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The authors have declared that no competing interests exist.

Conceived and designed the experiments: LLH JC. Performed the experiments: DLJ. Analyzed the data: DLJ LLH. Contributed reagents/materials/analysis tools: JC RH. Wrote the paper: LLH DLJ. Provided advice on analyses: SH. Contributed to manuscript: HER PMJB. Performed additional analyses for the revised manuscript: PMJB.

Understanding the characteristics and drivers of dispersal is crucial for predicting population dynamics, particularly in range-shifting species. Studying long-distance dispersal in insects is challenging, but recent advances in entomological radar offer unique insights. We analysed 10 years of radar data collected at Rothamsted Research, U.K., to investigate characteristics (altitude, speed, seasonal and annual trends) and drivers (aphid abundance, air temperature, wind speed and rainfall) of high-altitude flight of the two most abundant U.K. ladybird species (native

An estimated three billion insects fly through a 1 km^{2} ‘window’ of sky in England during a typical summer month

Ladybirds (Coleoptera: Coccinellidae) are the most abundant aphid predators in cereal crops worldwide, and are important biological control agents of aphids and coccids

Knowledge of the key characteristics of ladybird dispersal; specifically flight altitude, displacement speed, and seasonal and annual patterns, is crucial to understanding and predicting long-distance dispersal. Since wind speed increases with altitude, species that use high-altitude wind currents have greater long-distance dispersal potential than those that fly only a few metres above ground level (AGL), where wind currents are negligible

Another key question is whether dispersal is driven mainly by biotic or environmental cues, or by a combination of both. This is likely to vary depending on the scale of dispersal, as there are potentially different underlying causes for short and long-distance dispersal. Ladybird flight over short distances (classified as <2 m, and referred to as “trivial” or “appetitive flight” by

Both

Flight data for

Aerial density and displacement speed (i.e. speed relative to the ground) of radar targets identified as large ladybirds were estimated at each of the 15 altitude bands using the filtered VLR database. Potential duration and distance of flight were investigated using a combination of displacement speed data obtained from the VLR, and flight duration data from tethered flight experiments in a custom-built flight simulator. Full details of the tethered flight experiments are provided in the Supporting Information ^{3} Perspex cube using fine fishing line, and their flight activity video-recorded over a 2-hour period. Video footage was then analysed to determine the mean and maximum time spent in active flight during the 2-hour period.

Monthly averages for each variable (aerial density, number of records, temperature, wind speed, rainfall and aphid abundance) were calculated for May to October 2000–2010. Temperature, wind speed and rainfall data were obtained for Rothamsted from the U.K Met Office Unified Model ^{3} of air/s

All statistical analyses were performed in R v2.15.1

Second, the effects of aphid abundance, temperature, wind speed, and rainfall on ladybird aerial density were investigated more formally, using statistical modelling, in order to identify the main driver(s) of ladybird flight. We first used standard linear regression to investigate the relationship between aerial density and each explanatory variable. Next, because of the violation of assumptions for linear regression, discussed below, we used Generalised Linear Models (GLMs) and Generalised Least Squares (GLS) models to identify the main driver(s) of high-altitude flight. Full details of data exploration and model validation are given in the Supporting Information

In both the qpGLM and GLS analyses, we compared full (i.e. including aphid abundance, temperature, wind speed, and rainfall as explanatory variables), and partial (excluding wind speed) models to examine the effects of significant colinearity between wind speed and other environmental variables. The optimal minimal model (i.e. containing only significant explanatory variables) was found by dropping one explanatory variable in turn and each time applying an analysis of deviance (

A total of 8935 large ladybird-type targets (i.e. presumed ^{2}_{adj}_{1,9}

Figure 1a Box plot for ladybird aerial density summarized by month. Boxes correspond to the 25^{th} and 75^{th} percentile, horizontal bars within boxes to means, and whiskers to maximum values or 1.5 times the interquartile range (when there are outliers present, represented by open circles). For boxplots of aerial density by year, or number of target species records in the VLR database, see

The target species were detected in gate numbers 1–14 of the VLR (corresponding to altitudes between 150 and 1118 m AGL,

Mean displacement speed of the target species ranged from 8.5 m/s (S.D. = 4.2) for gate 1 to 16.4 m/s (S.D. = 1.3) for gate 14 (

Both basic time series plots (

Results of time series analysis for aerial density and each explanatory variable for May to October 2000–2010. Note the correspondence between peaks in temperature and aerial density, and the lag between peaks in aerial density and aphid abundance.

