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Forest Ecology and Management 331 (2014) 196–207

Contents lists available at ScienceDirect

Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco

Host and site factors affecting tree mortality caused by the spruce bark beetle (Ips typographus) in mountainous conditions Pavel Mezei a,⇑, Wojciech Grodzki b, Miroslav Blazˇenec a,c, Jaroslav Škvarenina d, Veronika Brandy´sová d, Rastislav Jakuš a,c a

Institute of Forest Ecology of the Slovak Academy of Sciences, Štúrova 2, 960 53 Zvolen, Slovak Republic Department of Forest Management in Mountain Regions, Forest Research Institute, ul. Fredry 39, 30-605 Kraków, Poland ´cká 1176, 165 21 Praha 6, Suchdol, Czech Republic Department of Forest Protection and Entomology, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences, Kamy d Department of Natural Environment, Faculty of Forestry, Technical University in Zvolen, TG Masaryka 2117/24, Zvolen, Slovak Republic b c

a r t i c l e

i n f o

Article history: Received 16 April 2014 Received in revised form 28 July 2014 Accepted 29 July 2014

Keywords: Ips typographus Outbreak Picea abies Mortality initiation Mortality severity Disturbance

a b s t r a c t To better understand the initiation and severity of tree mortality caused by the spruce bark beetle (Ips typographus (L.)) during an outbreak, we analysed the entire course of an outbreak from 1990 to 2000 in the Tatra Mountains (Western Carpathians, Central Europe). This time period represents the last complete bark beetle gradation in this area. We distinguished three outbreak phases: the incipient epidemic, epidemic and post-epidemic stages. The sampling unit was the forest subcompartment. We analysed a total of 315 forest subcompartments over more than 2000 ha. We investigated the influence of 11 environmental and stand variables on two processes in different phases of the outbreak: the initiation and the severity of spruce mortality. We used factor analysis, discriminant analysis, multiple linear regressions and boosted regression trees for the statistical analyses. The results showed that the roles of host and site factors in the initiation and severity of spruce mortality caused by the spruce bark beetle differed during the outbreak according to the exploitation of available host resources. The initiation of tree mortality was primarily related to host factors, and the severity of mortality was dependent on host size and insolation. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Bark beetle outbreaks are significant forest disturbances that affect wildlife, watershed quality and recreational uses and cause extensive timber losses. Because of these dramatic effects, ecologists and forest managers must understand the mechanisms that drive outbreaks, to better predict and mitigate them (Walter and Platt, 2013). Many authors have studied the factors that influence spruce mortality caused by bark beetles (Ips typographus) (Dutilleul et al., 2000; Becker and Schröter, 2001; Gilbert et al., 2005; Klopcic et al., 2009; Ogris and Jurc, 2010; Lausch et al., 2011; Marini et al., 2012; Overbeck and Schmidt, 2012; Albrecht et al., 2012; Thom et al., 2013; Mezei et al., 2014). The results of these investigations indicate that the mortality caused by I. typographus can be explained by characteristics such as forest age, potential solar radiation, and disturbance history. In these studies, favourable forest characteristics are understood to set the stage for outbreaks that are then triggered by climate and weather. An ⇑ Corresponding author. E-mail address: [email protected] (P. Mezei). http://dx.doi.org/10.1016/j.foreco.2014.07.031 0378-1127/Ó 2014 Elsevier B.V. All rights reserved.

I. typographus infestation on standing trees usually begins after wind damage. However, the tree has to first reach a size that is suitable for an I. typographus attack (Baier, 1996). The role of insolation, or sun effects (Kautz et al., 2013), is also an important factor in the spread of bark beetle infestations once they have been initiated. A substantial portion of the research on susceptibility to bark beetles describes how likely a tree or stand is to become infested if an outbreak occurs (Walter and Platt, 2013). Some authors, such as Boone et al. (2011), have highlighted the need for additional attention to research on the different phases of forest herbivore outbreaks. Most of the studies on this topic do not distinguish between the initial conditions leading to an outbreak and those that facilitate the spread of an outbreak, especially for I. typographus. According to Coulson et al. (1985) and Jakuš et al. (2003a), the mortality caused by bark beetles in mature coniferous stands is related to two main processes: the initiation and spread (expansion) of an infestation. The initiation of an infestation corresponds to the first spruce bark beetle attack on the living trees in a forest stand. These processes can be driven by different factors according to the stage of the outbreak. The process of initiation is not yet completely understood. Undisturbed spruce stands are well protected against

