Results

The emergent pattern is produced by behavioral traits of individual beetles, which, once emerged, can randomly search for suitable tree host. At specific time intervals, defined by time lag parameter (see (Kautz et al., 2014) paper for more details), the cohort of beetles emerged from the centered patch (Figure 3). Every beetle has its own energy level, efficiency, perceptual range, possibility of moving angle and distance. Its actual state is defined by its “status”: dispersing, staying, infesting, starved, killed or lost. Every beetle decides autonomously for its target tree, however, the beetles’ heterogeneity is introduces by its energy level (generated from Gaussian distribution) and by its efficiency (population-specific distribution). Thus, beetles conducted by same behavioral rules, react differently and the finer-scale patterns observed in a real world can occurred (Millington, O’Sullivan, & Perry, 2012).

Figure 3 Narrative approaches explaining emerging infestation pattern from individual agents’ decisions: sequence of beetles spreading over forest stand in IC model. One patch presents single tree, color intensity presents tree resistance (from the lightest to the darkest correspond from the most vigor to most susceptible tree). Over the simulation run, tree color could change from shade of green to pink (infested) and to brown (not more attractive to beetles = dead tree). Beetles are depicted as triangles with status: dispersing (red) or staying (orange). (1) Beetles start to spread from the centered patch. (2) A fraction of beetles moves randomly from the centered patch (the red ostensible “circle” is formed by amount of dispersing beetles), another fraction of beetles have already found their tree host and have status “staying”(orange). 3 trees are infested (pink patches), but the amount of beetles have not still overpass the threshold value of 5000, thus tree remains alive and increases its attractiveness by subsequent beetles aggregation pheromones. (3), (4), (5) Continuation of beetle spread and tree infestation. (6) Infested trees (previously pink) turn brown (dead, not attractive tree for beetle), beetle spreading continues, as marked by centered circles of dispersing beetles.

In the study, I was focused in i) sensitivity analysis, which was performed as a stepwise modification of clustering level, thus in changing radius values of clumps of weakened trees and its influence of selected system response variables:

% of beetle success,
number of infested trees,
max infestation distance.

Equally, to ii) changing number of beetle status during the simulation run depending on altering radius values and on iii) final number of beetle status’ at the end on the simulation run.

Figure 4 System response variables on i) % of beetle success, ii) count of infested trees, iii) maximum infestation distance depending on radius values.

At all clustering levels (Figure 4), % of successful beetles was more than 80%, with the lowest variability on the 0 radius value where one clump is presented by one patch. Beetle success is lowering until the lowest success value is reached at radius 2, corresponding to clump of 13 weakened trees. With increasing level of clusters the variability increase but remain relatively stable. At clustering level of 2, the variability of amount of infested trees was the highest and decreases with increasing radius value.

Maximum infestation distance was however more sensitive to clusters with radius more than 4 (49 clumped trees). The variability and length of maximum infestation distance grows with increasing radius value: at the threshold value of radius ~ 3 the length is about 100 m and increases up to 500 m for highest radius value.

Figure 5 # of mean beetle status after 10 simulation runs, where red = killed, yellow = staying, green = dispersing, orange = lost, blue = infesting, black = starved for different clustering level. The “fuzziness” of the dispersing beetles is caused by beetles emergence in cohorts chunked by time lag. At approximately 100 time steps, all beetles are emerged and are spreading over landscape selecting suitable host.

The proportion of beetles statuses’ changing over time step is evaluated at Figure 5. The most noteworthy is the ratio between dispersing and infesting beetles depending on radius value. At radius value equal to 0, the amount of dispersing beetles remains stable, increasing only with newly emerged beetles, but beetles seems to change their status rapidly to infesting or killed. However, with increasing radius value, the amount of dispersing beetles increases over time, meaning that in higher clustering level beetle aggregation behavior seems to be partially suppressed by waste brooding availability. Beetles spend more time by searching available host, thus more of them become starving or killed by tree until waiting for other beetles leading to overpass tree resistance.

Figure 6 Final proportions of the beetles' status at the end of the simulation run, depending on radius value. Note number on y axe is * 1000.

At the end of simulation run, the amount of beetle statuses is evaluated on Figure 6. The radius value 2 (clump of 13 weakened trees) seems to be a threshold value for increase of killed, starved and infesting beetles. On radius values beyond this level the amount of beetle statuses remain stable, with increasing variability, which can be caused by original placement of the clump of weakened trees in forest stand.