Research Collection50457/et… · Luzia Götz, ETH Zürich . Title page: View from the edge into the windthrow area facing east. ... development of the larvae is strongly temperature

Research Collection

Master Thesis

Predisposition of Norway spruce to European spruce barkbeetle infestation and spatial development of an outbreak afterwindthrow

Author(s): Opiasa, Michael

Publication Date: 2016

Permanent Link: https://doi.org/10.3929/ethz-a-010819425

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Predisposition of Norway spruce to European

spruce bark beetle infestation and spatial

development of an outbreak after a windthrow

Master Thesis at the Chair of Forest Ecology

Institute of Terrestrial Ecosystems

Department of Environmental Systems Science D-USYS

ETH Zürich

Michael Opiasa

October 2016

Supervisors:

Dr. Christof Bigler, ETH Zürich

Luzia Götz, ETH Zürich

Title page: View from the edge into the windthrow area facing east. Personal photograph.

Table of Contents 1 Abstract ........................................................................................................................................... 1

2 Introduction ..................................................................................................................................... 2

3 Material and Methods ..................................................................................................................... 4

3.1 Study site ................................................................................................................................. 4

3.2 Sampling campaigns ................................................................................................................ 5

3.3 Tree-related variables ............................................................................................................. 6

3.3.1 Tree condition ................................................................................................................. 6

3.3.2 Bark thickness .................................................................................................................. 7

3.3.3 Heart rot .......................................................................................................................... 7

3.3.4 Diameter at breast height ............................................................................................... 7

3.3.5 Tree height ...................................................................................................................... 8

3.3.6 Crown length ................................................................................................................... 8

3.3.7 Distance to the nearest dead tree ................................................................................... 8

3.3.8 Basal area ........................................................................................................................ 9

3.3.9 Slope ................................................................................................................................ 9

3.3.10 Damage at the tree .......................................................................................................... 9

3.3.11 Discoloration in the wood ............................................................................................... 9

3.3.12 Vitality index .................................................................................................................. 10

3.3.13 Cambial age ................................................................................................................... 10

3.3.14 Shading towards south .................................................................................................. 10

3.3.15 Exposition ...................................................................................................................... 10

3.4 Core samples ......................................................................................................................... 11

3.5 Statistical modelling .............................................................................................................. 12

3.5.1 Variable selection and data partitioning ....................................................................... 12

3.5.2 Model selection ............................................................................................................. 14

3.5.3 Model assessment ......................................................................................................... 15

3.6 Spatial projection .................................................................................................................. 15

4 Results ........................................................................................................................................... 16

4.1 Descriptive results ................................................................................................................. 16

4.1.1 Continuous variables ..................................................................................................... 16

4.1.2 Categorical variables ..................................................................................................... 17

4.2 Prediction of tree mortality ................................................................................................... 18

4.2.1 Model selection for global model 1............................................................................... 19

4.2.2 Model selection for global model 2............................................................................... 24


5 Discussion ...................................................................................................................................... 31

5.1 Prediction of tree mortality ................................................................................................... 31


6 Conclusions .................................................................................................................................... 35

7 Acknowledgements ....................................................................................................................... 36

8 References ..................................................................................................................................... 37

9 Appendix ........................................................................................................................................ 41

9.1 Appendix 1: Windthrow and cluster close ups ...................................................................... 41

9.2 Appendix 2: Model details ..................................................................................................... 44

9.3 Appendix 3: COFECHA outputs .............................................................................................. 47

Abstract

1

1 Abstract This master thesis is a research project about European spruce bark beetle infestation in subalpine

spruce dominated forests after a windthrow. The study took place in Uaul Prau Nausch, a natural

forest reserve in the canton of Grisons (GR) in Switzerland, where a spruce bark beetle outbreak

followed a foehn storm induced windthrow in 2012. The main objective was to quantitatively assess

the predisposition of single spruce trees based on individual tree related variables (e.g. diameter at

breast height (DBH), tree height, distance to the nearest dead tree, slope, crown length), which were

recorded in two sampling campaigns in 2015 and 2016. 217 dead and living trees were sampled in

total. The variables consisted of twelve continuous and four categorical variables. Multiple logistic

regression was used as a classifier to determine the influence of important variables on mortality risk

by spruce bark beetle attack. A further objective was to qualitatively assess, whether the pattern of

infestation followed any particular direction in the vicinity of the windthrow area after the foehn

storm. The sample consisted of 102 dead trees for which the year of death was determined using

dendrochronological techniques and their exact position was measured with a GPS.

Results of the logistic regression models showed that the distance to the nearest dead tree has the

greatest influence on the probability to die in a spruce bark beetle outbreak subsequent to a

windthrow. The mortality probability increased significantly for living trees, if a dead tree was less

than 20 m away. Further important predictors were, whether discoloration is present on the

extracted core or not. This generally increased the mortality probability, indicating a combined attack

of spruce bark beetle and its symbiotic fungi, which cause stain in the wood. DBH and tree height,

both growth related variables, indicated that spruce bark beetles rather attack bigger than smaller

trees. Trees with medium crown length were more frequently attacked than trees with smaller or

bigger crowns, indicating that the beetle pressure was high enough that they selected rather

unstressed trees over stressed ones to increase breeding substrate quality. Slope also showed an

effect on mortality probability. Trees on steeper slopes were more frequently attacked than trees on

smoother slopes, which could be caused by different soil water regimes and hence different water

stress levels. The spatial projection revealed that the two major dieback waves in 2013 and 2014

spread into two different directions away from the windthrow area. In 2013 it spread towards

southwest and in 2014 it spread towards north. The calamity in Uaul Prau Nausch is in its decreasing

phase. Combined findings of the two research aspects indicated that management measures in a

situation like this should be focused on the northern edge of a windthrow area and in a radius of 20

m around dead trees.

Keywords: Picea abies, Ips typographus, Windthrow, Calamity, Outbreak, Logistic regression, Tree

related variables, Predisposition, Spatial projection, Infestation pattern

Introduction

2

2 Introduction In Switzerland, Norway spruce (Picea abies) is one of the most important tree species considering the

proportion of the growing stock it represents in forests. Approximately 13’000 km2 are forested area,

while the most common species is Norway spruce by making up 45 % of the growing stock. In all of

the five main biogeographical regions of Switzerland Norway spruce is the dominant tree species and

in the lowlands it is mostly planted due to economic reasons (Stadelmann et al. 2013), while its

natural range of occurrence is above 800 m (Baier et al. 2002). This means that not only it is a

crucially important species for wood supply, but also as a protective measure against avalanches or

rockfall in pre-alpine and alpine regions (Wermelinger et al. 2014).

In spruce stands the most devastating biotic disturbance agent is the European spruce bark beetle

(Ips typographus), causing 8 % of all forest damage in the period between 1950 and 2000 only in

Europe (Stadelmann et al. 2013). There are several events, which could lead to an initiation of a mass

outbreak of European spruce bark beetle like windthrow, snow damage or heat waves and severe

drought. Several other factors like the proportion of spruce, especially outside its natural range, tree

vigor, stand age, density and structure, exposition and other stand related factors could drive such

mass outbreaks. But also climatic variables like temperature and precipitation play an important role

in the initiation of increased population growth of European spruce bark beetle (Stadelmann et al.

2013). For Switzerland windthrows are amongst the most important factors for the initiation of mass

outbreaks of the European spruce bark beetle. Since windthrows occur more likely in homogeneous

spruce stands, these forests are particularly vulnerable, because large areas of fresh lying dead wood

provide a lot of substrate for bark beetles to start developing at an increased rate. Therefore

approximately 60% of the sanitation fellings are due to storm damage in mature spruce dominated

forests in Switzerland (Stadelmann et al. 2014). In the subalpine zone, where the study site is

situated, spruce bark beetle populations are expected to develop only one generation a year,

although with future climate change this number may increase in the next 100 years, because the

development of the larvae is strongly temperature dependent (Wermelinger et al. 1998). It is

important to keep in mind that current climate warming will change the relationship between

European spruce bark beetle and Norway spruce. More than one beetle generation could develop in

a year in the subalpine zone and hence the pressure on spruce increases. Therefore it is important to

assess, what stand and tree related variables could drive the dynamics of such a mass outbreak.

At the stand level there is much known about what factors may affect the infestation probability of

an outbreak. Netherer and Nopp – Mayr (2005) showed with a Predisposition Assessment System

(PAS) that potential solar irradiation, water deficiency caused by water supply affecting soil

conditions, slope position, predisposition of sites to storm damage like e.g. a windthrow, species

composition and stand age significantly influence the susceptibility of a stand to spruce bark beetle

infestation (Netherer et al. 2005). Baier et al. (2007) developed PHENIPS, a predisposition model,

which models air temperature under the bark and its dependency on incoming solar irradiation at

stand and tree level. Since the development of high population levels of spruce bark beetle is also

temperature dependent, the model can predict outbreak risk on large scales (Baier et al. 2007).

However not much is known at the tree level about the likelihood of individual spruces of getting

infested or not. To examine possible relationships between tree related variables and the probability

of single trees of getting infested and eventually die back, data was collected from dead and living

spruces in autumn 2015 and summer 2016. The observational study was carried out in Uaul Prau

Nausch, a natural forest reserve in the canton of Grison (GR) in Switzerland, which was hit by a foehn

storm in 2012. This caused a windthrow and subsequent outbreak of European spruce bark beetle.

The question remains, why certain trees die and neighboring trees survive in this situation. Although

the spatial aspect of such an outbreak was addressed at a landscape level (Lausch et al. 2013), no

Introduction

3

literature was found describing the spatial development of an outbreak in the vicinity of a windthrow

area.

Hence, the research questions of this master thesis are:

1. Is there a relationship between tree- and stand-related variables of a Norway spruce and the probability of infestation by European spruce bark beetle after a storm induced outbreak? One can expect that bark beetles rather tend to attack spruces, which exert certain expressions of traits and that these traits differ significantly between dead and living trees. It is expected that the infestation risk and hence mortality probability changes with e.g. the distance to the nearest dead tree. A thicker bark could prevent spruce bark beetles from successfully boring into the phloem or a long crown could protect the trunk from solar radiation and the tree from water stress and therefore trees with a longer crown are less likely to get infested by spruce bark beetles.

2. Is there a spatial pattern underlying the yearly development of infestation by European spruce bark beetle in the Uaul Prau Nausch? To conduct this research the spatially measured positions are compared between dead trees, which died in the same year after the windthrow in 2012 within and in the vicinity of the windthrow area. This should reveal a temporal development pattern of infestation in the years after 2012. The trees were dated, using dendrochronological techniques. It is expected that the visually explored spatial development of die back events is clustered in a way that it is more probable to observe another killed tree in the current year in the near vicinity of an already killed one.

The research project in the natural forest reserve of Uaul Prau Nausch is a great opportunity to

observe, which tree related variables increase susceptibility of a spruce and how the infestation

dynamics of the European spruce bark beetle on Norway spruce develops spatially and over time,

since no sanitation felling or salvage logging is undertaken. Therefore the results of this master thesis

are expected to provide insights into the mechanisms driving a mass outbreak of European spruce

bark beetle in a subalpine Norway spruce dominated stand under natural conditions.

