The Effect of Beech (Fagus sylvatica L.) Bark Stripping by Deer on Depreciation of Wood

Abstract

The aim of the study was to analyse the changes in the infection rate development inside the beech stem as a result of browsing by deer (Cervus elaphus). The research materials were collected from three research plots located in the Polanów Forest Inspectorate from March to April 2020. For the study, 80 beech trees were selected, for which the size of the fallow tree, the percentage of the section taken from its centre infected with rot, and the number of years passed since the tree was wounded were determined. The study shows that the infection affects only the rings formed before the tree was injured. The average size of stem rot was 7.75% of its area, and it spread at the rate of 2.52% of the cross-sectional area per year. The analysis of the obtained results proved that both the size of the wound (splits) and the time elapsed since the tree was damaged are significantly correlated with each other. It is also possible to build a model for estimating the size of decay in stunted beech trees based on easy-to-determine predictors, such as maximum wound width and elapsed time since tree damage.

1. Introduction

For many years, the large number of herbivorous mammals has been perceived as one of the main factors influencing the structure and function of forest ecosystems [1,2]. As far as economic viewpoints are concerned, the way animals impact the forest vegetation will always be viewed through the prism of the damages that they cause. Among the stresses the ungulate exerts on the forest, browsing and bark stripping are the most common ones. This contributes to an exponential economic loss in forests. The Polish forest administration spends about 37 million euros every year to reduce the damage caused by big mammals in forests [3]. As the number of the deer increases, the percentage of damaged trees due to bark stripping increases, but also the preferences regarding the species chosen for bark stripping are changing [2]. Important factors that have an impact on reducing the amount of damage caused by bark stripping are the age and size of the tree, game management, stand characteristics, e.g., afforested agricultural land, and, in the contrary, less fertile stands, thinning regimes, and landscape context. It has been observed that there are significant differences between species as far as susceptibility to the damage is concerned. Hence, the Norway spruce (Picea abies (L.) Karst.) and the Sitka spruce (Picea sitchensis (Bong.) Carrière) are sensitive between the ages of 5 and 50, the European beech (Fagus sylvatica L.) up until 70, the Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) between the ages of 12 and 44, and the Scots pine (Pinus sylvestris L.) between the ages of 5 and 16 [4].

Depending on the size and the nature of the damage, bark stripping can lead to the inhibition of growth increments, i.e., thickness and height increments [5,6,7], and as a result, the tree volume. In extreme cases, the tree damages can be so extensive that they lead to the premature removal of the tree stand. There are about 20 tree species stripped by the red deer in Europe, the Norway spruce being among the most favourite [8,9,10,11], together with the Scots pine [12], the European ash (Fraxinus excelsior L.) [11], the Tilia (Tilia spp.) [13], the Norway maple (Acer spp.) [14], and recently, the European beech (F. silvatica) [15]. However, the species which appears to be the least susceptible to damage is the Sitka spruce (Picea sitchensis) [4]. In 2020, the total area of the tree stands damaged by the red deer reached 29.1 thousand hectares, which constitutes 0.4% of the forests managed by the State Forests in Poland. A significant percentage of these damages is from summer bark stripping in deciduous trees stands, including natural beech forests (reports on the state of forests in Poland 2020).

Beech bark stripping in summer is connected with an easier separation of the bark from the stem [16] and causes deep wounds, which include layers of bark and phloem reaching the layers of the wood. Such a type of damage undoubtedly decreases the quality of the wood because in the summertime, it may enable the infection of parasitic and saprophytic fungi [17,18] as well as insect infestation in xylem, including technical pests. In the case of separation of the bark from phloem on the entire circumference of the trunk or stem, a dieback of the damaged trees takes place within one vegetation period. The studies conducted by Kurek et al. [19] reveal that in young beech stands, up to 30% of the trees are damaged, and in extreme cases, even 100%. The average extent of these damages is 36% of the tree circumference and 0.06 m² of the trunk area.

According to the literature of the subject matter, the causes of bark stripping by deer vary. It seems that the most important one is the need for enhancing and diversifying the feeding base. Additional crucial factors are the supplementation of vitamin and mineral deficiencies; the need to obtain food rich in dietary fibre, which is important for the functioning of the rumen; the use of bark as an additional food source rich in water, which is particularly important in summer time; and as a direct result of stress to which the red deer is exposed [20]. According to Ueckermanna [21], the Cervidae, and the red deer in particular (Cervus elaphus L.), search for juicy food in the summertime and especially during heatwaves. Kurek et al. [19] believe that summer deer bark stripping is a result of searching for attractants, mainly sugars.

