Colonization of weakened trees by mass-attacking bark beetles: no penalty for pioneers, scattered initial distributions and final regular patterns

Bark beetles use aggregation pheromones to promote group foraging, thus increasing the chances of an individual to find a host and, when relevant, to overwhelm the defences of healthy trees. When a male beetle finds a suitable host, it releases pheromones that attract potential mates as well as other ‘spying’ males, which result in aggregations on the new host. To date, most studies have been concerned with the use of aggregation pheromones by bark beetles to overcome the defences of living, well-protected trees. How insects behave when facing undefended or poorly defended hosts remains largely unknown. The spatio-temporal pattern of resource colonization by the European eight-toothed spruce bark beetle, Ips typographus, was quantified when weakly defended hosts (fallen trees) were attacked. In many of the replicates, colonization began with the insects rapidly scattering over the available surface and then randomly filling the gaps until a regular distribution was established, which resulted in a constant decrease in nearest-neighbour distances to a minimum below which attacks were not initiated. The scattered distribution of the first attacks suggested that the trees were only weakly defended. A minimal theoretical distance of 2.5 cm to the earlier settlers (corresponding to a density of 3.13 attacks dm−2) was calculated, but the attack density always remained lower, between 0.4 and 1.2 holes dm−2, according to our observations.

S1. Impact of tree age on the colonization pattern The experimental setup, with trees felled at different times, did not bias the results  Landing rate at each time step is considered proportional to the number of available beetles and the temperature: →There was a linear relationship between the average temperature (T avg ) and the daily fraction of the still available beetles that had landed (∆L avail  Point process pattern rescaling test computes the scaling between the observed pattern and the SSI-simulated pattern to determine if the interaction between points is dependent or not on attack density. →Analysis indicated that hole density was the main factor controlling the nearest-neighbor distance and that the experimental attack pattern behaved like an SSI process. S14. Location of entrance holes over the available length throughout the observations Display and summarize the statistical test of attack spread along segments throughout the infestation →There was a linear relationship between the spreads of entrance holes along the X-axis at the first (spread 1 ) and last (spread END ) counts. →There was no significant relationship between observation time and entrance hole location along the X-axis.

S15. Comparison between the basal and upper segments
Summarize the statistical test Characteristic values of settlement dynamics, spread of points and spatial pattern for each segment size compared with a Mann-Whitney rank sum test →There were no statistical differences between the basal and upper segments. S16. Regulation of the colonization dynamics by the inhibition distance Theoretical exploration of the control of segment saturation by the inhibition distance Random attacks were simulated with an SSI algorithm on 13 segments with different susceptibilities. Different inhibition distances were simulated. Simulation stopped when it was no longer possible to add new entrance holes (=termination regulated by inhibition distance). →Termination of the attacks (plateau) during our observations cannot be explained by the inhibition distance (MAD=2.5 cm). →Infestation under the rule of a 2.5-cm inhibition distance can lead to densities close to those measured in the literature on standing trees (ca 4 holes/dm²). S17. Influence of attack age on establishment behaviour Test the possible impact of a delay between successive attacks and the inhibition distance around pre-existing entrance holes Linear regression: distance to the closest neighbour versus the time difference between the two attacks involved. →The very weak linear relationship indicates that inhibition distance is not influenced by the age of pre-existing neighbouring holes.
When the normality of the distributions was confirmed (Shapiro-Wilk test), the results were presented as mean±sd (N); otherwise, medians [Q1; Q3] (N) were used. The significance level for all statistical tests was α=0.05. S1. Impact of tree age on the colonization pattern . Setup of the main experiment Figure S1. Sketch of a tree (top view). Each tree is separated into 2 observation segments of different sizes (basal and upper segment; distances indicated in metres) by a 1-metre-long PVC sheet. Pheromone dispensers were removed when 20 entrance holes were counted anywhere around the trunks within 50 cm on both sides of the dispensers (area marked by grey shading).