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direct insolation (sun effects) by individual and/or collective shading and are usually not attacked by the spruce bark beetle (Jakuš et al., 2011a), but natural disturbances such as windthrows or severe droughts can create conditions that favour a bark beetle attack (Jakuš et al., 2011b; Kautz et al., 2013). An approach in which disturbances were studied according to their initiation and severity was applied in a previous study by our group (Mezei et al., 2014), where we examined the wind – bark beetle disturbance regime. In that study, tree mortality caused by wind or by wind and spruce bark beetles together was examined. In the first stage of an outbreak in mountainous conditions (incipient epidemic population), I. typographus predominantly colonises wind-thrown trees or trees on fresh forest edges (damage initiation), and the beetles are more likely to attack trees adjacent to the initial infestation (Jakuš et al., 2003a; Mezei et al., 2011). The subsequent spread of the infestation is caused by bark beetle attacks on trees neighbouring the primary attacked tree or group of trees. In the broader sense, spreading represents any further attack on trees after the initiation of infestation (during the years after the initial attack). The key factor influencing the spread of an infestation is the resistance of trees to bark beetle attack (Lieutier, 2004). In this study, we analysed the entire course of a spruce bark beetle outbreak from 1990 to 2000 in the Tatra Mountains, as this time period represents the last completed bark beetle outbreak in this area. Data from this study area have also been analysed by Grodzki et al. (2006), Jakuš et al. (2003a) and Mezei et al. (2014). Grodzki et al. (2006) compared different management strategies on both sides of the Tatra Mountains and found that there was no difference in the course and collapse of an outbreak. Jakuš et al. (2003a) studied the spread of an outbreak using terrestrial and remote sensing techniques. They found that the course and spread of the outbreak were related to the phase of the outbreak and to insolation. Neither of these studies considered environmental variables as factors affecting the initiation and spread of an outbreak. Mezei et al. (2014) found that factors affecting the initiation and intensity of tree mortality (caused by wind and bark beetles) changed during the outbreak period according to the phase of the outbreak. In the current study, we only examined the factors underlying the initiation and severity of tree mortality caused by the spruce bark beetle. Therefore, this work focus more on the population dynamics of I. typographus itself than on the interactions between disturbances. We find this approach reasonable because the findings of the present study can be used for modelling of the population dynamics of I. typographus. In addition, if the environmental characteristics of infested areas tend to change from the beginning of an outbreak cycle through the final crash of the outbreak, then understanding those dynamics may improve predictions regarding the spread of outbreaks (Walter and Platt, 2013). Additionally, by examining the environmental characteristics associated with bark beetle infestations through time, we can improve our understanding of how bark beetles use resources across the landscape (Nelson et al., 2007). Following Coulson et al. (1985) and Jakuš et al. (2003a) we describe tree mortality using two related metrics: the initiation and the severity of tree mortality. According to our experience, mature stands tend to be completely attacked (destroyed) by bark beetles after such initial damage. Because we worked with database data without any spatial considerations, we were able to analyse the severity of spruce bark beetle-caused tree mortality as a variable related to the spread of bark beetle damage or to spot expansion. A more detailed analysis of the spread of damage (infestation) would require a different type of data (detailed infestation maps) and a different type of analysis than we present in this paper. The advantages of the dataset used here are the length of