Material and Methods

4

3 Material and Methods

3.1 Study site The study was conducted in the natural forest reserve of Uaul Prau Nausch nearby the village of

Sedrun in the canton of Grisons (GR) in Switzerland. The forest site has an extent of 65.6 ha, a basal

area of 34 m2/ha, a standing wood volume of 281 m3/ha and a stem number of 263 ha-1. Of the stems

sampled in the sampling inventory 2014, a survey of the Swiss Federal Institute for Forest, Snow and

Landscape (WSL), 96% were spruce (Picea abies) (Brücker 2014). Since the 1st of January 2007 Uaul

Prau Nausch is a natural forest reserve, meaning that no management will be carried out for 50 years

until 2057. The reserve stretches from 1300 to 1900 m.a.s.l., has a mean exposition of 113° (ESE) and

a mean slope of 308% (72°). The forest site is mostly a coltsfoot – spruce forest with reedgrass and a

lingonberry – spruce forest with laserwort with spruces in cluster structure (Brücker 2014). In spring

2012 the forest reserve was hit by a foehn storm, causing a major windthrow in the center of the

forest site with an extent of approximately 1.5 ha (Figure 1). Since then, no sanitation fellings (felling

of infested remaining standing trees) or salvage loggings (removal of infested windthrown trees)

have been carried out. In the last four years the spruce bark beetle (Ips typographus) has caused

infestation of standing trees to occur on the edges of the windthrow area. Populations built up in the

fresh lying deadwood within the windthrow and even three new clusters of standing infestations

emerged away from the main windthrow area. Because no management should be carried out, Uaul

Prau Nausch (Figure 2) is a scientifically interesting opportunity to observe, how the infestation

progresses naturally. But since spread is suspected by local foresters, concern was expressed,

because Uaul Surrein, an adjacent north facing forest site, has a protection target profile and a

spruce bark beetle outbreak could cause a dangerous transition period for Uaul Surrein, where the

forest could not offer adequate protection.

Figure 1: Overview map of the windthrow area in Uaul Prau Nausch after the foehn storm in 2012 (Base map Swissimage\swissimage_25cm_2016 © 2016 Swisstopo).


5

3.2 Sampling campaigns All samples of living and dead trees were collected in two sampling campaigns. The first one was

carried out by Luzia Götz from ETH Zürich in September and November 2015 and the second one by

Michael Opiasa in June 2016 (Table 1), when two additional variables and the spatial distribution of

dead trees were recorded. In both campaigns trees were cored with an increment borer (5 mm) and

several tree variables were measured for living and dead trees. One core was taken for every tree. In

total 217 trees were sampled in the two campaigns, 159 in the first campaign in fall 2015 and 58 in

Figure 2: Overview map of Uaul Prau Nausch and the location of the windthrow area (Base map 1:25000 with Relief\1:25000 with Relief_2016 © 2016 Swisstopo).


6

the second campaign in summer 2016. The first campaign contained 78 dead and 74 living trees, the

second 29 dead and 28 living trees. The remaining trees were still alive but infested or their condition

was not recorded. The one missing tree from fall 2015 was not revisited in the 2016 campaign,

because it was not found anymore. The sampled trees were considered as a representative sample of

all living and dead trees near the windthrow area. It was a paired sample and for each dead tree a

corresponding living one of similar DBH was sampled and vice versa. It also needs to be mentioned,

that the sampling ratio of living and dead trees was kept constant at approximately 1, meaning, that

for every living tree one dead tree was sampled and vice versa. Cores were taken for every living and

dead tree. The borer was drilled into the trees at 1 m height and parallel to the slope to prevent

boring into compression wood. In the laboratory, the raw cores were glued on core mounts and

sanded on a belt sander. The grit was increased from 180 to 400 to obtain a smooth surface. The tree

rings were measured in 0.01 mm with a LINTAB 5 measurement bench and the TSAP-Win software

(both from Rinntech, Heidelberg, Germany). After measuring the tree rings for dead and living trees,

the cores of dead trees were quantitatively crossdated, using the COFECHA software (Holmes 1983)

(Section 9.3, contains all 232 collected cores).

Table 1: Total number of sampled trees according to condition in the two sampling campaigns.

Dead Living Infested NA Total

Fall 2015 78 74 6 1 159

Summer 2016 29 28 1 0 58

Total 107 102 7 1 217

3.3 Tree-related variables This section describes, how the different variables were recorded in the field and shows their

relevance and different ecological meanings for the infestation probability by spruce bark beetles. In

total there were 16 independent variables, consisting of twelve continuous and four categorical

variables and one categorical dependent variable. Tree related variables are the dependent variable

condition and the independent variables bark thickness [mm], heart rot, diameter at breast height

(DBH) [cm], tree height [m], crown length [m], damage at the tree, distance to the nearest infested

and dead tree [m], slope [%], discoloration in the wood, two vitality indices [%], cambial age [a] of a

tree, basal area total and south [m2/ha], shading towards south [m] and exposition [°].

3.3.1 Tree condition The dependent variable was the condition of the tree and it was recorded as a categorical variable

with two levels. It was assessed by looking at the color of the crown and also the degree of

defoliation. Total defoliation or an overall brown hue were strong indicators for recording a tree as

dead. Normally the change of crown color from green to brown is a good indicator, whether a tree

died from spruce bark beetle attack or if it is still alive. One can expect to see consequences of a

successful spruce bark beetle attack on a spruce approximately after twelve months in the case of

Uaul Prau Nausch (Forster et al. 2010). Some trees however were partially defoliated and therefore

recorded as a third category, called infested but living. However the third condition category,

infested but living, was left out in the statistical analysis, because tree infestation risk and mortality

was modelled, not only infestation risk. That caused seven more trees to drop out of the analysis. But

using the inferred models from the calibration, mortality probabilities could be predicted for this

group. Only for one tree the condition was not recorded. So the losses of information through this

variable is minor.


7

3.3.2 Bark thickness Bark thickness was measured at the tree in the drill hole, where the cores were taken. Bark beetles

feed either on the phloem or the sapwood of a tree. The spruce bark beetle feeds on nutritious

phloem tissues during its larval development, especially and most fatally during maturation feeding,

when most of the nutrition transportation system of the tree is damaged (Lieutier et al. 2004).

Although bark thickness varies with the height of a tree and cores were only taken at 1 m height, it is

still an indicator for comparison between trees. Also it has been shown that after a certain time, the

upper third of a tree was not used as a breeding substrate anymore, because it dries out quickly

(Göthlin et al. 2000). It was hypothesized that the first arriving male bugs were more likely to be

hindered to bore into the tree, if bark thickness is high. Bark thickness was available for 206 trees.

3.3.3 Heart rot Heart rot is considered a major disturbance factor in mature stands and is caused by fungi (Wagener

et al. 1954). Because heart rot destroys the water transport system of the trees in the sapwood, such

trees could be prone to spruce bark beetle infestation and mortality, due to the additional

investment to repair damages by heart rot. It is assumed that heart rot, caused by fungi, play an

important ecological role, especially by causing or facilitating disturbances, such as the spruce bark

beetle, which may have an easier task to overcome the defensive systems of such weakened trees

(Hennon 1995). Heart rot was available for all 206 trees.

3.3.4 Diameter at breast height DBH was measured with a measuring tape. It was not expected that DBH shows an effect on the

mortality probability, because the sampled dead and living trees were paired by DBH. For forests

with a more dispersed age and hence diameter distribution, we can expect lower risk of spruce bark

beetle infestation, because defensive abilities decrease and hence susceptibility of trees increases

with age. For Ips typographus this means that a tree with large diameter is a better substrate for

feeding than with small diameter. Göthlin, Schroeder et al. (2000) found that trees with diameter

larger than 42 cm were attacked twice as often than smaller ones in a spruce bark beetle outbreak

following a windthrow (Göthlin et al. 2000). DBH was available for all 206 trees.

Figure 3: DBH distribution of Uaul Prau Nausch based on data from the sampling inventory by WSL (Brücker 2014). The data was recorded on 29 plots with a radius of 12.62 m, which represent the area of 65 ha of Uaul Prau Nausch.


8

In Uaul Prau Nausch there are a lot of young trees growing under the old trees or in gaps or on dead

wood (Figure 3). But a remarkable part of the trees has a DBH around and above the critical

threshold of 42 cm, meaning that according to DBH, Uaul Prau Nausch could be rated a susceptible

forest stand to spruce bark beetle infestation. The data for the DBH distribution was also obtained

from the sampling inventory 2014 (Brücker 2014).

3.3.5 Tree height Tree height was measured, using the Vertex device (Haglöf, Langsele, Sweden). Normally tree height

and DBH correlate in an allometric relationship, an asymptotic dependency of tree height on DBH

(Mehtätalo 2004). Still there is variance in this relation, causing some trees to have a higher stability

in comparison to others, i.e. a lower tree height to DBH ratio (h/d). Trees with a higher h/d ratio

could be prone to wind-swaying and therefore their susceptibility to spruce bark beetle infestation is

increased, because these trees would have to invest carbon into the reparation of damaged root

parts and are generally more stressed (Jakuš et al. 2011). Tree height was also available for all 206

trees.

3.3.6 Crown length Crown length was recorded differently in the two sampling campaigns. In the 2015 campaign, it was

recorded by estimation of the proportion in thirds of the tree height. Like this, < 1/3, > 1/3 and < 2/3

and > 2/3 were the three different levels (1, 2 and 3) for this variable. In the 2016 campaign it was

recorded as a continuous height measurement. In the analysis, the crown length of the trees from

the 2016 campaign was calculated to the three different crown length categories with the given tree

height. For a separate analysis of the data only from the 2016 campaign, crown length was left

continuous. The lower end of the crown for living trees was defined as the spot, where the lowest

branch with green needles was attached to the stem. For dead trees we used visual comparison of

branch thickness to assess, which of the lowest branches must have been part of the green crown,

when the tree was still alive. Crown length can influence, how much solar radiation reaches the trunk

of a tree. The shorter the crown, the more solar radiation reaches the trunk and therefore the trunk

gets heated up. This could cause water stress for the tree and expose it to spruce bark beetle

infestation. Trees with higher shading by green crowns could be more likely to survive a spruce bark

beetle outbreak. It can also be used as a vitality index, because the longer the crown, the bigger the

assimilation apparatus and hence the resistance to spruce bark beetle attacks (Jakuš et al. 2011).

Crown length was available for all 206 trees with a core.

3.3.7 Distance to the nearest dead tree The distance to the nearest infested and dead tree was measured using the Vertex device. The

nearest infested dead tree was not necessarily part of the sample. The spruce bark beetle is known

to be able to actively disperse around 500 m. Within these 500 m the beetle is searching for suitable

host trees. It has been reported that within the first 200 m around the windthrow area, the density

of attacks on standing spruce trees was higher than beyond that range and dropped even further

after 450 to 500 m (Gall et al. 2003). During dispersal, aggregation pheromones play a major role in

forming a distribution pattern. These pheromones are exerted by beetles, which found a suitable

tree to reach a critical beetle density, which is necessary to overcome the tree’s defense (Fahse et al.

2011). Such phenomenon may raise the question, whether this aggregation and dispersal of spruce

bark beetles is dependent on other factors than just the distance between trees, respectively how

important the distance to the nearest dead tree is, in relation to other small scale tree related

variables. The distance to the nearest dead tree was available for 204 trees, so this variable has

almost no effect on the sample depth.


