Spatial Structure of Uneven-Aged Stands of Fir and Beech on the Borja Mountain (Bosnia and Herzegovina) ^†

Abstract

In the territory of Bosnia and Herzegovina, uneven-aged stands of fir and beech are very important from the economic and ecological points of view. A major lack of information on the simple structure of stands is that it cannot be used to draw valid conclusions about the spatial distribution of woody species and about the position and dimensions of trees, and this is one of the bases for the sustainable management of mixed and uneven-aged forests. In four mixed uneven-aged fir and beech stands and one pure fir stand on Mt Borja, the basic elements of tree growth were measured and the data needed to determine the indicators of the spatial stand structure were determined. According to the Clark–Evans aggregation index, there is a tendency towards a uniform spatial distribution of trees in the stand in the case when all trees are observed. When only fir trees are observed, it is evident that there is a tendency to group fir trees in the stand. The diameter differentiation index shows that there is average tree diameter differentiation on all sample plots. The determined values of the Weber height competition index by stands are approximately the same, that is, it can be stated that there is no significant difference between stands in terms of competition between trees as regards the vertical structure of stands.

1. Introduction

According to the forest inventory data in Bosnia and Herzegovina, the total area of forests and forest land is 3,231,000 ha. High forests with natural regeneration occupy more than 50% of the total forest area. The area of high forests with natural regeneration is dominated by deciduous forests, which make around a 50% share, whereas the share of mixed deciduous and coniferous forests is around 30%. The remaining 20% are coniferous forests [1]. In the mountain belt of Bosnia and Herzegovina, fir and beech form a community of beech-fir forests (Abieti fagetum) as one of the most important forest communities in this area.

Over the past decades, a large number of researchers of various profiles have pointed to the numerous ecological and economic advantages of mixed uneven-aged stands over pure even-aged ones. The advantages are primarily manifested in the more efficient use of habitat potential and space for growth, in greater stability and resilience of mixed uneven-aged stands and in positive impact on biodiversity [2,3,4,5]. The orientation of modern forestry towards mixed and uneven-aged stands raises numerous new issues on the growth characteristics of tree species that make up the mixture and their mutual relations [6]. The most important systemic characteristic of mixed and uneven-aged forests, where forest, growth conditions and growth flows are highly variable, is detailed structural determination [7]. Defining and analyzing structural indices that characterize the horizontal and vertical structure of stands are among the most important tasks in modern forestry research [8,9,10,11,12,13]. Based on the above, the aim of the research is to obtain information that will enable the structural determination of mixed fir and beech uneven-aged stands in the area studied.

2. Materials and Methods

The research area is Mt Borja (Dinaric Massif), located between the rivers Velika and Mala Usora in the northern part of Bosnia and Herzegovina (Figure 1). On this mountain, mixed stands of Silver fir (Abies alba Mill.) and European beech (Fagus sylvatica L.) predominate, with pure stands of Silver fir appearing as well. The required data have been collected by setting up 5 sample plots (2500 m²). The altitude of the sample plots ranges from 494 m to 940 m, the slope of the terrain changes from 7° to 22° and there are various exposures (except the western one) represented. The average age of fir trees in the sample plots is in the interval from 63 to 110 years (41% of trees are aged between 70 and 90 years), and beech trees vary from 58 to 107 years of age (the age has been determined by counting tree rings at breast height).

On sample plots 1, 2 and 4, the presence of the Rusco hypoglossi-Abietetum Brujić 2004 association was determined, and on sample plots the 3 and 5 the presence of the Galio rotundifolii-Abietetum M. Wraber 1959 association was determined. In addition to the survey of the basic elements of tree growth (diameter and height), the necessary data for determining the indicators of the spatial structure of the stand were determined. The investigated stands are managed by a system that is a combination of group selection and single selection of trees for felling, which results in a very heterogeneous state.

In this study, the spatial structure of stands is presented on the basis of the stand structure index and the Weber height competition index (CI) [14]. From the stand structure index, that is, stand structure indicators, the following were calculated: Clark and Evans aggregation index (R) [15] and diameter differentiation index (T_d) [10,16]:

$$CI=\frac{{\displaystyle {\sum }_{j=1}^n{H}_j}}{n};if(h_i>h_j)\Rightarrow H_j=1;else\Rightarrow H_j=0$$

where:

• CI_2i—the competition index for the subject tree i;
• h_i—the height of the subject tree i;
• h_j—the height of the competitor tree j;
• n—the number of competitors in the neighborhood zone.

$$R=\frac{\mathrm{observed}\mathrm{mean}\mathrm{distance}\mathrm{between}\mathrm{neighbour}\mathrm{trees}}{\mathrm{expected}\mathrm{mean}\mathrm{distance}\mathrm{between}\mathrm{neighbour}\mathrm{trees}}=\frac{\frac{1}{n}{\displaystyle \sum _{i=1}^n{r}_i}}{0.5\sqrt{10000/N}}$$

where:

• r_i = distance of tree i to next neighbor;
• N = number of trees per ha;
• n = number of sample trees.

$${{\displaystyle T}}_d=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left(1-r_i\right)}$$

where:

• r_i = (thinner dbh)/(thicker dbh) of tree pair i;
• n = number of measured tree pairs.

