Simulating bark beetle population dynamics in response to windthrow events

Ecological Complexity 32 (2017) 21–30

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Original Research Article

Simulating bark beetle population dynamics in response to windthrow events Mária Potterfa,* , Christopher Boneb a b

Institute of Forest Ecology, Slovak Academy of Sciences, Ludovíta Štúra 2, 960 53 Zvolen, Slovak Republic Department of Geography, University of Victoria, Victoria, BC V8W 2Y2, Canada

A R T I C L E I N F O

Article history: Received 29 January 2017 Received in revised form 23 August 2017 Accepted 29 August 2017 Available online xxx Keywords: IPS Windthrow Bark beetles Agent-based model Disturbance interaction

A B S T R A C T

The relationship between windthrow disturbance and outbreaks of European spruce bark beetle Ips typographus L. in European Norway spruce forests has been the focus of recent studies. However, the nature in which the spatial characteristics of windthrow events influence bark beetle population dynamics is rarely examined. This represents a significant gap in the literature, as our understanding of how spatial windthrow patterns influence bark beetles can be useful for management efforts to help mitigate large-scale bark beetle disturbance. The objective of this study is to simulate how windthrow events facilitate bark beetle population state transitions from endemic and epidemic levels using a spatially explicit agent-based model. We examined how the spatial extent of windthrow events and the size of tree clusters impacted by windthrow influence this state transition. The results show that the beetle population transition slows with increasing spatial extent of a windthrow event and with larger clusters of windthrown trees, while scattered patterns of windthrown trees accelerate the timing of this transition. This study contributes to our understanding of the role of large-scale wind disturbance in European bark beetle outbreaks. Moreover, it provides a basis for further research to discover the impact of potential forest management applications aiming to mitigate the risk of bark beetle outbreaks. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Wind disturbance plays a significant role in shaping Norway spruce Picea abies (L.) Karst. forest ecosystems in central and northern Europe (Kuuluvainen et al., 2014; Panayotov et al., 2011). Severe wind events lead to tree mortality, resulting in gaps in the forest canopy that encourage the growth of younger unaffected trees. At the same time, wind events can change the composition of the forest by facilitating large-scale outbreaks of bark beetles, such as the European spruce bark beetle (ESB) Ips typographus L. (Christiansen and Bakke, 1988; Marini et al., 2013; Økland and Berryman, 2004). Native to spruce forests in Europe and Asia (Wood and Bright, 1992), the ESB typically occurs in low (endemic) population numbers where it attacks unhealthy trees in order to reproduce. The low number of compromised trees constrains beetle population numbers; however, after a windstorm, beetles have a greater number of available compromised trees to infest (Göthlin et al.,

* Corresponding author. E-mail addresses: [email protected] (M. Potterf), [email protected] (C. Bone). http://dx.doi.org/10.1016/j.ecocom.2017.08.003 1476-945X/© 2017 Elsevier B.V. All rights reserved.

2000; Schroeder and Lindelöw,2002). In the year following a windstorm, beetles almost exclusively infest windthrown trees (Göthlin et al., 2000). This leads to higher reproductive success and increased population numbers, but at the same time depletes available hosts (Økland and Bjørnstad, 2006). The combination of increased population numbers and depletion of breeding materials can force beetles to attack healthy, living trees (Bouget and Duelli, 2004; Schlyter and Anderbrant, 1989), typically starting in the second year after a wind disturbance event (Göthlin et al., 2000; Kärvemo et al., 2014; Schroeder and Lindelöw,2002). At this point, beetle populations transition to an epidemic state in which widespread tree mortality ensues (Christiansen and Bakke, 1988). The nature in which windthrow events lead to a state transition between endemic and epidemic beetle populations is a complex process guided by multi-scale interactions between insects and host trees, leading to landscape-level patterns of forest cover change. Until recently, the spatial scalar divide in methods for examining spruce beetles and windthrow has challenged our ability to investigate the complexity of the relationship between these two disturbance agents. On the one hand, there is a depth of micro-scale research related to beetle physiology, including life cycle development (Sauvard, 2004), timing of beetle emergence from host trees and subsequent dispersal behaviour (Botterweg,

