Assessing the Flight Potential of the Four-Eyed Fir Bark Beetle Polygraphus proximus Blandford in Natural Conditions

Abstract

The four-eyed fir bark beetle Polygraphus proximus Blandford (Coleoptera, Curculionidae, Scolytinae) has become an aggressive invader in Siberia’s fir forests in recent decades. However, its spread in the invaded area is not yet complete; this species is absent so far in most of the Siberian fir Abies sibirica Ledeb. range. To predict this process, appropriate models are needed, including at the local level. One of the essential parameters for modeling is the flight characteristics of imago. To evaluate its flight potential, we placed slabs (sections of the bark with a thin sapwood layer) in an area without forests or with forests with an absence of fir at the end of May. The beetles overwintered under the bark in these slabs. We also placed short fir trap logs at distances ranging from 50 to 1500 m in the four cardinal directions from the release point to attract migrating beetles. After the beetles from the slabs had completed their migration, we evaluated the number of parental pairs (male and female) of the four-eyed fir bark beetle on the trap logs (p) and their number per dm² (p_S). The sole factor that affected the colonization of host objects in our experiment was the distance from the release point. The relationship between p and p_S and the distance to the release point can be accurately represented by a negative exponential curve. This experiment established a flight distance of 1500 m, with calculated values of 4919 m for p and 2965 m for p_S. However, an analysis of similar experiments and studies using flight mills suggests that these values may not be extreme in an environment with few and sparse host objects. In conditions of abundant food supply, the actual flight distance of P. proximus beetles is significantly less than the theoretically possible maximum.

1. Introduction

Over the past two centuries, the rate at which forest insects spread to non-native areas with human assistance has steadily increased. This includes species that have a significant impact on local natural and anthropogenic ecosystems in their new range. These species are commonly referred to as invaders. They are found among insects that differ in their feeding guild and biological characteristics, including bark beetles and wood borers, i.e., species that feed aboveground on phloem, cambium, or wood [1]. The damage that can be caused by members of this group of insects can be considerable. The emerald ash borer Agrilus planipennis Fairmaire, 1888 [2] and European elm bark beetle Scolytus multistriatus (Marsham, 1802) [3] are well known for their destructive properties. The four-eyed fir bark beetle Polygraphus proximus Blandford, 1894 (Coleoptera, Curculionidae, Scolytinae), which is monophagous on Abies ssp. [4], is one of the species that has a significant impact on ecosystems in invaded areas [5,6].

The four-eyed fir bark beetle is native to the Russian Far East and nearby areas such as Sakhalin, the Kuril Islands, and northern Japan [7,8]. However, in the late 2000s, there was evidence of its presence in Siberia (Tomsk Oblast, Krasnoyarsk Krai) and Moscow [9]. Its new range was found to be much wider, covering a significant part of Siberia [10]. Furthermore, using the methods of dendrochronology [11] and genetics [12], it has been shown that its spread beyond its domestic area occurred much earlier than its discovery and more than once. The expansion of their invaded area is still continuing, and recently this species has been found in the Volga and Ural regions [13].

In its native range [8,14], P. proximus is known to be aggressive. In Siberia, it causes severe damage to the Siberian fir Abies sibirica Ledeb., 1833 [5,6], and in the Tsitsin Main Botanical Garden of the Academy of Sciences in Moscow, it has been observed to damage some other fir species [15]. This species primarily feeds on fir species, although it can attack most genera of Palearctic conifers [4]. Tree size is also a factor for the bark beetle when selecting hosts. Although there are few records of four-eyed fir bark beetles being found on small fir trees (with a diameter of 3 cm), P. proximus still prefers larger trees. In the outbreak area, the average diameter of fir trees inhabited by the beetle is around 20 cm, whereas uninhabited trees have an average diameter of 12 cm [16].

One of the challenges of forest health monitoring is the need for forest health professionals to gather data and information that will allow them to take action when invasive pests are detected. The capacity to act rapidly and cost-effectively hinges on an understanding of the rate at which an invasive species spreads into new, non-native areas. The intensity of surveillance, for instance, is contingent upon the probability of an invader’s arrival. Additionally, the migratory capacity of an invader influences the probability of its range expansion. The higher this capacity, the more challenging it is to prevent its spread [17]. One approach to assess the spread potential of alien species is to develop models that describe the path of invasion into new areas [18,19]. This is particularly crucial in the case of invasive bark beetle and wood borer species, which tend to repopulate and spread aggressively [18].