According to White et al. [22], some trees are chosen multiple times, while other are never chosen and remain intact. The selected trees tend to grow faster with thicker cambium and the flow of their phloem sap is at its peak. Kutiers et al. [15] claim that beeches with a smoother bark are more susceptible to bark stripping than those with a coarser bark. Bobrowski et al. [23] state that the reason behind browsing of the beech is the availability of young trees stands. Moreover, they have proven that the extent of damage in the young beech tree stands is significantly correlated with the occurrence of the European blueberry (Vaccinium myrtillus L.) and is negatively correlated with the occurrence of old spruce tree stands.

In extreme cases, browsing and damaging young trees can lead to eliminating large portions of forest harvest. According to the study conducted by Zlotina and Khodashova [24], due to deer browsing and bark stripping in harvest and sampling stands, the dynamics of biomass increments can be lowered even by 37%. The wounds caused by bark stripping are vulnerable to pathogenic fungal infections for a long period of time. It is even more important to remember that beech wounds heal and close at a pace of about 0.6-1cm per year, so closing a 10cm-wide wound can take 10–15 years [25].

An total of 64% of the wounds in beeches (as stated by Schumanna et al. [26]) and 84% of the wounds in beeches [27] can be inhabited by fungi. Hecht et al. [28] investigated the susceptibility of beech wounds towards fungal infections that cause discolouration and rot. They compared the wounds caused by the removal of the bark at the base of the trunk with the wounds inflicted by fraying during stand treatment procedures in the upper part of the trunk. It was observed that the wounds in the upper parts of the trunk were more susceptible to be infected by fungi causing discolouration and rot than the wounds inflicted 0.5 m above the ground. They also compared wounds that were inflicted in July and October. Twice as many wounds from July were infected with fungi than those from October, which indicates that summer bark stripping has a greater risk of developing rot as a result than winter bark stripping. Apart from the fungi causing rot such as Fomes fomentarius or Stereum rugosum [29], they also isolated fungi that cause blue stain (Phoma spp., Phialophora spp.). Moreover, the wounds can also be infected with fungi that cause bark canker, such as Hypoxylon fragiforme, Hypoxylon cohaerens, Cylindrobasidium evolvens, Neonectria coccinea, and Neonectria galligena [28], which may lead to a long-lasting illness and damaging health and, in the end, dieback of the tree. The studies conducted by Hart and Hart [30] observed a relationship between tree mortality caused by pathogenic fungi and previous damages of the trunk caused by deer. Archipova et al. [31] analysed the process of infecting a wound with Pinus contorta fungi. It appeared that the length of the wound was of vital importance for stem rot area, while the area of wood discolouration outside the edge of wound was limited and reached 20 cm at most.

The issues of the damages caused by the deer in the forests are extraordinarily complex. The complexity stems from the complicated connections between animate and inanimate matters. The choice of a particular plant species, including trees, by the deer varies according to the season together with the chemical changes that take place in the plant tissues [32]. Timber, which has an external rot, cannot be used, and the extent of the damage may lead to premature removal of the tree stand, and is obviously connected with substantial economic losses.

The study assumed that there is a correlation between the size of the wound and its age with the size of the rot within the trunk of the European beech (F. sylvatica). It was also assumed that based on these correlations, it is possible to use algorithms to estimate the development of rot in tree trunks depending on the size of the wound and the time elapsed since the tree was damaged. The obtained models can support the calculation of economic losses and can help in the decision to remove the stand prematurely.

2. Materials and Methods

The studies were carried out in an area with great pressure from the ungulate on the beech tree stands. The study took place at a Regional Directorate of the State Forests in Szczecinek, Polanów Forest Inspectorate (Figure 1) in the following Forest Districts: Żydowo 16.695846 54.054176 (556g), Warblewo 16.775723, 54.124299 (326b), and Puławy 16.605219, 54.174964 (165k) during commercial thinning in the beech stands.

In Żydowo Forest District (section 556g, forest site type: fresh forest) 42 tree samples from trees in the ages between 18 and 33 were collected. In Warblewo Forest District (section 326b, forest site type: fresh forest), 27 samples from trees in the ages between 13 and 33 were collected. In Puławy Forest District (section 165k, forest site type: fresh forest), 11 samples from trees in the ages between 33 and 48 were collected.