9

3.3.8 Basal area Basal area around the tree and towards south was estimated, using the angle count method of

Bitterlich (Bitterlich 1952). To calculate the basal area around the tree, 360° were considered and for

the basal area towards south, the angle of observation was defined between 90° and 270°. The

relationship between basal area and the counted stem number between the angle of observation

and the slope is given by:

𝐵𝐴 = 𝑓𝑎𝑐𝑡𝑜𝑟1(𝑤, 𝑙) ∗ 𝑁𝑟. 𝑇𝑟𝑒𝑒𝑠 ∗ 𝑓𝑎𝑐𝑡𝑜𝑟2(𝑠)

where factor 1 is a value, which is dependent on the width and the length of the angle count device

and factor 2 is dependent on the measured slope. The result is the local basal area [m2/ha] in the

respective angle of observation. Basal area was reported as a stand related risk factor for spruce bark

beetle attack. The focus was on host tree share in basal area, which increased stand predisposition

(Seidl et al. 2007). In Uaul Prau Nausch the dominant species is spruce and basal area was recorded

locally and included as a variable for each single tree and could be considered to consist almost 100%

of spruce. Basal area was recorded for all 206 trees with a core.

3.3.9 Slope The slope was measured with an inclinometer at the spot of the tree and facing towards the

estimated steepest gradient. It was measured in a 5% resolution and was initially necessary for

determining the correction factor in the calculation of the local basal area (Section 3.3.8). However

Akkuzu et al. (2009) showed that the slope had a significant effect not only on the abundance of

spruce bark beetles in an oriental spruce (Picea orientalis) dominated forest, but also their body

length and weight, which are indicators of the population’s vitality (Akkuzu et al. 2009). Less steep

slopes showed to increase the abundance of spruce bark beetles. Therefore this variable was kept in

the data set for determining its effect in the presence of other variables, since there is a relation

between abundance of spruce bark beetles and damaged volume of timber (Faccoli et al. 2004).

Slope could also influence soil properties and hence soil water content, which could affect water

stress for spruces (Blume et al. 2009). The slope was recorded for all 206 trees.

3.3.10 Damage at the tree Damage at the tree was recorded by evaluating the tree from afar, to see, if snow break occurred

and close, to detect, if the tree was damaged on the lower trunk by e.g. rockfall. Such deformations

could cause carbon allocation to wound regeneration or less assimilation by photosynthesis, because

a part of the crown is missing. Göthlin et al. (2000) reported that one year after a windthrow,

damaged trees were more frequently attacked than uprooted trees. The attack frequency decreased

in the year after due to breeding suitability loss (Göthlin et al. 2000). Damage at the tree was

recorded for 192 trees.

3.3.11 Discoloration in the wood Discoloration was mainly a weak to strong change towards a blueish hue on the sampled core. The

blue color appears due to the presence of a symbiotic fungi of the spruce bark beetle, blue-stain

fungi Ceratocystis polonica, which is introduced to a tree by the spruce bark beetle itself

(Christiansen et al. 1987). This fungi symbiotically facilitates infestation by spruce bark beetles and

the occurrence can vary greatly among different trees, since the defense against such facilitators is

dependent on phenolic compounds in the resin of the tree (Lieutier et al. 2003). Therefore it is

expected that this variable could influence the mortality probability of individual spruces under

spruce bark beetle attack. This variable was recorded as a two level factor, stating, if discoloration

was visible or not. Discoloration was missing for four cores (NA), since it was not certain, if

discoloration occurred or not. 202 trees remained, which Discoloration was recorded for.


10

3.3.12 Vitality index The vitality index was calculated similar to Mulock and Christiansen (1986). An increasing vitality

index showed a significant effect on the threshold of necessary number of spruce bark beetles,

attacking a single tree, given a certain vitality index value (Mulock et al. 1986). This could imply that

an increased vitality index could be a predictor of spruce mortality in the context of a calamity after a

windthrow. However, circumference does not play an important role in predicting tree resistance

towards fungal inoculations and hence spruce bark beetle infestation still occurred at elevated tree

vitality in other studies (Lieutier et al. 2003). For defensive capabilities of spruce this means that the

circumference, independent of tree age, does not dependably indicate resistance. But the faster a

tree grows, the higher the threshold of necessary spruce bark beetles for successful infestation is.

However, there is a debate about this so called plant stress hypothesis with some evidence for the

plant vigor hypothesis. It says that many herbivore species rather fed on vigorous plants or plant

modules, as opposed to the plant stress hypothesis (Price 1991). The question is, which of the

hypotheses holds true for single spruces prone to spruce bark beetle attacks after a windthrow with

a subsequent spruce bark beetle calamity. Since this variable is restricted by the year of death and

the number of missing rings (r), this variable reduced the amount of available data points to 98 trees

of which 42 were dead and 56 were living.

3.3.13 Cambial age Older forest stands tend to become more vulnerable to agents of disturbance like wind, fire, fungi or

bark beetles. Naturally disturbances or “pests” as the spruce bark beetle play an important role in

gradually replacing old forest patches with new tree generations. Older trees could be more prone to

the infection by root pathogens, which may also predispose them to spruce bark beetle infestation.

More importantly, as trees age an increasing fraction of their photosynthate is used, to maintain the

living tissue, leaving less energy for e.g. building more resin ducts and hence increase the first line of

defense against spruce bark beetles (Christiansen et al. 1987). The truth may be somewhere in

between, because infesting older trees may be less risky for spruce bark beetles, but the tissue that

they feed on is probably of minor quality (Price 1991). Cambial age is under the same restrictions like

the vitality index, reducing the sample size in the same way as mentioned above.

3.3.14 Shading towards south Shading towards south [m] was assessed in a similar way as crown length in the 2016 campaign. It

was measured with a Vertex as height of the onset of the south facing crown in meters. This variable

describes the crown length facing south of a tree and hence the protection, a trunk has against high

solar radiation coming from south. Since the exposition of Uaul Prau Nausch is mainly ESE, we expect

higher radiation coming in at sunny days. It is possible that trees with a longer crown towards south

are more likely to survive and that having a long crown towards south is even more important than

having just a long crown in general. This variable was only recorded for the 58 trees in the 2016

campaign.

3.3.15 Exposition Exposition [°] was measured in degrees deviation from north. It was assessed using a compass, facing

along the line of the steepest gradient at the spot of the tree. Topography on a small scale could play

a role and trees with a less south exposed root system may suffer less from water stress than trees

with more south exposure, where incoming radiation could cause the soil to dry up. As mentioned

above, such stress could cause higher vulnerability to spruce bark beetle attacks. This variable was

only recorded for the 58 trees in the 2016 campaign.


11

3.4 Core samples From the cores several variables were extracted. Heart rot and discoloration were recorded as

presence/absence factors, stating, if heart rot respectively discoloration was visible on the core or

not. The vitality index was calculated similar to Mulock and Christiansen (1986) by dividing the area

of the tree rings of the last one or five years by the sapwood area. But in comparison to Mulock and

Christiansen (1986) the vitality index was calculated using the total basal area and not only the

sapwood area of a tree. For the calculation of Vit1 and Vit5 only the years 2011 and 2008 up to 2011

were used respectively. This is a measure of how well the tree was growing in the last one to five

years before the windthrow in 2012 and how much resources the tree invested into growth. Mulock

and Christiansen (1986) reported that the necessary beetle density for successful infestation was

always higher for a given Vit5 than for Vit1. To overcome this uncertainty, both indices were used in

the analysis.

𝑉𝑖𝑡𝑖 =𝐵𝐴𝐼𝑖

𝐵𝐴; 𝑖 = {1,5}

Viti is the ratio of the basal area increment of the last one or five years (BAIi) to the total basal area

(BA) of a tree. Further the cambial age of each dead and living tree was assessed, using the method

of Duncan (1989), but for the determination of missing rings, only the first four years apart from the

arc were taken into account instead of 20 (Duncan 1989). For trees where the pith was available on

the core, this procedure was skipped and only the output of COFECHA for the cambial age was taken.

The formula for the number of missing rings is:

𝑟 =𝐿2

8 ∗ ℎ+

ℎ

2

where L is the length of the arc on the core, h its height and r is the length of the missing radius from

the arc to the pith of the tree. The number of missing rings r was added to the age, which was

determined by COFECHA, to obtain the cambial age of the tree at 1 m height. For the spatial

projection of the dead trees the year of death was needed to show, where dead trees died in which

year. From the cores of the 2015 campaign, 11 were useless, because the heart rot was too strong

and the cores fell apart when removed from the storing tube. The cores from the 2016 campaign

were all usable, leaving a total of 206 out of 217 trees of all three condition categories with a core,

which were used for the analysis. Further exclusions were necessary, if variables like the vitality index

or the cambial age were included in the analysis. If the arc of the last recorded tree ring, which is

needed for the estimation of the number of missing rings (r), was missing, the core was excluded for

the estimation of r and hence also the estimation of cambial age and the vitality index. This affected

57 of the 148 usable cores of the 2015 campaign, leaving 91 cores from the 2015 campaign. Cores

which indicated that the tree died before 2011, were excluded, since they do not give any

information about what happened after the windthrow and subsequent spruce bark beetle attack.

I.e. their information about the cambial age and vitality indices is without any relation to the

windthrow and the subsequent mortality through spruce bark beetle attacks. Trees with too many

missing rings (r > 20) also had to be excluded, since the uncertainties when predicting cambial age

would be too high, if too many missing rings were present. For the 2015 campaign this procedure left

56 cores of the 2015 campaign and 44 of the 2016 campaign, for which cambial age and the vitality

index were calculated. From these 100 cores, two belonged to the third condition, infested but living.

This dropped the sample size down to 98 trees, which had cores, giving reliable information about

cambial age and the vitality indices, but also indicating, which trees were relevant for the research

questions to be answered in this thesis, i.e. the trees, which died after the year 2011 subsequent to

the windthrow and spruce bark beetle outbreak.


12

3.5 Statistical modelling To predict the mortality probability of single spruce trees, based on measured and calculated tree

variables, multiple logistic regression was used. In logistic regression the response variable is binary

and probabilities are calculated that an observation belongs to either one or another group. It has

become a standard model for the prediction of a binary response variable (Hosmer et al. 2004). In

this study the binary outcome Y was, whether the tree is dead or if it is still alive. Dead trees were

labeled as 1 and living as 0, since the model should predict, whether it is likely that a given tree dies

from spruce bark beetle attack or not, given a combination of tree related variables.

The response variable of the linear predictor is the logit link function, i.e. the natural logarithm of the

odds, called log-odds. We describe a linear function of β, a vector which contains the regression

coefficients and X, a design matrix. In multiple regression we have βn parameters and xn variables.

ln (𝑝(𝑋)

1 − 𝑝(𝑋)) = 𝛽𝑋

The parameter vector β holds as many estimates as variables included in the model, which is equal to

the number of columns in the design matrix X (Kéry 2010). The multiple linear regression model and

hence its parameter estimates are fitted on this so called logit scale. Increasing logit values generally

mean increasing probability and vice versa (Hosmer et al. 2004). If we solve the logit for p(X) we get

the probability to belong to either one or another group, dependent of X:

𝑝(𝑌 = 1|𝑋) =𝑒𝛽𝑋

1 + 𝑒𝛽𝑋

This is, what the model is assigning to each tree as y, or more precisely ŷ, the estimated mortality

probability given X for the respective tree. The model estimates are the values contained in the

parameter vector β. At any given X, the estimated probability p(Y=1|X) is a parameter of the binomial

distribution, which is defined as:

𝑃(𝐾 = 𝑘) = (𝑛

𝑘) 𝑝𝑘(1 − 𝑝)𝑛−𝑘

with k as the number of dead trees (Y=1), K as any natural number, n as the number of dead and

living trees, p as p(Y=1|X) and P as the probability of observing K dead trees (Y=1).

3.5.1 Variable selection and data partitioning All independent variables were used as they were recorded. Different partitioning of the data is

shown, to illustrate, how different global models were formulated based on the available data and

how the used variables restricted the sample size. The trees with condition NA or the third category,

infested but living, were dropped from the 206 trees with usable cores for the analysis, leaving 200

trees, of which 102 were dead and 98 were living available for variable selection and modelling

(Table 2).