It is now recognized that the range expansion of invasive species occurs through two distinct processes (local and long-distance). The first is the spread to neighboring biotic communities. This depends on the ability of the species to migrate and is possible in a more or less homogeneous environment. The second is migration by passive dispersal to biotic communities that are separated by distances that are insurmountable for the species and by physical barriers. A specific modeling approach is required for both processes [19,20].

In the context of modeling the local spread of invasive pests, distance is one of the most crucial factors to consider. The ability of individuals to fly over distances has been identified as one of the most significant predictors of invasive species distribution and is therefore a key feature in modeling this process [19,21,22,23]. However, the lack of data on the dispersal distance of the species under investigation represents a significant challenge for the development of effective models [24].

The dispersal distance of bark beetles and wood borers can be estimated by direct or indirect methods. Indirect methods include dendrochronological techniques and the study of tree mortality dynamics [20,21,22,23]. Direct methods include using flight mills, mark–recapture experiments, and in rare cases, observing dispersal at the initial stages of invasion [20,25,26,27]. For P. proximus, only one similar study has been conducted at the local level. The study assessed the beetle’s migratory ability by analyzing a time series of images from an unmanned aerial vehicle. Conclusions about the flight range of the beetles were made based on the distance between recently colonized fir trees and those that were colonized some time ago, which were considered a source of insects [23]. However, when estimating the speed of local migration of other borer insects, it was found that the results obtained using different methods [21,28] can vary significantly. Notably, the flight distance of young individuals decreases sharply with the increasing abundance of host objects [20,28].

To date, a number of studies have been conducted that have enabled the direct estimation of the flight range of bark beetles. The majority of these studies employed the mark–recapture method [29,30,31,32,33,34,35,36,37]. In contrast, a smaller number of studies [38,39] employed an approach similar to ours, conducting research at sites where the population of the target species was absent.

The subjects of such studies were primarily the most aggressive species of bark beetles. In Europe, the flight range of European spruce bark beetle Ips typographus (L., 1758) has been extensively studied under natural conditions [29,30,34,36,39,40]. In North America, mountain pine beetle Dendroctonus ponderosae Hopkins, 1902 [33,38,41,42] and several other members of the genus Dendroctonus [31,32,35] have been observed. With the exception of southern pine beetle Dendroctonus frontalis Zimmermann, 1868, all of these species are significantly larger than P. proximus. A number of studies have demonstrated a direct correlation between body weight and flight performance [20]. Consequently, the results of these studies may not be applicable to the four-eyed fir bark beetle. For instance, on a flight mill, the maximum flight range of D. ponderosae was found to exceed 24 km [43].

In addition, the distance that bark beetles can fly is also dependent on the availability of trees that are suitable for attack. Although it has been shown that bark beetles are capable of longer flight distances [20], the majority of the population will limit their flight distances to a few tens or hundreds of meters in the presence of a sufficient food supply [20,23,28].

In the majority of the studies enumerated in the preceding paragraph, the beetles were released at a distance from the trap objects that was as far as possible. In some instances, marked bark beetles were observed outside the boundaries of the experiment site [44]. Consequently, in order to estimate the maximum distance over which bark beetles can spread during local migration, it is necessary to employ calculation methods. To supplement the observational data on bark beetles, calculations were carried out [31,35,36,39].

In light of the limited understanding of the migratory ability of P. proximus, the objective of our study was to ascertain, through empirical and modeling approaches, the maximum distance that young beetles of this species can fly under natural conditions. To ensure the integrity of the experimental design, we excluded the potential influence of food availability on the results. This was done because, under conditions of sufficient food supply, the actual flight distance of bark beetles and wood borers is significantly lower than the maximum possible.

2. Materials and Methods

2.1. Study Site and Experimental Set Up

The experimental plot was selected based on specific criteria related to the biological features of P. proximus. The first criterion was the absence of hosts for the four-eyed fir bark beetle, meaning large fir trees.