The study was conducted between March and May 2020, and it was executed in two stages. The first stage was conducted on standing trees and the second stage on felled trees. The selection of trees was made on the basis of thickness classification (DBH). First, the breast height of all trees was measured. Then, the stand was divided into four thickness classes (5.0–9.0; 9.1–13.0; 13.1–17.0; 17.1–21.0), and 20 damaged trees were selected from each class while assuming a minimum threshold of damage to the trunk circumference of no less than 30%. Each measurement was recorded in a field report and then the data was imported into an Excel spreadsheet. In total, 80 trees were measured between 1 and 8 years after bark stripping occurred.

The first stage of the study focused on measuring the biometric characteristics of trees and, in addition, measuring the tree circumference in the place where the wound occurred as well as the height and width of the damage in its widest and narrowest places. Next, the trees were felled, and from the middle height of the wound, the samples (cross-sections) were collected for further lab analysis.

The second stage focused on measuring the collected samples (discs). In order to measure the area of the rot, a scanner with a computer software was used. Next, the measured area was related to the area of the entire disc (Sa/Ra), which means they are without the annual increments since the time bark stripping occurred. On the basis of annual ring increments after the damage, the number of years that had passed since the damage occurred as a result of bark stripping was calculated.

On the basis of the measurement, mean values for the following characteristics were calculated:

• Height of the wound [cm];
• Width of the wound [cm];
• The trunk circumference at the height of the maximal width of the wound [cm];
• The ratio of trunk circumference to the maximal width of the wound (Tc/Ww);
• Years after the damage;
• Rot area (Ra) [cm²];
• Area of the cross-section without the increments after bark stripping (Sa) [cm²] (Figure 2, area marked with red circle);
• Ratio of the area of the cross-section without the increments after bark stripping to the area of the rot (Sa/Ra) (Figure 2).

Basic statistical values were calculated for each characteristic using Statistica 13.1 software (TIBCO Software Inc., Palo Alto, CA, USA). Next, the distribution of variables analysis was conducted, and then correlations between the studied characteristics were determined. In order to determine the correlations between the characteristics, Spearman’s rank correlation coefficient was calculated for each of the characteristics. The level of statistical significance was established at α = 0.05. For this particular study, a zero hypothesis was adopted, which states that the parameters of tree damage (years since the bark stripping, size of the wound, width of the wound to the circumference of the trunk ratio) do not impact the size of the rot. The next step was to conduct hierarchical clustering, factor analysis, and in order to build the model backward, stepwise regression was done as well. All the analyses were conducted at the statistical significance of α = 0.05.

3. Results

3.1. Analysis of Variables

In the analysed samples, the mean trunk circumference was 34.96 cm. The thinnest tree was 18 cm whereas the thickest tree was 63 cm. The variability of tree circumference in the studied group was low at only 25%. The tapped trees were characterised by a damaged trunk with a mean height of 54.13 cm and a mean width of 10.24 cm. The coefficient of variation for this characteristic was quite high and was as much as 56% for the height and 71% for the width of the wound (

Table 1. Statistical values of the studied characteristics.

Variables	N	X	Min	Max	St. Dev	CV
Tree circumference [cm]	80	34.96	18.00	63.00	8.86	25.33
Maximum wound height [cm]	80	54.13	9.00	118.00	30.31	56.00
Maximum wound width [cm]	80	10.24	1.00	32.00	7.28	71.12
Stem rot area [cm2]	80	9.93	0.25	93.94	17.78	178.94
Sectional area [cm2]	80	65.46	7.55	188.69	35.70	54.54
Years since stem damage has occurred	80	3.16	1.00	7.00	1.93	61.09
Sa/Ra	80	32.83	1.02	196.11	43.75	133.25
Tc/Ww	80	6.11	1.00	44.00	6.39	104.60

N—number of samples; X—mean; Min—minimum; Max—maximum; Std. dev—standard deviation; CV—coefficient of variation.

).

The mean rot area in the studied tree population was 9.93 cm², and the coefficient of variation for this characteristic was very high, reaching as much as 179.94%; hence, in the studied sample, there were trees with trace amounts of rot as well as trees with a highly developed and extensive rot. The age of the trees since the moment of the damage was between 1 and 7 years old.