13

Table 2: Number of observations (n) per variable only for dead and living trees after exclusion of NA and infested but living trees and proportion of dead and living trees per variable.

Independent Variable Observations (n) Dead Living Ratio (dead/living)

Bark thickness 200 102 98 1.04

Heart rot 200 102 98 1.04

DBH 200 102 98 1.04

Tree height 200 102 98 1.04

Crown length 200 102 98 1.04

Distance 198 102 96 1.06

Slope 200 102 98 1.04

Basal area total 200 102 98 1.04

Basal area south 200 102 98 1.04

Damage 186 92 94 0.98

Discoloration 196 98 98 1.00

Cambial age 98 42 56 0.75

Vit1 98 42 56 0.75

Vit5 98 42 56 0.75

Shading south 57 29 28 1.04

Exposition 57 29 28 1.04

The most restricting variables, recorded in both campaigns in the dataset were the ones, which

depended on intact cores, i.e. cambial age and the two basal area increment indices for tree vitality.

Shading south and exposition were only recorded in the 2016 campaign and one tree was in the third

condition category, infested but living, leaving 28 living and 29 dead trees for these variables. In

general the ratio of dead and living trees was quite constant over all independent variables with a

mean of 0.98 and a standard deviation of 0.12. By combining these variables into global models, the

sample size still got smaller, because the missing values occurred at different observations, causing

more samples to drop out of the analysis, since no missing values (NA) should be present in the

dataset before modelling. This also had an effect on the ratio of dead and living trees in the available

sample.

Table 3: Global models, the used independent variables, the sample size and number of available dead and living trees.

Included variables n Dead trees Living trees

Model 1 Bark thickness, Heart rot, DBH, Tree height, Crown length, Distance, Slope, Basal area total, Basal area south, Damage, Discoloration, Cambial age, Vit1, Vit5

92 38 54

Model 2 Bark thickness, Heart rot, DBH, Tree height, Crown length, Distance, Slope, Basal area total, Basal area south, Damage, Discoloration

180 88 92

Model 3 Bark thickness, Heart rot, DBH, Tree height, Crown length, Distance, Slope, Basal area total, Basal area south, Damage, Discoloration, Shading south, Exposition

57 29 28


14

The first global model, model 1 (Table 3), consisted of all 14 independent variables, except the two,

which were only recorded in the 2016 campaign, shading south and exposition. This reduced the

dataset to 92 observations with no NA in the dataset, consisting of 38 dead and 54 living trees for

model calibration.

The second global model, model 2 (Table 3), consisted only of the first eleven independent variables,

excluding the strongly restricting core related variables cambial age and the vitality indices, as well as

shading south and exposition. The sample size in this dataset was 180. The sample size almost

doubled in comparison to model 1. It consisted of 88 dead and 92 living trees.

Another model was fitted (Table 3), but not commented in the results. Model 3 was fitted, using only

the data from the 2016 campaign. Crown length could be included as a continuous variable and the

new variables shading south and exposition were included in the global model. The strongly

restricting variables cambial age and the vitality indices were excluded, because the sample size was

already small. For the outputs of this global model refer to Section 9.2.

3.5.2 Model selection Models, inferred from several different global models (Section 3.5.1), were fitted and selected at the

same time, using maximum log-likelihood estimation and the Akaike information criterion (AIC)

(Akaike 1974). Rather than restrictively looking at models with single variables, an information

theoretic approach was used by comparing models with different numbers and combinations of

independent variables (estimation and selection) (Anderson et al. 2000). Based on maximum

likelihood theory and Kullback-Leibler information the AIC is formulated as:

𝐴𝐼𝐶 = −2 ln(ℓ(𝜃|𝑑𝑎𝑡𝑎)) + 2𝑝

with ln(l(θ|data)) as the value for the log-likelihood over the unknown parameters θ (given by the

data in the respective model), which is maximized and p as the number of parameters included in the

respective candidate model. Multiple models, inferred from a global model are tested by computing

an AIC for each candidate model. After ranking according to the AIC, the model with the lowest AIC

score is selected, or a model set is built, based on differences in AIC scores (ΔAIC). The relative

support for an individual model is given by the Akaike weight (wi), which is defined as:

𝑤𝑖 =exp (−

12 𝛥𝐴𝐼𝐶𝑐

𝑖)

𝛴𝑗=12𝑝

exp (−12 𝛥𝐴𝐼𝐶𝑐

𝑗)

with ΔAICc as the AICc difference of model i and the model with the lowest AICc and parameter p as

the number of independent variables used in the global model. So rather than testing one single

hypothesis, i.e. one single model against a null hypothesis, we infer multiple hypotheses from a

global model and rank them against each other by evaluating the relative support in the observed

data. For small sample sizes, i.e. if the number of free parameters (p) exceeds n/40 (n is the sample

size), the corrected Akaike information criterion (AICc) is used, which includes a correction factor

(Johnson et al. 2004).

𝐴𝐼𝐶𝑐 = −2 ln(ℓ(𝜃|𝑑𝑎𝑡𝑎)) + 2𝑝(𝑛

𝑛 − 𝑝 − 1)

All models were fitted and inferred using the “MuMIn” library in R (Barton 2013). For model selection

the dredge function was used, which generates 2p models and computes the Akaike weight and AICc

for each candidate model.


15

3.5.3 Model assessment A further statistic was computed to assess the predictive capabilities of the inferred models, i.e. the

discrimination power. The receiver operating characteristic (ROC) was computed for each model.

This statistic is useful for determining, if a classifier like a logistic regression model is assigning

positive observations, based on independent variables at random or not. It shows, whether a model

is discriminating well between observed positive cases and negative cases in the available data or if

its predictions are independent or contradicting the observed data. This method also became

important in the presence of unbalanced classes (Fawcett 2006). This assessment is based on a so

called confusion matrix (Figure 4).

The count of true positives is a, false positives b, false negatives c and true negatives d. From the

confusion matrix two metrics are relevant for the calculation of the ROC. The sensitivity, which

ranges from zero to one and is given by a/(a + c) and specificity ranging from zero to one and given

by d/(b + d). Sensitivity quantifies the avoidance of false negatives, as the specificity does for false

positives. While the sensitivity could be termed as true positive rate, the specificity defines the true

negative rate. For the calculation of the ROC curve, we use 1 – specificity or the false positive rate on

the x axis and the true positive rate on the y axis. The ROC curve is the interpolated curve made

of points whose coordinates are functions of the threshold, which is a cut point between 0 and 1,

beyond which a prediction by a fitted model is defined as positive. The AUC, a threshold independent

measure for model discrimination, is the area under this curve, which emerges, when plotting

sensitivity against 1 – specificity for an increasing threshold. The observations are sorted according to

increasing predicted probabilities (Fielding et al. 1997). The area under the curve varies between 0.5

(straight line) and 1.0 (asymptotic shape). Since a good classifier, e.g. a logistic regression model, is

expected to discriminate well between two groups, we expect the area under the curve to be greater

than 0.8. With an AUC of 0.5, the model would not perform better than random guessing. The

Hosmer – Lemeshow test was used to assess the goodness of fit of the model. It compares the

expected and the observed positive and negative cases in groups of fitted probabilities, which all

have the same interval size (Hosmer et al. 2004).

3.6 Spatial projection In the 2016 campaign, the dead trees were spatially surveyed. Every dead tree was measured with

the Postex system and a DP II caliper computer (both from Haglöf, Langsele, Sweden), to obtain the x

and y coordinates relative to a plot center. These values were added to absolute center coordinates

of a plot with a radius of 15 m, within which all dead trees have been calipered. There were 110 dead

trees contained in 32 plots. The plots were established with the HiPer SR Construction Kit LongkLink

BASE & Rover, a highly precise GPS device, which measured coordinates in the CH1903_LV03

coordinate system (Topcon, Tokyo, Japan). The point coordinates of trees, calculated from the

addition of a respective plot coordinate with each relative tree coordinate on this plot, and the

respective years of death were calculated and prepared in R (R Core Team 2016) and afterwards

displayed as a point pattern in ArcMap (Desktop ESRI ArcGIS 2011) with a digital elevation model and

a false color image of the landscape in the background. The trees were partitioned into six point

layers, which could be projected individually, grouped by the attached year when the trees died. Like

this it could be tracked, where which tree died in which year in the sample.

Figure 4: A confusion matrix (from Fielding and Bell (1997)).

Results

16

4 Results This section is split in three parts. First the descriptive results are shown for the continuous and for

the categorical variables. Mean values for all continuous variables were calculated and compared

between dead and living trees and contingency tables for the categorical variables were made. The

sample sizes for each variable are according to Section 3.5.1. Next the results of the different models

are shown and it is important to point out, that Model 3 is not described in the results section, but

discussed in the subsequent Section 5.1. Finally the results of the spatial projection of the dead trees

are shown in an overview map.

4.1 Descriptive results

4.1.1 Continuous variables Only four of the twelve variables differed significantly (Table 4), when comparing them solely in a

paired t – test between dead and living trees. Distance differed most strongly between dead and

living trees with a p – value of 1.634*10-13.

Table 4: Mean values for all continuous variables and the p – values of paired t – tests for the comparison of sample means between dead and living trees. The standard error is shown in brackets (se).

Variable Mean over all (se) Mean of dead (se) Mean of living (se) p - value

Bark thickness [mm] 12.69 (0.33) 12.57 (0.47) 12.82 (0.46) 0.707

DBH [cm] 43.30 (0.92) 43.16 (1.27) 43.44 (1.34) 0.879

Tree height [m] 26.24 (0.51) 26.74 (0.70) 25.72 (0.74) 0.322

Distance [m] 4.43 (0.29) 2.40 (0.25) 6.59 (0.45) < 0.001

Slope [%] 55.55 (0.99) 54.95 (1.29) 56.17 (1.52) 0.539

Basal area total [m2/ha] 48.81 (1.54) 52.19 (2.38) 45.28 (1.89) 0.024

Basal area south [m2/ha] 25.92 (1.14) 29.05 (1.88) 22.66 (1.19) 0.005

Cambial age [a] 167.33 (3.36) 172.02 (3.36) 163.80 (5.29) 0.193

Vit1 [%] 0.90 (0.10) 0.78 (0.11) 0.99 (0.16) 0.290

Vit5 [%] 4.38 (0.44) 4.05 (0.56) 4.63 (0.65) 0.504

Shading south [m] 19.33 (1.27) 18.52 (1.71) 20.16 (1.89) 0.525

Exposition [°] 119.49 (4.64) 130.17 (5.50) 108.43 (7.04) 0.018

On average, the living trees had a 175% higher distance to another dead tree than trees, which died.

However, some dead trees also had relatively long distances (Figure 5). Dead trees had higher values

than living trees for the stand related variables basal area around the tree and basal area towards

south. Dead trees had a 15% higher basal area around the tree and a 28% higher basal area towards

south than living trees on average. Exposition also differed significantly, when comparing dead and

living trees. Dead trees were rather facing south than living trees. The average tree height of all the

sampled trees was quite appropriate for a coltsfoot – spruce forest with reedgrass, where the

maximum tree height is around 25 to 35 m and rather high for a lingonberry – spruce forest with

laserwort with a maximum tree height of 20 to 25 m (Ott et al. 1997). DBH and bark thickness

showed the smallest differences between dead and living trees. Shading towards south, i.e. the south

facing crown length, was on average 74% of tree height. This proportion was 69% for dead trees and

increased to 78% for living trees. The core dependent variables cambial age and the two vitality

indices all showed no significant differences. But compared to the vitality index over the last five

years, the vitality index of one year had a greater difference between dead and living trees.

