Byers, J.A. 1999. Effects of attraction radius and flight paths on catch of scolytid beetles dispersing outward through rings of pheromone traps. Journal of Chemical Ecology. 25:985-1005. pdf

Department of Crop Science
Swedish University of Agricultural Sciences
SE 230-53 Alnarp, Sweden
Present address:

Paths of insects dispersing outward through pheromone traps Abstract-- see it in
Results were analyzed from six previous studies in which marked bark and ambrosia beetles, Ips typographus, I. paraconfusus and Trypodendron lineatum (Coleoptera: Scolytidae), were released at the center of concentric rings of pheromone traps. Assuming nearly straight flight paths, a `filtering' equation model predicts recapture percentages on several trap rings of specified radii, trap numbers, and effective attraction radius (EAR) of a pheromone trap. The equations were used to calculate recapture percentages on concentric trap rings as a function of increasing EAR, and gave polynomial relationships for each ring with terms equal to the number of inner rings plus one. These results were confirmed by computer simulations. The filtering equations were iterated with increasing EAR values to find one that gave a recapture percentage for the innermost trap ring that matched the field results. The estimated EAR for a synthetic pheromone bait of I. typographus was similar in five tests (range 1.39 to 1.78 m), but in two other tests was larger (3.27 and 15.9 m). The EAR for pheromone of 75 male I. paraconfusus in ponderosa pine logs ranged from 0.35 to 34.5 m (mean of 4.7 m), and was generally larger for previously pheromone-responding beetles than for freshly emerged ones. For T. lineatum, the EAR of lineatin-baited traps at 100 m radius was 2.43 m. Recaptures of I. typographus were reasonably predicted by the estimated EARs in the filtering model. To obtain perfect fits, another model assumed the EAR could vary with ring radius (dispersal distance) and found that the EAR for I. typographus decreased with dispersal distance in four experiments, but increased or was variable in two others. The EAR decrease is probably due to catch of more responsive beetles on inner rings. However, in I. paraconfusus and T. lineatum, the EAR increased with dispersal distance possibly due to changes in responsiveness with flight exercise. Simulations that varied combinations of the EAR and random angles of maximum turning (AMT) of beetles stepwise, found that a nearly straight flight path for I. typographus explained the observed catches on trap rings best, while a higher AMT of 36° was better to explain catches of T. lineatum. Simulations show that catch per trap ring in relation to radial distance can be influenced significantly by the beetle's AMT (still unobserved in the field). A conceptual model of dispersal and host selection in "aggressive" bark beetles with regard to pioneer and joiner colonization strategies is presented.

Key Words--Effective attraction radius, dispersion, dispersal, host finding, host selection, Scolytidae, Coleoptera, Ips typographus, I. paraconfusus, Trypodendron lineatum, computer simulation model


In California, Gara (1963) released marked bark beetles, Ips paraconfusus, at the center of one ring of five traps containing ponderosa pine logs infested with 75 males each. The ring radius varied in individual tests from 3 to 2000 m. Since then, several studies in Europe have released marked spruce bark beetles, Ips typographus, at the center of several concentric rings of traps releasing pheromone components (Botterweg, 1982; Zumr, 1992; Zolubas and Byers, 1995; Duelli et al., 1997). The striped ambrosia beetle, Trypodendron lineatum, also was released from the center of three trap rings baited with the synthetic pheromone lineatin (Salom and McLean, 1989). Duelli et al. (1997), marked 6898 I. typographus termed "unflown" (freshly emerged) and 5123 considered "flown" (collected in pheromone traps) and released them at the center of three rings of pheromone-baited traps in a nonhost Scots pine forest (Table 1).

Table 1. Trap ring radii and number of synthetic pheromone-baited traps per concentric ring in previous studies in which Ips typographus were released at the center of the rings and a portion recaptured on the pheromone traps.
Duelli et al. (1997) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Ring radius (m) 5 200 500
Number traps 4 80 80
Catch unflown (6898)a 2445 650 195
Catch flown (5123) 2070 95 38
Zolubas and Byers (1995) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Ring radius (m) 10 or 30b 60 90 120
Number traps 1 or 4b 4 4 4
Catch (5030 or 5920)b 284 or 384b 208 64 7
Zumr (1992) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Ring radius (m) 50 100 200 300 400
Number traps 4 4 4 4 4
Catch (6600)c 2673 1254 719 317 290
Botterweg (1982) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Ring radius (m) 50 100 200 350 500
Number traps 4 8 16 28 40
Catch (1500 and 7000)d 125 or 198d 56 or 36 55 or 66 22 or 90 9 or 167

aValues in parentheses in first column are number of released I. typographus.
bValues for experiments 1 and 2, respectively, single values for experiment 2.
d1989 and 1990 results pooled.
eExperiments 1 (1980) and 3 (1981), respectively.

Zolubas and Byers (1995) and Zumr (1992) released marked I. typographus at the center of four lines of pheromone traps in cardinal directions which can be considered as concentric rings (only the first four or five rings considered here) in a spruce forest (Table 1). Botterweg (1982) also released marked spruce bark beetles at the center of pheromone trap rings in an area of meadow and Scots pine forest (Table 1). Among the purposes of these studies were to describe how far bark beetles disperse and whether flight behavior or responses to pheromone traps varies with distance from the release point. The authors of these studies concluded based on trap catches that bark beetles fly away from a release site in all directions when wind speeds are below 1 m/s.

The "effective attraction radius" (EAR) was proposed as an index of attractive strength for a trap releasing semiochemicals (Byers et al., 1989). Given a population density that is proportional to the unbaited (passive) trap catch, the EAR is the radius that a spherical passive trap would need to be in order to catch, merely by interception, as many dispersing insects as were actually caught on the baited trap. Comparison of catches on passive and pheromone-baited traps gave an EAR of 1.9 m for I. typographus response to a release of pheromone components, 50 mg 2- methyl-3-buten-2-ol (MB) and 1 mg (S)-cis-verbenol (cV) per day (Byers et al., 1989). Similar amounts of MB+cV were also released in trap ring studies using Pheroprax® baits (Zumr, 1992; Duelli et al., 1997) and `Ipslure' baits (Botterweg, 1982; Zolubas and Byers, 1995). For simulation studies, the EAR can be considered more simply in two dimensions rather than three because at large EARs the ground and beetle's flight height essentially flatten the theoretical sphere into a cylinder.