The absence of nearby populations of the four-eyed fir bark beetle was the second criterion for selecting the experimental plot. It was assumed that this criterion is satisfied by sites that are at least 2 km away from the nearest forest stands where fir grows.

The third criterion followed from the ability of bark beetles to migrate long distances: the size of the experimental plot must be sufficient to place objects that attract insects at a considerable distance from the release point. To determine the appropriate plot size, information about the flight capacity of other Scolytinae species [20] was considered, and an experimental plot with a size of approximately 1.5 × 1.5 km was selected.

Finally, the release of the four-eyed fir bark beetle specimens during the experiment should not have led to an expansion of its new range. Therefore, the experimental plots were placed in a region where P. proximus populations had already been formed.

The experiment used slabs (sections of the bark with a thin sapwood layer) with beetles hibernating under the bark as the source of the insects, and short logs of Siberian fir trees with no signs of bark beetle attacks nor galleries were used as trap objects [45]. The slabs were constructed from A. sibirica trees that had been infested with overwintered P. proximus beetles beneath the bark. These trees were situated in a fir-dominated stand on the Chulym–Yenisei plateau (Emelyanovsky District, Krasnoyarsk Krai, 56.18 N, 92.19 E). To confirm infestation, small pieces of bark were removed along the entire trunk and the beetles were warmed to check for activity and viability. The bark of trees infested with the four-eyed bark beetle was divided into several pieces along with the sapwood for storage. The slabs were prepared in such a way as to preserve a large number of bark beetles [4]. Compared to intact logs, the slabs were more compact and easier to transport. Both trap logs and slabs with wintering bark beetles were prepared on 4 April 2023 and stored under the snow until the start of the experiment. Previous studies [46] have demonstrated the efficacy of this method in preserving active and viable beetles for several months. Furthermore, it impairs the capacity of trap log tissues to generate an induced resin flow, which is essential for successful colonization.

Prior to conducting the field experiment, eight slabs were transferred to the laboratory. Then, they were placed in a closed cardboard box with a transparent plastic cup embedded at the bottom. At ambient temperature (~22 °C), viable bark beetle individuals left the slabs and, due to positive phototaxis, accumulated in the cup. The number of bark beetle imagoes was counted after they ceased to emerge. The surface area of the bark was measured, and the number of young beetles per dm² was determined [45].

The field experiment began when temperatures stabilized above zero and the forest roads were in good condition after spring.

To conduct the experiment, we selected a site located on the Chulym–Yenisei plateau (Emelyanovsky District, Krasnoyarsk Krai, 56.36 N, 93.02 E) as shown in Figure 1. The site has a flat relief and is dominated by forest vegetation, with Scots pine (Pinus sylvestris L., 1753) being the dominant tree species and birch (Betula ssp.) and common aspen (Populus tremula L., 1753) as co-dominants (Figure 2A). During the examination of the selected area in 2022, we only observed sparse fir trees with a diameter of ≤6 cm. These trees did not have any signs of P. proximus attacks (pale green, yellow, or red crone; entry holes; resin flow on the bark surface; galleries [45]). The nearest stand with the presence of fir is at a distance of about 8 km. The experimental plot is surrounded by either open spaces or forest stands with a similar species composition. Despite the presence of the four-eyed fir bark beetle in this region [10], we can exclude the migration of P. proximus from outside the experiment area [33,39], as well as the damage associated with the flight of the beetles we released.

A total of 132 slabs, covering an area of 380 dm², were used. The number of beetles per dm² was 9.7 ± 1.1, resulting in a total of approximately 3700 emerging beetles. The slabs were laid out in the center of the experimental plot (Figure 2C), and two trap logs (Figure 2B) per point were placed along lines oriented to the cardinal points at distances of 50, 100, 150, 300, 500, 750, 1000, 1250, and 1500 m from the center, except for the southern direction where the length only allowed for logs to be placed up to a distance of 750 m. The mean length of these logs was 33 (31 to 34) cm (Figure S1B), which is quite attractive for P. proximus [47]. The diameter of these logs was 6 to 16 cm (Figure S1A), while the bark surface was 6.2 to 16.7 dm² (Figure S1C). For laying out the slabs, a well-lit place was chosen, which was supposed to speed up the drying of the bark and stimulate the emergence of overwintered beetles from it [48].

