This page provides a detailed description of the iLand bark beetle sub module. A more technical description is given by the barkbeetle module page.
The iLand bark beetle module dynamically simulates the interactions between climate, bark beetle disturbance, and forest development. It explicitly considers bark beetle phenology and development, spatially explicit dispersal of the beetles, colonization and tree defense reactions, as well as temperature-related overwintering success and predation by antagonists. The design of the models follows recent findings on multi-scale drivers of bark beetle outbreaks, considering drivers at the tree (defense, susceptibility), stand (thermal requirements and beetle phenology), landscape (host distribution, beetle dispersal) and regional (climate variation and extremes as triggers of outbreaks) scale. It is a process-based model, using specific findings from the literature to parameterize individual processes. The iLand bark beetle model is currently parameterized and implemented to simulate the Norway spruce (Picea abies) – European spruce bark beetle (Ips typographus L.) system, but is general enough that adaptation to other host – bark beetle systems is possible with moderate efforts.
Table of contents
Description of the bark beetle module
Initiation of an outbreak
An annual probability for the occurrence of a bark beetle disturbance P_{base} is derived from the observed disturbance rotation period (DRP) for bark beetles. This can either be specified as a single (i.e., spatially uniform) probability for the entire landscape, but can also be supplied as map that accounts for spatial differences on the simulated landscape. However, even if a spatially uniform outbreak probability is supplied to the model the realized bark beetle disturbance regime in the simulation will vary strongly for landscapes that feature strong climatic gradients, as a result of the explicit effect of climate on beetle development – see below. To derive P_{base} for the simulation from DRP, the average size of a bark beetle outbreak area per year (size) and the reference size of the calculation (here 100 × 100 m cells) (area) need to be accounted for as described in Eq. 1:
\[\begin{aligned} P_{base}=\frac{1}{DRP}\cdot\frac{area}{size} \end{aligned} \] | Eq. 1 |
Values for DRP can be derived for instance by means of dendrochronology (e.g., Čada et al. 2013) or from recent disturbance records (e.g., Thom et al. 2013). Temporally, outbreak probabilities vary strongly between years, and recent studies on the multi-scale drivers of bark beetle outbreaks show that regional-scale variation in climate is an important trigger for outbreaks (Seidl et al. 2016). The outbreak probability P_{bb} is thus derived from P_{base} by accounting for the climatic conditions of a given year. This is accomplished using a climate-sensitive modifier of bark beetle probability r_{c}. as described in Eqs 2-4:
\[\begin{aligned} {odds}_{base}=\frac{P_{base}}{1-P_{base}} \end{aligned} \] | Eq. 2 |
\[\begin{aligned} {odds}_{bb}={odds}_{base}\cdot r_c \end{aligned} \] | Eq. 3 |
\[\begin{aligned} P_{bb}=\frac{{odds}_{bb}}{1+{odds}_{bb}} \end{aligned} \] | Eq. 4 |
The climate modifier r_{c} is related to interannual climate variation at the regional level and is thus uniform over the landscape. It is a measure of relative change, where the baseline (i.e., a value of 1) is related to the climate conditions for which P_{base} was specified (e.g., the long-term mean climate over the disturbance observation period). It can be determined using climate-sensitive outbreak relationships that are derived either based on detailed modeling analyses by means of meta-modeling (e.g., Seidl et al. 2009), or from empirical analyses of the large-scale climatic drivers of bark beetle outbreaks (e.g., Seidl et al. 2011). For the P. abies – I. typographus system currently parameterized in iLand we followed the in-depth analysis of Seidl et al. (2016) and related outbreak probability to regional variation in summer precipitation.
If a wind disturbance event is simulated P_{bb} is increased by the probability that windfelled and –broken trees are colonized by bark beetles, currently set to 0.30, based on previous empirical analyses (Eriksson et al. 2005; Eriksson et al. 2008). Salvaging windthrown trees can thus strongly dampen the probability of outbreak initiation in the simulation (see also Stadelmann et al. 2013). Bark beetle outbreaks are initiated by drawing a random number and comparing it against P_{bb}. A prerequisite for initiation at a given location on the landscape is the availability of viable host trees, defined as Norway spruce trees exceeding a certain threshold diameter (here set to 15 cm dbh). The spatial grain of the simulation of outbreak initiation and spread are 10 x 10 m cells (i.e., the approximate area covered by the crown of an old-growth tree (Lexer and Hönninger 2001). For these cells the dominant Norway spruce tree is evaluated in order to determine whether the cell is a potential host cell for the beetle.