Moreover, the Sa/Ra index, which is a ratio of the cross-section area to the rot area, was calculated as well. The value of this index was between 1.02 and 192.11, and its mean value was 32.83. The second of the determined indexes was Tc/Ww, which determined the ratio of the circumference at the height of the wound to the maximal width of the wound, whose mean value was 6.11 and was characterised by its variability at the level of 104.6% (Table 1).

3.2. Correlation Analysis

Another step was conducting the analysis of correlation between the studied characteristics and indexes. The analysed characteristics were not normally distributed; hence, the correlation analysis was conducted using Spearman’s rank correlation coefficient (

Table 2. Spearman’s rank correlation coefficient for the studied characteristics and indexes.

Spearman’s Rank Correlation Coefficient	Tree Circumference [cm]	Maximum Wound Height [cm]	Maximum Wound Width [cm]	Stem Rot Area [cm2]	Sectional Area [cm2]	Years since Stem Damage has Occurred	Sa/Ra	Tc/Ww
Tree circumference [cm]	1.0000	0.2400	0.3043	0.5019	0.7182	0.3832	−0.2211	−0.0335
Maximum wound height [cm]	0.2400	1.0000	0.7024	0.6499	0.1159	0.1401	−0.6485	−0.6652
Maximum wound width [cm]	0.3043	0.7024	1.0000	0.6207	0.2982	0.3038	−0.5144	−0.9490
Stem rot area [cm2]	0.5019	0.6499	0.6207	1.0000	0.1838	0.6404	−0.9149	−0.5006
Sectional area [cm2]	0.7182	0.1159	0.2982	0.1838	1.0000	−0.1621	0.1559	−0.1124
Years since stem damage has occurred	0.3832	0.3038	0.1401	0.6404	−0.1621	1.0000	−0.6608	−0.0249
Sa/Ra	−0.2211	−0.6485	−0.5144	−0.9149	0.1559	−0.6608	1.0000	0.4701
Tc/Ww	−0.0335	−0.6652	−0.9490	−0.5006	−0.1124	−0.0249	0.4701	1.0000

). The majority of the analysed variables were correlated with each other positively or negatively. A particularly noteworthy correlation is the time correlation that has passed since the damage and the rot area (0.6404) as well as the time since the damage occurred and the width of the wound (0.3038).

Moreover, it is important to emphasise the relationship between the tree circumference and the rot area (0.5019) and the Tc/Ww index and the stem rot area (−0.5006).

Another issue is that the relative areas of the stem rot were strongly and negatively correlated with the width of the wound (−0.5144), its length (−0.648), and time that had passed since the damage of the trunk (−0.6608) (Table 2).

On this basis, it can be assumed that the analysed variables can be independently taken into consideration as potential predicates while modelling the studied correlations.

3.3. Creating the Model

The data were subjected to a statistical analysis: hierarchical clustering. Exploratory clustering of observations indicated that if the mean distance aggregations are assumed at between 300 and 400, then the variables focus basically around three groups, i.e., Sa/Ra, sectional area, maximum wound height, and other variables. A separate group with a great agglomeration distance is the Sa/Ra index, and while this index is significantly correlated with all the variables, it is apart from the sectional area. However, relatively closely clustered around stem rot area were the variables: years since stem damage has occurred, maximum wound width, tree circumference, and Tc/Ww index (Figure 3). In further analysis, sectional area was acknowledged as the least significant variable and impractical for predicting the development of rot; as a result, it was omitted in the further analyses. Its rejection was determined by the fact that it was a characteristic that was poorly correlated with the other variables. In addition, it is difficult to measure in the forest, which limits its practical use in modelling.

In order to construct a model for predicting the development of stem rot, the next step was to conduct a factor analysis to reduce the number of attributes and to detect a structure in the relations among the attributes of bark stripping by deer and the depreciation of the timber as a result of the rot. After determining the correlation between the variables, on the basis of Kaiser criterion, the analysis of eigenvalues, and adopting the graphic scree test, it was possible to indicate the significant factors. An additional test which verified the accuracy of factor isolation was determining the correlation matrices of residuals. Assuming that the Sa/Ra and Tc/Ww indexes are derivatives of other variables, then the principal components analysis indicated that the variables clustered around three factors at most, as illustrated in a three-dimensional diagram of factor loads (Figure 4). The maximum wound height and the maximum wound width have been described by one factor; stem rot area and years since stem damage has occurred, by another; and tree circumference has been described by a third factor.