The flight of the four-eyed fir bark beetle is heavily influenced by weather conditions. Previous studies have shown that flight is disrupted when the air temperature drops below 15 °C, and during precipitation or when there is a light breeze [4,14]. As the last two weather conditions affecting flight are not quantitatively characterized, we defined cloudy weather as a cloud cover above 50%. To describe the wind influence quantitatively, we used the Beaufort scale. A light breeze was defined as having a lower speed limit of 3.3 m/s, below which we considered the flight of P. proximus to be possible. We processed the weather data for synoptic times and hours from the nearest available weather station (Emelyanovo airport, 36 km) [49] for the period from the day of laying out the material to the day of its collection. The meteorological data obtained at this distance were found to be highly accurate in reflecting the meteorological conditions observed in the study area [50,51].

One of the reasons for the failure of the first experiment (2021, unpublished) was the unfavorable weather conditions for the flight of P. proximus. To prevent a recurrence of this outcome, weather data were analyzed on a daily basis in 2023. Weather data were recorded until 14 June. During the initial period of the experiment, beetle flight was also generally unfavorable. This was mainly due to a combination of heavy wind and low temperatures. Weather conditions that allowed for the dispersion of the four-eyed fir bark beetle began in early June 2023. The best conditions during the observation period occurred from 4 June to 9 June, with west winds dominating the wind rose (Figure 3).

The activity related to the beetle flight period lasted for 45 days, from 19 May to 3 July 2023. During an intermediate inspection (14 June), entry holes were found on the trap logs. An opening in the bark on the slabs with overwintering beetles confirmed their flight; no individuals were found remaining under the bark but exit holes were presented. This bark beetle species is monogamous; the nuptial chamber is constructed by males and egg galleries by both sexes [52,53]. Hence, we considered nuptial chambers with a system of egg galleries (Figure 2D) as a sign of a pair (male and female) of mated beetles’ presence. In the laboratory, we counted the number of pairs and unsuccessful attacks (entry hole or nuptial chambers only) by P. proximus, as well as the presence of non-target bark beetle and wood borer species on the trap logs.

Additionally, the developmental stage and sex of the beetles were identified by opening the bark of the trap logs. The objective was to examine the potential variation in the time of settlement of trap logs at varying distances. The assumption was that the more distant logs would be populated later and that the brood in them would be at an earlier developmental stage.

The laboratory studies were conducted two days after the completion of the field portion of the experiment (3 July).

2.2. Statistical Processing and Modeling

The four-eyed fir bark beetle exhibits selectivity in host selection, with a focus on tree size [4,16,54]. To eliminate the possibility that the size of the trap logs influenced the distribution by cardinal directions and/or distance from the release point, we conducted a non-parametric Kruskal–Wallis test [55]. The cardinal directions and distances were used as grouping variables, and the length, diameter, and bark surface area of the trap logs were the dependent variables. A significance level of 0.05 or greater was used to confirm the uniform distribution of trap logs of different sizes.

As predictors in the simple linear modeling of the dispersion of beetles, we used the orientation to the cardinal directions (Cdi), the distance from the trap logs to the release point (dist, m), and the total bark surface area (S, dm²) of the trap logs at a point (

Table 1. Combinations of predictors (dist—distance from release point to trap objects, S—bark surface of the trap objects, Cdir—cardinal direction) used to model the population characteristics of the four-eyed fir bark beetle Polygraphus proximus Blandford in trap objects.

Model	Dist	S	Cdir
1	+
2	+		+
3	+	+
4	+	+	+

). In linear mixed-effect modeling, Cdi was treated as a random-effect variable, while dist and S were treated as fixed-effect variables. The diameter and length of the trap logs were excluded from the list of predictors, since their values were both used in calculating the value of S and exhibited no significant variations across cardinal directions and distances from the release point (Figure S2). Both the number of pairs (p) and the number of individuals of the brood generation at stages from larva to adult (b) were considered as dependent variables. The second group of dependent variables was obtained by converting them to the bark surface area: the number of adult beetles per dm² (p_S) and the number of insects of the brood generation per dm² (b_S).

