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Dynamic in-flight flock organizationIt is commonly assumed that during flocking, flock members follow three basic interaction rules: Attraction, Repulsion and Alignment, to coordinate spatial positions between each other18. To study the spatial organization of our zebra finch flock during flight, the spatial positions of all birds in the flight section were tracked in every fifth frame (sample rate: 24 Hz (that is, frames per second)) of the synchronized footage recorded by two high-speed digital video cameras (Camera 1: centred upwind view, Fig. 1a,b; Camera 2: upturned vertical view, Fig. 1a,c) for the entire duration (51.7, 58.3, 69.2 and 127 s) of four (session 2, 5, 8 and 13) out of 13 flight sessions. Flight paths were reconstructed from the tracking data for each bird in the flock, with horizontal and vertical coordinates delivered by Camera 1 and coordinates in wind direction delivered by Camera 2. The data show that each bird mainly occupied a particular area in the flight section, and that this spatial preference was stable over different flight sessions. Bird Green, for example, was preferentially flying very low above the flight section’s floor, and bird Lilac preferred to fly at upwind positions in front of the flock (Fig. 1d, Extended Data Figs. 1 and 3 and Supplementary Information).Despite their preference in flight area, all birds constantly changed their spatial positions fast and rhythmically along the horizontal dimension of the flight section (Fig. 1e–g, Extended Data Figs. 2 and 4, Supplementary Video 1 and Supplementary Information). This behaviour is reminiscent of the flight behaviour of wild zebra finches: when being surprised in flight by a predator, zebra finches fly in a rapid zig-zag course low above the ground, heading for nearby vegetation16. Whether the sideways oscillating flight manoeuvres, which are performed by both wild birds in open space and domesticated birds in the wind tunnel’s flight section, are caused by the close proximity to the ground or are part of an escape reaction is yet unknown.From the tracking data, we further calculated the spatial distances in all three dimensions between all pairwise combinations of birds throughout the four flight sessions (sample rate: 24 Hz). When normalized to the maximum distance detected for each bird pairing, each dimension and each flight session, mean distances of bird pairings in all dimensions were narrowly distributed within a range of 27.7–38.0% of maximum distance (Fig. 1h and Supplementary Table 1). This may indicate that during flocking flight, zebra finches actively balance Attraction and Repulsion to maintain a stable 3D distance towards all other members of the flock. Owing to the spatial limitations in the wind tunnel’s flight section, we did not expect the zebra finches to perform large-scale flight manoeuvres with movements aligned between all flock members (Extended Data Fig. 5 and Supplementary Information), as can be observed, for example, in freely flying flocks of homing pigeons (Columba livia domestica)19 and white storks (Ciconia Ciconia)20.Visually guided horizontal repositioningWhen observing the dynamic spatial organization of our zebra finch flock, a question immediately arises: how do the birds prevent collisions during their frequent horizontal position changes? When considering the spatial limitation experienced by the flock of six birds during flight in the flight section and their highly dynamic flight style, collision rates seemed to be astonishingly low (median: 0.02 Hz; interquartile range (IQR): 0–0.03 Hz; n = 13 sessions) during flocking flight (in total 16 collisions in 13 min of analysed flight time). In birds, the visual system represents the main input channel for environmental information. To tackle the above question, we therefore first investigated the role of vision during flocking flight, and tested whether a bird’s viewing direction was correlated with the direction of horizontal position change. As gaze changes are governed by head movements in birds21, we used a bird’s head direction as an indicator for the orientation of its visual axis. We tracked (sample rate: 120 Hz) the position of a bird’s beak tip and neck in each frame of the footage during ten horizontal position changes (Fig. 2a and Supplementary Video 2) per bird, and found a strong interaction between a bird’s head angle relative to the wind direction and its direction of horizontal position change. During horizontal position changes, the birds always turned their heads in the direction of the position change (Fig. 2b). While the population’s median absolute angle of position change was 84.0° (IQR: 78.6–87.2°; n = 60) relative to 0° in wind direction, the population’s median absolute head turning angle was 36.0° (IQR: 26.4–42.5°; n = 60; see Supplementary Information for results on head movements during solo flight). The eyes of zebra finches are positioned laterally on their heads22 and each retina features a small region of highest ganglion cell density (fovea, that is, region of highest visual spatial resolution) at an area that receives visual input from horizontal positions at 60° relative to the midsagittal plane23. By turning their heads by about 36° during horizontal position changes, the zebra finches roughly align the foveal area in the retina of one eye with their direction of position change, and in the retina of the other eye with the wind direction (Fig. 2c,d). Thus, head turns in the direction of position change may indicate that the birds use visual cues while repositioning themselves within the flock. This hypothesis is supported by a study on zebra finch head movements performed during an obstacle avoidance task. In this study, instead of fixating on the obstacle, zebra finches turned their head in the direction of movement while navigating around the obstacle24.Fig. 2: Horizontal position changes are accompanied by head turns.a, Head and body orientation of bird Orange (ventral view) during one example of position changes to the right, tracked (sample rate: 120 Hz) in the footage of Camera 2. Circles: beak tip positions; plus signs: neck positions; upward pointing triangles: tail base positions. Cutouts of freeze frames of the footage taken with Camera 2 show the bird’s head and body posture for 11 time points during the position change. b, In all birds, the median angle of head turn during horizontal position change in flocking flight is positively correlated (linear mixed effects model (LMM), estimates ± s.e.m.: 2.05 ± 0.1, P  More