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1982; Byers and Lofqvist, 1989; Öhrn, 2012; Zumr, 1992), reproduction (Wermelinger and Seifert, 1999), lifespan (Austara and Midtgaard, 1986), and chemical communication between beetles (Byers, 2004; Sun et al., 2006). On the other hand, there exists substantial landscape-scale research based on observations of windthrow severity and beetle-induced tree mortality (Kärvemo et al., 2014; Økland and Bjørnstad, 2006; Schroeder and Lindelöw, 2002; Wermelinger et al., 2002). Yet, minimal research exists that directly explores how individual beetle physiology and beetle-host interactions collectively influence the landscape-scale patterns of beetle-induced tree mortality resulting from windthrow events. Agent-based modelling (ABM) provides an opportunity to explicitly represent spruce beetle physiology and how interactions between beetles and host trees lead to emergent patterns of tree mortality in post-windthrown landscapes. Beetles, either individuals or collections of beetles, can be represented as a single agent that interacts with trees, as represented by cells in a grid. ABM can simulate windthrow by specifying time steps at which tree resistance is diminished, subsequently decreasing the number of beetles required to infest a tree. The resulting increase in beetle population numbers acts as a catalyst for a state transition between endemic and epidemic populations. ABM can therefore serve as an approach to understanding how the characteristics of wind events facilitate epidemics. Previous studies have demonstrated the utility of ABM for simulating specific characteristics of ESB population dynamics. Examples include examining how variations in individual beetle traits impact subsequent tree mortality during a single generation (Kautz, 2016; Kautz et al., 2014), and estimating

the level of forest management activities required to mitigate outbreaks (Fahse and Heurich, 2011). Additionally, Kausrud et al. (2011) have used ABM for modelling ESB population dynamics, while inspected the importance of beetle aggregation behaviour in beetle-killed forest patches. This relatively small yet compelling collection of existing research has set the groundwork for conceptualising ESB as agents in a simulation model, and has facilitated an opportunity to explore the role of windthrow events in driving ESB outbreaks. The objective of this study is to evaluate the relationship between windthrow and ESB dynamics in causing emergent patterns of tree mortality using agent-based modelling. The model incorporates existing knowledge of beetle reproduction, mortality, host selection, and beetle–tree interaction in order to better understand how the spatial extent and size of clusters of windthrown trees influence the state transition between endemic and epidemic beetle populations. 2. Methods 2.1. Model description The IPS-wind model developed in this study is an extension of the IPS model (Infestation Pattern Simulation, version 1.0) published by Kautz et al. (2014). The original IPS model simulates I. typographus L. dispersal and infestation patterns within a single generation, over a hypothetical forest stand. Our study modifies this existing model by simulating ESB dispersal and aggregation behaviour, and tree mortality over multiple generations. We

Fig. 1. Simplified model flow chart showing processes, decisions, resulting alternatives, and beetles’ states.

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include annual small-scale and large-scale wind disturbances that permit us to observe emergent system-level patterns of beetle population dynamics, dispersal, and tree mortality, both in and between endemic and epidemic conditions. We developed the IPS-wind model in the NetLogo environment (Wilensky, 1999), a standard modelling tool in agent-based modelling in ecology (Railsback and Grimm, 2012). We provide the complete IPS-wind model version used in this study in Appendix A (Supplementary material). The model description follows the Overview, Design Concepts, and Details (ODD) protocol originally proposed by Grimm et al. (2006) and updated by Grimm et al. (2010). Here we describe the Overview component of the ODD protocol; the Design concepts and Details components are provided in Appendix B (Supplementary material). 2.1.1. Overview 2.1.1.1. Purpose. The purpose of the model is to simulate the interactions between wind disturbance and ESB population dynamics. Specifically, the model simulates how the spatial extent of windthrow, as well as the cluster size (i.e. the size of a group of trees affected by windthrow), influence beetle population size, the shift from attacking windthrown to healthy trees, and how this shift potentially leads beetle populations to change from endemic to epidemic beetle population numbers. Our study offers novel contributions to the literature on ABM of bark beetle simulations by evaluating how the spatial characteristics of one disturbance (windthrow) influence the timing and transition state of a secondary disturbance (ESB outbreak). 2.1.1.2. Entities, state variables, and scales. The model consists of two types of interacting entities: beetles and trees. We employ a ‘super-agent’ approach (Régnière et al., 2015) in which multiple beetles are represented by a single computational agent in the model. In our case, each beetle-agent (referred hereafter as a