A set of models was created for each dependent variable that differed in the set of predictors used. The predictor combinations employed are listed in Table 1. The best models from the sets were selected by minimizing the Akaike information criterion (AIC) value. As direct comparisons of linear and mixed-effect models by AIC do not give information about the effects of grouping factors, we used the information regarding random-effect variation for this purpose [56]. The quality of the model was assessed using the adjusted coefficient of determination ($r_{adj}^2$) and Pearson’s correlation coefficient (r) between the actual and predicted results. The R base package v. 4.3.2 was used to construct simple linear models [55], while the lme4 package v. 1.1-35.1 was used for linear mixed-effect modeling [56].

When modeling the flight range of beetles nonlinearly, we used a neg-exponential function that had previously been successful in solving similar problems [31,57,58]. The function’s value asymptotically approaches the x-axis, meaning that the dependent variable (p, b, p_S, or b_S) will never be equal to zero, and therefore has no biological meaning. To address this issue, we introduced, in addition to coefficients a and b, the coefficient n to the function:

$$y=a\times e^{b\times dist}-n$$

(1)

The formula used to calculate the maximum flight distance of insects is as follows:

$$dist={\displaystyle \frac{{log}_e\left(n/a\right)}{b}}$$

(2)

The nls2 v. 0.3-3 [59] and minpack.lm v. 1.2-4 [60] packages were used for nonlinear modeling.

3. Results

3.1. Analysis of Trap Logs

Pairs of the four-eyed fir bark beetle, detected by nuptial chambers with galleries, were found at all distances and in all cardinal directions from the release point. Unsuccessful attacks, indicated by an entry hole without a nuptial chamber, were observed at distances of 150 (E), 750 (N), and 1250 (E) meters from the release point (

Table 2. Number of nuptial chambers with egg galleries p (in parentheses, pairs per dm² p_S) of the four-eyed fir bark beetle on trap logs, depending on the direction and distance from the release point. Unsuccessful attacks are indicated by the white circle symbol (○). Empty cells show the absence of both successful and unsuccessful attacks.

Distance	N	E	S	W
50	3 (0.12)	9 (0.39)	12 (0.46)	1 (0.06)
100	1 (0.04)		5 (0.28)
150		○	11 (0.37)	2 (0.10)
300	3 (0.14)	6 (0.22)
500	1 (0.04)	3 (0.15)
750	○	1 (0.04)
1000	6 (0.24)	1 (0.04)		7 (0.31)
1250		○		1 (0.03)
1500				1 (0.04)

).

Of the galleries with a developing brood, only seven contained adults of the parental generation (females only). Broods from larvae to young adults were present in 26 cases, representing 35.1% of the total (

Table 3. The occurrence of four-eyed fir bark beetle immature stages (L—larvae, P—pupae, A—young adults), depending on the cardinal direction and distance from the release point. The figures in parentheses indicate the number of galleries at each stage.

Distance	N	E	S	W
50	L (3), P (3)	L (2)	L (4)
100
150			L (1)
300	L (1), P (1)	L (3)	L (4)
500
750		L (1), P (1)
1000	L (1)			L (3), P (3), A (2)
1250				L (1), P (1)
1500

). In terms of the number of individuals found, larvae (24) were significantly more numerous than pupae (9) and young adults (2).

3.2. Modeling

In linear modeling, the best results for all the dependent variables with the lowest AIC values were obtained for Model 1 (Table 1). These models included only distance as a predictor (

Table 4. Characteristics of the best linear models for number of pairs (p) and brood (b) and for their number per dm² (correspondingly, p_S and b_S), including the model coefficients for distance (dist), the values of the Akaike information criterion, the adjusted coefficient of determination, and Pearson’s correlation coefficient.

Dependent Variable	Predictors and Coefficients	AIC	${\mathit{r}}_{\mathit{a}\mathit{d}\mathit{j}}^2$	r
p	dist, –0.0021	175.77	0.061 (0.090) 1	0.300
b	dist, –5.21 × 10−4	142.20	−0.015 (0.470)	0.130
pS	dist, –8.83 × 10−5	−37.18	0.074 (0.069)	0.320
bS	dist, −2.07 × 10−5	−67.80	−0.016 (0.489)	0.125

¹ p-level is given in parentheses.

