey oak are irrefutably close in values as the zero hypothesis is not refused but assumed. It follows from the proximity of the rows of the normal numbers, or the qualitative characteristics, of thickness structure to Tyurin's uniform average curve that the thickness structures of seed-tree Hungarian oak, durmast and Turkey oak dendrocoenoses are statistically very close, and that it is possible to develop general models for the three tree species on the basis of thickness level.
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Таблица 3. Average curves of normal numbers for the seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses as compared with Tyurin's uniform curve of normal numbers
Belonging of the curve Natural levels of thickness Test after Wilcoxon (<x=0.5)
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Wst at. Wc rit. P Zer 0 hyp
Average curves of the normal numbers for thickness structure /qualitative characteristics/ - (qxav)
Hungarian oak 0.07 0.13 0.23 0.35 0.48 0.6 0.7 0.8 0.87 0.91 0.96 0.98 1 33 15 0.64 assu med
Durmast 0.05 0.14 0.2 0.32 0.47 0.62 0.64 0.84 0.9 0.93 0.98 0.99 1 31 15 0.53 refit sed
Turkey oak 0.05 0.14 0.26 0.4 0.54 0.68 0.78 0.86 0.9 0.94 0.98 0.99 1 25 15 0.27 assu med
Tyurin's uniform average curve 0.01 0.04 0.14 0.3 0.48 0.66 0.79 0.88 0.95 0.98 0.99 1 1 - - - -
INFERENCES
As a result of the investigation, the following inferences can be drawn: What is known from earlier investigations about the investigated seed-tree dendrocoenoses of Hungarian oak, durmast and Turkey oak has been confirmed, namely the availability of three types of thickness structure - of right-hand-side and left-hand-side asymmetries and of a symmetric type.
One and the same tendency as of the distribution of the sample plots according to types of asymmetry has been observed with the Hungarian-oak, durmast and Turkey oak dendrocoenoses (of the genus Quercus). With all other conditions equal, it can be presumed about durmast that it has better productivity owing to that the curves of its thickness levels are more often of a right-hand-side asymmetry in terms of its average diameter.
The dendrocoenoses' ages influence negligibly the trees' distribution according to types of asymmetry, regardless of the tree species.
Comparing the average curves of the normal numbers (or of the qualitative characteristics) of the thickness structures of the investigated seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses with Tyurin's uniform average curve of normal numbers has shown close similarities in the aspects of the curves for the three tree species. This suggests the possibility of developing general models of their timber volumes and assortment structures, as long as these depend on the trees' thickness structures.
CONCLUSION The thickness structures of seed-tree Hungarian-oak, durmast and Turkey-oak dendrocoenoses do not depend significantly on tree species and age; it is possible to develop a general model of their thickness structure, as well as to develop other models such as volumetric and assortment tables.
Acknowledgement: The sample plots we used had been delivered to us by Prof. Kiril Bogdanov, for which we express our gratitude to him.
Literature Cited
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