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beetle) represents the mean characteristics of 500 I. typographus L. individuals. We used a super-agent approach in this study because the large number of beetles required to simulate the transition between endemic and epidemic levels at the landscape-scale requires substantial computational resources. This approach was proposed by Scheffer et al. (1995) and justified by previous research in simulating similar bark beetle species (Régnière et al., 2015), as well as other applications of agent-based modelling (Hellweger and Bucci, 2009; Parry and Evans, 2008). Each individual beetle is characterised by age (Austara and Midtgaard, 1986), energy (Botterweg, 1982; Byers, 2004), consumption efficiency, perceptual range, and moving angles that determine flight dispersal and host selection. During its lifetime, a beetle passes through consecutive states related to its life cycle: dispersal, host selection, infestation, and reproduction (Fig. 1). A summary of the description of beetle’s state variables is presented in Table 1. An individual tree is represented as a single cell that is characterised by its attractiveness, level of infestation by beetles, health state, minimal resistance, and maximum carrying capacity. Total attractiveness of the tree is the sum of primary and secondary attractiveness. Primary attractiveness represents the release of chemicals called monoterpenes, where weak trees emit more monoterpenes then the healthy ones (Erbilgin et al., 2007). Secondary attractiveness represents the aggregation pheromones emitted by attacking beetles to facilitate a collective beetle attack (Berryman, 1982; Sun et al., 2006). If a tree is fully occupied by beetles, its total attractiveness decreases to zero, and the tree dies. This represents a density-dependent communication strategy in which beetles emit a repellent chemical that causes additional beetles to avoid the tree when the tree’s maximum carrying capacity is reached (Byers, 1989; Schlyter et al., 1989). Tree resistance represents the minimum number of collectively attacking beetles required to surpass a tree’s defences. Maximum carrying capacity defines the physical limitation of the tree to

Table 1 List of beetle’s state variables. Variables are fully adopted (***), adopted and modified (**) from the IPS model of Kautz et al. (2014), or developed for the IPS-wind model (*). AUM: abstract unit of measurement. Variable

Description

Energy level energy***

Energy level assigned to every beetle (for the initial setting and for newly 3 < energy < 30 AUM born beetles); energy is chosen randomly for each individual from a population-specific distribution and linearly reduced during dispersal flight

Consumption efficiency

Determines energy consumption during dispersal flight, related to 1 time 1 < efficiency < 100 AUM step (consumption = 1/efficiency); chosen randomly for each individual from a population-specific distribution

Range, limitation, calculation

efficiency*** State state**

Current status of the beetle may vary over the course of the simulation

disperse: ability of dispersal flight and search for suitable host attack: beetle lands on tree and waits for sufficient number of conspecifics to collective attack with aim to overpass tree resistance, beetle can die due to tree resistance reproduce: beetle may reproduce after 1 generation, simulating the length of offspring development mortality: beetle dies due to age, post-reproduction or due to tree resistance

Age birth-tick*

Time of beetle's birth, define the length of beetle's life

2 * generation time (2 * 150 = 300 time steps = 1 growing season)

Dispersal time t_dispers*

Time length of beetle's dispersal

0 < t_dispers < 150 time steps

Dispersal distance flightdist***

Cumulative beetle's dispersal distance

0 < flightdist < 3000 patches (3000 patches correspond to 15000 m)

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Table 2 List of tree’s state variables. Variables are fully adopted (***), adopted and modified (**) from the IPS model of Kautz et al. (2014), or developed for the IPS-wind model (*). AUM: abstract unit of measurement. Variable

Description

Range, limitation, calculation

Primary attractiveness primattract**

Monoterpenes emitted by host trees, weakened trees emit higher quantities of monoterpenes then healthy trees

1–8 AUM

Low attractiveness = 1 (healthy) High attractiveness = 8 (windthrown)

0 if nrepr = nmax

Secondary attractiveness secattract**

Aggregation pheromones released by attacking beetles in order to attract conspecific to facilitate a mass attack.

