Purpose

The model’s purpose is to study the Influence of the level of Clustering (IC) of wind-fallen trees on the bark beetle flight dispersal and emerging infestation pattern. Weakened trees and their level of clustering represent natural wind-fallen trees present in coniferous stand caused by wind or snow. Disturbed trees change suddenly their vigor status from healthy to susceptible to bark beetle attack. Hereafter, the terms weakened and wind-fallen tree are considered as synonyms. The term weakened is used in NetLogo environment but represents the reality of wind-fallen trees in forest stand. Term cluster is used for clumps of wind-fallen trees, which extent is defined by radius (r) value.

 

Entities, State Variables, and Scales

The model includes two types of entities. Bark beetles are mobile entities (agents), moving by random walk by step length of 5 – 1250 m over the forested landscape from single centered patch. Trees are patches of 5 × 5 m, where each patch represents single tree and is defined by its BB attractiveness value. Entire simulated landscape include 501 × 501 patches (627.5 ha), however, for the analysis, only the inner circle of the forested landscape is relevant, defined by the maximal beetle dispersal distance of 1250 m, so 490.9 ha. Under different simulations, the increasing or decreasing level of clustered trees is created using grading radius value. Beetles are released from the centered patch searching for suitable tree host. During simulation, beetle can be i) successful in finding suitable trees host or ii) can die due to run off its energy value or because of tree resistance. The tree can i) be infested and increase its further attractiveness value or ii) remain intact. One model run simulates the course of a single dispersal wave which wage in natural conditions only several days (Botterweg, 1982). A onetime step corresponds to beetle movement from one patch to another. Bark beetles are characterized by its energy level, perceptual range, moving angle, moving distance and its current status (dispersing, infesting, staying, lost, and starved). Tree is defined by its attractiveness value, infestation level and sensitive to number of attacking beetles. First the beetles act, followed by trees. State variables are updated every time step.

 

Process overview and scheduling

In each time step beetles move in order to find a suitable tree host. Depending on their behavioral traits, the individual beetle can die because of running-off energy level or tree resistance, or it is successful in tree colonization. Depending on the number of beetles landing on the three, the last one can be either infested or it remains unaffected. In the agent processing sequence the beetles are set first, followed by trees. State variables are updated every time step.

 

Basic principles

The IC model is focused on detection and quantification of effect clustering of disturbed trees to emerging infestation pattern, BB mortality and successful attacks. It constitute the BB outbreak triggered by small to large-scaled climatic disturbance (Sauvard, 2004). In IC model, this concept is included using different level of clustering of weakened trees, presenting from scattered to centered windbreaks.

 

Emergence

From interactions between beetles and trees individuals and their individual traits the infestation pattern, dispersal level and beetles’ and trees’ mortality are emerging.

 

Objectives

Beetles search for suitable tree host for colonization and disperse over space. They have to accomplish specific density number to overpass tree resistance. If they don’t attempt this threshold value, they are killed by tree. The system level responses are captured by the mortality rate within the dispersing beetle population and the maximum tree infestation distance to the entered world patch or source. Tree defense is encounter by infestation rate and spatial location.

 

Sensing

Beetles are able to sense their energy level, movement direction, trees’ attraction within their sensing radius and the number of aggregated beetles on an encountered tree host. Sensing strongly affects their dispersal and infestation behavior. Tree sense the number of attacking beetles and change its status from non-infested to infested. Equally its attractiveness depends directly on the BB attack density.

 

Interaction

Interaction among beetles and trees is representing by trees attraction to bark beetles coordinate attack. Tree attractiveness is increasing by number of colonizing beetles until the 5000 beetles/tree. From this threshold, the newly coming beetles are repulsed from the infested tree. This behavior corresponds to real beetle-tree and beetle-beetle interaction, when the primary attractiveness of the tree is expressed by terpenes attracting bark beetles. Once the tree is infested, positive feedback is created by pheromones released by beetles, attracting higher beetle number. Once the attack density is sufficient to overpass tree resistance (5000, stable for all trees), beetles are repulsing each another, equally tree is not more attractive.

 

Stochasticity

Randomness is involved by several processes: i) bark beetle energy levels is derived from Gaussian population distribution, ii) individual beetle’s consumption energy depends on negative exponential distribution, iii) beetles (agents) are moving using Correlated random walk (CRW) with different step length and iv) primary attractiveness and cluster position is random.

 

Observation

In the study, attention is paid to selected system-level responses variables recorded after completed simulation runs. Variables quantifying emergent dispersal and infestation pattern are:

 

• Mortality rate – how many beetles are not successful in suitable host finding

• Total number of infested trees

• Maximum net distance of an infested tree in meters to the source tree.

The aim of the study is to quantify the influence of the clustering level on these variables and determine its sensitivity.

 

Initialization

A simulation starts with the beetle dispersal from the centered source. At the beginning, all the beetles have the status dispersing and all the trees are noninfected. Although trees’ primary attractiveness is different, depending on the selected scenario of weakened tree clustering level. Tree stand position is random. Total number of dispersing individual range from 0 – 200.000 beetles.

 

Sensitivity analysis

Sensitivity analysis includes altering clustering level of weakened trees in forest stand. Common ratio is stable among clustering levels, only the total amount and clumps’ size is altered. As system level responses, the BB mortality rate, number of infected trees and maximum net distance will be recorded. 10 simulations run were calculated.

 

Model will be evaluated by comparison the complex system behavior through traits generated by individual entities to actual knowledge about beetle and tree behavior and their interaction.