In the dispersal studies above, catches on pheromone traps decreased as a function of distance from the release point as described by power and exponential regressions (Zolubas and Byers, 1995). This is expected based on the movement of beetles outward into increasingly greater areas. However, the relationships can be greatly affected by several factors, for example, the EAR of a trap could change with flight distance (proportional to distance from release site). Another factor, previously ignored, is that there is a "filtering" effect such that some beetles would be caught on the first rings of traps while those remaining would pass through to be possibly caught on outer rings. There could also be a selective catch of pheromone-responding beetles on the inner rings while unresponsive beetles would pass through to be caught on traps of the outer rings by chance interception. Bark beetles might even change their angle of turning (or frequency of turning) with flight distance from the source which ought to affect catch rates. The previous studies were done in spruce, pine, or Douglas-fir forests so interceptions by trees, expected every 67 m for a 70-year old Norway spruce forest of 30 cm diameter trees (Byers, 1996a), might affect the dispersal directions when beetles that had landed took flight again in random directions.

My first objective was to develop equations that can calculate the theoretical filtering effect of any arrangement of concentric trap rings of specified dimensions, numbers of traps, and attractive power (EAR) in order to predict the catch of insects dispersing outward from a central release site. A second objective was to determine the influence of trap EAR and the beetle's angle of maximum turning at random (AMT) on catches of scolytid beetles in various trap ring arrangements in computer simulations. The comparison of predicted catches using equations and simulations with those catches observed in the field in the previous studies may provide insights concerning the behavior of bark and ambrosia beetles during the initial dispersal from brood trees and overwintering sites. Finally, I develop a theory that during dispersal and host seeking, a beetle exhibits either a "pioneer" or a "joiner" strategy of colonization behavior that is based on competition, host resistance, presence of aggregation pheromone, and the bark beetle's fat reserves.


Sequential equations to predict catches. A general series of equations can predict the catch on any number of concentric rings of traps depending on the respective ring radii, number of traps per ring, and radii of the traps (assumed to be equal). Considering three rings as in Duelli et al. (1997), the number caught on rings one to three, C1 to C3, and the number escaping each ring, E1 to E3, can be calculated by three successive pairs of equations assuming a nearly straight flight path (no beetles can come back once they have left a ring):

where N is the initial number of insects released, T1 to T3 are the number of traps in rings 1 to 3, EAR is the effective attraction radius of the pheromone trap, and R1 to R3 are the radii of trap rings 1 to 3, respectively. The catch on a fourth ring, or more, can be considered by adding a fourth equation, or more, as indicated.

The sequential equations were used repeatedly by computer to graph the effect of changing the EAR on the percentage of released beetles caught on each trap row. The best-fitting EARs to the data of four studies, and various experiments, were found by incrementing the EAR from 0 to the maximum possible without overlap (MAX) in steps of MAX/10000 m using sequential equation (1) by computer to find the least difference in the actual percent catch on ring 1 compared with the predicted. This EAR was then used to calculate the predicted catches on the outer rings for comparison to observed catches. Assuming, however, that the EAR can vary with distance from the center, an optimal EAR was found for each ring based on the maximum number that could have passed through the inner rings (by subtracting the catches from the number released) and again on the dimensions and trap numbers of the ring (as calculated for the first ring above).

Simulations to predict catches. Insect flight movement can be simulated in two dimensions by taking steps in a forward direction with possible random deviations up to an angle of maximum turn (AMT), either right or left at random (Skellam, 1973; Byers, 1991, 1993a, 1996a, b). An insect is caught when intercepting a trap, no matter how large the step size, according to the algorithm in Byers (1991). A computer model was made to simulate the trapping designs used in previous studies, e.g. by Duelli et al. (1997). The input parameters of the program are dispersal time, number of released insects, average insect speed, step size, AMT, number of trap rings, number of traps per ring, radii of trap rings, and the EAR of a trap. The release site is centered on the screen and coordinates of the traps are calculated and traps drawn. Insects are given random initial directions (random number 0 to 360° ).

In all simulations, flight speed was 2 m/s which is about what large bark beetles such as Ips typographus can maintain in still air (Byers, 1996a). Simulated dispersal periods were limited to 1 hr when AMT was varied, although a few beetles on flight mills have flow up to 6 hrs (Forsse and Solbreck, 1985; Forsse, 1991; Gries et al., 1990). The AMT was varied from 0° to 45° and steps were 2 m (possible turn every sec). Catch was recorded for each trap ring. The "flown" bark beetles have a catch distribution on the three rings that was different from the "unflown" (Duelli et al., 1997) and did not fit well to the predicted based on the best-fitting EAR calculated for ring 1. Therefore, the EAR and the AMT were varied two-dimensionally (AMT varied at each varied EAR) in an attempt to find an EAR-AMT combination of simulated results that could predict the field data. The EAR was the same for all traps in the rings. Other catch distributions (Zolubas and Byers, 1995, I. typographus; Salom and McLean, 1989, experiment 1, T. lineatum) were modeled similarly.

The expected catch per trap with an EAR of 1.9 m at increasing distances from the release point of 1000 insects was estimated by simulation when only one trap was present (no filtering effect). Insects had either an AMT of 5° or 20° and flew for 30 min. In another series of related simulations, competing traps were placed in 10 concentric rings of 20, 10, and then 4 traps each, respectively, every 25 m, with the same EAR and an AMT of 5° . Nonlinear regressions were fitted to the data when appropriate.


Sequential equations to predict catches. The computer-iterated equations (1-3) found that increasing the effective attraction radius (EAR) of a trap from 0 to the maximum without overlap between traps, linearly increases the recapture percentage (of those released) on trap ring 1 (for the trap configuration of Duelli et al., 1997, Y = 25.465X, r2 = 1, Figure 1).

FIG. 1. Percentage caught on each trap ring of the number of insects released in relation to the effective attraction radius (EAR) of the trap. The curves are based on equations (1-3) for four traps in ring 1 (5 m radius), 80 traps in ring 2 (200 m radius), and 80 traps in ring 3 (500 m radius). The maximum trap radius of 3.927 m is based on four non-overlapping traps in ring 1. Concentric rings of dots represent trap ring dimensions and number of traps (3 m radius).