0.1 * nattack + 0.1 * nrepr

Secondary attractiveness is additive to primary attractiveness during a simulation; increased by number of attacking 0 if nrepr = nmax beetles in attack or reproduce state

Total attractiveness totalattract***

Sum of primary and secondary tree attractiveness; increases while tree is infested by beetles, decreases to 0 while tree primattract + secattract is fully occupied by beetles 0 if nrepr = nmax

Infestation level

Current tree status reflecting the number of attacking beetles per tree; may vary over the course of simulation

Infestlev**

non-infested: nattack < nmin infested: nmin< nrepr < n max

dead: nrepr = nmax Health status of the tree, indicating if the tree was impacted by large-scale disturbance or not

healthy: primattract < 4 AUM windthrown: primattract = 8 AUM

Maximum carrying capacity nmax***

Maximum carrying capacity of the tree, same for healthy and windthrown trees

10 AUM

Minimal resistance nmin**

Minimum number of beetles necessary for a successful collective attack, various for healthy and windthrown trees nmin< nmax nmin = nmax

Health state health_status*

primattract

Beetles in attack state Number of attacking beetles in attack state per tree, vary over the simulation run nattack**

nattack 2 nmin

Beetles in reproduce state nrepr*

nmin < nrepr < = nmax

Number of attacking beetles in reproduce state per tree, vary over the simulation run

support beetle breeding (Raffa and Berryman, 1983). A summary of the description of tree’s state variables is presented in Table 2. The model operates on a cellular grid of 101 101 cells representing a total area of 25.5 ha, in which one cell represents a single Norway spruce tree with an extent of 5  5 m. We parameterised time based on the number of time steps required to complete a single beetle generation (i.e. dispersal flight and host selection). We determined that one generation is represented as 150 time steps. ESB has two generations per growing season and hibernates over the winter (Sauvard, 2004). We omitted the process of overwintering; two growing seasons thus represent a single year (i.e. 300 time steps). The temporal extent of the model is 3000 time steps, representing a time span of 10 years. 2.1.1.3. Process overview and scheduling. Fig. 1 depicts the life cycle of a beetle. The simulation run starts with beetles in the disperse state, in which a beetle performs a correlated random walk (Byers, 1996). A beetle’s energy decreases linearly in relation to its consumption efficiency and the distance over which it disperses (Atkins, 1969). While dispersing, a beetle senses the total attractiveness of the trees within its perceptual range. Decreasing the energy level of the beetle increases the likelihood of beetle attacking the attractive tree (Byers, 2004). Host selection occurs if a beetle’s energy value drops below the total attractiveness of the most attractive tree within the beetle’s perceptual range. Otherwise, the beetle dies due to energy depletion.

The beetle moves directly towards the selected host tree and attacks it. The beetle verifies if the tree’s resistance has been overcome. If it has not been overcome, the beetle enters the infestation process and switches to attack state. It waits for conspecifics (additional beetles) for half of its generation time in order to allow additional beetles to come and collectively attack the tree. If a sufficient number of conspecifics joins the attacking beetle, it switches to the reproduce state, in which it produces progeny and then dies. Otherwise, the tree’s defences kill the beetle before it is able to reproduce. Every tree starts in a non-infested state, and potentially encounters a number of attacking beetles in the attack and reproduce states in each time step. A tree switches from the noninfested to the infested state if its minimal resistance has been overcome by the number of beetles in the attack state. A tree in the infested state may house additional attacking beetles until the point at which it is fully occupied. Synchronously, tree secondary attractiveness and total attractiveness increase each time step, along with the number of beetles in the attack and reproduce states. When the tree is fully occupied by beetles in the reproduce state (i.e. its maximum carrying capacity is reached), its total attractiveness decreases to zero and the tree enters the dead state. Fig. 2 shows the interaction between attacking beetles and the attractiveness of a host tree. Beetle variables are updated first, followed by the tree variables. A simulated windthrow disturbance reduces a tree’s minimal resistance and increases its primary attractiveness. We simulated

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Fig. 2. Schematic diagram of the dynamic interactions between two dispersing beetles and total host tree attractiveness varying from (i) non-infested, (ii) infested to (iii) dead state. The red beetle starts with a higher energy level but is less efficient in its consumption than the blue one. This allows beetles in our example attack the same tree. Tree attractiveness is (i) stable in non-infested state, (ii) increases when localised and attacked by beetles, and (iii) decreases to zero when maximum tree carrying capacity has been reached (based on Kautz et al. (2014), modified). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

two levels of disturbances: annual (small-scale) and wind (largescale) disturbance. Annual disturbance affects a small number of random trees in the forest stand every year (300 time steps) that mimics the usual conditions within a stand where a scattered number of less resistant trees are always present, whereas largescale wind disturbance affects a large number of trees once per simulation run (3000 time steps). Wind disturbances take place at the beginning of a growing season, allowing beetles to benefit from the disturbance. Each tree can be disturbed only once per simulation run. The simulation starts on the endemic level with low beetle population numbers, sustained by annual disturbances. The epidemic increase of the beetle population is not explicitly modelled; instead, it emerges from the large-scale wind disturbance and the greater number of available low-defence breeding material.