Beetle development
Bark beetle development is simulated by means of a phenology-based process model (Seidl et al. 2007; Baier et al. 2007). A cumulative sum of maximum air temperature of 140.3 degree days above the beetles’ lower developmental threshold (DTL = 8.3 ◦C; (Wermelinger and Seifert 1998)) accumulated from the April 1^{st} onward is used to predict the onset of spring swarming and first colonization of trees. Beetles only swarm on days with air temperature maxima of >16.5°C. Essential for brood development, however, is bark temperature rather than ambient temperature. To derive bark temperature, a previously established empirical relationship between bark temperature, air temperature, incoming radiation above the canopy, and relative light level (the latter derived here from the local leaf area index simulated in iLand) is employed (Baier et al. 2007). Brood development is estimated using upper and lower temperature thresholds (8.3 and 38.9°C, respectively) and a non-linear function for calculating effective bark temperatures and thermal sums necessary for successful bark beetle development (Wermelinger and Seifert 1998; Wermelinger and Seifert 1999). If the effective bark temperature sum reaches the heat sum of 557 degree days beetle development is completed. If the maximum air temperature exceeds the required lower limit of swarming (16.5°C), and day length is still >14.5 h, beetles disperse (see below) and start sister broods (i.e., new broods established by the initial parental generation of beetles) and/ or a new filial generation. If the accumulated effective bark temperature exceeds beetle 278.5 degree days and the swarming requirements are met a sister brood is initiated. Sister broods develop in analogy to the main filial generations using the same developmental thresholds. Beetle development stops either through bark temperatures below the lower developmental threshold or through day lengths of <14.5 h (Seidl et al. 2007; Baier et al. 2007).
Beetle dispersal
Every completed beetle generation disperses from the colonized host if the swarming requirements are met. The tree is killed once the beetles leave the host, and is no longer available as potential host tree for future beetle attacks. All mature Norway spruce trees above the colonization threshold growing on the focal 10 × 10 m cell are assumed to be colonized and killed in the same time step. Spatially explicit beetle dispersal follows a two-step approach:
In a first step, beetle flight follows a symmetrical dispersal kernel (see e.g., Fahse and Heurich 2011; Kautz et al. 2011). The direction of dispersal is randomly chosen and the distance is determined from the probabilistic kernel function. In a second step, the thus determined landing location is further modified by the beetle actively searching for potential hosts in the vicinity. The perceptual range of the beetles for this search was previously estimated to be in the range of 15 m ( Fahse and Heurich 2011; Kautz et al. 2014). We here used the Moore neighborhood around the initial landing cell of the beetle to constrain the beetles search for potential hosts. If no potential host is present in this 30 × 30 m area the beetle cohort is assumed to die (dispersal mortality). If both living and freshly windthrown host trees are available, the beetles preferentially colonize the latter. If selected by managers, salvage harvesting of windthrown trees is assumed to occur before the brood of the colonizing beetles leaves the tree, and thus reduces the local bark beetle pressure. Trap trees, frequently used to monitor beetle development and reduce local beetle pressure by managers, are treated as freshly windthrown trees, but are assumed to be removed from the site before the next beetle generation can emerge.