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the time series and the precise quantification of tree morality caused by bark beetles. Our working hypothesis was that the role of host and site factors in the initiation and severity of spruce mortality caused by bark beetles differs through the course of an outbreak. The initiation of spruce mortality due to bark beetles is mostly related to the age or size of the host trees, while the expansion (growth) or severity of tree mortality is related to factors associated with the age or dimensions of the host trees and to factors associated with insolation (Jakuš et al., 2003a). We hypothesised that host factors would be most important in the early stages of the outbreak and that the role of insolation would be more important in later stages. 2. Methods The study area and applied statistical methods were similar to those described in our previous work (Mezei et al., 2014). However, we did not consider any disturbance or disturbance regime other than spruce bark beetle-caused tree mortality in the present study. This factor was omitted in our previous study, where we focused on interactions between disturbances. 2.1. Study area Our study was conducted in the High Tatra Mountains in the Javorová, Široká and Bielovodska/Białki valleys. The Tatra Mountains are located in the Western Carpathians on the border between Slovakia and Poland. The study area encompassed both the Slovak and Polish sides of the mountains, which comprise two national parks: Tatrzan´ski Park Narodowy (TPN) in Poland and Tatransky´ Národny´ Park (TANAP) in Slovakia. This area remains under the administration of three Forest Divisions: Łysa Polana and Morskie Oko on the Polish side and Javorina on the Slovak side. The dominant tree species through the upper timberline is the Norway spruce, Picea abies (L.) H. Karst. At higher elevations, Pinus cembra L. and Pinus mugo Turra are observed. The average altitude in these areas ranges from 970 m.a.s.l. to 1670 m.a.s.l. A more detailed description of the study area was published by Grodzki et al. (2006). The area of subcompartments, which are the basic forest management areas in Slovakia and Poland, covers 2824 ha. The size of the subcompartments ranges from 0.28 to 68.3 ha. The average subcompartment area is 8.9 ha. 2.2. Response variable and predictors Because the outbreak lasted for 11 years, the data were divided into three outbreak phases (Grodzki et al., 2006): (1) incipient epidemic (Phase I), from 1990 to 1994, when the number of trees being killed was increasing; (2) epidemic (Phase II), from 1995 to 1996, when the killing of trees by spruce bark beetles reached its peak; and (3) post-epidemic (Phase III), from 1997 to 2000, with the numbers of trees dying was declining. We used two sources of data: forest inventories (updated every 10 years) containing data on independent variables and a database indicating the volume of trees killed by bark beetles in cubic metres (updated every year in the 1990–2000 period) providing data on tree mortality (both sources were kindly supplied by the two national parks governing the area, i.e., the Polish Tatrzan´ski Park Narodowy – TPN, and the Slovak Tatransky´ Národny´ Park – TANAP, administration). Based on the data on the yearly volume of attacked trees, mean indices of yearly tree mortality per hectare (ha) were calculated for each forest compartment. For each subcompartment, we examined 11 environmental and stand variables (Table 1), and we calculated the global potential solar radiation for the entire year from a DEM (digital elevation

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Table 1 List of variables used in the analysis of the initiation and severity of bark beetle-caused spruce tree mortality together with the results of a factor analysis (listed in the last four columns) between the variables. Numbers in bold indicate the variables that were combined into factors. Forest management plans were provided by TPN and TANAP (see Section 2.2 Response variable and predictors). Variable

Stand age Percentage of spruce Stand height Stand DBH Slenderness ratio Site quality Slope Elevation pH Vegetation period Solar radiation Eigenvalue % Of total variance

Short description

Mean age of stand (years) Percentage of spruce in stand (%) Mean height of stand (m) Mean stand diameter at breast height (cm) Ratio of mean stand height and stand DBH Potential mean height of stand at 100 years (m) Relief slope (°) Stand elevation (m.a.s.l.) pH of soil Maximum duration of vegetation period (days) Potential global solar radiation (Wh/m2) – –

Source

Abbreviation

Forest management Forest management Forest management Forest management Forest management Forest management Forest management Forest management Kukla (1993) Hancˇinsky´ (1972) Derived from DEM – –

model) with the ArcGIS 9.2 solar radiation tool (Huang and Fu, 2009). First, we calculated solar radiation for the whole study area, and we then used the zonal function to calculate the mean solar radiation for each subcompartment. Forest management planning in Slovakia is based on the use of a site-related phytocenology classification (Hancˇinsky´, 1972). Therefore, we employed site-related data obtained through the quantification of vegetation types. The relationship between the potential forest vegetation types and the maximum duration of the vegetation period was used to calculate the variable ‘‘vegetation period’’ (Hancˇinsky´, 1972). In addition, the relationship between the potential forest vegetation types and the upper ecological limit of soil acidity (Kukla, 1993) was used to calculate the variable ‘‘soil pH’’. Any subcompartments with missing values for any of the variables listed in Table 1 were not subjected to further analysis. A total of 315 forest subcompartments were used.