Results

17

4.1.2 Categorical variables Considering only the share in dead and living trees, we get for the contingency tables a χ2 of 13.54 at

2 degrees of freedom and a p – value of 0.001 for crown length (Table 5). But it is still unknown, what

effect the different crown length categories do have on the mortality individually. Generally more

trees have a longer crown, but with decreasing crown length the proportion of dead trees increases

compared to living trees. Discoloration has a χ2 of 2.94 at 1 degree of freedom and a p – value of

0.086 (Table 6) and similarly damage and heart rot have a χ2 of 1.90 and 0.27 at 2 and 1 degrees of

freedom with a p – value of 0.386 and 0.602 respectively (Tables 7 and 8).

Table 5: Contingency table of crown length and the distribution of dead and living trees.

Crown length Total Share in dead Share in living

< 1/3 of tree height (1) 21 13 8

> 1/3; < 2/3 of tree height (2) 51 36 15

> 2/3 of tree height (3) 128 53 75

Table 6: Contingency table of discoloration and the distribution of dead and living trees.

Discoloration Total Share in dead Share in living

Absent (0) 97 42 55

Present (1) 99 56 43

Figure 5: Boxplot of distance vs. condition for living and dead trees, n = 198.

Results

18

Table 7: Contingency table of damage at the tree and the distribution of dead and living trees.

Damage Total Share in dead Share in living

None (0) 132 65 67

Broken top (1) 31 18 13

At the stem (2) 23 9 14

Table 8: Contingency table of heart rot and the distribution of dead and living trees.

Heart rot Total Share in dead Share in living

Absent (0) 174 87 87

Present (1) 26 15 11

The vitality index based on the basal area increment of dead and living trees seemed to increase, if

crown length increases (Figure 6). But this trend obviously was not true for dead trees, because the

vitality index had a lower median than for living trees, if the proportion of crown length was bigger

than 2/3 of tree height. DBH and bark thickness increased for both conditions and total basal area

decreased similarly for both conditions with increasing crown length (results not shown).

4.2 Prediction of tree mortality The models were always fitted to the whole dataset during global modelling. The data was not split

into training and testing datasets. The predictions for all trees are based on the full available datasets

for the included variables in the global model (Table 3 in Section 3.5.1) and are the resulting

probabilities assigned by the model fitting process for each tree. Fielding and Bell (1997) refer to this

as resubstitution (Fielding et al. 1997). Note that the predicted probabilities are relative probabilities,

because the ratio of the sampled dead and living trees was kept close to 1 (Table 2) and thus was not

Figure 6: Boxplot for Vit1 vs. crown length for living and dead trees, n = 98.

Results

19

representative of the observed mortality in the forest. On the presented graphs (Figures 8 to 13 and

16 to 19) the solid lines represent the fitted values of probabilities, predicted for varying continuous

variables, by the model. The color represents different levels for categorical variables. The bands

represent confidence intervals for the predictions. The different interval widths among the crown

length categories are due to the unequal abundance of the different categories in the data (Table 5).

4.2.1 Model selection for global model 1

Model selection for global model 1 resulted in the construction of 214 different models for which the

AICc and the Akaike weight was computed. From these 16384 candidate models, those with the

lowest AICc scores are listed in Table 9.

Table 9: Comparison of logistic regression models after model selection for global model 1. Models with an Akaike weight < 1% or a ΔAICc > 2 were excluded.

Model number Variables AICc ΔAICc Akaike weight (%)

11809 Distance + Tree height + Crown length + Slope + Discoloration

89.17 0.00 1.27

11937 Distance + Tree height + Crown length + Slope + Basal area south

89.37 0.20 1.14

Six variables remained in model 11809 (Table 10). For further comments on the results of global

model 1, only the best scoring model (model 11809) is considered, although the two top models

from global model 1 had a very similar AICc score. Note that the relative support for the two models

is relatively low.

Table 10: Description of mortality model 11809 with parameter estimates, standard errors and p - values.

Variable Estimate Standard error p – value

Intercept -5.789 2.443 0.018

Distance -0.569 0.144 < 0.001

Tree height 0.094 0.045 0.035

Crown length 2 Crown length 3

2.034 -0.177

1.367 1.192

0.137 0.882

Slope 0.070 0.028 0.013

Discoloration 1 1.127 0.607 0.064

The model parameters indicate, that an increasing distance has a negative effect on the log odds as

does crown length > 2/3 of tree height. Therefore the mortality probability decreases, if distance to

the nearest dead tree increases or if we change from crown length category 1 to 3. Note that crown

length < 1/3 is a reference level, which is at the intercept, if all other variables are at the hypothetical

zero. A crown length > 1/3 and < 2/3 increases the mortality probability compared to crown length <

1/3. Increasing tree height and slope increase mortality probability weakly, while if discoloration is

present, the mortality probability increases.

4.2.1.1 Mortality probability predictions per tree condition by model 11809

The model discriminated well between dead and living trees (Figure 7). The models were fitted and

selected including all data (n = 92). The model assigned a mean mortality probability of 0.21 for living

trees and 0.71 for dead trees. The p – value of a t – test for the difference of the means between the

groups is 7.659*10-16.

Results

20

4.2.1.2 Prediction plots of different variables of model 11809

Since model 11809 is built of one 3 level and one 2 level factors together with three continuous

variables, there are six plots (Figures 8 to 13) to describe the model predictions for the three

continuous variables in different combination with the two categorical variables in the model.

4.2.1.2.1 Distance

Discoloration is shown as absent (0) and present (1) in two figures separately (Figures 8 and 9). Slope

and tree height were kept at the sample mean of the respective variable. The varying variables are

crown length and distance to the nearest dead tree. Generally mortality probability increases with

decreasing distance. It ranges from 0 to almost 100% for crown length category > 1/3 and < 2/3 and

from 0 to approximately 62% and from 0 to approximately 85% for the other two crown length

categories, depending whether discoloration was absent or present respectively. The mortality

probabilities, dependent on distance, vary differently for different crown lengths. Whether

discoloration was present or not, trees with crown length > 1/3 and < 2/3 had the highest risk of

getting infested and dying, depending on the distance with a sharp decrease between 3 to 10 m. If

crown length was < 1/3 or > 2/3 the maximum mortality probability is around 85%, if discoloration is

present. Without discoloration the maximum mortality probability is around 62%. For these crown

length categories the mortality probability is already below 10%, if the distance to the nearest dead

tree is approximately above 6 m. For a given distance the mortality probability is only marginally

larger for trees with crown length < 1/3 than for trees with crown length > 2/3. If discoloration is

absent, the probabilities are generally lower for a given distance to the nearest dead tree for all three

crown length categories.

Figure 7: Predicted mortality probability for living and dead trees of model 11809. n = 92.

Results

21

4.2.1.2.2 Tree height

Figures 10 and 11 have the same setting for the categorical variables as Figures 8 and 9. Distance to

the nearest dead tree and Slope were kept at the sample mean of the respective variable and the

varying variables are crown length and tree height. Mortality probability generally increases with

increasing tree height. The variation of mortality probabilities for a given tree height dependent on

the different crown lengths is similar to the probabilities dependent on distance. Again, whether

discoloration was present or not, the mortality probability was highest for trees with crown length >

1/3 and < 2/3, however the increase is not very abrupt. Without discoloration the mortality

probability of this crown length category starts to increase more strongly beyond a tree height of 20

m and less strongly afterwards. With discoloration the probability is high from the beginning and the

Figure 8: Predicted mortality probability vs. distance by model 11809 for each crown length category without discoloration on the core. The available data for the distance to the nearest infested tree ranged from 0.14 to 15.89 m. n = 92.

Figure 9: Predicted mortality probability vs. distance by model 11809 for each crown length category with discoloration on the core. The available data for the distance to the nearest infested tree ranged from 0.14 to 15.89 m. n = 92.

Results

22

increase declines after 20 m and reaches almost 100% at a tree height of 60 m. Note that due to

uncertainties, the mortality probability is still above 0% for the hypothetical tree height of 0 m. The

other two crown length categories seem to develop similarly in mortality. The mortality probability is

generally 12 to 15% higher, if discoloration is present but the development dependent on tree height

is similar.

4.2.1.2.3 Slope

Crown length varies in the graphs and discoloration is kept at either absent (0) or present (1). Slope

has a positive effect on mortality (Figures 12 and 13). The steeper the slope is, i.e. the closer to 100%,

the more probable it is for a tree to die from spruce bark beetle attacks. Probabilities range from 0 to

approximately 75% for trees with crown length < 1/3 or > 2/3, if discoloration is absent and from 0 to

Figure 10: Predicted mortality probability vs. tree height by model 11809 for each crown length category without discoloration on the core. The available data for tree height ranged from 10 to 44 m. n = 92.

Figure 11: Predicted mortality probability vs. tree height by model 11809 for each crown length category with discoloration on the core. The available data for tree height ranged from 10 to 44 m. n = 92.

Results

23

around 90%, if discoloration is present. For the medium crown length category the mortality

probability reaches almost 100% at 100% slope, whether discoloration is present or not. But although

the probabilities are similar towards 100% slope, the differences below 75% slope are quite large,

dependent on the presence or absence of discoloration. For example at a slope of 50%, mortality

probability for trees with discoloration is almost 25% higher. Again trees with crown length < 1/3 had

a slightly higher mortality probability than trees with crown length > 2/3. For these two categories,

discoloration has an stronger effect after 50% slope, where mortality probability starts to increase by

approximately 25%, depending on whether discoloration is present or not.

Figure 12: Predicted mortality probability vs. slope by model 11809 for each crown length category without discoloration on the core. The available data for the slope ranged from 10 to 90%. n = 92.

Figure 13: Predicted mortality probability vs. slope by model 11809 for each crown length category with discoloration on the core. The available data for the slope ranged from 10 to 90%. n = 92.

Results

24

4.2.1.3 Assessment of model 11809

The receiver operating characteristic curve (ROC) in Figure 14 shows that model 11809 discriminates

well between dead and living trees. For an increasing threshold the false positive fraction drops,

while the true positive fraction stays quite high and drops relatively quickly around 10% false positive

fraction. The area under this ROC curve is 0.9059 and relatively high on a range of 0.5 to 1.0. The

Hosmer – Lemeshow test for model 11809 has a p – value < 0.05 with a group size of 10.

4.2.2 Model selection for global model 2 Model selection for global model 2 resulted in the construction of 211 different models, for which the

AICc and the Akaike weight was calculated. The inference resulted in 2048 candidate models of which

the ones with the lowest AICc are shown in Table 11.

Table 11: Comparison of logistic regression models after model selection for global model 2. Models with an Akaike weight < 1% or a ΔAICc > 2 were excluded.

Model number Variables AICc ΔAICc Akaike weight (%)

1158 DBH + Distance + Crown length + Discoloration

184.39 0.00 8.92

1190 DBH + Distance + Crown length + Discoloration + Basal area total

186.13 1.75 3.73

Table 12 lists details about the parameter estimates for model 1158. For further investigation of the

results of global model 2, only the best scoring model (model 1158) is considered. The best scoring

model 1158 had a quite low AICc compared to the other models and hence its Akaike weight is

relatively high.

Figure 14: ROC curve for model 11809. The dots on the curve denote the threshold value, at which the true positive fraction and the false positive fraction are calculated.

Results

25

Table 12: Description of mortality model 1158 with parameter estimates, standard errors and p - values.