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We recorded multiple system-level responses. Peak beetle population represents the maximum number of beetles at a specific time. During the epidemic phase, beetles infest healthy trees (Økland et al., 2016; Wermelinger, 2004); therefore, we considered the shift from infestation of windthrown to healthy trees as the transition from the endemic to epidemic population state. We identified two thresholds in the transition phase: (1) the moment when the first healthy trees are infested, and (2) the moment when the infestation of windthrown and healthy trees is equal. Dispersal distance represents the distance a beetle has overcome during dispersal, and the dispersal time is the length of dispersal in time steps. Mean and maximum dispersal distances and mean dispersal time were recorded per beetle population. Beetle aggregation (i.e. number of beetles per windthrown tree) was recorded during two years after a windthrow event. A full factorial sensitivity analysis was performed with 30 repetitions for 3000 time steps. 3. Results 3.1. Model evaluation Beetle populations declined during the first generation in approximately 30% of simulation runs, regardless of the presence of wind disturbance. The decline of the beetle population can be attributed to stochasticity in energy and consumption efficiency affecting beetle dispersal, and to location of the annually disturbed trees. Otherwise, the model fully replicated the fluctuation of beetle numbers due to natural birth and death rates, as would be expected under the endemic conditions. In such conditions, the number of weakened trees remained scarce, and beetle populations experienced an exponential increase due to the higher number of windthrown trees (Fig. 3).

2.2. Simulation experiments and system-level responses We designed a simulation experiment framework to first verify that the model was able to produce relatively stable endemic beetle population sizes in the absence of windthrow disturbance, as well as producing endemic population numbers when wind disturbance was included. The evaluation procedures involved 1000 repetitions with a temporal extent of seven years (2100 time steps). Secondly, we conducted a full factorial sensitivity analysis to identify the impact of various large-scale windthrow scenarios, characterised by a combination of extent and cluster sizes (Table 3), on selected system level responses. The spatial pattern of wind disturbance varied over simulation runs to exemplify the variability of windthrow events on terrain conditions. Hereafter, we use the terms extent and cluster size to denote the spatial pattern of windthrow disturbance per simulation run.

Fig. 3. Impact of absence (black, solid line) and presence (red, dashed line) of windthrow on dynamics of beetle population size (windthrow scenario: extent 5%, cluster size 500). Peak beetle population is not shown. The numbers of beetles refer to super-agents (comprising 500 individual beetles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 3 List of parameters and values that were swept across in full factorial sensitivity analysis in the presence of a large-scale windthrow disturbance. Parameter name

Value

Units

Extent Cluster size

5, 10, 15, 20 1, 25, 100, 250, 500

% of windthrown forest number of windthrow trees in a cluster

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Fig. 4. Results from two scenarios demonstrating variability in (a) the timing of peak beetle population, and (b) the timing of transition between endemic and epidemic states in response to different extents and cluster sizes. Solid lines: extent 20%, cluster size 1. Dashed lines: extent 5%, cluster size 500. Timing of large-scale windthrow is marked by red arrow. The numbers of beetles refer to super-agents (comprising 500 individual beetles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.2. Sensitivity analysis 3.2.1. Timing of peak population size and transition state Relatively low numbers of beetles and infested trees were recorded before a large-scale windthrow event (Fig. 4). The infestation of windthrown trees was then observed starting in the first year after windthrow. The preference for infestation of windthrown trees over healthy trees persisted until the third year after the windthrow, followed by an exponential beetle population growth. Subsequently, the increased size of the beetle population facilitated the infestation of healthy trees, which further amplified the size of the beetle population over the next three to four years. This eventually resulted in the depletion of the host tree and subsequent beetle population decline. Windthrow extent influenced the timing of when beetles reached peak population size (Fig. 5). Increasing extent accelerated the timing of peak beetle population by approximately one year for large cluster sizes, and by approximately a third of a year for small cluster sizes. At the same time, the smaller windthrow extent