3. Results and Discussion

Basic data on the elements of the structure of stands by sample plots are given in

Table 1. Characteristics of sample plots.

Sample Plots	N (trees ha−1)			dq (cm)		hL (m)		V (m3 ha−1)
	Fir	Beech	Total	Fir	Beech	Fir	Beech	Fir	Beech	Total
1	604	128	732	29.1	23.4	26.5	25.3	518.3	71.9	590.2
2	268	124	392	38.7	20.5	27.6	23.6	416.0	49.9	465.9
3	604	8	612	28.8	25.4	27.2	24.4	524.5	5.1	529.6
4	200	276	476	39.3	31.7	30.1	31.3	354.1	356.0	710.1
5	520	68	588	22.8	37.3	18.7	20.5	195.6	78.1	273.7

Note: N—number of trees per hectare on the sample plot; d_q—quadratic mean diameter; h_L—Lorey’s mean height; V—wood volume per hectare.

. On sample plot 3 there is a pure fir stand, whereas on the remaining ones there are mixed stands of fir and beech. The number of trees (per hectare) per sample plots is in the range from 392 to 732, that is, the number of fir trees is within the range from 200 to 604. The quadratic mean diameter (d_q) for fir is within the range from 22.8 cm to 39.3 cm and for beech within the range from 20.5 cm to 37.3 cm. The volume of wood (V) per sample plots is within the range from 273.7 to 710.1 m³ ha⁻¹.

The Clark and Evans aggregation index, an indicator of stand structure, represents the ratio of the observed and expected mean distance between the nearest neighboring trees. Two forms of competition have been observed. In the first case, all trees (fir and beech) have been taken into account, and in the second only fir trees (

Table 2. The index of aggregation of Clark and Evans.

Sample Plots					Mean	SD	CV(%)
1	2	3	4	5
Fir and Beech–Fir and Beech (all trees)
1.253	1.121	1.057	1.063	0.980	1.095	0.102	9
Fir–Fir (only fir trees)
1.044	0.746	1.044	0.599	0.842	0.855	0.193	23

Note: Mean—arithmetic mean; SD—standard deviation; CV_(%)—coefficient of variation.

). In this first form of competition, when all trees (fir and beech) are taken into account, with a random distribution on individual experimental surfaces, there is a tendency towards the uniformity of the spatial distribution of trees in the stand. In the second case, only fir trees were selected. In this form of competition, the lower values of calculated indices are evident. On average, in this case when only fir trees have been taken into account and with a random distribution on individual experimental areas, there is a tendency to group fir trees in the stand. Compared to the previous case of competition, there is a higher coefficient of variation of the determined indices per sample plots.

According to Lafond et al. [17], the individual selection of trees for felling led to a random or uniform distribution of trees, while the group selection of trees for felling (formation of groups) enabled greater grouping of trees in space. Vacek [18] analyzed the structure of natural mixed forests (spruce-beech-fir) in the Orlické hory nature reserve (Czech Republic). Of the four permanent sample plots, only one has a tendency to group trees. In mixed old forests (spruce-fir-beech) in the Western Carpathians, based on the value of the aggregation index, Parobekova et al. [19] determined a random arrangement of trees in all layers by stages of development: initial (1.03), optimal (1.08) and terminal (1.05).

In order to more fully define the stand structure, it is necessary to analyze the differences in the dimensions of trees and their immediate neighbors. For this purpose, the diameter differentiation index (T_d) was determined (

Table 3. The diameter differentiation index.

Sample Plots	n	Mean	Min	Max	CV(%)	Mean	Min	Max	CV(%)
		Td1				Td3
1	183	0.478	0.021	0.837	49	0.449	0.098	0.830	31
2	98	0.479	0.011	0.880	52	0.470	0.178	0.790	31
3	153	0.430	0.019	0.848	58	0.405	0.076	0.828	40
4	119	0.381	0.002	0.792	59	0.355	0.063	0.791	43
5	147	0.442	0.003	0.845	47	0.434	0.116	0.751	29
total	700	0.442	0.002	0.880	53	0.423	0.063	0.830	36

). All trees (fir and beech) were selected as the main (reference) trees for which the diameter differentiation index was calculated. The form of competition observed was as follows: fir and beech trees–fir and beech trees. The average value of the index based on the differentiation of diameters of the two observed trees (reference tree and the first neighbor) by the sample plots is within the range from 0.381 to 0.479. The mean value of the diameter differentiation index of all five sample plots is 0.442. This practically means that, on average, a randomly selected tree and its immediate neighboring tree are in such a relationship that the diameter of a thinner tree is 56% of the diameter of a thicker tree. This can be stated in all cases of the average differentiation of tree diameters according to Pommerening [12]. In order to gain the most realistic idea of the level of diversity of tree diameters, the (T_d3) index (difference in diameters between the reference tree and its three closest neighbors) was determined. The size of the (T_d3) index at the stand level is within the range from 0.355 to 0.470. The mean value of the diameter differentiation index of all five sample plots is 0.423. These are approximately the same values as the values obtained on the basis of the reference tree and the first neighbor, with the variation of the determined individual values by stands, expressed by the coefficient of variation, being significantly less.