The conducted factor analysis (

Table 3. Intrinsic value.

Value	Intrinsic Value	% Total	Cumulative	Cumulative
1	3.152834	45.04049	3.152834	45.04049
2	1.242978	17.75683	4.395813	62.79732
3	1.020765	14.58236	5.416578	77.37969 1

¹ statistically significant.

and

Table 4. Factor loads.

	Factor	Factor	Factor
Tree circumference [cm]	0.458273	−0.342340	−0.722560
Maximum wound height [cm]	0.800213 1	0.094173	0.125873
Maximum wound width [cm]	0.837161	0.392808	−0.122307
Stem rot area [cm2]	0.710678	0.062073	−0.349816
Years since bark stripping occurred	0.513003	−0.752850	0.187869
Sa/Ra	−0.698082	0.318476	−0.513964
Tc/Ww	−0.588293	−0.539028	−0.214580
Variation explained	3.152834	1.242978	1.020765
Participation	0.450405	0.177568	0.145824

¹ Statistically significant

) allowed us to isolate three factors, the first of which explains 45%; the second, 17.8%; and the third, 14.6% of the total variance (Figure 4, Table 4). This means that together, the three factors explain over 77% of the total variance of the rot that occurred as a result of bark stripping by the deer. As a result, in order to fairly and precisely describe the stem rot area as a result of bark stripping, a three-dimensional space was required, in which the first factor determines the size of the wound; the second, the size since the damage had occurred; and the third one, the size of tree, i.e., tree circumference (Table 4).

Moreover, scree test indicates that in order to prepare a proper description of the correlations and to construct the model, 2 or 3 factors should be taken into account, of which three eigenvalues are higher than 1 (Figure 5). On the basis of the factor loadings analysis, correlation matrices of residuals analysis and Kaiser criterion, three attributes which shaped the stem rot area the most (years since stem damage has occurred, maximum wound width and tree circumference) were initially selected.

A significant correlation between the analysed factors indicates that knowledge contributed to regression equation by two, significantly correlated variables is not usually much higher than the knowledge contributed by one of them. In order to eliminate the least meaningful variables from the equation, a backward stepwise regression approach was used to determine the coefficients for this equation. The first step to achieve this is to construct a model which includes all potential explaining variables, and then the next step gradually eliminates the variables in such a way to achieve the model with the highest value of the coefficient of determination while preserving the significance of the parameters.

In order to construct the model, a regression equation was used which looks the following:

Y = β₀ + β₁ X₁ + β₂ X₂ +…+ β_k X_k + E,

(1)

where: β₀, β₁,…, β_k are regression coefficients (structural parameters) of the equation model in the population; X₁, X₂,…, X_k are explaining variables or explaining variable functions; E is a random component.

The conducted backward stepwise regression analysis showed that the proper predictors of the rot area after bark stripping by the deer are years since bark stripping occurred and maximum wound width, which explain over 65.5% of the total variable of the stem rot area.

The interpretation of the estimated value of the particular parameters leads to a conclusion that with each year after bark stripping the internal rot increases, on average, by 2.52% (provided the unchanged values of other independent variables, ceteris paribus assumption). However, the increase of the width of the wound by 1 cm causes the increase of the internal rot by 1.43% (also provided the determined values of other variables) (

Table 5. Correlation coefficients of stem rot area and the independent variables of years since bark stripping occurred and maximum wound width.

N = 81	b*	Statistical Error	b	Statistical Error	t (76)	p
Constant term			−9.30241	3.794010	−2.45187	0.016507
Years since bark stripping occurred	0.274096	0.109674	2.52212	1.009174	2.49919	0.014577
Maximum wound width [cm]	0.584128	0.120504	1.42549	0.294073	4.84739	0.000006

). The margin error of the stem rot estimation model is 3.6%.

The regression equation of the model is expressed by the following formula:

stem rot area = 2.52212 × years since bark stripping occurred [years] + 1.42549 × maximum wound width [cm] − 9.30241

In the case when there is a difficulty estimating the time when the bark stripping occurred it is possible to use only maximum wound height to construct the model, in such a case the variable explains 60.5% of the common variance and seems the most appropriate to estimate the stem rot area. As the analysis of regression model with only one independent variable (maximum wound height) has shown, it allows to the explain over 60% of the variable variance of stem rot area. In such a case increasing the wound by 1cm increases the rot area by 1.48% (

Table 6. Correlation coefficients of stem rot area and the independent variable maximum wound width.