The innermost trap ring always will have a linear increase in recapture percentage as a function of EAR, regardless of the ring radius or number of traps in the ring. The recapture percentage on the second ring of traps has a quadratic relationship to EAR, first increasing then decreasing (Figure 1), again regardless of the ring radii or number of traps. For the trap configuration of Duelli et al. (1997), the relation follows Y = - 3.242X2 + 12.732X, r2 = 1 (Figure 1). The third ring of traps catches insects similarly (Figure 1) but even less according to a cubic relationship, Y = 0.165X3 - 1.945X2 + 5.09X, r2 = 1. Trap placements with four or more rings are related as polynomials of four or more terms; however, the specific coefficients depend on the actual EAR, ring radii and number of traps per ring.

The EAR of pheromone-baited traps in previous studies can be estimated using sequential equation (1) and incrementing the EAR until the predicted catch percentage matches the observed catch. Trap ring 1 is the only reliable one to use since the relation is monotonic while rings 2 and 3 are unimodal with two values of X for each Y (Figure 1). In the study by Duelli et al. (1997), the pheromone traps would need to have an EAR for "unflown" I. typographus of 1.39 m to account for the observed catch of 35.45 % recaptures on ring 1 (Table 2).
Table 2. Percentages of recaptured Ips typographus in previous studies compared with predicted percentages calculated from the filtering model with an effective attraction radius (EAR) of pheromone traps best fitting the observed percentage for trap ring 1.
Percentage recaptured
Duelli et al. (1997) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Catch unflown (6898) 35.45 9.42 2.83
Predicted (1.39 m EAR) 35.45 9.42 2.83
Catch flown (5123) 40.41 1.85 0.74
Predicted (1.59 m EAR) 40.41 12.04 3.84
Zolubas and Byers (1995) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Catch (5030 or 5920)a 5.65 or 6.49a 3.51 1.08 0.12
Predicted (1.78 or 1.53 m EAR)a 5.65 or 6.49a 3.03 1.96 1.44
Zumr (1992) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Catch (6600) 40.5 19.0 10.89 4.8 4.39
Predicted (15.9 m) 40.5 12.05 4.8 2.88 2.01
Botterweg (1982) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Catch (1500 or 7000)b 8.33 or 2.83b 3.73 or 0.51 3.67 or 0.94 1.47 or 1.29 0.6 or 2.39
Predicted (3.27 or 1.11 m EAR)b 8.33 or 2.83b 7.64 or 2.75 7.0 or 2.67 6.42 or 2.6 5.88 or 2.52
aValues for experiments 1 and 2, respectively, single values for experiment 2.
bExperiments 1 (1980) and 3 (1981), respectively.

This value also predicts recapture percentages on rings 2 and 3 that are quite close to observed values. The best-fitting EAR for the "flown" beetles was 1.59 m yielding 40.41 % catch on ring 1 as observed, but the predicted catches on rings 2 and 3 of 12.04 and 3.84 % are much larger than the observed values of 1.85 and 0.74 %, respectively (Table 2). The sequential equations predict a similar EAR of 1.78 or 1.53 m in the studies by Zolubas and Byers (1995) and 3.27 or 1.11 m in two studies by Botterweg (1982), and even the recapture rates on rings 2 to 5 are similar to predicted catches with some exceptions (Table 2). The EAR calculated for traps used by Zumr (1992), however, is much larger at 15.9 m, but the predicted catch rates are reasonably similar to that observed, again with some unexplained deviations (Table 2).

In contrast to a constant EAR assumed above, it is possible that bark beetles change their responsiveness to pheromone as they fly away from the release site (or as a function of flight time), thereby resulting in a variable EAR. The same result could occur if bark beetles varied inherently in their responsiveness to pheromone so that more pheromone-sensitive individuals would be filtered out by the inner rings of traps. The best-fitting EAR can be predicted based on the number expected to pass through each succeeding ring. The EAR for I. typographus appears to decline significantly with distance of dispersal from the release (Table 3), for example, from 1.59 to 0.15 m (Duelli et al., 1997) and from 1.53 to 0.11 m (Zolubas and Byers, 1995) or from 3.27 to 0.24 m in experiment 1 of Botterweg (1982).
Table 3. Estimated effective attraction radii of synthetic pheromone traps for each concentric trap ring of previous studies in order to obtain the observed catches of Ips typographus with the filtering model.
Effective attraction radius (EAR) in m
Duelli et al. (1997) Ring 1 Ring 2 Ring 3 Ring 4 Ring 5
Unflown 1.39 1.15 1.01 --
Flown 1.59 0.24 0.25 --
Zolubas and Byers (1995)
Experiment 1 or 2a 1.78 or 1.53a 1.77 0.85 0.12 -
Zumr (1992)
pooled release 15.9 25.1 42.3 38.2 55.7
Botterweg (1982)
Experiment 1 or 3b 3.27 or 1.11b 1.6 or 0.21 1.64 or 0.38 0.68 or 0.53 0.28 or 0.99
aValues for experiments 1 and 2, respectively, single values for experiment 2.
bExperiments 1 (1980) and 3 (1981), respectively.

However, the EAR was consistently large (11 to 17 m) in Zumr (1992), but went down and then increased again with trap ring distance in experiment 2 of Botterweg (1982).

In the study with I. paraconfusus (Gara, 1963), nine experiments had a trap ring of radii from 3 to 2000 m (5 traps in a ring) with EARs estimated to range from 0.35 to 34.5 m, average of 4.68± 4.13 m (95% CL, Table 4).

Table 4. Estimated effective attraction radii (EAR in m) of traps with natural pheromone of Ips paraconfusus (75 males in logs) for nine experiments of various trap ring radius in order to obtain the observed catches (Gara, 1963).
Emerging beetles Responding beetles
Ring radius (m)a Recapture % EAR (95% C.L.)b Recapture % EAR (95% C.L.)
3 18.58 0.35(0.31-0.40) 19.05 0.36(0.32-0.41)
5 28.18 0.89(0.80-0.97) 26.73 0.84(0.77-0.92)
10 20.62 1.30(1.14-1.47) 25.92 1.63(1.35-1.95)
25 15.74 2.47(2.22-2.74) 16.96 2.66(2.44-2.91)
50 5.97 1.88(1.31-2.67) 16.39 5.15(4.45-5.93)
100 2.31 1.45(0.57-3.64) 11.89 7.47(5.22-10.52)
500 1.45 4.56(2.20-9.27) 10.98 34.49(29.72-39.93)
1000 0.70 4.40(1.19-15.71) 1.27 7.98(4.21-15.08)
2000 0 - 0.13 1.68(0.25-9.30)
aFive traps equally spaced in ring.
bConfidence limits for proportions (from Gara, 1963) were used to calculate 95 % confidence limits for EAR.