Variable Estimate Standard error p – value

Intercept -0.421 0.828 0.611

DBH 0.040 0.016 0.014

Distance -0.453 0.077 < 0.001

Crown length 2 Crown length 3

0.902 -0.538

0.745 0.667

0.226 0.419

Discoloration 1 1.136 0.393 0.004

The categorical variables have their reference level at the intercept, if all other variables are at the

hypothetical value of zero. The model parameters indicate that an increasing distance has a negative

effect on the log odds of mortality as does crown length > 2/3 of tree height. If discoloration is

present, the log odds of mortality increase by 1.136 compared to if it is absent.

4.2.2.1 Mortality probability predictions per tree condition by model 1158

As shown in Figure 15 this model discriminates quite well between the two groups. The model was

fitted and selected using the full available data for the independent variables (n = 180). The mean

prediction of mortality probability for living trees was 0.30 and 0.69 for dead trees. The p – value of a

t – test for the difference of the means between the groups is < 2.2*10-16.

4.2.2.2 Prediction plots of different variables of model 1158

Since model 1158 is built of one 3 level and one 2 level factor together with two continuous

variables, there are four plots (Figures 16 to 19) to describe the model predictions for the two

continuous variables in different combination with the two categorical variables in the model.

Figure 15: Predicted mortality probability for living and dead trees of model 1158. n = 180.

Results

26

4.2.2.2.1 Distance

Discoloration is either absent (0) or present (1) respectively (Figures 16 to 19). DBH was kept at the

sample mean. The varying variables are crown length and distance to the nearest dead tree. Like in

model 11809 the mortality probability increases with decreasing distance to the nearest dead tree.

Mortality probability range and change dependent on distance are very similar to Figures 8 and 9,

except that it is slightly increased for the prediction with DBH at its mean (Figures 16 and 17) and a

distance beyond 5 m, if discoloration is absent or present. For example mortality probability is at 50%

for 7.5 m distance to the nearest dead tree for model 1158, while it is already at approximately 37%

for model 11809, with discoloration and crown length > 1/3 and < 2/3. A further difference is that the

difference between the mortality probability for crown length < 1/3 and crown length > 2/3 is larger

in Figures 16 and 17 and that they are generally higher than in Figures 8 and 9. They range from 0 to

approximately 77% and 70% respectively, if discoloration is absent and from 0 to 93% and 87%

respectively, if discoloration is present. Generally the mortality probabilities are again higher, if

Figure 16: Predicted mortality probability vs. distance by model 1158 for each crown length category without discoloration on the core. The available data for the distance to the nearest infested tree ranged from 0.10 to 19.90 m. n = 180.

Figure 17: Predicted mortality probability vs. distance by model 1158 for each crown length category with discoloration on the core. The available data for the distance to the nearest infested tree ranged from 0.10 to 19.90 m. n = 180.

Results

27

discoloration is present for a given distance to the nearest dead tree for all three crown length

categories.

4.2.2.2.2 Diameter at breast height

Figures 18 and 19 show that an increasing DBH raises mortality probability of a tree, depending on

crown length and with the distance to the nearest dead tree kept at its sample mean. DBH ranges

from 8 to 100 cm in the graphs, while the range of measured DBH in the data was 15 to 83 cm. The

differences in prediction between the different crown length categories is similar as in Figures 16 and

17. Discoloration again raises the mortality probability, however the increase is quite strong and the

difference between mortality for crown length < 1/3 and for crown length > 2/3 is quite big,

approximately 10 to 12%. For a DBH of 50 cm for example, the increase of mortality probability is

almost 25% for all crown length categories, depending whether discoloration is absent or present.

The range of mortality probability is 22 to 91%, 11 to 81% and 6 to 72%, if discoloration is absent and

Figure 18: Predicted mortality probability vs. DBH by model 1158 for each crown length category without discoloration on the core. The available data for DBH ranged from 15 to 83 cm. n = 180.

Figure 19: Predicted mortality probability vs. DBH by model 1158 for each crown length category with discoloration on the core. The available data for DBH ranged from 15 to 83 cm. n = 180.

Results

28

47 to 97%, 27 to 93% and 18 to 89%, if discoloration is present for crown length > 1/3 and < 2/3, <

1/3 and > 2/3 respectively. Mortality increases quite steadily dependent on DBH.

4.2.2.3 Assessment of model 1158

The receiver operating characteristic curve (ROC) in Figure 20 shows, that the model discriminates

quite well between dead and living trees. However the curve seems to develop a bit closer to the

straight line than in Figure 14. The area under this ROC curve is 0.8712 and still quite high on a range

of 0.5 to 1.0. The Hosmer – Lemeshow test for model 1158 has a p – value < 0.05 with a group size of

10.

4.3 Spatial projection The proportion of the trees with the same year of death varied over time (Figure 21). In total, there

were 102 dead trees, which had coordinates and a core for determining the year of death. 23.5% of

the sampled trees died before the windthrow in 2012. The amount of dead trees increases strongly

after the windthrow in 2012 and culminates in the year 2014. In the consecutive years 2015 and

2016 only a few trees died. Some trees had brown crowns during the 2016 sampling campaign, which

means that they were recorded as dead, but they were still developing tree rings in 2015.

Figure 20: ROC curve for model 1158. The dots on the curve denote the threshold value at which the true positive fraction and the false positive fraction are calculated.

Results

29

The black circles in Figure 22 represent the position of all 102 spatially surveyed trees. The biggest

proportion is within or in the vicinity of the windthrow area and from 2012 to 2016, three new

clusters developed further away from the windthrow area. Two are situated in the north and one

emerged towards southwest. For each group of dead trees with the same year of death, one distinct

color was chosen (Figure 22). The trees, which died before 2012 are shown in green. They are

clustered mostly at the edge of the windthrow area and some are spread northwards. There are 24

trees in this group. Red dots indicate that three trees died in the same year of the windthrow and

they are all situated within the perimeter of the windthrow area. After the windthrow 27 trees died

in the year 2013. They were mostly distributed at the southwestern edge of the windthrow area. Five

trees died in the cluster southwest of the windthrow area and one in the closer northern cluster. The

biggest proportion of trees died in the year 2014. These 44 dead trees primarily died at the

northeastern edge of the windthrow area. However 11 of these trees were measured in the northern

clusters. In these northern clusters, the trees, which died in 2014 have the biggest share in the

amount of trees. Only three trees of this group belonged to the southwestern cluster. The trees

which died in 2015 and 2016 are shown in yellow. The two trees which died in 2015 are located at

the northeastern edge of the windthrow area and one of the two, which died in 2016, is located at

the northeastern edge too, while the other is situated in the nearer northern cluster. For pictures at

a smaller scale of the windthrow area and each individual cluster, refer to Section 9.1.

Figure 21: Proportion of dead trees and their respective year of death. n = 102.

Results

30

Figure 22: Spatial distribution of dead trees which died before the foehn storm in 2012 and in the consecutive spruce bark beetle outbreak from 2012 to 2016. The numbers and the related colors in the legend indicate the trees with a common year of death (Base map Swissimage\swissimage_25cm_2016 © 2016 Swisstopo).

Discussion

31

5 Discussion

5.1 Prediction of tree mortality Distance had the most significant influence on mortality overall. This means that spruce bark beetles,

which built up an epidemic population in lying dead wood, attack trees randomly, while they swarm

from tree to tree. Against expectations the tree related variables like heart rot, cambial age, the tree

ring related vitality indices and damage at the tree never had an important influence on the mortality

of spruces. Even if damage at the tree appeared several times in the inferred models of the first

global model (Section 9.2). Bark beetles seem not to select old trees, which are expected to have

lower defensive capabilities or trees which rather invested into vigorous growth than defensive

structures, but just mainly infest the nearest available spruce. The clusters may have emerged due to

wind dispersion of spruce bark beetles or locally available lying dead wood.

Three models were fitted and inferred using maximum likelihood and a different set of variables,

which strongly affected the available sample size for model fitting (Table 3 in Section 3.5.1). After the

models were selected, three variables remained in both of the investigated top models, i.e. distance

to the nearest dead tree, crown length and discoloration.

In both models the effect of distance to the nearest dead tree on mortality risk was highly significant

and increases, if distance to the nearest dead tree decreases with a sudden rise below 10 m, if crown

length is around half of tree height. It has been shown that whitebark pine trees, which grew in a

more aggregated cluster were more frequently attacked and killed by mountain pine beetles (Perkins

et al. 2003). It is possible that such an effect could be generalized to the relationship between the

European spruce bark beetle and Norway spruce and the presented results could be an attempt to

quantitatively report such a dependency. It has been found that 90% of new infestations occurred

within 100 m of an earlier infestation spot under epidemic conditions (Wichmann et al. 2001).

However the findings of this master thesis state that the actual risk of die back only increases

substantially in a radius of 20 m in the vicinity of a dead tree, which died due to spruce bark beetle

infestation (Figures 8, 9, 16 and 17).

A further commonality among the two investigated models was crown length. Crown length was a

categorical variable with three levels in both models. If the crown length proportion was > 1/3 and <

2/3 of tree height, the mortality risk was always highest (Figures 8 to 13 and 16 to 19). Crown length

has two major effects in relation to spruce bark beetle development and pressure. First, crown

length is expected to decrease the temperature in the trunk and hence limit the filial beetle

generation, which in turn lowers the beetle pressure overall (Seidl et al. 2007). Second, a bigger

crown increases the availability of carbon, which could be allocated into a better defensive system

and decrease tree susceptibility (Jakuš et al. 2011). According to these findings we would expect that

trees with the shortest crowns have the biggest mortality risk, which would agree with the plant

stress hypothesis (Seidl et al. 2011). However it could be shown in the results that, if predicted over

all the different continuous variables, trees with a crown length around half the tree size are

expected to die back more frequently, which could be partially in accordance with the plant vigor

hypothesis (Price 1991). The beetles change their strategy from a safety to a risk strategy, where in

comparison to the former, more vital trees are infested (Boone et al. 2011). But obviously the link

between different definitions of vitality is not constant, dependent on whether the tree in the

sample was dead or alive (Figure 6). Vitality defined by growth related measures should be treated

differently than crown related vitality measures.

The two models both included discoloration. It had a stronger effect in the second model 1158. But

in every prediction made for the other independent variables, discoloration increased the risk of die

back by moving the curves in Figures 8 to 13 and 16 to 19 upwards, which indicates a higher risk.

Discussion

32

Generally trees, which failed to stop beetles from penetrating into the sapwood with resin ducts, get

infested by their symbiotic fungi. Thus follows the hypersensitive wound reaction, which is stronger

in more vigorous trees than in suppressed ones. This reaction depletes the carbohydrate reservoir of

the tree, causing more successful penetrations by spruce bark beetle, which could cause a positive

feedback loop and hence a tree to die quickly (Christiansen et al. 1983). Therefore including this

predictor in a risk estimation model, like the one presented in this master thesis, may be

problematic, if classifying a still living tree as endangered depends strongly on this predictor.

Deviating from the first model, the second best scoring model 1158 included DBH as a predictor and

vice versa model 11809 included tree height as a predictor. DBH had a positive effect on mortality

risk. After a windthrow trees were reported to be more frequently attacked, if the stem diameter

increased (Göthlin et al. 2000). But because DBH and tree height are in an allometric relationship for

spruce (Mehtätalo 2004), it is possible to interpret the separate presence of those variables in the

two models as a result of this correlation and both factors could be equally important, when

predicting tree mortality by spruce bark beetle attack. But since the sample was paired according to

DBH, it is possible that the presence of these variables is an artifact due to the reduction of the

sample size, if different variables were included in the global model (Table 3).