2.3. Statistical analysis To reduce the number of variables and to detect structure in the relationships amongst variables, we applied a factor analysis. All of the variables listed in Table 1 were included in the factor analysis. The factors necessary for representing the data were differentiated via a principal components analysis. To make the factors more interpretable, varimax normalisation was performed, and only the factors showing eigenvalues greater than 1 were extracted. The scores for each factor were computed for each subcompartment in Statistica 8.0 (StatSoft 2007). These scores were then used in discriminant analyses and multiple linear regressions. To analyse outbreak dynamics, we used data from forest inventories to assemble a database containing detailed data on the yearly (1990–2000) volume of trees killed by I. typographus (for details, see the Section 2.2 Response variable and predictors). This is the largest difference in comparison with our preceding study (Mezei et al., 2014), where we examined the mortality of trees caused by wind or by wind and bark beetles altogether (wind – bark beetle disturbance regime). The results from our previous study did not allow us to interpret results that are relevant to I. typographus population dynamics alone. The volume of killed trees (spruce mortality) is a standard metric used to estimate spruce bark beetle populations in managed forests. This variable is carefully measured under field conditions by counting the attacked trees from the ground and calculating the volume attacked based on stand characteristics or through precise measurements of the volume of cut wood (salvage cutting). It is also a reasonable proxy for the abundance of beetles and therefore permits qualified

plan plan plan plan plan plan plan plan

Age Spruce H D H/D. SiteQ Slope Elev pH VegPer Radiation – –

Factors Site

Host

Soil

Sun

0.47 0.35 0.21 0.20 0.75 0.81 0.55 0.83 0.02 0.61 0.02 3.55 32.30

0.82 0.30 0.94 0.96 0.22 0.06 0.02 0.05 0.06 0.04 0.05 2.43 22.05

0.07 0.06 0.02 0.04 0.01 0.05 0.44 0.32 0.90 0.39 0.11 1.23 11.16

0.07 0.53 0.12 0.02 0.14 0.26 0.46 0.00 0.11 0.24 0.85 1.10 9.92

inferences of population dynamics (Marini et al., 2012). I. typographus must generally kill its host trees to reproduce, and tree mortality is therefore positively related to beetle population abundance (Faccoli and Stergulc, 2004; Franklin et al., 2004). As in our previous study (Mezei et al., 2014), we analysed two different processes involved in outbreak development: the initiation and the severity of tree mortality. We applied two different statistical approaches. In the first approach, we conducted factor analysis, discriminant analysis and multiple linear regression (MLR) (StatSoft, 2014). In the second approach, we employed boosted regression trees (BRTs, Elith et al., 2008), which is a suitable statistical technique for studying the main drivers of forest disturbances. This method was used, for example, by Albrecht et al. (2012) for the assessment of storm damage amongst Norway spruce and Douglas-fir trees. Both approaches have been used to evaluate both processes (initiation and severity). The first approach is an example of a traditional statistical technique, while the BRT approach is an example of a machine learning technique. The advantage of BRTs is that there is no need to drop prior predictors as the BRTs can handle interaction effects between the predictors, and they can handle different types of response data (Elith et al., 2008).

2.3.1. Initiation of tree mortality caused by spruce bark beetles Our analysis was focused on processes at the stand level. Thus, damage initiation corresponds to the first detection of damage in a particular stand (local level), and the initiation of local stand damage can occur in any year of a bark beetle outbreak. It was not possible to precisely track the initiation of infestation in some cases because some infestations began before the study period. The initiation of tree mortality was analysed as the presence (1) or absence (0) of tree mortality in the different outbreak phases. In a particular stand, an absence of tree mortality was assigned to years without any record of mortality. Beginning with the first record of mortality caused by bark beetles, the presence (1) of mortality was assigned to the particular stand, and that stand was removed from the analysis of mortality initiation in all of the subsequent outbreak phases. Therefore, stands in which mortality was initiated at the first (incipient epidemic) phase were removed from the analysis of initiation in the second (epidemic) phase, while stands initiated in the second phase were removed from the analysis of mortality initiation in the last (post-epidemic) phase. Thus, in each outbreak phase, we only analysed stands initiated in that particular phase, and we compared them to the remaining stands that had not been initiated by bark beetles in discriminant analysis. In the analysis of the whole outbreak period, presence was