S3. Influence of the pheromone dispensers on the spatial patterns
The potential influence of the pheromone dispensers on the locations of the entrance holes was tested by a deviation test, in which the statistic is defined by the integral deviation measure where T computes the number of entrance holes within a disc of radius r centred on the pheromone dispenser p, i.e., = . # < ∈ ( , ) , and uses Ripley's isotropic edge correction weights, e r , to correct for edge effects. In (eq. S1), r max denotes the maximum permissible distance to the pheromone dispenser, T obs . The function T is evaluated from the cumulative entrance hole locations at the time of dispenser removal, and is the mean of T 1 , …, T N obtained from N=999 simulated homogeneous Poisson point processes with intensity related to the number of data locations within the convex hull encompassing the holes. The deviation measure (eq. S1) has been evaluated for each simulated Poisson pattern, and we obtained values u 1 , … , u N . The p-value of the deviation test can be estimated as The p-values for the basal and upper segment were 0.355 and 0.366, respectively. This shows that the location of the pheromone dispenser does not influence entrance hole locations. Complementary analysis also suggests that the pheromone dispensers had no effect on the dynamics of the attacks (see Appendix S12).
S4. Validation of the segment experiments. Results of a side study of the spatio-temporal patterns of colonization on whole trees without pheromone dispensers  Table S1. Statistical results of the analysis of whole trees.
S5. Impact of bark texture on entrance hole location S7. Impact of weather on male landing dynamics Weather data (daily average (T avg ), minimum (T min ) and maximum (T max ) temperature) were obtained from the Belgian Royal Meteorological Institute weather station at Beauraing. The impact of temperature on the colonization dynamics was assessed for the overall colonization process by characterizing the relationship between the number of beetles landed on the 4 traps and the 3 corresponding daily temperature values (T max , T avg and T min ) (Figure S4 a) There is a linear relationship between the average temperature (T avg ) and the ∆L avail , whose slopes correspond to the relationship between the landing rate α=0.036/°C at T avg =17.7±3.2°C (N=16) (Figure S4 b).   segment whose Λ i is on the ordinate axis segment whose Λ j is on the abscissa axis S10. , P=0.036). λregular: final hull densities with regular patterns; λrandom: final hull densities with random patterns; λdetection: hull densities whose patterns are detected as regular.

S12. Pattern comparison
To test for independence between point patterns at times >t and times ≤t, we adapted Lotwick and Silverman's [1] and Van Lieshout and Baddeley's [2] approaches for classifying the spatial pattern of points into distinct types. These authors test the null hypothesis that the sub-patterns of the points of each type are independent point processes by wrapping the study window into a torus, fixing locations of type-1, shifting locations of type-2 on the torus and comparing the nearest-neighbour distributions. In our case, type-1 events (resp. type-2 events) correspond to locations at times >t (resp. times <t). For half of the replicates, we concluded that there is a repulsion between the two point patterns, meaning that the points do interact and that new entrance holes fill the empty spaces. These results were obtained when comparing the attack patterns before and after any arbitrary time t (including before the removal of pheromones, which also strongly suggests that the pheromone dispensers did not influence the location of the entrance holes). For the remaining replicates, non-significance may have been linked to the small number of points used to test for independence.