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Key delimitation trapping survey performance factorsTrap attractivenessThe 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. Despite all those factors, p(capture) for the leek moth grid with 1/λ = 20 m was 15 percentage points greater than that for Medfly at 30 days duration. Thus, trap attractiveness was the key determinant for delimiting survey performance, as it was for detection13.One straightforward 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 attractants48 and traps based solely on visual stimuli36. But developing better traps is difficult. Pheromone-based attractants generally perform best49, 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 success50. Common issues include the complexity of components, costs of synthesis, and chemical stability.Trap densitiesAll else being equal, increasing the trap density will generally improve p(capture) for any survey grid, and intuitively this can help compensate for using less attractive traps. However, the impact of increasing density is limited when attractiveness is low13,47, and large surveys or grids with many traps can become prohibitively expensive51. The Medfly grid designers likely understood that the available trap and lure was not highly attractive, and used higher densities in inner bands to try to reach some 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 and lure were known to be relatively strong. Here, for both species, marginal ROI decreased as densities increased (Tables 2, 3). Hence, increasing densities has limited benefit, but may be useful when better lures are unavailable13.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 lower densities could be used in outer bands because captures there were less likely. However, doing so 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 particular52.Generally, however, we think the variable Medfly grid densities run counter to delimitation goals. Greater core and Band 2 densities have proportionally more impact on p(capture), but only a few detections in the core are necessary to confirm the presence of the population (Goal 1), and inner area detections probably contribute little to boundary setting (see below). Therefore, lower or intermediate densities (at most) may be optimal for the core when considering ROI. For the outer bands, increasing densities might improve boundary setting (Goal 2) and help mitigate potential egress, but the sizes of those bands already limit cost efficiency (Table 2), making greater densities less advisable. Our simulation results can help elucidate how to balance these interests to achieve delimitation goals while minimizing costs47.Grid size considerationsThe simulation results indicated that the standard survey sizes for these two pests were excessive. We have verified that empirically for Medfly using trapping detections data53. A 14.5-km grid has been widely used for many other insects in the CDFA (2013) guidelines10, such as Mexfly and OFF, and the same analysis indicated that those are also oversized for use in short-term delimitation surveys53. From the same analysis, the predicted survey radius for leek moth, with D = 500 m2 per day, would be 2,382 m, or a diameter of nearly 4.8 km, which matches the results here. Similarly, Dominiak and Fanson45 analyzed trapping data for Qfly and found that the recommended quarantine area distance of 15 km could be reduced to 3 to 4 km.Grids with radii larger than 4.8-km only seem necessary for highly vagile insects, those with D ≥ 50,000 m2 per day47. This should not be surprising. Small insect populations are unlikely to move very far31,54, especially if hosts are available20,39,55. The (proposed) short duration of a delimitation survey would also limit dispersal potential (see below). Many delimiting survey plans may be oversized, because they were developed before much dispersal research had been done37, thus uncertainty was high. Our dispersal distance analysis included species with a wide range of dispersal abilities, so it can be used generally to choose smaller survey grid radii53.Reducing grid sizes down to about 4.8-km diameters may have little impact on p(capture), since detections in bands outside that distance contributed little to overall performance. The cores of both the leek moth and Medfly grids accounted for 86 percent or more of overall p(capture). While core area detections will confirm the presence of the population, they are less useful for defining spatial extent. The furthest detections from the presumed source are usually used to delimit the incursion46,56 (although in our experience formal boundary setting exercises seem rare). Delimiting surveys may often yield few captures anyway, because adventive populations can be very small and subject to high mortality31. Because size reductions eliminate traps in proportionally larger outer areas, the impact on survey costs is substantial. Removing just the outermost bands of each grid would directly reduce costs by $11,200 for leek moth (400 traps) and by $7,488 for Medfly (288 traps; Table 1).Another reason for the large size of the standard Medfly grid may be that it was designed for monitoring and management in addition to delimitation57. Medfly quarantines end after at least three generations without a detection, so the surveys may last for months. The 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 per 30 days. Thus, the design may not have been built for the 30-d duration used here, but our recommended design is valid if a shorter delimitation activity without further monitoring is appropriate.