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assigned to every stand initiated any time during the outbreak, and an absence of tree mortality was assigned to stands without any record of mortality during the outbreak. This analysis was performed in Statistica 8.0. We used a stepwise selection algorithm with Wilk’s lambda method. Under this method, the standardised coefficients for canonical variables are shown. Discriminant classification correctness describes how many samples are classified correctly. The correlation between the discriminating variables and discriminant functions was used to assess the contributions of the variables to the discriminant functions. In the analysis described above, we worked with variables combined into factors to minimise the influence of correlated variables. Subsequently, we sought not only to analyse the influence of the variables listed in Table 1 on the initiation of tree mortality but also to examine at what values/rates these changes were occurring (at least for the most important variables). For this purpose, we used boosted regression trees (BRT) because they do not require the transformation of prior data; outliers do not need to be eliminated; they can fit complex nonlinear relationships; they automatically handle interaction effects between predictors; and they can be fitted to a variety of response variable distributions (e.g., Gaussian, Poisson). The BRT method combines two algorithms: (1) regression trees, obtained from the classification and regression tree group of models (De´ath and Fabricius, 2000); and (2) boosting, which builds and combines a collection of models (De´ath, 2007). This methodology does not produce a single best model but instead combines large numbers of simple tree models. Under this method, unlike conventional statistical techniques, there are no P values to indicate the relative significance of the model coefficients. The relative significance of individual variables is estimated based on how often the variable is selected and its ability to improve the model. The relative influence of the variables is scaled so that the sum adds up to 100%. Models are also selected based on how well each model explains observed data (training data correlation) and predicts excluded data (CV correlation) (Elith et al., 2008). For better comparison of the results gained using BRTs and the results gained through discriminant analysis and MLR, we grouped the predictor variables into categories according to a factor analysis (Site, Host, Soil, Sun), and we added one category (Other), where we listed all of the variables that were not selected into any of factors during the factor analysis. These categories listed in the BRT results are solely informational and present no direct relationship to the factor analysis results. Visualisation of the fitted functions in a BRT model is achieved using partial dependence functions that show the effect of a variable on the response after the average effects of all other variables in the model have been taken into account (Elith et al., 2008). All of the models were fitted using R software, version 2.14.1 (R Development Core Team, 2013), with the gbm package (Ridgeway, 2007) and an extension developed by Elith and Leathwick (2011). We employed the default 10-fold cross-validation procedures described by Elith et al. (2008). The models were fitted using the gbm.step function with a Bernoulli response type for the analysis of mortality initiation. The models were then reduced to the most important variables with the gbm.simplify function (Elith and Leathwick, 2011).

the dependent variable and the factors from the factor analysis as the independent variables. We applied backward stepwise regressions, and the intercept was set to zero. Only factors showing statistical significance at the 0.01 significance level are reported in the results. The obtained statistical significance and the variance explained, based on the R values, were used to evaluate the reliability of the models. Boosted regression trees were employed to analyse the thresholds of these changes (see previous chapter). For this purpose, the models were fitted using the gbm.step function (Elith and Leathwick, 2011) with a Gaussian response for bark beetle damage severity (m3 ha 1), and the models were then reduced to the most important variables with the gbm.simplify function (Elith and Leathwick, 2011).

2.3.2. Severity of tree mortality caused by spruce bark beetles Due to working with data from a database without spatial references, we analysed the severity of tree mortality caused by spruce bark beetles using variables related to the expansion or growth of a bark beetle infestation. Multiple linear regression analyses were performed with Statistica 8.0 to find the most important factors influencing the severity of spruce mortality caused by spruce bark beetles. We employed the volume of trees felled/attacked by bark beetles per hectare as

3.2. Initiation of tree mortality caused by spruce bark beetles

3. Results 3.1. General results Because of the different methodologies used to examine the initiation and severity of tree mortality, the number of attacked stands differed not only between the phases of the outbreak but also between the two different processes. Under our approach regarding tree mortality initiation, every attacked stand could be recorded only once. As soon as a stand was attacked in one phase of the outbreak, we did not examine it in the next phase. We did not account for the possibility that one stand might be attacked at the beginning of the outbreak, after which the attack might pause for some period and then continue again, because it would violate our assumptions that the initiation of an attack on a stand can occur only once in an outbreak. In the incipient epidemic phase, bark beetle-caused spruce tree mortality was initiated in 93 stands, while in the epidemic phase, 46 stands were initiated, and in the post-epidemic phase, only 8 stands were initiated. In the analysis of the severity of spruce bark beetle-caused tree mortality, we analysed all of the stands where any attack was recorded, and we can therefore say that we analysed all of the stands where I. typographus was ‘‘active’’ in a particular outbreak phase. A total of 93 stands were under attack in the incipient epidemic phase, while 115 stands were under attack in the epidemic phase, and 100 stands were under attack in the post-epidemic phase. Overall, 146 stands were attacked during the entire outbreak. Here, one stand could be analysed in more than one outbreak phase. The results of the factor analysis are summarised in Table 1. All of the variables were reduced to four main factors, which we refer to as Site, Host, Soil and Sun. The correlated variables Slenderness (ratio of the mean stand height to stand DBH), Site Quality and Elevation were combined into the Site factor. Three other correlated variables – the Mean age of the stand, Mean stand height and Mean DBH – were combined into the Host factor. The variables pH and Solar radiation stood alone, as the Soil and Sun factors, respectively. Only the factors showing eigenvalues greater than 1 were extracted, and the extracted factors represented 75.43% of the total variation. Scores for each factor were computed for each case. These scores were used in subsequent analyses.