Beetles that had freshly emerged were marked with one color of fluorescent powder while another group that had responded previously to pheromone was colored differently and both groups were released simultaneously. The EARs for both groups increased similarly as trap rings were enlarged from 3 to 25 m radius, then the EAR for the emerged group increased little with increases in ring radii while the EAR for the previously responding group continued to increase (Table 4). T. lineatum released in three concentric rings of traps (Salom and McLean, 1989) had EARs that increased from only 0.32 m close to the release to 1.72 m at 100 m radius (Table 5). In the one ring tests, the EAR also seems to increase up to 7.1 m at 500 m radius (Table 5).

Table 5. Estimated effective attraction radii of lineatin-baited traps for each concentric trap ring in order to obtain the observed catches of Trypodendron lineatum with the filtering model (Salom and McLean, 1989).
Effective attraction radius (EAR) in m
Ring 1 Ring 2 Ring 3
Experiment 1a 0.32(0.30-0.34)b 1.04(0.98-1.10) 1.72(1.61-1.84)
Experiment 2c 2.43(2.29-2.59) - -
Experiment 3d 7.07(5.11-9.74) - -
aTrap ring radii of 5, 25 and 100 m with 4, 8 and 16 traps for rings 1 to 3, respectively; and recaptures of 8.1, 9.7 and 7.2 % per trap ring, respectively, of 10535 released in six replicates.
b Confidence limits for proportions were used to calculate 95 % confidence limits for EAR.
cOne trap ring of 16 traps in a radius of 100 m; and recapture of 12.4% of 6780 released in four replicates.
dOne trap ring of 4 traps in a radius of 500 m; recapture of 35 of 1985 released.

Simulations to predict catches. The catch of simulated insects dispersing outward through rings of traps (Figure 2) verifies the sequential equations (Table 2, unflown) when the flight path was nearly straight, meaning that the angle of maximum turn at random (AMT) was only a few degrees.

FIG. 2. Percentage caught on each trap ring of the number of insects released in relation to the insect's angle of maximum turn (AMT) at random assuming a 1.39 m effective attraction radius (EAR) for a trap. The curves are based on release of 1000 simulated insects for each X-value with trap arrangement as in Figure 1 (see text for details).

An extension of the AMT to 90° caused paths to twist wildly and this caused the relationships between the AMT and the recaptured percentage on the various rings to be complicated (Figure 3).

FIG. 3. Percentage caught on each trap ring of the number of insects released in relation to the insect's angle of maximum turn (AMT) at random assuming a 1.39 m effective attraction radius (EAR) for a trap. The curves are based on release of 1000 simulated insects for each X-value with trap arrangement as in Figure 1 (see text for details).

It was thought that simulations varying both the EAR and AMT could find values that would predict the percentages of catch of "flown" I. typographus on the various rings that were not fitted well by the equation model (Table 2). However, none of the stepwise values of EAR from 0 to 3.93 m (maximum without overlap) while varying AMT from 0 to 90° were able to predict the distribution of catch percentages of "flown" beetles on the three trap rings of Duelli et al. (1997). For example, using an EAR of 1.39 m and varying the AMT (0-90° ) shows that no relative catch distributions on the three rings were similar to that found in the field (Figure 3, Table 2). The "best" fit, although unsatisfactory, was an AMT of 0° or straight flight path.

The best fit for the data of Zolubas and Byers (1995) for each ring was better, giving an EAR of 1.6 m and AMT of 0° ; and recapture percents of 6.3, 3.5, 0, and 0% per ring, respectively (observed were 6.5, 3.5, 1.1, and 0.1%). Using the data of Salom and McLean (1989) for T. lineatum, an EAR-AMT combination was found that fit the observed catch percentages best with an AMT of 36° and EAR of 0.2 m, giving percentages of 8.5, 9.4 and 8.0 (compared to the observed 8.1, 9.7 and 7.2 % recapture). A flight duration of only 10 min did not change the results much as the best EAR was 0.3 m and AMT of 36° . This method does not work for experiments with only one ring. For example, in the second experiment, they recaptured 12.4% on the 16 traps in a ring of 100 m radius (Table 5) which in simulations was fit by many combinations of EAR-AMT, from an EAR of 0.2 m and AMT of 38° to an EAR of 2.5 m and AMT of 0° . In this case, the EAR and AMT vary inversely (in a negative logarithmic relation: EAR = 14.78 - 13.27 ln AMT, r2 = 0.97), and thus no conclusions can be drawn about flight paths.

The catch per trap as a function of trap distance from the release site has been plotted in most earlier studies as summarized by Zolubas and Byers (1995). Simulations using an ideal situation of only one trap, so that competition among traps could not occur, showed a power relationship between catch and distance (Y = 540.19X-0.98, r2 = 0.98) that depended on the AMT (Figure 4).

FIG. 4. Catch on one trap as a function of distance from the point of insect release at two different random angles of maximum turn (AMT). Each point represents an average of ten simulations of 1000 insects each, that flew for 30 min. The effective attraction radius of the trap was 1.9 m.

For example, a more twisting AMT of 20° causes a higher catch on the trap at all distances compared to a more straight path with an AMT of 5° (Figure 4). When traps were competing and filtering the beetles with flight paths of 5° AMT, the catch per trap was less, as expected, compared to the situation with only one trap (Figure 5).

FIG. 5. Comparison of catch per trap in simulations with only one trap versus many competing traps in rings at indicated distances from the release site. The number of competing traps in each successive ring was 20, 10, and then constant at four traps per ring. Each point represents an average of ten simulations of 1000 insects each, AMT of 5° , and EAR of 1.9 m, with flight for 30 min.

However, the first ring of traps filtered out many beetles which biased the catch on the second ring so that it did not fit the general curve compared to the outer rings (Figure 5). This effect is evident in earlier studies where many beetles were caught on the first ring (Fig. 7 of Botterweg, 1982; Fig. 2 of Duelli et al., 1997) but is minimal in other studies where only 4 traps per ring were used at farther distances (Zumr, 1992; Zolubas and Byers, 1995). This effect tends to confound the regressions in a way that was not realized earlier (Zolubas and Byers, 1995).


