The performance of the current Medfly design was unexpectedly inferior to that of the leek moth even with a more vagile target insect, 2.8 times greater trap density in the core, and a grid size over three times larger. The leek moth grid performed better despite all those factors because of much greater trap attractiveness. Thus, trap attractiveness was the key determinant for delimiting survey performance, as it was for detection 12.
The Medfly grid designers likely understood that the available trap was not highly attractive, and chose higher densities to try to reach their desired (non-quantitative) survey performance level. By contrast, the designers of the leek moth grid used a (constant) density three times smaller, likely because the trap was known to be much more attractive. Higher densities can help compensate for less attractive traps, but the impact is limited when attractiveness is low 36.
The cores of both the leek moth grid and the Medfly grid accounted for more than 86 percent of overall p(capture), and even the second band had greater p(capture) than outer bands. Therefore, in many delimiting activities we can expect that most captures will occur in the core and Band 2. This should not be surprising. Small insect populations are unlikely to move very far 26,37, especially if hosts are available 34,38,39. In addition, the short duration of a delimitation survey limits dispersal potential for the insects (see below). Core area captures confirm the presence of the target pest population but may not contribute much to boundary setting.
No captures occurred in Band 3 of the leek moth grid and Bands 3 to 5 of the Medfly grid, which indicated that those bands could be eliminated. The resulting smaller grids would be more cost-effective without compromising performance. Smaller survey grid radii can be predicted based on insect dispersal abilities 40.
All else being equal, increasing the trap density will generally improve p(capture) for any survey grid. However, large surveys can become prohibitively expensive for agencies to run 41. In that context, the use of variable densities in the Medfly grid is understandable. At its standard size, the survey grid would require 8,100 traps if the core trap density were constant (Table 1). The designers likely intuited that captures in outer band were less likely, and that lower densities could be used in those bands. However, that reduces the likelihood of detection in outer bands, and could increase the possibility of undetected egress, especially with longer survey durations. As far as we know, natural egress has not been raised as a concern following the numerous Medfly quarantines that have used this survey grid over the years, in Southern California in particular 42.
There are limited situations in which increasing densities to improve p(capture) would be worthwhile. Generally, p(capture) increases with density because the insects have more chances to interact with traps. However, gains are limited for less attractive traps, and the marginal ROI decreased quickly as densities increased (Table 2). Higher densities in the core had much more impact on grid performance, but once the presence of the population has been confirmed additional captures are unnecessary. Therefore, low or intermediate density may be optimal for the core. For the outer bands, increasing densities would improve detection of potential escapees but larger grid sizes already limit cost efficiency (Table 2). Further increasing those densities would reduce cost efficiencies even more. Investigating the relationship between the outer band densities and the accuracy of boundary setting could help resolve how to balance costs.
One way to improve p(capture) and the accuracy of boundary setting, while also cutting costs, would be to develop more attractive traps. Poorly attractive traps include food-based attractants 43, and traps based solely on visual stimuli 31. But developing better traps is difficult to achieve. Pheromone-based attractants generally perform best 44, but these are unavailable for many insects. For instance, scientists have searched for decades for effective pheromones for Anastrepha suspensa (Loew) and A. ludens (Loew) without success 45. Common issues include the complexity of components, costs of synthesis, and chemical stability.
The 14.5-km grid with variations has been widely used for many other insects in the CDFA (2013) guidelines, such as Mexican fruit fly (Anastrepha ludens), Oriental fruit fly (Bactrocera dorsalis), and melon fly (Zeugodacus cucurbitae). In the current study, a 4.8-km grid provided adequate containment of pest populations with moderate or lower dispersal abilities, including Medfly. Leek moth, with even lower dispersal ability, might require only a 3.2-km grid. Grids larger than 4.8-km only seemed necessary for highly vagile insects, those with D ≥ 50,000 m2 per day 36. Dominiak and Fanson 46 analyzed trapping data for Queensland fruit fly (Qfly, Bactrocera tryoni (Froggatt)) and obtained a similar result: the recommended quarantine area distance of 15 km was oversized, and could be reduced to 3 to 4 km. In that case, managers had also seemed to overestimate the needed size based on uncertainty about likely pest dispersal distances.