S13. Spacing versus attack density
In our observations, the nearest-neighbour distance between points decreases as the number of points increases. A relevant question is whether the interaction strength (e.g., inhibition distance) between points remained constant over time independent of hole density. We considered the point pattern at time t to be a scaled version of the pattern at time t+1 [3]. Thus, for each point pattern X t at each time t, we computed a scale factor c t such that the intensity of X t /c t is equal to one. Then, we computed the mean nearest-neighbour distance between the points of X t /c t and X t+1 /c t, which should tend toward a constant if the interaction between points does not depend on attack density. We computed the nearest-neighbour distances obtained from the patterns of attacks and from 99 regular processes simulated with an SSI algorithm (see Methods -Statistical analysis) with the same densities. Figure S7 compares the nearest-neighbour distances of the rescaled patterns, and it clearly suggests that entrance hole density is the main factor controlling nearest-neighbour distance and that, from this point of view, the experimental attack pattern behaves like an SSI process. Figure S7. Nearest-neighbour distance between patterns at times t and t+1 after rescaling. S14. Location of entrance holes over the available length throughout the observations Figure S8. a The spreads of entrance holes along the X-axis at the first (spread1) and last (spreadEND) counts show a strong linear relationship (spread1=0.782×spreadEND+22.120, F1,11=25.5, P<<0.001, R 2 =0.67). b Entrance holes are randomly scattered over the whole segments throughout the observations. Replicate 16, which is represented here, as well as the 8 other replicates, does not show any significant relationship between observation time and entrance hole location along the X-axis (linear regression parameters in Table S3).   There are no statistical differences between the basal and upper segments in terms of both the establishment dynamics (colonization rate β) and the density at the final observation (λ END ), indicating that the available space at the investigated ranges did not influence colonization intensity. The comparison of the different variables characterizing pheromone removal (time, λ pherom , and the fraction of the total number of entrance holes at H END ) also supports this result. Similarly, the spatial pattern on both segment types did not show any difference (spread over time, nearest-neighbour distance between holes, and the density at which the pattern was characterized as regular).

S16. Regulation of the colonization dynamics by the inhibition distance
The effect of the inhibition distance on the colonization dynamics was tested by simulating random attacks until the available surface was saturated. Random attacks were simulated within an environment consisting of 13 segments of area A i and susceptibility α i using an SSI algorithm (see Methods) with various inhibition distances, MAD (cm). In this simulation, the location of the new entrance holes was determined using weighted random sampling (weighted by segment susceptibility α i ). The simulation terminated when the number of entrance holes stopped increasing for giveup=10,000 successive iterations (maximal number), suggesting that it was no longer possible to add new entrance holes. Hence, the infestation dynamics and termination were only regulated by the inhibition distance. The total number of entrance holes at the end of the simulation is H. The area and susceptibility of each segment were similar to those of an experimental segment; the MAD value ranged from 0 cm to 25 cm (MAD=0 cm indicates no inhibition; in this case, the simulation terminates when the total number of entrance holes reaches N=8,000 holes). Each segment i bears a number of holes H i defined as and has an infestation density of λ i < = < < < AX <YA Thus, there is a theoretical linear relationship between the susceptibility α i , and the density of the segments with a slope At the end of our simulations, this linear relationship between susceptibility and density was verified throughout the entire colonization process when MAD=0 cm (no inhibition, Figure S9 a & b). In contrast, for MAD≥2.5 cm, the density tended to reach a plateau on the most receptive segments while continuing to increase on the others. This is particularly visible for large values (MAD≥15 cm), at which the final hole density was similar on each segment, but this was not compatible with our observed results of MAD≈2.5 cm. Moreover, at MAD values closer to our observed results (MAD≤9 cm), the total number of entrance holes at the end of the simulation was far greater than the total number recorded on any segment throughout the observations was H END =1614 holes (Table S6, Figure S9 a). Hence, when considering only the first 1614 entrance holes of our simulations, the relationship between segment susceptibility and density remained linear for MAD≤9 cm (Figure S9 b). This indicates that the termination of the attacks (plateau) that occurred during our observations cannot be explained by the inhibition distance (MAD=2.5 cm). Our simulations also show that infestation under the rule of a 2.5 cm inhibition distance can lead to densities close to those measured in the literature on standing trees (ca 4 holes/dm²) (Table S6 and  see Discussion).

MAD (cm)
N (holes) λ (holes/dm 2 ; min-max)  Table S6. Total number of entrance holes and density range at saturation for each MAD value. The pheromones emitted by male Ips typographus vary with the size of the galleries, i.e., with the time since gallery initiation [4]. Therefore, the question of whether galleries of different ages could have different spatial influences on further settlement arose. To explore this issue, we computed the distance to the closest neighbour and the time difference between two attacks. The results show a statistically significant but weak linear relationship (R 2 =0.02, Figure S10) between the age of an attack and the distance to its closest neighbour.