The sequential equations that filter out the dispersing insects on successive rings of traps were validated by simulation, and in some cases by a good match with field catches. Usually, the traps in a ring, both in the simulations and in the field, are spaced equally apart. However, actually it does not matter whether the traps are placed at random or spaced about the ring as long as there is no overlap of the EAR (or plume) and that beetles disperse in all directions equally at random. Also, it does not even matter if beetles fly in one general direction (e.g. downwind) with random deviations; non- overlapping EARs of traps would theoretically filter in the same proportions. In the simulations, on the other hand, if insects fly completely straight (0° AMT) then inner traps will prohibit outer traps along the same trajectory from catching (which did not happen in any studies). Therefore, the simulated traps must be offset or the insects must have some degree of random turning. However, too much random turning will cause them to turn back occasionally into a ring of traps they have already passed through, thereby possibly inflating the catch on that ring. The sequential equations do not consider the AMT or trap placement and thus give ideal results. The equations should not be used with an EAR that overlaps with other traps. In nature, the EAR could overlap but this should decrease the catches as the traps directly compete and also the insects could be confused by background levels of pheromone. Gara (1963) showed that bark beetles would fly past sources of natural pheromone when overlapped by pheromone from sources further upwind.

The EAR is expected to be much smaller than an envisioned average distance of oriented flight toward a semiochemical source, which in turn is most likely smaller than the average distance that bark beetles would first detect such a source (Byers et al., 1989; Schlyter 1992). One can imagine a pheromone plume as globules and filaments of higher and lower (or no) pheromone concentration snaking, splitting or exploding into larger and more uniform clouds that dissipate below the threshold detection of the insect (cf. Byers 1996b). The probability that an insect will orient to the pheromone source after entering this plume depends in large part on the entry point in relation to the source. It is obvious that all these probabilities, behavioral variations, and differences in wind turbulence over time make the calculation of an average orientation distance virtually impossible. What the EAR attempts to do instead is reform the plume and all the orientation probabilities into a sphere (or cylinder) where 100% orient to the source (Byers et al., 1989; Byers 1995, 1996a).

The EAR for a specific semiochemical release rate and insect species is in theory independent of the population density (or number released). Temperature and wind could have some affect on the EAR by influencing orientation behavior but this has not been studied. Most behavioral tests are done under similar weather conditions when insects can fly. The EAR can be estimated by comparison of a passive trap catch with the semiochemical trap catch and using the dimensions of the passive trap (Byers et al., 1989). This method does not depend, in theory, on the trap efficiency as a lower efficiency is like a lower population density, neither should change the ratio of catches between the pair of traps. Alternatively, the EAR can be estimated with a second method using the filtration model, as done here, by comparing the catches on semiochemical-baited traps with the number released from the center. However, in this case the trap efficiency would affect the EAR.

Increasing the dosage of semiochemical release in traps should give increasing EARs, until inhibition at the highest rates. According to Schlyter et al. (1987), 1 m of Pheroprax® tape one week old releases 50 mg MB and 1 mg cV per day (used by Duelli et al., 1997). Zolubas and Byers (1995) used Ipslure baits that released the same rates but also released ipsdienol (probably inactive, Schlyter et al., 1987). Botterweg (1982) used 0.25 m of Pheroprax® and Zumr (1992) used some unspecified portion thereof. These studies all appear to have used comparable rates so the much higher EARs of Zumr (1992) are probably not explained by release rate (Table 3). However, his was the only study that used a cluster of four traps as "the trap". This would both increase the trap surface area by four and broaden the spatial distribution. Byers et al. (1989) showed that enlargement of the sticky trap radius logarithmically increased trap catch of I. typographus. The EAR, as estimated with the filtering equations, depends on the trap efficiency which probably differed in each study: Duelli et al. (1997) used Theysohn traps for ring 1 and a mixture of these and Olesnik traps in outer rings; Zolubas and Byers (1995) used cross-vane barrier traps, while Botterweg (1982) used drain-pipe traps. There does not seem to be any consistent affect of nonhost Scots pine or host Norway spruce forest on the recapture rates in the studies with I. typographus.

Using paired sticky traps, an EAR of 1.9 m was calculated for a MB+cV release (Byers et al., 1989) that is similar to most of those estimated here for the inner trap ring (Tables 2 and 3). An effective catch radius (the same as the EAR) of about 2 m for a puddle trap, releasing the same MB+cV rate, in a grid of 49 (7x7) such traps at 6 m spacing was calculated for I. typographus (Byers, 1993b). The calculation was based on comparing the ratios of catch on the outer rectangular `ring' of 24 traps with the next inner ring of 16 traps with simulated results iterating larger EARs. The estimated EAR varied on different dates from 1.53 to 2.48 m (Byers, 1993b). All these estimates of EAR using different traps and methods are similar for the MB+cV release rate. However, in the experiments with multiple trap rings (I. typographus), the EAR appears to decrease with distance in several studies (Table 3). This is most probably due to a selective catch of responsive beetles on the inner trap rings leaving less responsive ones to be caught less often on the outer rings (smaller EAR) rather than due to changes in response with flight time.

In contrast, the EAR for T. lineatum attraction to lineatin (dose unspecified) in multiple funnel traps had the opposite trend, increasing from 0.32 to 1.72 m (Table 5). The low EAR value at 3 m from the release center may be the result of overlapping of plumes (or EARs) of the closely spaced traps so that their locations were obscured. When single ring tests were done at 100 and 500 m radius, the EAR still appears to increase with radius or dispersal distance (Table 5). The EAR for I. paraconfusus to natural pheromone also increased with distance (Table 4). Since there was only one ring in each test and thus no filtration, the increase in EAR would seem to be a function of dispersal flight distance. The initial increase in EAR close to the release center may result not only from overlapping plumes (or EARs) of the closely spaced traps but also from escape reactions as the beetles were ejected into flight mechanically (as opposed to the other studies where the beetles initiated flight at will). The EAR of 34.5 m seems to be an outlier. Both the `previously responding to pheromone' and `freshly emerged' groups of beetles behave similarly, at least out to 25 m due to the `overlapping and fright' hypothesis above. Then, the EARs enlarge for the previously responding beetles since they appear more willing to respond on average than the freshly emerged beetles that are in the dispersal stage with presumed higher fat reserves.