The results of the discriminant analysis of the relationship between the main factors and mortality initiation in the three outbreak phases are presented in Table 2. The factors that did not show a statistically significant influence were not included in the discriminant functions. The main factor influencing initialisation was the Host factor (i.e., parameters relevant to host size and geometry). In the incipient epidemic phase (Phase I), the Site factor

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Table 2 Results of discriminant analysis of the relationship between the main factors and the presence (1) and absence (0) of bark beetle damage according to the outbreak phase. Phase I – incipient epidemic phase, Phase II – epidemic phase, Phase III – post-epidemic phase. Factors

Standardised coefficients and factor structure coefficients Phase I n = 315

Site Host Soil Sun

0.42* 0.93** – –

DCC % Significance

69 0.0000

Phase II n = 222 0.38* 0.91** – –



Phase III n = 174 –

0.94** – –

0.94** – –

78 0.0005

– – – – – 0.3084

Whole outbreak n = 315 – – – –

0.14 0.99** 0.00 0.15

0.11 0.98** 0.00 0.12

70.8 0.0000

DCC – discriminant classification correctness. Standardised coefficients – discriminant function coefficients. Factor structure coefficients – correlations between the variables and the discriminant functions. * Significant at p = 0.05. ** Significant at p = 0.01.

also contributed to initiation. In the post-epidemic, phase none of the factors were important, but only 8 stands were initiated, which was too few stands to analyse the factors underlying mortality initiation at this particular outbreak phase. However, as we expected, only a few stands that were suitable for new colonisation attempts by spruce bark beetles remained in this phase. In the BRT analysis, which was conducted using a Bernoulli response type (i.e., values of 0 for the absence and 1 for the presence of tree mortality; Table 4), we found that the most important variables were the Mean stand height, Mean stand DBH, and Slope. For the post-epidemic phase, the BRT algorithm did not converge because of the insufficient amount of data. The main factors influencing the initiation of stand mortality came from the ‘‘Host’’ group of factors (the variables Mean tree height and Mean DBH). More than 40% of the overall influence

was explained by these predictors. Amongst the ‘‘Other’’ factors, only the Slope had any influence. The variables DBH and Radiation are presented as examples in Figs. 1 and 2. The role of DBH was quite clear: the greater the DBH, the greater the initiation of mortality. 3.3. Severity of spruce bark beetle-caused tree mortality Table 3 shows the relationships between the volume of the trees attacked by bark beetles per hectare and the main factors. The main factor influencing the severity of tree mortality in all three of the outbreak phases was the Host factor (i.e., parameters relevant to host size and geometry). In the epidemic phase, the Sun factor (i.e., solar radiation) also made a significant contribution.

Fig. 1. Relationship between DBH and the initiation of bark beetle damage analysed using BRTs in different phases of the outbreak and throughout the whole outbreak. The fitted function (y-axis) is the effect of the predictor variable on the response variable after accounting for the average effect of all other variables in the model. Phase I – incipient epidemic phase, Phase II – epidemic phase, Phase III – post-epidemic phase.

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Fig. 2. Relationship between solar radiation and bark beetle damage initialisation analysed using BRTs in different phases of the outbreak (in the phase that is not shown, solar radiation had no effect) (cf. Fig. 1 for details).

Table 3 Results of multiple linear regressions between the volume of trees attacked by bark beetles per hectare and the main factors. Phase I – incipient epidemic phase, Phase II – epidemic phase, Phase III – post-epidemic phase. r and p values, estimates and standard errors Factors

Phase I (n = 93)

Site Host Soil Sun Model r Model p

– 0.32 – – 0.32 0.0015

– 0.002 – –

Phase II (n = 115) – 18.48 – –

– 5.63 – –

– 0.53 – 0.25 0.57