Vacek [14], analyzing the structure of natural mixed forests (spruce, beech and fir) in the Orlické hory nature reserve on four permanent sample plots, determined the respective values of the diameter differentiation index (0.415, 0.428, 0.474 and 0.549) which are slightly higher than obtained in this study. In mixed old forests (spruce-fir-beech) in the Western Carpathians, Parobekova et al. [19] determined the values of the differentiation index by stages of development: initial (0.55), optimal (0.50) and terminal (0.56). The stated values are higher than those obtained in this study, that is, the differentiation of tree diameters is higher. An analysis of variance and Duncan’s test showed that two homogeneous groups can be formed as regards T_d1 and three homogeneous groups as regards T_d3, that is, greater differentiation is evident when looking at the reference tree and its three closest neighbors (

Table 4. Analysis of variance—the diameter differentiation index and the Weber height competition index.

Index	Sample Plots					ANOVA
	1	2	3	4	5	F	p	n
Td1	0.478 a	0.479 a	0.430 a,b	0.381 b	0.442 a	3.611	0.0064	2
Td3	0.449 a	0.470 a	0.405 b	0.355 c	0.434 a,b	10.113	0.0000	3
CI (fir)	0.472 a	0.550 a	0.487 a	0.467 a	0.474 a	0.6215	0.6474	1
CI (fir and beech)	0.474 a	0.488 a	0.486 a	0.484 a	0.508 a	0.1740	0.9520	1

n—number of homogeneous groups by Duncan’s test (α = 0.05). ^a, ^b, and ^c—tags for homogeneous groups.

).

Analyses that provide a detailed insight into the vertical structure of stands are important. One of the parameters that allows this is the Weber height competition index (CI). The index is equal to zero when all competing trees are higher than the observed tree, that is, it is equal to one when all competing trees are lower than the observed tree. Therefore, higher values of the index mean that the observed tree has a greater competitive power, that is, there is less competition in its environment. In the first variant (form of competition: fir–fir and beech), the determined average values of the Weber height competition index per sample plot are within the range from 0.467 to 0.550, that is, the average figure for fir trees from all sample plots is 0.486. In the second variant (form of competition: fir and beech trees–fir and beech trees), the determined average values of the Weber height index per sample plot are within the range from 0.474 to 0.508, that is, the average for trees from all sample plots is 0.487 (

Table 5. The Weber height competition index.

Sample Plots	Fir–Fir and Beech				Fir and Beech–Fir and Beech
	n	Mean	SD	CV(%)	n	Mean	SD	CV(%)
1	151	0.472	0.356	75	183	0.474	0.353	75
2	67	0.550	0.359	65	98	0.488	0.360	74
3	151	0.487	0.342	70	153	0.486	0.341	70
4	50	0.467	0.340	73	119	0.484	0.349	72
5	130	0.474	0.354	75	147	0.508	0.356	70
total	549	0.486	0.350	72	700	0.487	0.350	72

). The determined values of the Weber height competition index by stands are approximately the same, that is, it can be stated, based on the analysis of variance (Table 4), that there is no statistically significant difference between stands in terms of competition between trees as regards the vertical stand structure.

4. Conclusions

In the mountain belt of Bosnia and Herzegovina, fir and beech form a community of beech-fir forests as one of the most important forest communities in this area. The investigated uneven-aged, mixed stands are managed by a system that is a combination of group selection and single selection of trees for felling.

The Clark and Evans aggregation index shows that there is a tendency towards uniformity of the spatial distribution of trees in the stand when all trees (fir and beech) have been taken into account. On the other hand, there is a tendency towards the grouping of fir trees in the stand and a greater variation of index values by sample plots when only fir trees are observed. The diameter differentiation index shows that there is average tree diameter differentiation on all sample plots. It is also determined that there are statistically significant differences between individual sample plots in terms of tree diameter differentiation. The determined values of the Weber height competition index by sample plots are approximately the same, that is, it can be stated that there is no significant difference between stands in terms of competition between trees when it comes to the vertical structure of stands.

The research shows the possibility of using the index (CI, R and T_d) as an additional indicator of structure that helps quantify the condition and comparison of stands, that is, the structural determination of stands in mixed fir and beech uneven-aged forests in the area studied.