In addition, model 11809 included slope as a predictor variable of tree mortality. The steeper the

terrain was, the more likely a tree died. Slope is known to influence the formation and water supply

processes in the soil. In steeper slopes, soil erosion happens more frequently and run off below the

surface tends to be higher. The mass transport beyond the soil surface is more horizontal, if the slope

is steeper (Blume et al. 2009). The results for model 11809 (Figures 12 and 13) indicate that beyond a

slope of 25%, the mortality risk increases substantially for trees with crown length > 1/3 and < 2/3. If

discoloration is present, it increases earlier. If we imagine the sampled trees standing on differently

steep slopes, the trees on steeper slopes may be affected by less water availability and more washed

out soils, because of the horizontal mass transport. Such small differences in resource availability

may influence mortality risk by spruce bark beetle attacks after a windthrow as indicated by the

results from model 11809.

Two classification rules were used in this master thesis. Both indicated excellent discriminatory

abilities, i.e. the AUC is greater than 0.8 (Hosmer et al. 2004). However there are several

shortcomings of the models and their formulation. Although the Hosmer – Lemeshow test has been

criticized recently, especially in the presence of outliers in the covariates and the arbitrary group size

selection (Hosmer et al. 1997), it was still used to compare the inferred models among each other.

The presented models 11809 and 1158 had both p – values < 0.05, which means that the model fit is

relatively bad and interactions among the independent variables are needed, when formulating the

global models. An interaction between basal area and the distance to the nearest dead tree could be

possible. It seems intuitive that, if the local stand density is higher, it is also more probable for a tree

to be located near another dead tree than if local stand density is very low. However, if looking at the

residual deviance at the given degrees of freedom for both models, 11809 and 1158, the data could

emanate from these models respectively (Section 9.2).

The third inferred model 203 resulted from global model 3 (Section 9.2). The AUC was 0.9286. The

Hosmer – Lemeshow test for this model had a p – value of 0.8385, which indicated that the model fit

was better than in the two first models. The two new variables exposition and shading towards south

and the continuously measured crown length did not have a significant effect on mortality as

opposed to models 11809 and 1158. They were all not included in the inferred model 203. Obviously,

if measured as a continuous variable, crown length varied too little between dead and living tree and

the inclusion of crown length as a categorical variable was more meaningful for an assessment of

mortality risk by spruce bark beetles. In addition the model included bark thickness as a predictor for

Discussion

33

a decrease in mortality risk, if bark thickness increases. But once spruce bark beetles penetrate the

bark, it could actually shelter the brood from winter desiccation and parasitoids (Kostal et al. 2011).

This could also be the case in Uaul Prau Nausch, since the European spruce bark beetle has been

found more frequently in trees with a thicker bark than other bark beetle species (Grunwald 1986).

But it has been reported that bark thickness still aids to repel boring attempts (Wermelinger 2004).

The other variables of the inferred model 203 are in accordance with the two previous models 11809

and 1158.

Although model 11809 had the lowest AICc score among the inferred models, its relative support by

the Akaike weight was relatively low (Table 9). Also the AICc scores were very similar over a wide

range of models (Section 9.2), which means that other models up to a ΔAICc of 2 should be

investigated too. The low relative support may be due to the large number of candidate models,

which were derived from the 14 variables in the global model. Also it needs to be mentioned that the

assessment of the models by AUC could be overestimated, because resubstitution was used and it is

known to yield too optimistic results (Fielding et al. 1997). Attention should also be payed, when

looking at the predicted probabilities dependent on model variables (e.g. Figures 10 and 11).

Especially at extreme and hypothetical values like e.g. tree height of 0 m, the model still predicted a

mortality of almost 25 %, if the tree had medium crown length and discoloration was present. This is

due to the fact that the range of measured tree heights never included 0 m and the model fit is bad

and therefore the uncertainties of prediction are quite high outside the known range of data.

5.2 Spatial projection In Uaul Prau Nausch the infestation pattern followed two main directions. One tended to develop

towards southwest and one towards north. In the die back wave of 2013, one year after the

windthrow, the spruce bark beetles migrated out of the windthrow area for the first time. Bark

beetles were reported to be able to disperse around 500 m by their own (Wermelinger 2004), so the

cluster with the first dead trees from 2013 was within range. Since the storm took place in spring

2012, the population had time to infest many downed trees during the mating and oviposition period

in 2012, which changed the population level from endemic to epidemic in 2013, when much more

beetles emerged from the downed trees. Since temperatures in the subalpine zone are low and the

vegetation period is shorter than at lower elevations, spruce bark beetles do not recruit more than

one generation at the elevation of Uaul Prau Nausch, because a lot of aspects like swarming, larval

development etc. are dependent on higher temperatures (Nierhaus-Wunderwald et al. 2004).

Because the first generation after overwintering swarmed very directional towards southwest, many

trees were infested and died back in a very dense cluster at the southwestern edge of the windthrow

area (Section 9.1). Such high population pressures could lead to shorter maternal galleries and thus

reduced oviposition (Wermelinger 2004). This intraspecific competition through elevated population

density could have led to the recruitment of sister broods (Wermelinger et al. 1999). These could

have been established in the trees of the first cluster, which developed outside the windthrow area

towards southwest. Lying dead wood could be used up to two years by spruce bark beetles (Forster

et al. 2010). The huge number of standing trees dying of spruce bark beetle infestation in 2014 is

therefore still partially enhanced by beetles emerging from downed trees. The 2014 wave had its

main focus at the northern edge of the windthrow area and two new clusters emerged in this year. In

some of these clusters lying dead wood could also be found. This change in direction seems random.

Beetle dispersal is influenced by wind direction and pheromone sources. Since the infestation in 2014

occurred mostly at the northern edge of the windthrow area, it is possible that the southward

exposed stems were stressed by higher income of solar radiation after the windthrow in 2012, which

could make them prone to attacks by exudation of attracting pheromones from the bark (Nierhaus-

Wunderwald et al. 2004). Similar processes as mentioned above could have driven the spruce bark

beetles to migrate northwards. The only four trees which died after 2014 were in the northern part

Discussion

34

of the windthrow area and could be leftovers in the vicinity of the die back wave in 2014. In a

temporally large-scale study it has been reported that the movement of focal points of spruce bark

beetle infestation can change from undirected to directed during an outbreak and that it can be

influenced by wind or a variation in dispersal abilities among individuals (Lausch et al. 2013). The

relatively huge number of trees observed in this master thesis, which died before the foehn storm in

2012, could have been caused by either an increased mortality of spruces even at an endemic spruce

bark beetle population level, or due to the inclusion of problematic cores for the spatial projection,

as mentioned in Section 3.4, i.e. cores with many missing rings.

A major die back wave occurred one and two years after the windthrow. It is expected that one

growing season after a windthrow, the spruce bark beetle population size massively increases after

excessive reproduction in downed spruces. This caused the first die back wave in 2013. Afterwards,

natural enemies, intraspecific competition and a decrease in the quantity and quality of suitable

breeding material cause the exponential growth to start decreasing. If enough breeding material is

available, the outbreak could still continue for several years (Forster et al. 2003). In Uaul Prau Nausch

it seems that the outbreak reached its peak in 2014, when 44 (43%) of all spatially surveyed dead

trees died. The only significant differences between the trees of the two die back years was basal

area around the tree and towards south, which were higher in the 2014 die back wave (p – values of

0.019 and 0.047 respectively). This may reflect, that the two new clusters in the north were mostly

containing trees from the 2014 die back wave, where no adjacent windthrow area existed. The two

minor die back events in 2015 and 2016 should be handled with care, because the sample size in the

2016 campaign was smaller than in the 2015 campaign (Table 1) and maybe more trees, which died

in 2015 and 2016 would have been recorded, if the sample size was larger.

Conclusions

35

6 Conclusions This master thesis resulted in the formulation of three different classification rules, which were

based on different datasets respectively. Differences in the datasets were the available sample size,

the number of predictors and data structure. Mortality risk was assessed for Norway spruces in the

subalpine zone after a windthrow and a subsequent spruce bark beetle outbreak. In this setting all

three models point out the importance of tree size related variables like tree height or DBH, the

distance to the nearest dead tree and whether discoloration in the wood is present or not. When

assessing individual tree mortality risk in a spruce bark beetle outbreak after a windthrow, these

variables should definitely be taken into account. Although tree height and DBH might be artifacts.

Further important determining factors are crown length, slope and bark thickness, as pointed out by

the individual models (Section 9.2). These variables did not appear in all three models

simultaneously, but were of importance in the respective models and should be included, if using the

respective classification rule.

The models did not include any interaction terms and hence the model fit was bad. Further

investigation on such interactions is needed to improve the model fit. This could cause the models to

predict more accurately outside of the known range of data, which was used to fit the models. But

the discriminatory power of all models was quite high. An external validation of the models

formulated in this master thesis should be carried out anyway in future research about the outbreaks

of spruce bark beetles in spruce dominated forests of the subalpine zone. A further validation could

be done, using the trees from the third condition category, infested but living, and predict their

mortality with one of the models. In the long term it could be verified, if the trees died from spruce

bark beetle infestation or not, by revisiting the trees each following year.

From the results of the spatial projection it can be concluded that the calamity in Uaul Prau Nausch is

in its declining phase (Figure 21), although it needs to be pointed out that the sample size in the 2016

campaign was smaller. Measures should be taken within 20 m around dead trees, which surround

the windthrow area or died in a cluster. Water stressed trees occur more frequently at the northern

edge of a windthrow area on a south facing slope, but the direction of infestation away from the

windthrow area in the first year after the windthrow might be random.

In this study, no climatic influence was included. Wind and temperature do have a tremendous effect

on the spread and development of spruce bark beetles and should be considered in future research.

But on such a small scale of individual trees, the influence of such variables is hard to determine.

Under current climate change subalpine spruce dominated forests might see an increase in spruce

bark beetle outbreaks, because increasing temperatures favor the development of epidemic

population levels by increasing the number of generations per year and increasing the susceptibility

of spruces (Netherer et al. 2010). This stresses the need for such small scale mortality risk

assessment models in the future.

Acknowledgements

36

7 Acknowledgements First of all I would like to thank Dr. Christof Bigler and Luzia Götz from the Chair of Forest Ecology at

ETH Zürich for their supervision. This work was offered and very well assisted by them and their ideas

and inspiration were a driving force. I would like to thank Dr. Christof Bigler for his help in the

statistics and the implementations in the R software and Luzia Götz for her help in all the technical

related problems and difficulties in the field. Without their assistance, this master thesis would not

have been possible. Thanks also to Magdalena Nötzli for her instructions during the measurement of

the cores and to the whole Forest Ecology group for their support and the great time. Also I want to

thank my family, relatives and friends for supporting me during these six months, by helping me to

endure all difficulties and always encouraging me to achieve my goal. My brother, Pascal Opiasa, I

especially want to thank for helping me measuring the cores. Also I want to thankfully mention the

tremendous help in Sedrun by Florian Denzinger and Benjamin Seitz, who endured wind and rain in

the field with me. Considering the fieldwork, I also want to thank the ETH for supporting this master

thesis financially by carrying the expenses for the fieldwork.