N = 80	b*	Statistical Error	b	Statistical Error	t (78)	p
Constant term			−5.18378	2.760291	−1.87798	0.064121
Maximum wound width [cm]	0.604782	0.090174	1.47589	0.220057	6.70687	0.000000

).

In this case the model is very simple and is expressed by the following formula:

stem rot area = 1.47589 × maximum wound width [cm]

The margin error of the stem rot estimation model on the basis of only maximum wound height is 2.76%.

In the case when there is a need to determine the relative size of the stem rot area, Sa/Ra index needs to be adopted. In order to predict the relative area of the rot the most suitable are two explaining variables, i.e., years since bark stripping occurred and maximum wound height, which explain as much as 68% of the total relative variable of the stem rot area described by Sa/Ra index. The margin of error for this equation is 8.4% (

Table 7. Correlation coefficients of Sa/Ra index area, the years since bark stripping occurred variable, and the independent variable, maximum wound height.

N = 80	b*	Statistical Error	b	Statistical Error	t (77)	p
Constant term			95.5929	8.541677	11.19136	0.000000
Years since bark stripping occurred	−0.465883	0.087476	−10.5495	1.980810	−5.32583	0.000001
Maximum wound height [cm]	−0.376313	0.087476	−0.5432	0.126262	−4.30190	0.000049

).

The regression equation in this case is expressed by the following formula:

stem rot area = (−10.5495 × years since stem damage occurred [years]) + (−0.5432 × maximum wound width [cm]) + 95.5929.

4. Discussion

Tree damage caused by the ungulate has become a serious economic problem in recent years in Europe. The accumulation of extensively damaged trees in a single tree stand impacts its longevity, stability, and the ability to produce good quality wood. Preventing the mechanical damage caused by bark stripping is of vital importance for the future of the entire tree stand. The collected results during the field study observations allowed us to conclude that both tree diameter as well as the basal area of the damaged trees were significantly higher than those of the undamaged trees. This means that deer are more likely to select trees classified as Kraft Class I and II than trees from lower biosocial classes. When it comes to protecting beech stands from bark stripping by deer, the focus should be on protecting the main stand, i.e., trees classified as Kraft Class I, II, and possibly III, which are most readily selected by deer. Such information helps in evaluating the extent and value of the damages in a tree stand, which could be advantageous to plan further stand management activities [33]. According to Neely [34], the main factors that seem to be most strongly correlated with the wound healing index are tree longevity, time when the wound occurred, as well as location and size of the wound on the tree, which is reflected in the results of our study. According to Jones et al. [35], the more vigorous trees, those on better-quality sites, and those with intact, live crowns maintained wound-closure rates for longer periods of time than other trees. Wound-closure rates were reduced for trees with larger relative trunk damage, smaller live crown cross-sections, slower relative diameter growth, and greater crown competition.

An important factor that impacts the tree and tree stand stability is their regenerative and wound-closure abilities. The speed at which a tree returns to health after damage to the stem can significantly influence their survival and the future value of the wood [36]. A total wound closure increases the mechanical stability of trees due to shifting the damaged wood closer to the central axis of the stem, hence, shifting it away from the area with the highest compressive and stretching forces caused by wind [37]. According to Tavankar et al. [38], the wound-closure speed of the beech is 31.2 ± 7.7 cm² year⁻¹, and the wound-length-closure speed (4.5 ± 1.6 mm·year⁻¹) is significantly faster than the wound-width-closure speed (18.4 ± 3.4 mm·year⁻¹). This principle has been confirmed by the obtained results. A significant positive correlation between the age of the wounds and their maximal length was observed. The wound height in the studied beech lowered annually on average by 2.17%, and no correlation was observed between the size of the wound and its width. It is worth emphasising that this is not a rule for all trees, which was also confirmed by studies conducted on other tree species [13].

The main focus of the paper was on the possibility of estimating the depreciation of wood on stem caused by summer beech bark stripping by deer on the basis of easy-to-measure characteristics in the tree stand. The possibility of accurately determining the stem rot area in the stripped trees can facilitate and support the decision-making process in forestry and forest management. Thus, it is possible to determine the economic validity of either prematurely removing or leaving the stripped trees. Moreover, it can also help to estimate the reasoning behind removing the entire tree stand in which the number of damaged trees has exceeded a certain value.