The aggregation behavior of beetles via their chemical communication is not simulated explicitly in iLand. Rather than simulating the dispersal of pioneer beetles and the subsequent attraction of followers via pheromones, which eventually exhausts tree defenses and leads to a successful attack (Wermelinger 2004; Kausrud et al. 2012), we here aggregate this dynamics by simulating the dispersal of beetle cohorts, with a cohort defined as the minimum number of beetles that are jointly able to kill a tree (estimated to be 30 beetles in the case of I. typographus, (Kautz et al. 2014)). Every cell for which a successful brood is simulated disperses multiple beetle cohorts, with the number determined by the reproductive success of the beetle. For I. typographus, for instance, it can be assumed that 45 larvae are hatched per female colonizing beetle (Fahse and Heurich 2011), representing the upper limit of the reproductive rate. However, if also mortality and density-dependent competition for resources within a brood are considered, the reproductive rate of beetles is likely considerably lower than that (estimated to range between 4 and 24 by Wermelinger and Seifert (1999), and set to 20 in Seidl and Rammer (2016)). The reproductive success is a user-defined parameter in the model that can be parameterized based on empirical data and specified separately for main generations and sister broods.
Host colonization
A beetle cohort attacking a tree has to overcome the trees defense system, including stored and induced resin production as well as induced wound reactions (Baier 1996; Wermelinger 2004). These defense mechanisms are closely related to the availability of non-structural carbohydrates in the tree, and thus bark beetle susceptibility is frequently found to be related to drought stress and low tree vigor (Christiansen et al. 1987; Netherer et al. 2015). iLand dynamically simulates tree stress based on the carbon balance of a tree, and the thus derived stress index (where 0 means no stress and a full carbohydrate reserve, while 1 indicates high stress and a fully depleted carbohydrate reserves pool) is used as an indicator for tree defense in the simulation of bark beetle host colonization. Kautz et al. (2014) suggested that a healthy, vigorous tree (i.e., a host tree at its maximum defense capacity) requires 6.67 times more attacking beetles to be successfully colonized compared to a stressed tree. Consequently, we here formulated the probability of successful colonization (P_{colonize}) by a single beetle cohort (representing the aggregation of 30 beetles) to (Eq. 5)
\[\begin{aligned} P_{colonize}=0.85\cdot SI+0.15 \end{aligned} \] | Eq. 5 |
with SI is the C-balance derived stress index 0,1. Windthrown trees are assumed to be essentially defenseless, and area assigned a P_{colonize} of 1.0. A uniform random number is compared against P_{colonize} to determine whether a tree is successfully colonized by an attacking cohort of beetles. Please note that during any given dispersal wave multiple beetle cohorts can attack a tree.
Overwintering of the beetle
Only the last beetle generation developing in a year is assumed to overwinter. Of that generation, all immature beetles are assumed to experience 100% winter mortality (Faccoli 2002; Jönsson et al. 2012). For mature beetles, simulated winter mortality consists of two components: First, a background winter mortality rate (M_{bg}) is assumed, i.e., a fixed proportion of adult beetles is killed every winter (here set to M_{bg}= 0.40, following Jönsson et al. (2012)). Second, additional mortality is caused by exposure to strong winter frost. Specifically, days with minimum temperatures below -15 °C are assumed as frost days (fd), and beetle mortality (M_{w}) increases with days of exposure (Eq. 6):
\[\begin{aligned} M_w=1-e^{a_1\cdot fd } \end{aligned} \] | Eq. 6 |
The empirical parameter a_{1} was estimated to be -0.1005 by Koštál et al. (2011) under wet conditions, with more than 95% of the beetles dying from 30 days of frost exposure.
Collapse of outbreaks
How and why bark beetle outbreaks stop is not yet fully understood. However, observations for the P. abies – I. typographus system show that regional eruptions of beetles die down regularly after six years on average (Kautz et al. 2011; Tomiczek et al. 2012; Lausch et al. 2013; Seidl et al. 2016). Antagonists, such as predatory beetles (Cleridae) and flies (Dolichopodidae), as well as parasitic wasps (Pteromalidae, Braconidae) and birds, play an important role in mitigating and containing bark beetle outbreaks (Wermelinger 2002; Wermelinger 2004). A further aspect in the collapse of outbreaks is likely to be a decreased fitness of individual beetles due to intraspecific competition and density-dependent feedbacks (Marini et al. 2013; Kautz et al. 2014). However, modeling population dynamics of the diverse community of antagonists as well as the fitness level of individual beetles was beyond the scope of the iLand bark beetle disturbance module. Consequently, we assumed a fixed negative feedback in later stages of bark beetle outbreaks, parameterized to mimic the observed pattern of periodic collapses of bark beetle populations. Specifically, we defined the effect of negative feedbacks (as represented by an additional beetle mortality component M_{nf}) to depend on the time elapsed since the initiation of an outbreak spot (t_{ob}), following Eq. 7,
\[\begin{aligned} M_{nf}=min\left ( max\left ( 2\cdot\frac{t_{ob}}{t_{max}}-1,0 \right ),0 \right ) \end{aligned} \] | Eq. 7 |
with t_{max} an empirical parameter randomly selected for each year between 5 and 6 to mimic the observed periodicity of outbreaks in the P. abies – I. typographus system.