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37

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Appendix

41

9 Appendix

9.1 Appendix 1: Windthrow and cluster close ups

Fig

ure

23

: Sp

ati

al d

istr

ibu

tio

n o

f d

ead

tre

es w

hic

h d

ied

bef

ore

th

e fo

ehn

sto

rm in

20

12

an

d in

th

e c

onse

cuti

ve s

pru

ce b

ark

bee

tle

ou

tbre

ak

fro

m 2

01

2 t

o 2

01

6

in t

he

win

dth

row

are

a. T

he

nu

mb

ers

an

d t

he

rela

ted

co

lors

in t

he

leg

end

ind

ica

te t

he

tree

s w

ith

a c

om

mo

n y

ear

of

dea

th (

Ba

se m

ap

Sw

issi

ma

ge\

swis

sim

ag

e_2

5cm

_20

16

© 2

01

6 S

wis

sto

po

).

Appendix

42

Figure 24: Spatial distribution of dead trees which died before the foehn storm in 2012 and in the consecutive spruce bark beetle outbreak from 2012 to 2016 in the southwestern cluster. The numbers and the related colors in the legend indicate the trees with a common year of death (Base map Swissimage\swissimage_25cm_2016 © 2016 Swisstopo).

Figure 25: Spatial distribution of dead trees which died before the foehn storm in 2012 and in the consecutive spruce bark beetle outbreak from 2012 to 2016 in the first northern cluster. The numbers and the related colors in the legend indicate the trees with a common year of death (Base map Swissimage\swissimage_25cm_2016 © 2016 Swisstopo).

Appendix

43

Figure 26: Spatial distribution of dead trees which died before the foehn storm in 2012 and in the consecutive spruce bark beetle outbreak from 2012 to 2016 in the second northern cluster. The numbers and the related colors in the legend indicate the trees with a common year of death (Base map Swissimage\swissimage_25cm_2016 © 2016 Swisstopo).

Appendix

44

9.2 Appendix 2: Model details

Mo

de

l Nr.

(In

terc

ep

t)B

AI1

SAB

AI5

SAB

HD

Bo

rDca

geD

ist

fau

lG

sud

Gto

tH

oe

KrL

Ne

igSc

had

en

Ve

rfar

bd

flo

gLik

AIC

cd

elt

aw

eig

ht

1180

9-5

.788

7552

6N

AN

AN

AN

AN

A-0

.568

93N

AN

AN

A0.

0940

01+

0.06

9511

NA

+7

-36.

9175

89.1

6842

00.

1125

82

1193

7-5

.257

4678

42N

AN

AN

AN

AN

A-0

.640

77N

A-0

.033

86N

A0.

1063

73+

0.07

4855

NA

+8

-35.

8192

89.3

7341

0.20

4986

0.10

1614

1603

3-6

.382

3609

56N

AN

AN

AN

AN

A-0

.641

46N

A-0

.043

62N

A0.

1200

12+

0.09

747

++

10-3

3.48

0789

.677

360.

5089

410.

0872

88

1194

0-6

.117

7694

79-2

.748

491

0.71

6987

NA

NA

NA

-0.7

6627

NA

-0.0

4322

NA

0.10

7189

+0.

0916

15N

A+

10-3

3.73

6590

.189

051.

0206

280.

0675

84

1590

5-6

.795

0416

32N

AN

AN

AN

AN

A-0

.555

7N

AN

AN

A0.

0982

41+

0.09

0819

++

9-3

5.00

2990

.200

91.

0324

830.

0671

84

1130

1-4

.468

4627

96N

AN

A0.

0481

28N

AN

A-0

.585

33N

AN

AN

AN

A+

0.06

0981

NA

+7

-37.

503

90.3

3937

1.17

095

0.06

269

1206

5-5

.399

8326

03N

AN

AN

AN

AN

A-0

.633

09N

AN

A-0

.016

540.

1108

27+

0.07

2168

NA

+8

-36.

3059

90.3

4674

1.17

8318

0.06

246

1590

7-8

.002

9708

62N

A0.

1416

52N

AN

AN

A-0

.629

34N

AN

AN

A0.

1195

66+

0.09

9167

++

10-3

3.83

5790

.387

491.

2190

660.

0612

1603

6-7

.783

3963

25-2

.467

537

0.69

911

NA

NA

NA

-0.8

188

NA

-0.0

523

NA

0.12

8926

+0.

1180

77+

+12

-31.

2298

90.4

0899

1.24

0571

0.06

0545

3617

-5.5

9772

1441

NA

NA

NA

NA

NA

-0.5

4629

NA

NA

NA

0.10

0909

+0.

0678

1N

AN

A6

-38.

7444

90.4

7701

1.30

8587

0.05

8521

1603

5-7

.508

4902

87N

A0.

1248

58N

AN

AN

A-0

.708

76N

A-0

.041

01N

A0.

1369

4+

0.10

4642

++

11-3

2.59

1490

.482

791.

3143

680.

0583

52

1181

2-6

.696

5810

23-2

.130

349

0.60

0461

NA

NA

NA

-0.6

5504

NA

NA

NA

0.09

7627

+0.

0799

22N

A+

9-3

5.17

1790

.538

571.

3701

550.

0567

47

1181

1-6

.167

7512

58N

A0.

1004

08N

AN

AN

A-0

.606

16N

AN

AN

A0.

1029

85+

0.06

9632

NA

+8

-36.

4021

90.5

3913

1.37

071

0.05

6731

1181

3-5

.960

5591

05N

AN

A0.

0233

21N

AN

A-0

.587

44N

AN

AN

A0.

0706

15+

0.06

8932

NA

+8

-36.

6578

91.0

5062

1.88

2204

0.04

3929

1182

5-6

.824

3386

34N

AN

AN

AN

A0.

0065

25-0

.578

27N

AN

AN

A0.

0873

23+

0.07

0867

NA

+8

-36.

6892

91.1

1328

1.94

4862

0.04

2574

Tab

le 1

: Fu

rth

er c

an

did

ate

mo

del

s fo

r g

lob

al m

od

el 1

up

to

ΔA

ICc

= 2

. BA

I1SA

= V

it1

, BA

I5SA

= V

it5

, BH

D =

DB

H, B

orD

= B

ark

th

ickn

ess,

ca

ge

= C

am

bia

l ag

e, D

ist

= D

ista

nce

, fa

ul =

H

eart

ro

t, G

sud

= B

asa

l are

a s

ou

th, G

tot

= B

asa

l are

a t

ota

l, H

oe

= Tr

ee h

eig

ht,

KrL

= C

row

n le

ng

th, N

eig

= S

lop

e, S

cha

den

= D

am

ag

e, V

erfa

rb =

Dis

colo

rati

on

.

Fig

ure

27

: Su

mm

ary

ou

tpu

t in

R f

or

mo

del

11

80

9.

Appendix

45

Mo

de

l Nr.

(In

terc

ep

t)B

HD

Bo

rDD

ist

fau

lG

sud

Gto

tH

oe

KrL

Ne

igSc

had

en

Ve

rfar

bd

flo

gLik

AIC

cd

elt

aw

eig

ht

1158

-0.4

2137

9754

0.03

9555

NA

-0.4

5278

NA

NA

NA

NA

+N

AN

A+

6-8

5.95

1518

4.38

850

0.70

5362

1190

-0.0

0169

7834

0.03

8861

NA

-0.4

6497

NA

NA

-0.0

0578

NA

+N

AN

A+

7-8

5.74

1618

6.13

441.

7459

240.

2946

38

Tab

le 2

: Fu

rth

er c

an

did

ate

mo

del

s fo

r g

lob

al m

od

el 2

up

to

ΔA

ICc

= 2

. BH

D =

DB

H, B

orD

= B

ark

th

ickn

ess,

Dis

t =

Dis

tan

ce, f

au

l = H

eart

ro

t, G

sud

= B

asa

l are

a s

ou

th, G

tot

= B

asa

l are

a t

ota

l, H

oe

= Tr

ee h

eig

ht,

KrL

= C

row

n le

ng

th, N

eig

= S

lop

e, S

cha

den

= D

am

ag

e, V

erfa

rb =

Dis

colo

rati

on

.

Fig

ure

28

: Su

mm

ary

ou

tpu

t in

R f

or

mo

del

11

58

.

Appendix

46

Mo

de

l Nr.

(In

terc

ep

t)B

AB

ark

BA

SC

olo

rC

row

nD

amag

eD

BH

Dis

tan

ceEx

po

siti

on

Gra

die

nt

HR

ot

Shad

ingS

df

logL

ikA

ICc

de

lta

we

igh

t

203

0.47

1976

594

NA

-0.4

5733

NA

+N

AN

A0.

1516

42-1

.120

879

NA

NA

NA

NA

NA

5-1

7.37

3845

.924

020

0.19

8478

1227

-0.0

6223

9596

NA

-0.4

8496

NA

+N

AN

A0.

1160

53-1

.207

5372

NA

NA

0.08

6794

NA

NA

6-1

6.67

6247

.032

51.

1084

780.

1140

27

1675

-2.3

8605

046

NA

-0.3

9983

NA

+N

AN

AN

A-1

.481

8256

NA

0.07

0448

030.

1627

39N

AN

A6

-16.

8383

47.3

5667

1.43

2653

0.09

6965

459

-2.5

0971

4039

NA

-0.5

1573

NA

+N

AN

A0.

1918

28-1

.001

5286

0.01

6771

543

NA

NA

NA

NA

6-1

6.85

4647

.389

261.

4652

430.

0953

98

715

-1.1

1432

7451

NA

-0.5

1935

NA

+N

AN

A0.

1549

32-1

.225

6003

NA

0.03

8708

27N

AN

AN

A6

-16.

9036

47.4

8715

1.56

3131

0.09

0841

4299

0.44

8432

357

NA

-0.4

5219

NA

+N

AN

A0.

1336

19-1

.186

1884

NA

NA

NA

NA

0.04

5890

686

-16.

949

47.5

7809

1.65

4072

0.08

6803

207

-0.4

6946

0589

NA

-0.4

7847

0.03

189

+N

AN

A0.

1481

06-0

.990

3185

NA

NA

NA

NA

NA

6-1

6.96

3747

.607

411.

6833

940.

0855

4

1739

-2.7

0898

7479

NA

-0.5

8782

NA

+N

AN

A0.

1036

73-1

.402

3552

NA

0.06

0697

280.

1217

9N

AN

A7

-15.

7418

47.7

6935

1.84

5326

0.07

8887

204

-0.4

7771

9172

0.01

9116

-0.4

705

NA

+N

AN

A0.

1448

5-1

.002

8003

NA

NA

NA

NA

NA

6-1

7.06

647

.812

091.

8880

690.

0772

19

1163

0.90

6704

42N

A-0

.262

65N

A+

NA

NA

NA

-1.2

6354

91N

AN

A0.

1297

51N

AN

A5

-18.

3358

47.8

4806

1.92

4041

0.07

5842

Tab

le 3

: Fu

rth

er c

an

did

ate

mo

del

s fo

r g

lob

al m

od

el 3

up

to

ΔA

ICc

= 2

. BA

= B

asa

l are

a t

ota

l, B

ark

= B

ark

th

ickn

ess,

BA

S =

Ba

sal a

rea

so

uth

, Co

lor

= D

isco

lora

tio

n, C

row

n =

Cro

wn

len

gth

, H

= Tr

ee h

eig

ht,

Ro

t =

Hea

rt r

ot,

Sh

ad

ing

S =

Sha

din

g t

ow

ard

s so

uth

.

Fig

ure

29

: Su

mm

ary

ou

tpu

t in

R f

or

mo

del

20

3.

Appendix

47

9.3 Appendix 3: COFECHA outputs

Appendix

48

Appendix

49

Appendix

50

Appendix

51

Appendix

52

Documents

Research Collection50457/et… · Luzia Götz, ETH Zürich . Title page: View from the edge into the windthrow area facing east. ... development of the larvae is strongly temperature