At the beginning of a dispersal flight, bark beetles are considered to be rather unresponsive to pheromone or host volatiles. The theory is that fat reserves are higher in freshly emerged beetles so that they have the ability for extended flight and can gain adaptive benefits from dispersal before responding to hosts (Borden et al., 1986; Anderbrant et al. 1985; Gries et al., 1990). Graham (1959) showed that continued flight exercise by T. lineatum caused an increase in responsiveness to visual and olfactory stimuli of the host. Freshly emerged T. lineatum and D. pseudotsugae required 30 or 90 min of flight, respectively, before responding to pheromone from female frass (Bennett and Borden, 1971). Atkins (1966) found that female D. pseudotsugae with more than 20 % fat (dry weight) were usually not responsive to the host, while those under 20 % fat were responsive and still could fly. Beetles with less than 10% fat had trouble flying since fat was required as an energy source (Atkins, 1969). The fat metabolized by D. pseudotsugae consists mainly of C16 and C18 fatty acids (Thompson and Bennett, 1971). Other studies have found that scolytid beetles in the genera Trypodendron, Dendroctonus, Scolytus, and Ips increase their responsiveness or upwind orientation to host and pheromone after continued flight exercise (Choudhury and Kennedy, 1980; and cf. Borden et al., 1986).

However, some bark beetles appear rather responsive to pheromone upon emergence. Lindelöw and Weslien (1986) found that overwintered I. typographus, taken from emergence tents in the field and marked, were caught in synthetic pheromone traps within minutes of release. Also, the majority of I. paraconfusus will respond to aggregation pheromone soon after emergence (Wood and Bushing, 1963; Gara, 1963; Hagen and Atkins, 1975). Botterweg (1982) also found that I. typographus can immediately respond to pheromone when beginning dispersal, and this is in accordance with his finding that beetles lost 40-50% of their fat over the winter. Possibly second generation beetles in southern Europe would have higher fat and disperse further.

Increasing competition among larvae due to increasing densities of parents laying broods was shown to reduce size and fat content of bark beetles (Atkins, 1975; Anderbrant et al., 1985). This seems in conflict, however, with the statement of Forsse (1991) that flying time of I. typographus on flight mills was "similar among populations and appeared unaffected by outbreak conditions". Earlier, Forsse and Solbreck (1985) could not find any affect of sex or body size on the duration of flight on mills. Botterweg (1982) also concluded that there was little, if any, affect of beetle size or fat content on dispersal distance as monitored in field traps. However, he did find that fat content of beetles declined over the flight period. This was probably due to consumption of fat during host-seeking rather than later emergence of lower- fat beetles since beetle's sizes (elytral weights) did not decrease over the spring season.
Newly emerged D. pseudotsugae fly on flight mills an average of 2 h before resting (3 h total) but some individuals can fly up to 8 h uninterrupted (Atkins, 1961). Jactel and Gaillard (1991) flew I. sexdentatus on rotary flight mills and found that 50% of the beetles could fly more than 20 km and 10% more than 45 km based on about 50 interrupted flights. About 25% of I. typographus taken from litter in an outbreak area can fly for over 1 h and 10% for more than 2.5 h on flight mills, with a maximum flight of 6 h and 20 min recorded (Forsse and Solbreck, 1985). At free- flying speeds of 1.9 to 2 m/s (Gries et al., 1989; Byers, 1996a), a maximum range would be 41 to 45.6 km without wind transport. However, wing beat frequency declines with flight duration which may affect flight range. In the only case studied, the wing beat frequency of D. pseudotsugae of about 95 Hz declines 18 % with flight time over 4 h to about 75 Hz (Atkins, 1960). Speed on flight mills also declined from 1.11 m/s to 0.99 m/s (Atkins, 1961).

The view that bark beetles can fly some tens of km is based less on mark- recapture studies and more on collections of beetles far from forests. Nilssen (1978) found two I. typographus in the stomach of a salmon 35 km from spruce forest. Miller and Keen (1960) report results of studies by the US Forest Service in California where the western pine beetle, D. brevicomis, infested `islands' of ponderosa pine, initially free of beetles, that were separated from the main forest by open sagebrush areas. They concluded that significant numbers of bark beetles must have flown a minimum of 3.2 km in one study, and 9.6 or even 20 km in another study, to reach the infested trees and kill them.

At some point during the flight, or throughout the flight, beetles respond to pheromone, avoid unsuitable trees, or land on trees and presumably determine their suitability. Encountering pheromone while flying, by definition, means that a suitable host is nearby. Other volatiles, notably ethanol (a diseased or decaying tree) and verbenone (signalling competition, fully colonized host, or decaying host), as well as green-leaf alcohols are avoided in flight and after landing (cf. Byers, 1995; Borden et al., 1997; Byers et al., 1998). Some bark beetles respond to host volatiles (e.g. Tomicus, Byers, 1995) but the aggressive, tree-killing bark beetles considered here are believed to find hosts by random landing without the aid of any long-range host volatiles (Raffa and Berryman, 1979; Moeck et al., 1981; Byers, 1995, 1996a). For example, Scolytus ventralis in one area made borings in 74% of the grand fir but only 3.5% of the trees were colonized (Berryman and Ashraf, 1970). Hynum and Berryman (1980) also found no differences between landing rates on killed and non-killed lodgepole pine or between host and nonhost trees for D. ponderosae. There was a direct relationship between the magnitude of the flying population (as measured by total catch) and the number of trees landed upon (catch in window traps) indicating a random landing pattern (Raffa and Berryman, 1979). Ponderosa pines that were injured by freezing were as likely to be landed upon by D. brevicomis as healthy control trees (Moeck et al., 1981).