The mean percentage of the rot area in the studied beeches was over 15% (±17.78 cm²) of the cross-sectional area of the studied trees. Pach [6] in the study conducted on the fir achieved a slightly better result, 17%; however, Vasiliauskas and Stenlid [18] conducted the same study for the spruce and their mean result was 36.8%, whereas Vacek et al. [10] achieved as much as 39% of the rot for tree volume. The obtained results indicate that species such as the beech are less susceptible to rot development in the stem caused by wounds, unlike the spruce, for example, which is very sensitive.

As a consequence of the conducted studies, it was ascertained that the wound height and width, the ratio of wound width to tree circumference (Tc/Ww), and the years since the damage occurred are factors that influence the rate at which the stem rot in beeches develops. The analysis indicates that the wound height and width significantly influence the rate at which the tree tissue depreciates after the stripping. Vasiliauskas [17] arrived at similar conclusions studying the common oak and Hahn et al. [39] studying the spruce; however, they both emphasised that the key parameter indicating the stem rot area was the wound length. In addition, they did not observe a significant correlation between the age of the wound and the extent of the rot in the studied tree species. Barszcz and Jamrozy [40] stated that the size and the number of wounds in the fir and the ash indicated a strong relation with the extent of the rot, and the age of the wound was the weakest among the studied characteristics. This last observation, however, cannot be related to the results achieved for the beech. In the experiment, there was a statistically significant positive correlation (0.6404) between the age of the wound and the rot area; another much weaker, but still significant correlation was noted between the age of the wound and maximal width of the wound (0.3038) and the tree circumference (0.3832). Moreover, we have concluded that both the length of the wound as well as its width can be good predictors for estimating the stem rot area in the European beech (F. sylvatica).

The mean rate of the rot development in the core direction was 2.52% in the studied trees and encompassed only annual rings that occurred before bark stripping. Pach [6] in his research of the fir achieved a similar result with the rot growth annually as 2% of the area of the disc; however, for the spruce, the values were between 1 and 70 cm per year for Čermák et al. [8], whereas the results for the pine were 0.9 cm annually⁻¹ for Cukor et al. [12]. Mercer and Kirk [41] obtained very similar results of the rot development in the beech, which encompassed only the annual rings before bark stripping. They have proven that the rot caused by bark stripping spreads, but is limited, in most cases, only to the last few annual rings that grew before the damage, which was also corroborated by our study. As the results have shown, a few easy-to-measure characteristics are enough to fairly precisely estimate the stem rot area in the beech. We have proposed very simple models to predict the size of the rot which are essentially based on three variables, i.e., length and width of the wound as well as its age. In the case of the described experiment, a relatively high accuracy of the model was achieved when only one variable was used, namely, maximal wound width. The results describing the influence of bark stripping on beech wood depreciation should not be treated as a final indicator used to determine the development of stem rot. However, they do allow to reach a conclusion that a fairly precise prediction of the stem rot area requires easy-to-determine characteristics (predictors).

5. Conclusions

• The stem damage of the European beech (Fagus sylvatica L.) due to summer bark stripping has a significant impact on the development of rot inside the stem. Owing to a considerable depreciation of the beech wood caused by rot, which occurred as a result of bark stripping, the future of the damaged tree is uncertain. The trees are more susceptible to break. There is also a high probability that the damage will contribute to decreasing the biosocial position of the tree in the tree stand, thus leading to considerable economic loss.
• In each of the studied cross-sections, the rot was observed at various stages; it spread from the wound and infected only the annual rings that grew before the stripping. The mean rate at which the rot developed in the direction of the core was 2.52% per annum.
• Significant correlations were found between the wound size and its age, and the beech stem rot size. The correlations were used to create a model which allows estimation of the stem rot area. In order to carry out a fairly precise prediction of the size of the rot, the maximum wound width and perhaps the number of years since bark stripping occurred are enough. The proposed models are based on simple characteristics which can prove beneficial and helpful in the decision-making process. This is particularly true in the case of severe and recurring damages of beech tree stands where there are doubts concerning the economic validity to continue maintaining such tree stands. They can also be helpful in managing the quality of raw timber in stands damaged by bark stripping.
• Further research is needed on the applicability of the proposed models to manage the quality of stands other than beech trees.