One likely reason for the large size of the standard Medfly grid is that it is also used for monitoring and management 47. Medfly quarantines end after at least three generations without a detection, so the surveys may last for 90 days or more. The standard grid size was reportedly originally determined by multiplying the estimated dispersal distance by three (PPQ, personal communication), to account for uncertainty. This implies that the estimated distance was about 2,400 m (duration unknown).
Examining diffusion-based movement for these two insects in TrapGrid can give insight into why simulations indicated that smaller grids may be adequate 36, which has been verified empirically 40. The expected spread of insect pests is a normal distribution centered from the epicenter 48 with a standard deviation (σ) proportional to the time (t) elapsed, as follows 12:
σ = 4 × (Dt)0.5 [1]
The value of σ for Medfly after 30 days is only about 1,550 m. In a normal distribution, σ = 1,550 m gives a 95th percentile distance of 2,550 m, which is similar to the estimated distance above of 2,400 m. Over 90 days, σ = 2,700 m for Medfly, which gives a 95th percentile distance of 4,441 m, still much shorter than the grid radius of 7,250 m. A 95th percentile of 7,250 m requires σ ≈ 4,408 m, which equals t = 253 days. In addition, the maximum total distance we observed in trapping detections data for Medfly in Florida was about 4,800 m 40. Hence, depending on survey objectives, some Medfly grid sizes could be significantly reduced, while achieving significant cost savings and maintaining containment. While a large grid size has been suggested for most exotic fruit flies 9, the most vagile species may be the Oriental fruit fly, which requires a delimiting survey radius of only 4 km 40.
The same calculations for leek moth give σ ≈ 490 m for 30 days, with a 95th percentile distance of only 806 m. That is half the distance of the recommended shortened radius above of 1.6 km (i.e., a 3.2-km grid), and nearly five times less than the radius of the standard 8-km grid. A 95th percentile of 4,000 m requires σ = 2,432 m, which implies t = 740 days, which is about two years. Therefore, the leek moth grid is arguably even more oversized than the Medfly grid.
Although it seemed too large for leek moth, an 8-km grid for delimitation could be appropriate for some other moths. For example, the delimiting survey plans for Spodoptera littoralis and S. exempta use this size 8. S. littoralis is described as dispersing “many miles” and S. exempta can travel hundreds of miles 8, which clearly exceeds the described dispersal ability of leek moth. On the other hand, the survey plan for summer fruit tortrix moth (Adoxophyes orana) also specifies an 8-km grid for delimitation, but contains little information on dispersal, suggesting only that most movement is local 7. Like leek moth, a 3.2-km grid for that species seems likely to be more appropriate.
Many survey designs in use were often primarily based on local experience 49 rather than “hard” science. Scientists have recognized the need for more cost-effective surveillance strategies 50,51. Results here demonstrated that the sizes and densities of these two survey grids could be optimized to save up to $22,960 per survey for the leek moth, and $38,168 per survey for the Medfly. In practical terms, that means more than 11 leek moth surveys could be run for the cost of one under the previous plan, while over seven Medfly surveys could be funded by the budget of one the original plan. The magnitudes of reduction seen here may be typical, since about 90 percent of the costs in trapping surveys are for transportation and maintenance related to traps 52.
Circular grids perform as well as square grids but use fewer traps and less service area to achieve equivalent p(capture) 36. Moreover, detections in the corners of a square grid are evidence that insects could have traveled beyond the square along the axes, resulting in uncertain boundary setting. Most published survey grids are square 9,53 but many field managers tend to use approximately circular trapping grids in the field (PPQ, personal communication). Converting to a circular grid with a radius of half the side length reduces the area and number of traps by around 21 percent 36. Our findings here were consistent with that. The circular leek moth grid used 80 traps while the square grid would require 100 traps at the same density (9.7 trap per mi2). For Medfly, only 232 traps were needed for 4.8 km circular grid (Table 3), while a square grid would require 300 (not shown).