A beetle that lands on a tree and attempts to find a place on the bark to bore is termed a "pioneer" if there are few others present. Pioneers are presumed to encounter significant host resistance and resin when attacking compared to later arrivals ("joiners") when the tree has succumbed (Berryman, 1974; Raffa and Berryman, 1979; Wood, 1982; Byers, 1995). Only males, in the case of Ips, or females, in the case of Dendroctonus, initiate the entrance tunnel and can be pioneers, but the joining sex in the early stages of colonization must incur some increased risks of resinosis. One hypothesis is that since pioneers must attack the tree and survive to produce pheromone before the rest of the population can exploit the resource, pioneers must be the largest and most vigorous beetles of the population. In Figure 6, a scheme is presented for the dispersal flight under various conditions and circumstances. An individual would undertake a pioneer strategy, in my view, only if no pheromone was encountered during the dispersal, or after leaving unsuitable colonization areas, so that finally fat reserves became low (cf. Fig. 5.6 in Byers, 1995).

FIG. 6. Conceptual model of dispersal and host-seeking ecology of "aggressive" bark beetles that use aggregation pheromones. Factors such as the beetle's amount of fat reserves, encountering of pheromone, and level of competition and host suitability determine whether a beetle joins resident beetles in colonizing a tree or is the first "pioneer" to attack.

In this desperate state, the beetle attempts to bore into any tree and if lucky will find a tree of low resistance (Figure 6). Thus, the smaller beetles, those that suffered severe larval competition, or those that have used up their fat reserves in flight, regardless of size, are hypothesized to be the pioneers.

There are still many questions regarding the behavior of bark beetles during the dispersal and host selection period. For example, for how long do beetles fly in nature, how random are the paths, and how often do they land? There is a large body of literature on observations but few experiments from which conclusions can be drawn. The question as to what the flight paths of beetles might look like was investigated in the simulations that varied combinations of the EAR and AMT stepwise to find that the data for I. typographus ("unflown" in Duelli et al., 1997, and Zolubas and Byers, 1995) were best fit if the beetles have a straight flight path after release. This is in accordance with the theory that newly emerged beetles would have fat reserves and tend to initially ignore pheromone and hosts. The data for "flown" I. typographus (Duelli et al., 1997), however, could not be fit by any combination of EAR-AMT. The method also focused on a combination of EAR-AMT for T. lineatum, where a quite small EAR of 0.2 m was needed with a winding AMT path of 36° to predict the recapture rates by Salom and McLean (1989) on the three trap rings of 5, 25 and 100 m radii. Although the flight time of beetles is unknown, this may not affect the recapture rates significantly because most beetles disperse outward and do not return (a 10 min flight gave similar results to the hr flight). One trap ring allows too many possible EAR- AMT pairs to be of any use in predicting flight paths, although some degree of circuitous path is indicated. In any case, simulations reveal that catch per trap ring in relation to radial distance can be influenced significantly by the beetle's AMT, which has not been measured directly in the field.

The equation and simulation models useful for analyzing other systems of trap rings can be obtained as a compiled program for IBM-compatible personal computers by downloading the software (RINGTRAP.ZIP) from the internet
Opening screen of RINGTRAP.EXE
The study was supported by a grant from the Swedish Council for Forestry and Agricultural Research (SJFR). Reviews were done by F. Schlyter, Q. Zhang, and J. Jönsson. The paper was inspired by discussions supported by the "Bayersische Landesanstalt für Wald und Forstwirtschaft" about the large outbreak of Ips typographus in the Bayerischer Wald National Park.


ANDERBRANT, O., SCHLYTER, F., and BIRGERSSON, G. 1985. Intraspecific competition affecting parents and offspring in the bark beetle Ips typographus. Oikos 45:89-98.

ATKINS, M.D. 1960. A study of the flight of the Douglas-fir beetle Dendroctonus pseudotsugae Hopk. (Coleoptera: Scolytidae) II. Flight Movements. Can. Entomol. 92:941-954.

ATKINS, M.D. 1961. A study of the flight of the Douglas-fir beetle Dendroctonus pseudotsugae Hopk. (Coleoptera: Scolytidae) III. Flight capacity. Can. Entomol. 93:467-474.

ATKINS, M.D. 1966. Laboratory studies on the behavior of the Douglas-fir beetle, Dendroctonus pseudotsugae Hopkins. Can. Entomol. 98:953-991.

ATKINS, M.D. 1969. Lipid loss with flight in the Douglas-fir beetle. Can. Entomol. 101:164-165.

ATKINS, M.D. 1975. On factors affecting the size, fat content and behavior of a scolytid. Z. Angew. Entomol. 78:209-218.

BENNETT, R.B., and BORDEN, J.H. 1971. Flight arrestment of tethered Dendroctonus pseudotsugae and Trypodendron lineatum (Coleoptera: Scolytidae) in response to olfactory stimuli. Ann. Entomol. Soc. Amer. 64:1273-1286.

BERRYMAN, A.A., and ASHRAF, M. 1970. Effects of Abies grandis resin on the attack behavior and brood survival of Scolytus ventralis (Coleoptera: Scolytidae). Can. Entomol. 102:1229-1236.

BORDEN, J.H., HUNT, D.W.A., MILLER, D.R., and SLESSOR, K.N. 1986. Orientation in forest Coleoptera: an uncertain outcome of responses by individual beetles to variable stimuli, pp. 97-109, in T.L. Payne, M.C. Birch and C.E.J. Kennedy (eds.). Mechanisms in Insect Olfaction. Clarendon Press, Oxford.

BORDEN, J.H., CHONG, L.J., SAVOIE, A., WILSON, I.M. 1997. Responses to green leaf volatiles in two biogeoclimatic zones by striped ambrosia beetle, Trypodendron lineatum. J. Chem. Ecol. 23:2479-2491.

BOTTERWEG, P.F. 1982. Dispersal and flight behaviour of the spruce bark beetle Ips typographus in relation to sex, size and fat content. Z. Angew. Entomol. 94:466-489.

BYERS, J.A. 1991. Simulation of mate-finding behaviour of pine shoot beetles, Tomicus piniperda. Anim. Behav. 41:649-660.

BYERS, J.A. 1993a. Simulation and equation models of insect population control by pheromone-baited traps. J. Chem. Ecol. 19:1939-1956.

BYERS, J.A. 1993b. Orientation of bark beetles Pityogenes chalcographus and Ips typographus to pheromone-baited puddle traps placed in grids: A new trap for control of scolytids. J. Chem. Ecol. 19:2297-2316.

BYERS, J.A. 1995. Host tree chemistry affecting colonization in bark beetles, pp. 154-213, in R.T. Card‚ and W.J. Bell (eds.), Chemical Ecology of Insects 2. Chapman and Hall, New York.