Parameters of the bark beetle module
The following table lists the parameter values used in the application described by Seidl and Rammer (2016). See also barkbeetle module for implementation notes.
Parameter | Value | Description |
Initiation of an outbreak | ||
P_{base} | 0.000685 | Annual outbreak probability per hectare. Estimated from a disturbance rotation period of 365 years and a mean disturbance size of 4 ha (Thom et al. 2013; Thom et al. 2016). |
r_{c} | ${P_{summer,rel}}^{-0.9609}$ | Climate sensitive modifier of outbreak probability. Based on a reanalysis of data given in (Seidl et al. 2016). P_{summer,rel} is the relative summer precipitation (JJA) of the previous year relative to the long-term average. |
P_{windthrown} | 0.3 | Probability of bark beetles colonizing windthrown trees. Based on empirical data from Eriksson et al. (2005) and Eriksson et al. (2008). |
Beetle dispersal | ||
K_{spread} | $e^{-\frac{\left ( \frac{x}{4.5} \right )^2}{40.5\cdot4}}$ | Bark beetle dispersal kernel, calculating the probability that beetles spread to x m from the center of the originating cell. The thus defined kernel is scaled to a sum of 1. The kernel function is taken from Fahse and Heurich (2011) (see also Kautz et al. (2011) for alternative kernel functions, which, however, include the compounding spread of multiple generations per year). |
N_{cohorts, main} | 20 | Reproduction rate of the beetle, i.e. the number of beetle cohorts spreading from infested pixels for each main beetle generation. Empirical evidence points to values between 4 and 24 (Wermelinger and Seifert 1999), with a theoretical upper limit of 45 (Fahse and Heurich 2011). |
N_{cohorts, sisterbroods} | 30 | Reproduction rate of beetles if - in addition to the filial generation - a full sister brood develops. It is assumed that the reproductive rate in sister broods is 50% lower than that of a main generation. |
Host colonization | ||
DBH_{min} | 15 | Threshold diameter at breast height for colonization (cm). Cells occupied by Norway spruce tree above the threshold are considered as potential host cells. |
P_{colonize} | $0.85\cdot SI + 0.15$ | Probability of successful colonization by one beetle cohort as a function of SI, the C-balance derived stress index (Seidl et al. 2012). Following Kautz et al. (2014) it is assumed that healthy trees require 6.7 times more beetles for successful colonization compared to stressed trees. |
Overwintering of the beetle | ||
M_{bg} | 0.4 | Background winter mortality rate (Jönsson et al. 2012). |
M_{w} | $1-e^{-0.1005\cdot fd}$ | Additional probability of beetle mortality due to days with minimum temperature below -15°C, following Koštál et al. (2011). |
Collapse of outbreaks | ||
M_{nf} | See Eq. 7 above | Additional beetle mortality due to antagonists and decreased fitness of beetles in later stages of an outbreak. t_{ob} is the time elapsed (in years) since the initiation of an outbreak spot. t_{max}'' is the maximum duration of an outbreak and is selected randomly each year from an user-specified interval, here set to 5,6. Sources: Kautz et al. (2011); Tomiczek et al. (2012); Seidl et al. (2016). |
Seidl, R., Rammer, W., 2016. Climate change amplifies the interactions between wind and bark beetle disturbances in forest landscapes. Landscape Ecol (2016). doi:10.1007/s10980-016-0396-4