delayed the time of peak beetle population, but increased peak beetle population size. The transition from endemic state to epidemic state started two to three years after a windthrow event, and lasted approximately one to one and a half years (Fig. 6). Higher windthrow extent postponed the transition to epidemic state by approximately one year. Furthermore, increasing cluster size postponed the beginning and the ending point of that transition. 3.2.2. Dispersal time and distances The results revealed relatively small variability among various combinations of windthrow extent and cluster size on beetle dispersal behaviour (Fig. 7). Yet, the simulation results revealed three distinct observations. First, we recorded variable dispersal distances and time lengths at a low beetle population before windthrow and for approximately one generation after the windthrow. Second, lower and relatively stable dispersal distances and dispersal time characterised beetle dispersal three to four years after windthrow. Finally, after completion of a transition state, dispersal time and distances increased and became highly variable (Fig. 7a), as beetles adapted their search strategy in response to the spatial pattern of trees affected by annual disturbances (Fig. 7b). 3.2.3. Beetle aggregation on windthrown trees The mean number of aggregated beetles per windthrown tree within two years after a wind disturbance decreased linearly with increasing windthrow extent (Fig. 8a). The highest mean beetle aggregation was recorded in cluster sizes up to 25 trees and decreased in larger clusters (Fig. 8b). Windthrow cluster size affected the potential of beetle aggregation, which modified the likelihood of successful collective beetle attack needed to overcome a tree’s resistance. 4. Discussion

Fig. 5. Timing of peak beetle populations by cluster size, in response to different extents and cluster sizes. The numbers of beetles refer to super-agents (comprising 500 individual beetles).

This study has demonstrated that the spatial and temporal characteristics of windthrow disturbance can influence the timing and extent of subsequent beetle outbreaks. The results reveal that increasing windthrow extent increases beetle population size in a non-linear fashion as beetle populations exponentially increase from aggregation on selected trees. We found, however, that beetle aggregation decreases with increasing windthrow extent, which

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Fig. 6. Timing of transition from endemic to epidemic, in response to different extents and cluster sizes. The numbers of beetles refer to super-agents (comprising 500 individual beetles).

Fig. 7. Results from two scenarios demonstrating variability in maximal (dotted, grey line) and mean (solid, black line) dispersal distances and mean dispersal time (dashdoted, red line) in response to different extents and cluster sizes. a) extent 20%, cluster size 1, b) extent 5%, cluster size 500. Timing of large-scale windthrow is marked by red arrow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. Mean number of aggregated beetles per windthrown tree in the two years following a wind disturbance in response to various a) extents and b) cluster sizes. Red dots represent mean values. The numbers of beetles refer to super-agents (comprising 500 individual beetles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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results from dispersing beetles over a larger number of windthrown trees (Fig. 8a). A plausible explanation for the non-linear rise of beetle populations in scenarios with a higher windthrow extent is due to obstructed local beetle aggregation. Large-scale windthrow creates a relatively homogenous area of trees with high attractiveness, which assists beetle dispersal. The capacity of beetles to collectively target a single tree within a specific time is thus restricted. Scattered windthrows (smaller cluster sizes) were shown to accelerate and increase the peak beetle population compared to larger, clumped cluster sizes (Fig. 5). This finding contradicts Eriksson et al. (2007), who considered gap sizes of 20 windthrown trees as not increasing the risk of subsequent tree mortality caused by I. typographus in managed forests. The difference in study results may stem from the different levels of spatial scales used in each study, as our model works on a small scale as 25.5 ha, whereas Eriksson et al. (2007) operated on a landscape scale. Some studies report that the transition between endemic and epidemic states arises from the depletion of available windthrown trees (Bouget and Duelli, 2004; Schlyter and Anderbrant, 1989). In contrast, our results indicate that infestations of healthy trees start in the first year after large-scale windthrow (i.e. before the depletion of windthrown trees; Fig. 4b). Two processes may underlie the infestation of healthy trees while windthrown trees remain available. First, the susceptibility of a healthy tree to beetle attack decreases with increasing distance of the tree from the location of the infestation (Kautz et al., 2011; Lausch et al., 2011). Second, the probability of infestation of a healthy tree increases with a higher number of attacking beetles releasing aggregation pheromones to reinforce a collective attack (Byers, 1996). We argue that during state transition, increases in beetle population size lead to healthy and windthrown trees being approximately equally attractive due to beetle communication strategies. The benefits of beetle infestation shifting to healthy trees are not well understood for the ESB. Studies related to mountain pine beetle (Dendroctonous ponderosae Hopkins), however, discuss the gain of higher nutritional value from infestation of larger, healthier trees (Boone et al., 2011; Six et al., 2014). In our model, we consider the increased synchronisation of beetle emergence from healthy trees as crucial for subsequent tree infestation. Healthy trees have higher resistance, and thus require a higher number of beetles to successful collective attack within a specific time. The temporal synchronisation in attack leads to synchronisation of beetle emergence, which thus further amplifies the increase in beetle population and subsequent tree attack. Our study agrees with previous findings that suggest that the presence of windthrow reduces the length of dispersal time and dispersal distances (Jakuš et al., 2003; Kausrud et al., 2011; Kautz et al., 2011; Hlásny and Tur9 cáni, 2013). Within one year after largescale windthrow, individual beetles require less time to select and infest a suitable host tree, and such a tree is likely close to a beetle’s brood tree. Decreasing dispersal distances and time indicate a more effective process of tree selection, which further accelerates beetle reproduction and growth of the beetle population. Scattered clusters of windthrown trees facilitate beetle aggregation and successful infestation of windthrown trees. Windthrow cluster size is considered as one of the measures of spatial pattern of large-scale windthrow over the real landscape. In our study, we found that the cluster size of 25 trees was the most beneficial for beetle aggregation (Fig. 8b). In contrast, Eriksson et al. (2007) reported that a wind gap of 20 trees does not increase the risk of beetle-induced tree mortality. Information enabling a reliable prediction of local tree mortality based on the size of storm gaps would be highly valuable from the management perspective (Kärvemo et al., 2014). Hence, our results provide a base for