). The cardinal direction and bark surface area of the trap object did not have any significant effect on the colonization of trap logs by the four-eyed fir bark beetle or the number of its brood. If we include the bark surface area in models, the AIC values were higher as compared to Model 1. The interpretation of the modeling results according to Bates et al. [56] demonstrated the absence of cardinal direction influence on the dependent variables, and random-effect variance was close to zero.

The coefficient of determination for linear models is generally low, as unaccounted factors determine the bulk of the variability of characteristics. However, models that describe the number of parents (p, p_S) (Figure 4A,B) provide a relatively accurate representation of the current situation (0.05 < p < 0.1) (Table 4). Attempts to model the number of offspring (b) and the number of broods per dm² (b_S) were unsuccessful (Table 4).

Nonlinear models were used to determine the number of pairs p and their density p_S using Equation (1). The model of density p_S was found to be the best fit for the real data (AIC = −38.10) with coefficients a = 0.182, b = −1.75 × 10⁻³, and n = −0.001. The correlation between the real and predicted p_S values was statistically significant (r = 0.362, p = 0.038), which is slightly better compared to the linear model (Table 4). The negative exponential model for p yielded better results compared to the linear model (Table 4). The AIC value for the negative exponential model was 174.98, with r = 0.339, p = 0.054, and a = 4.28, b = −1.70 × 10⁻³, and n = −0.001.

The flight range predictions for the four-eyed fir bark beetle vary significantly depending on the model used. The linear modeling of p_S indicates that this value reaches zero at 1622 m from the release point, while a nonlinear model shows p_S = 0 at a distance of 2965 m. For p, these values are 1649 and 4929 m, respectively.

4. Discussion

4.1. Eliminating Possible Sources of Result Distortion

The flight range of the four-eyed fir bark beetle may be biased by the attractiveness of trap logs with beetles tunneled in the bark, and it is important to consider this potential source of bias when analyzing flight range data to ensure objectivity. Male beetles, who have begun constructing the nuptial chamber, emit an aggregation pheromone that attracts both sexes to inhabited objects [61]. Based on this, it was assumed that overwintered beetles may concentrate and fly out of fir slabs onto the trap logs closest to them. As a result, a significant proportion of the individuals that emerged later would attempt to populate these logs, reducing the likelihood of them settling on trap logs located at greater distances. This could lead to an underestimation of the flight range of P. proximus.

The micropopulation density p_S increases as one approaches the release point (Figure 4B). However, it is believed that the inhabited trap logs closest to the release point did not lose their attractiveness to the four-eyed fir bark beetle. Nevertheless, the beetles still flew towards more distant trap objects. The evidence indicates that P. proximus simultaneously colonized trap objects at different distances from the release point. This is demonstrated by the lack of a correlation between the developmental stage of the young generation and the distance (Table 3). This perspective is based on the biology of bark beetles. It was demonstrated that olfactory communication enables the regulation of population density. The signals involved have divergent effects. As the micropopulation approaches the p_S optimum, the release of the aggregation pheromone is replaced by the emission of repellents that cause avoidance of the area occupied by this micropopulation [62]. The optimal density for the four-eyed fir bark beetle varies widely, from two to eight pairs of P. proximus per dm². This range was established in a controlled experiment [46] and confirmed by numerous data from natural populations [63,64,65,66,67]. In our experiment, the maximum value of p_S was significantly lower than the lower limit of this range (Table 2). This finding does not provide evidence that trap objects lost their attractiveness for P. proximus. Additionally, it excludes the possibility of experimental results being distorted due to their influence.

It is crucial to acknowledge that the area of the experimental plot allocated to each trap object increases in proportion to the distance from the release point. This may result in the flight path of the beetles extending beyond the range within which they could be attracted by the trap objects. Nevertheless, an experiment that excluded this possibility in its methodology [39] yielded results that were consistent with our own, demonstrating that the attractiveness of the traps exhibited a similar dependence on the distance from the release point as we describe.

