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Study areasThe technique of harmonic radar tracking has been applied in nine different localities of Liguria (Italy), in the framework of the control activities developed to contain the spread of V. velutina in this region19,21,30. Four of these study areas (Ameglia, Arcola, Riccò del Golfo in La Spezia district and Finale Ligure in Savona district) were new invasive outbreaks characterised by a low nest density of V. velutina and low predation pressure on honey bee colonies. The other five study areas of Imperia district (Camporosso, Dolceacqua, Ospedaletti, and the two villages of Calvo and Latte in the municipality of Ventimiglia) were located inside the colonised range of the species21, and were characterised by a high nest density and an intensive predation pressure on honey bee colonies (Supplementary Table S1).Harmonic radar trackingThe harmonic radar and the tags that have been used for tracking the flight of V. velutina were designed and developed ad-hoc for following insects in complex environments; their technical and innovative characteristics have been previously described by the authors18. At the beginning of a new tracking session, worker hornets are trapped, usually in apiaries while preying on honey bees, and the transponders are attached on their thorax using an orthodontic glue, without anesthetising the insects. Subsequently, hornets are released from the tagging location and are immediately able to resume their activity, such as flying and preying on honey bees (Fig. 6). The whole tagging procedure requires less than one minute per hornet. Tag weight (15 mg) is approximately 4–7% of the weight of V. velutina workers (mean worker’s weight changes over the season between 189 and 386 mg)26. Moreover, the tag is 3–4 times lighter than the weight of prey’s pellet generally transported to the nest by this species. This information, together with multiple observations of tagged hornets in apiaries and the results achieved by other authors with a radio-tracking experiment (in which it was found that hornets equipped with a tag of weight lesser than 80% of their body weight are considered good flyers)22, suggest that the tags used in this study do not affect the behaviour and the flying abilities of V. velutina.Figure 6Tagged hornets performing their usual predatory behaviour. Tagged individuals of V. velutina hovering in front of honey bee colonies for preying on forager bees (a,b). A tagged hornet that is disjointing a honey bee for gathering the thorax (most energetic part of its prey), that will be brought back to the nest for feeding the brood (c). Two tagged hornets in proximity of the entrance hole of the nest (d).Full size imageThe harmonic radar records independently all the tracks of flying hornets that are inside its detection range. The real-time analysis of the recorded tracks allows understanding the main flying directions. If the nest of V. velutina is located outside of the maximum detection range of the radar (about 500 m in flat terrain)18 or behind physical obstacles, the harmonic radar is moved according to the flying directions of the hornets. The presence of a diffused road network, as in many of our study areas, facilitated the movement of the radar from one position to another. This operation is repeated until the position of the nest is determined. The area where the nest is located is generally highlighted by the presence of several tracks that converge or begin from the same site. The visual inspection of the area permits the exact detection of the position of the nest. In several cases, tagged hornets were visually observed on the surface of the nests (Fig. 6d).The total number of tagged hornets was recorded for each tracking session, together with the radar operation time, the number of radar movements per session, the number of detected nests per session and the minimum distance between the nests and the apiaries where hornets were hunting honey bees (Supplementary Table S2). Hornets were trapped with standard entomological procedures for trapping insects, and experiments were conducted ethically since no hornets were killed, injured, or kept captive after being tagged.Tracking lengths and environmental characteristicsThe main parameter selected for estimating the performance of the harmonic radar in tracking V. velutina in different natural and complex environments is the length of the tracks of tagged insects. To obtain this parameter, fixes (hornets detected by the harmonic radar at each radar’s rotation) were extracted for each tracking session and uploaded on a GIS software32. Afterwards, consecutive fixes of the same track were connected with the shortest line, so to obtain hornet tracks and calculate their length. The advanced radar analyses used for processing the received signals18 allow discriminating the true fixes (position of the hornet) from clutter (reflected signals received from objects in the landscape). However, the presence of obstacles may generate gaps in the received signals (e.g. when a hornet is temporarily flying behind an obstacle such as a house), but these gaps were rare and never occurred for long periods of time. In these cases, if fixes were not clearly recognizable to a track of the same hornet, these were excluded from the analysis. The exclusion of the tracks was performed also in the rare cases during which the presence of multiple tagged hornets did not allow a clear identification of the tracks.The length of the tracks in each fix position (n = 2580) was modelled with a GLMM (see “Data analysis”) to evaluate the effect of environmental features (land cover, elevation above sea level, slope gradient, road density). The land cover layer was obtained through a photo interpretation of satellite images (in a buffer area of 100 m around the minimum convex polygon that encompass all the tracks in each locality) and classification in three macro-levels: open terrains (landscapes predominantly characterised by open areas, such as fields), urban areas (matrices formed by buildings/roads) and woodlands (matrices formed by forests). Elevation above sea level and slope degree were obtained by a digital elevation model (resolution of 20 m).Visual tracking of flying hornetsThe length of the tracks recorded by the harmonic radar was compared with the length of the tracks recorded when adopting a customary technique for tracking insects, such as the visual tracking and triangulation of flying directions20,25. In six of the nine localities where the harmonic radar tracking has been applied (Fig. 4), an operator was waiting near a honey bee colony till one V. velutina worker caught a honey bee. Subsequently, after the hornet disjoined the most energetic parts of its prey (the thorax)33, the operator visually tracked the flight of the hornet when flying back to its nest, using a binocular and by recording with a GPS the position where the hornet disappeared from view. In some cases (n = 4), common flying routes were identified, and we were able to resume the visual tracking with other hornets from the previous disappearance position. Finally, GPS positions were uploaded on a GIS software to calculate the length of the tracks with this technique.In this study, the visual tracking technique has not been implemented systematically for nest detection, therefore the two approaches are compared only by evaluating the recorded length of the tracks. The effectiveness in locating nests, the required time and the associated costs are discussed in the framework of previous studies for tracking V. velutina, taking into account advantages and limits of the different techniques20,22,25.Estimation of V. velutina ground flying speedHarmonic radar tracking allows estimating the ground flying speed of V. velutina, by analysing the distance between each recorded position at consecutive radar rotations. Giving that the time of each radar rotation is fixed (3 s), it is possible to estimate the hornet’s speed between each detection8.The ground flying speed of V. velutina has been estimated in the three localities of La Spezia district, due to the availability of a subsample of clear tracks with consecutive detections per each rotation of the radar and good weather conditions. Furthermore, based on their direction, tracks were classified in homing tracks (H), which belong to hornets flying from the apiary to the nest, and foraging tracks (F), which belong to hornets flying towards the apiary for hunting honey bees. Data on wind speed and direction were obtained from weather stations close to the study areas.Data analysisData analyses were performed with the software R34. Environmental characteristics of the localities were analysed with a Principal Component Analysis (PCA; package factoextra), to understand affinities between study areas and correlations between the considered variables. The length of the tracks between localities recorded with the harmonic radar was compared with the Kruskal–Wallis and the Dunn tests with Bonferroni correction, while the flying speed between foraging and homing hornets was compared with the Wilcoxon rank-sum test (two-tailed).Generalized linear mixed models (GLMM; package lme4) with gamma distribution and log link function were used to assess (1) the influence of environmental variables on the length of the tracks and (2) compare tracking methods between study areas. In the first case, a random slope model has been implemented, by defining the locality and the slope degree as random effects (uncorrelated). In the second case, a standard random intercept model has been implemented, by selecting the locality as random effect. In both cases, continuous variables were standardized, and multi-collinearity of environmental variables was taken into account by calculating the Variance Inflation Factor (VIF). This was 1.5 for elevation and slope degree, and 1.0 for road density. More

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