Grid size reductions have little impact on p(capture), since outer band detections contributed little to overall performance. Egress potential is the main consideration when setting survey size, and the simulation results indicated that the standard survey sizes for these two pests were excessive. The optimal designs for these two species both used smaller grids. We have verified these results empirically using trapping detections data for six species with varying dispersal abilities 40, and, as mentioned above, similar results were observed for Qfly quarantine area size 46. Many delimiting survey plans may be oversized because they were developed before much dispersal research had been done 32. Because size reductions eliminate traps in proportionally larger outer areas, the impact on survey costs is substantial. In the case of leek moth, removing the outermost band, with 400 traps, would directly reduce the cost by $11,200.
Quantitatively assessing p(capture) in different designs for the same target pest allows us to find trap densities that lower costs while maintaining performance. This quantification was not possible until very recently, so survey performance has only been discussed very generally in the literature 4,54 and no standard thresholds exist. We think a reasonable minimum threshold for the choice of p(capture) might be p(capture) > 0.5, to try to ensure that population detection is “more likely than not”. It seems designs that try for p(capture) = 1.0 could be realistic for traps with high attractiveness but seem very likely to have lower ROIs (e.g., Table 2). Even for the most serious insect pests, we think targeting near-perfect population detection during delimitation is likely not justified. Rather than specifying a single, optimal performance level, designs achieving p(capture) from 0.6 to 0.75 could be effective in terms of both cost and performance (see above).
However, some delimiting survey designs in the United States may not be performing as well as expected 36. For instance, the delimiting survey design for Mexican fruit fly (Anastrepha ludens (Loew, 1873)) uses approximately 31 traps per km2 in the core of a 14.5 km square grid 9 but the traps are poorly attractive (1/λ = 5 m). In this scenario, with a 30-d survey duration, p(capture) is only around 0.23 36. A much greater density (> 80 traps per km2) could be used to achieve p(capture) ≥ 0.5, but this may not be feasible, depending on the survey budget.
The current version (Ver. 2019-12-11) of TrapGrid is not sensitive to population size and does not consider effect of ambient factors. The recommendations for leek moth and Medfly are based on the relatively small population size and in situations where a consistent early detection is spotted. If the outbreak population is very large and have extensively spread out, area-wide delimitation survey should be considered, which we are currently studying. Additionally, except for the model parameters specified above, many factors can impact trapping survey, such as weather conditions, topography of the environment, availability of host plants, seasonality of pest, and population dynamics. These factors are not considered in the current version of TrapGrid.
Still, our results indicated that inner area detections are likely to predominantly determine p(capture). Delimiting surveys may often yield few detections, because adventive populations can be very small and subject to high mortality 26. Captures assure managers that the surveys are viable, but while inner area detections confirm the presence of the population, they seem much less useful for defining spatial extent. Usually the furthest detections from the presumed source are used to delimit the incursion 53,55. Thus, increasing inner area densities to inflate p(capture) may not produce a more effective survey, even if ROI seems comparable (Table 2). The most effective surveys will achieve the two goals of delimitation and limit the likelihood of egress while minimizing both trap density and grid size.
Using TrapGrid simulations to decouple and isolate different survey design factors in the two grids examined here demonstrated the utility of simulations to investigate something that would be extraordinarily costly and time-consuming to experiment with in the field. It may not be possible to use TrapGrid to optimize delimiting survey designs for all combinations of dispersal abilities and trap attractiveness levels, because of the very large number of simulations that would require, but our results demonstrate that such optimization is possible for select insects. Although TrapGrid has not been completely validated for all insects and situations, it has performed well with two studied species 12, and its accuracy with regard to recommending smaller grid sizes has now also been empirically verified 40. Follow-up field studies could always be done to try to validate more surprising results.