4.2. The Impact of Wind Direction on the Flight of the Four-Eyed Fir Bark Beetle

The results of the experiment showed no correlation between the colonization of trap logs by the four-eyed fir bark beetle and the cardinal direction (Table 4). Despite the predominance of west winds (Figure 3B) and the location of the most distant galleries in this direction (Table 2), the largest number of successful attacks was recorded in the southern part of the experimental plot (Table 2). Previous studies have produced contradictory results, indicating a lack of connection between the direction of flight of bark beetles and the direction of the wind [29,34], more active flight against the wind [33], or downwind [42].

Bark beetle searches for hosts typically last no longer than one day [29,35,39]. It is therefore imperative that data collected during this period, rather than averaged over a longer period, be used for accurate assessments. Furthermore, the flight direction may vary. In the absence of an aggregation pheromone source, scolytinae beetles tend to fly downwind. Nevertheless, following the secretion of this pheromone by pioneers, a preference for flying against the wind is observed [33,42]. Therefore, the beetles face a constantly changing situation during the flight period, which lasts from two weeks to one month in P. proximus [4,63,68]. This experiment, which closely mimics natural conditions, seems to best reflect the actual impact of wind direction on the dispersal of beetles emerging from their wintering sites. The age structure of the immature stages (Table 3) may indicate that the dispersal of bark beetles lasted for at least several days. Given the potential for significant change over the specified time period in environmental conditions that may influence the orientation of parent-generation beetles, it is reasonable to assume that their behavior would likewise change. The flight behavior of these beetles may be influenced by environmental conditions at a given time. For instance, they may fly with or against the wind, which would result in a negligible impact of wind direction on the model over several weeks.

4.3. Effectiveness of Attracting the Four-Eyed Fir Bark Beetle with Trap Logs

This experiment showed that only a small proportion of beetles were attracted by trap logs. Based on the number of emerging beetles (see Section 2.1), the monogyny of P. proximus [52,53], and the number of nuptial chambers with egg galleries on trap logs (Table 2), it can be concluded that approximately 4.0% of the emerged beetles were recaptured. However, the value obtained was relatively high. Previous studies have predominantly utilized traps to measure the flight range of beetles (I. typographus or Dendroctonus ssp.) containing synthetic aggregation pheromones [29,30,31,33,34,35,36,38,39,44] or trap trees treated with such pheromones [41]. If trap trees [40], barrier traps with kairomones [37], or without semiochemicals [42] were used as trap objects, the proportion of recaptured beetles did not exceed 5.2% [37].

The high proportion of beetles recaptured in our experiment may be due to the lack of other points of attraction. In contrast, only a very low proportion of Dendroctonus frontalis Zimm., 1868 (no higher than 0.066%) were recaptured in pheromone traps [31], which appears to be linked to the presence of numerous other attractive objects at the experimental sites. In an experiment to study the flight range of I. typographus, pheromone traps were hung in a spruce forest that had been damaged by a hurricane several years prior to the start of the experiment [36]. In the selected area, there were no suitable objects for the colonization or maturation feeding of P. proximus, as the bark beetle feeds exclusively on fir trees [4].

4.4. Flight Range of the Four-Eyed Fir Bark Beetle and Its Modeling

The results of our experiment indicate that the maximum flight distance achieved by the beetles was 1500 m (Figure 4A,B, Table 2), which exceeds the results obtained in the majority of full-scale experiments conducted on other bark beetle species. It is probable that this discrepancy is attributable to the specific characteristics of the experimental design rather than to the flight capacity of the species under study. In most of the studies cited [33,34,35,37,38,39,40,41,42], the maximum distance from the release point to the furthest trap object was several times less than in our own study. Alternatively, the distance did not exceed 1 km [30,31,44]. However, in instances where the experimental design permitted a greater distance from the release point, the maximum confirmed flight distance of I. typographus was comparable to that observed in our own studies [29,36]. For six-toothed bark beetle Ips sexdentatus (Boerner, 1766), the flight of beetles between neighboring experimental sites demonstrated the possibility of flight up to 4 km [44].

Our experiment aimed to maximize the flight distance of the four-eyed fir bark beetle imago by limiting the number of objects that are attractive to them. This was achieved by using relatively sparsely located and small fir logs (see the study site and experimental set up details), which are unlikely to release significant amounts of kairomones. It has previously been suggested [34] that this situation stimulates bark beetles to fly away from the release point, resulting in an increase in the distance they cover. The technique used involved beetles that had just emerged from under the bark. This approach had a positive effect on flight range, as demonstrated in the example of D. ponderosae [43].