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 (Boisduval) and S. exempta Walker use this size9. S. littoralis is described as dispersing “many miles”, and S. exempta can travel hundreds of miles9, which clearly exceeds the described dispersal ability of leek moth. On the other hand, the survey plan for summer fruit tortrix moth (Adoxophyes orana Fischer von Röeslerstamm) also specifies an 8-km grid for delimitation but contains little information on dispersal, suggesting only that most movement is local8. Like leek moth, a 4.8-km grid for that species seems likely to be more appropriate.Limiting egress potential is probably the main consideration when setting survey size, but uncertainty about the source population location may also be a factor. Survey grids placed over the earliest insect detection may sometimes be off center from the location of the source population54. However, so far as we know for our agency, most adventive populations have been localized, based on post-discovery detections (PPQ, personal communication). Likewise, we have found53 and other researchers have found that dispersal distances for different species in outbreaks and mark-recapture studies are often less than 1 km58,59,60. That may often be the case for detection networks of traps (e.g., for high risk fruit flies), which increase the likelihood of capture before the population has had much time to grow and disperse. Here, we focused explicitly on localized populations, but allowed for uncertainty in the simulations by varying outbreak locations over one mile in the central part of the grid. If the outbreak population is very large and has extensively spread out (e.g., spotted lanternfly, Lycorma delicatula (White) in 201461), delimitation will not be localized, but “area-wide”2. The results here do not apply to area-wide outbreaks, and we are currently studying how to effectively delimit them.Optimizing delimitation surveysMany trapping survey designs in use were based not on “hard” science but on local experience62. Scientists have recognized the need for more cost-effective surveillance strategies63,64. Quantitatively assessing p(capture) in different designs for the same target pest allows us to determine grid sizes and densities that lower costs while maintaining performance. Results here demonstrated that the sizes and densities of these two survey grids could be optimized to save up to $20,244 per survey for the leek moth and $38,168 per survey for the Medfly. In practical terms, that means more than five leek moth surveys could be run for the cost of one standard design survey. Additionally, over seven Medfly delimitation surveys could be funded by the budget of one standard 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 traps65.Quantifying survey performance was not possible until very recently, so it has been little discussed in the literature5,66, and no standard thresholds exist. We think 0.5 may be a reasonable minimum threshold for the choice of p(capture), to try to ensure that population detection is “more likely than not”. Designs that aim to maximize p(capture) could be realistic with high attractiveness traps, but those designs 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. Designs achieving p(capture) from 0.6 to 0.75 could be highly effective in terms of both costs and performance.Another potential area of improvement is grid shape. Circular grids perform as well as square grids but use fewer traps and less service area to achieve equivalent p(capture)47. 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 square10,46, but many field managers tend to use approximately circular trapping grids in the field (PPQ, personal communication). The conversion to a circular grid with a radius of half the square side length reduces the area and number of traps by around 21 percent47. Our findings were consistent with that value.This new quantification ability also indicates that some delimiting survey designs in the U.S.A. may not be performing as well as expected47. For instance, the delimiting survey design for Mexfly uses approximately 31 traps per km2 in the core of a 14.5 km square grid11, but the traps are only weakly attractive (1/λ ≈ 5 m). In this scenario, p(capture) was only around 0.23 with a 30-d survey duration47. A much greater density ( > 80 traps per km2) could be used in the core to achieve p(capture) ≥ 0.5, but this may not be feasible depending on the survey budget.Technical and modeling considerationsExamining diffusion-based movement for these two insects in TrapGrid can give insight into why simulations indicated that smaller grids may be adequate47. 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 (up to 39 days after detection) we observed in trapping detections data for Medfly in Florida was about 4,800 m53.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 length of the recommended shortened radius above of 2.4 km, and nearly five times shorter 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.The default capture probability calculation in the current version (Ver. 2019-12-11) of TrapGrid is not sensitive to population size32 and does not consider the effects of ambient factors (e.g., wind speed and direction, rainfall, temperature). Many other factors can also impact trapping survey outcomes, such as 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. More