BYERS, J.A. 1996a. An encounter rate model for bark beetle populations searching at random for susceptible host trees. Ecol. Model. 91:57- 66.

BYERS, J.A. 1996b. Temporal clumping of bark beetle arrival at pheromone traps: Modeling anemotaxis in chaotic plumes. J. Chem. Ecol. 22:2133- 2155.

BYERS, J.A., ANDERBRANT, O., and LÖFQVIST, J. 1989. Effective attraction radius: A method for comparing species attractants and determining densities of flying insects. J. Chem. Ecol. 15:749-765.

BYERS, J.A., ZHANG, Q.H., SCHLYTER, F., and BIRGERSSON, G. 1998. Volatiles from nonhost birch trees inhibit pheromone response in spruce bark beetles. Naturwissenschaften 85:557-561.

CHOUDHURY, J.H., and KENNEDY, J.S. 1980. Light versus pheromone-bearing wind in the control of flight direction by bark beetles, Scolytus multistriatus. Physiol. Entomol. 5:207-214.

DUELLI, P., ZAHRADNIK, P., KNIZEK, M., and KALINOVA, B. 1997. Migration in spruce bark beetles (Ips typographus L.) and the efficiency of pheromone traps. J. Appl. Entomol. 121:297-303.

FORSSE, E. 1991. Flight propensity and diapause incidence in five populations of the bark beetle Ips typographus in Scandinavia. Entomol. Exp. Appl. 61:53-57.

FORSSE, E., and Solbreck, C. 1985. Migration in the bark beetle Ips typographus L.: duration, timing and height of flight. Z. Angew. Entomol. 100:47-57.

GARA, R.I. 1963. Studies on the flight behavior of Ips confusus (LeC.)(Coleoptera: Scolytidae) in response to attractive material. Contrib. Boyce Thompson Inst. 22:51-66.

GRAHAM, K. 1959. Release by flight exercise of a chemotropic response from photopositive domination in a scolytid beetle. Nature 184:282- 284.

GRIES, G., NOLTE, R., and SANDERS, W. 1989. Computer simulated host selection in Ips typographus. Entomol. Exp. Appl. 53:211-217.

GRIES, G., BOWERS, W.W., GRIES, R., NOBLE, M., and BORDEN, J.H. 1990. Pheromone production by the pine engraver Ips pini following flight and starvation. J. Insect Physiol. 36:819-824.

HAGEN, B.W., and ATKINS, M.D. 1975. Between generation variability in the fat content and behaviour of Ips paraconfusus Lanier. Z. Angew. Entomol. 79:169-172.

HYNUM, B.G., and BERRYMAN, A.A. 1980. Dendroctonus ponderosae (Coleoptera: Scolytidae) pre-aggregation landing and gallery initiation on lodgepole pine. Can. Entomol. 112:185-192.

JACTEL, H., and GAILLARD, J. 1991. A preliminary study of the dispersal potential of Ips sexdentatus Boern (Coleoptera: Scolytidae) with an automatically recording flight mill. J. Appl. Entomol. 112:138-145.

LINDELÖW, Å., and WESLIEN, J. 1986. Sex-specific emergence of Ips typographus L. (Coleoptera: Scolytidae) and flight behavior in response to pheromone sources following hibernation. Can. Entomol. 118:59-67.

MILLER, J.M., and KEEN, F.P. 1960. Biology and Control of the Western Pine Beetle. USDA misc. pub. # 800, 381 pp.

MOECK, H.A., WOOD, D.L., and LINDAHL, K.Q.Jr. 1981. Host selection behavior of bark beetles (Coleoptera: Scolytidae) attacking Pinus ponderosa, with special emphasis on the western pine beetle, Dendroctonus brevicomis. J. Chem. Ecol. 7:49-83.

NILSSEN, A.C. 1978. Development of a bark fauna in plantations of spruce (Picea abies [L.] Karst.) in north Norway. Astarta 11:151- 169.

RAFFA, K.F., and BERRYMAN, A.A. 1979. Flight responses and host selection by bark beetles, pp. 213-233, in A.A. Berryman and L. Safranyik (eds.). Dispersal of Forest Insects: Evaluation, Theory and Management Implications. Proc. second IUFRO conf., Canad. and USDA Forest Service, Washington State Univ., Pullman. Washington, USA.

SALOM, S.M., and McLEAN, J.A. 1989. Influence of wind on the spring flight of Trypodendron lineatum (Oliver) (Coleoptera: Scolytidae) in a second-growth coniferous forest. Can. Entomol. 121:109-119.

SCHLYTER, F. 1992. Sampling range attraction range and effective attraction radius estimates of trap efficiency and communication distance in coleopteran pheromone and host attractant systems. J. Appl. Entomol. 114:439-454.

SCHLYTER, F., BIRGERSSON, G., BYERS, J.A., LÖFQVIST, J., and BERGSTRÖM, G. 1987. Field response of spruce bark beetle, Ips typographus, to aggregation pheromone candidates. J. Chem. Ecol. 13:701- 716.

SKELLAM, J.G. 1973. The formulation and interpretation of mathematical models of diffusionary processes in population biology, pp. 63-85, in M.S. Bartlett and R.W. Hiorns (eds.), The Mathematical Theory of the Dynamics of Biological Populations. Academic Press, London.

THOMPSON, S.N., and BENNETT, R.B. 1971. Oxidation of fat during flight of male Douglas-fir beetles, Dendroctonus pseudotsugae. J. Insect Physiol. 17:1555-1563.

WOOD, D.L. 1982. The role of pheromones, kairomones, and allomones in the host selection and colonization behavior of bark beetles. Ann. Rev. Entomol. 27:411-446.

WOOD, D.L., and BUSHING, R.W. 1963. The olfactory response of Ips confusus (LeConte) (Coleoptera: Scolytidae) to the secondary attraction in the laboratory. Can. Entomol. 95:1066-1078.

ZOLUBAS, P., and BYERS, J.A. 1995. Recapture of dispersing bark beetles, Ips typographus L. (Col., Scolytidae) in pheromone-baited traps: regression models. J. Appl. Entomol. 19:285-289.

ZUMR, V. 1992. Dispersal of the spruce bark beetle Ips typographus (L.)(Col., Scolytidae) in spruce woods. J. Appl. Entomol. 114:348- 352.
Scientific Software