additional research to define a threshold value delimiting the cluster sizes leading to facilitated beetle aggregation, tree infestation, and creation of potential hotspots of beetle emergence. Further work on agent-based modelling for ESB outbreaks in windthrown environments should consider several opportunities for model improvement. The application of the super-agent approach could impact model results regarding beetle dispersal over time and space. The super-agent approach assumes beetles disperse in swarms of 500 beetles, which may overestimate the successful colonisation of the host tree. The uniform colonisation density of windthrown and healthy trees excludes the dynamic intraspecific competition within a tree and higher offspring survival at lower beetle densities (Anderbrant et al., 1985). Furthermore, omission of the sex of individual beetles ignores the role of sister broods in the spread of beetle infestation within a year (Sauvard, 2004). The absence of several initial environmental conditions, such as increased solar radiation on exposed forest edges, may reduce the exclusive role of cluster size on peak beetle populations. We found higher and earlier peak beetle populations in smaller clusters; these, however, might be shaded by surrounding living trees, which may slow down beetle development in comparison to that in sun-exposed large-opened clusters (Kautz et al., 2013). Moving forward, the model can be extended in two directions. First, empirical spatial and climate data are necessary to more accurately represent real forest conditions (Baier et al., 2007; Jakuš et al., 2003; Mezei et al., 2012) and locations relative to windthrow (Eriksson, 2007). Secondly, the model may be extended to explore the range of management applications related to windthrow, and the scheduling required mitigating the risk of subsequent beetle outbreaks. This will allow us to understand the effect of management strategies on ESB population dynamics. Here, we used the wind–ESB interaction as an example. The model, however, provides a tool to support the analysis of forest pest epidemics in general. 5. Conclusion Our study shows the potential of agent-based modelling in simulating an emergent bark beetle outbreak driven by large-scale wind disturbance. The possibility to model multi-scalar interactions among beetles, host trees, and environmental variables provides insights into beetle population dynamics, including the transition timing from infestation of windthrown to healthy trees. The spatial patterns of windthrown areas are highly variable over affected forests each time the wind hits the landscape. We found that scattered windthrow – opposed to clumped windthrown Trees – facilitates the transition from endemic to epidemic beetle population. Our findings may assist forest managers to prioritise the clearing of smaller clusters over the clumped windthrown trees in order to mitigate the risk of I. typographus L. outbreaks. Further research is required to identify potential thresholds in the timing, magnitude, and spatial distribution of salvage logging in order to prevent bark beetle outbreaks. Acknowledgements We thank Mike Nelson and Megen Brittell for their valuable comments on the IPS-wind model. We also thank two anonymous reviewers, whose comments helped to improve this manuscript. This work was supported by the Slovak Research and Development Agency (APVV-0297-12 and APVV-15-0425), by Fund of Štefan Schwarz, and by the National Science Foundation under grant No. 1414041.

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