Our results also agree well with previously obtained data on the flight potential of other bark beetles and wood borers. The dependence of the number of adult bark beetles attracted by trap objects on the distance from the release point usually [29,30,31,34,36,37,38,39] has a form that can be described by a function that, like Equation (1), can be reduced to the Taylor function [69]. Similar experiments have noted both linear [33] and non-monotonic (with a peak at a short distance from the source of insects) [34] distributions less frequently. The dispersion of bark beetles and wood borers in general can be described well by the monotonic nonlinear distribution described by the Taylor function [33]. Although it is methodologically difficult to conduct similar studies for other groups of phloem- or wood-feeding insects, this is suggested by an analysis of the relationship between the distribution of A. planipennis population density and the distance to the source of insects [70], as well as data from measuring the flight range of some species of longhorn beetles on flight mills [71,72].

The computational method was identified as the sole means of determining the maximum flight distance that beetles were capable of covering in the search for food. This was substantiated by the observation that their actual flight range was identical to that of the maximum distance of food items from the release point. Equation (2) was used to calculate this distance, resulting in a value of 4919 m for p and 2965 m for p_S. Both results should be treated with caution due to the significant discrepancy, but the first value appears to be closer to the true values. A confirmation of I. sexdentatus’ ability to fly over a distance of 4 km was previously mentioned [44]. Similar experiments showed that 1% of D. frontalis beetles, with a median flight range of 500 m, cover a distance of 3.29 km [31], and golden-haired bark beetle Hylurgus ligniperda (Fabricius, 1787) can cover a distance of 5 km [37].

The discrepancy between the previously published data regarding the assessment of the migration distance of P. proximus [23] and the present findings appears to be attributable to differences in environmental conditions. In the experiment described here, the insects were placed under limited food availability with widely spaced food sources, which led to the observed dispersal behavior in search of suitable hosts [40]. The study cited is based on observational data from an outbreak area, where approximately 4% of trees were found to be attractive for four-eyed fir bark beetle attacks [23]. Our results provide a better description of the beetle’s behavior when it is necessary to intensively search for food, such as in forest stands with a small number of fir trees. In contrast, the data from [23] characterize the beetle’s behavior when the food supply is sufficient. One possible reason for the differences between the maximum expansion distances predicted for p and p_S, and the source of uncertainty in general, is the value of the coefficient n. Even small changes in n can result in multiple changes to the calculated maximum flight distance. The smaller n, the bigger the calculated distance with a sharp increase for n ≤ 0.00125 (Figure 5).

It is important to note that the results obtained are limited to the interpretation of data from a single experimental site. It cannot be ruled out that the maximum flight range of P. proximus may change under different conditions, either decreasing or increasing. To clarify this issue, it would be desirable to conduct similar experiments as have been conducted for the much better studied I. typographus [29,30,34,36,39,40] and D. ponderosae [33,38,41,42].

5. Conclusions

In accordance with the parameters of our experimental design, the flight range of the four-eyed fir bark beetle is solely contingent upon the distance from the release point, largely due to the sparse distribution and limited number of trap logs. We were unable to confirm the previously stated dependence of bark beetle flight on wind direction. We observed that the experimentally confirmed maximum flight distance of P. proximus is 1500 m. However, our model estimated the potential flight range of P. proximus to be approximately 3000 to 5000 m. The number of beetles emerging from their wintering sites and attracted by the food objects decreases exponentially along with the distance to the breeding site. The number of pairs on trap logs and the number of individuals of the parental-generation individuals per dm² also decrease rapidly with distance from the release point. The maximum flight range of the four-eyed fir bark beetle was calculated based on two different sets of data. One set, using information on the number of pairs, resulted in a range of 4919 m. The other set, which used the number of beetles per dm² data, resulted in a range of only 2965 m. While there is a significant discrepancy between these results, an analysis of data from similar experiments on other bark beetle species suggests that the first value is a more accurate representation of the four-eyed fir bark beetle’s flight capacity.