Plots suggest linear trends for temperature and wind speed over the whole study period, and this was confirmed by linear regressions, which showed a significant increase in temperature (^{2}_{adj}_{1,58} = 24.77, ^{2}_{adj}_{1,58} = 13.49,

Significant auto-correlation in the same month of each year was found for ladybird aerial density, temperature and wind speed, but not for rainfall or aphid abundance (

We focus here only on results from partial auto-correlations since they are much more informative than auto-correlations for revealing relationships between variables as they account for correlation between successive points in the time series. All pair-wise cross correlations showed at least some significant peaks in the partial auto-correlation plots, suggesting influence of the explanatory variables on AD (

“ACF” is the auto-correlation function, and “AD” Aerial density. Peaks that cross the dotted blue lines are considered significant at the 5% level. All explanatory variables show at least some significant peaks suggesting some influence on aerial density, however patterns for temperature, wind speed and aphids are particularly strong (Figure 3 a, b and d).

Significant relationships were identified between AD and both temperature and aphid abundance in the standard linear regressions (^{2}_{adj}_{1,58}^{2}_{adj}_{1,58}^{2}_{adj}_{1,58}^{2}_{adj}_{1,58}

Graphs show the relationship between monthly mean aerial density and each of the explanatory variables (also monthly means). Units for the explanatory variables are: temperature: °C, wind speed: m/s, rainfall: mm, aphids: absolute number counted in suction trap. Note aerial density, rainfall and number of aphids are not normally distributed and are therefore log transformed (see main text). “Rsq” = adjusted ^{2}^{2}_{adj}

We found a strong, negative linear relationship between temperature and wind speed (correlation coefficient = −0.8, ^{2}_{adj}_{1,58}^{−12}) and a positive linear relationship between wind speed and rainfall (correlation coefficient = 0.3, ^{2}_{adj}_{1,58}

Temperature and aphid abundance were the only significant predictors of ladybird aerial density in the full and partial qpGLMs (

Variable | qpGLM |
qpGLM deviance ( |
GLS without auto-correlation |
GLS with auto-correlation |

Aphid abundance | −2.292 (0.026^{+}) |
23.750 (^{+}) |
−2.273 (0.027^{+}) |
−2.349 (0.022^{+}) |

Temperature | 3.847 (0.000^{***}) |
26.046 (^{*}) |
3.879 (0.000^{***}) |
3.601 (0.001^{**}) |

AIC | n/a | n/a | 185.729 | 184.958 |

BIC | n/a | n/a | 193.901 | 195.173 |

Log likelihood | n/a | n/a | −88.865 | −87.479 |

^{ Results for minimal qpGLMs and GLS models (See }

^{***}^{**}^{*}^{+}^{}

Temperature and aphid abundance were also the only significant predictors of aerial density in full and partial GLS models (

Together, the linear regression, qpGLM and GLS results demonstrate that both temperature and aphid abundance are significant drivers of high-altitude ladybird flight, with temperature being the most important explanatory variable. The results are robust to different methods of analysis, and are essentially unaffected by confounding factors such as co-linearity and auto-correlation.

Previous studies have been limited to studying coccinellids flying at or near ground level (e.g.

Direct estimates of the long-distance dispersal capability of coccinellids are crucial for accurately predicting spread beyond native ranges, and could inform risk assessment. Indirect estimates of the spread of

Time series analyses demonstrated clear seasonal cycles in ladybird flight, with peak aerial density corresponding to midsummer, and lowest aerial densities in May and October. Low aerial density in May corresponds to the period when

A complex but well-established link exists between aphidophagous coccinellids and the population dynamics of their prey

Although our results indicate that aphids clearly influence dispersal, they demonstrate that ambient temperature is a much more important driver of ladybird flight in the U.K. Time series analyses suggested a positive relationship between monthly temperature and ladybird aerial density, with peak measurements corresponding to high summer. This was confirmed with linear regressions, in which temperature (between 5 and 19°C) explained approximately 19% of the variation in aerial density. Moreover, temperature was retained, and highly significant in all of our statistical models. This is perhaps not surprising given that temperature has long been implicated as the single most important predictor of insect flight

We predicted that wind speed and rainfall would also influence high-altitude ladybird flight, since wind speed is thought to be either facilitative or inhibitory in insect flight depending on its magnitude

In the current study we were only able to consider environmental variables and aphid abundance as potential drivers of dispersal. Other potential drivers include the physiological state of beetles at the onset and completion of diapause. Further study is needed to determine the relative importance of physiological compared to other biotic and abiotic cues.

In conclusion,

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We are grateful to Alan Smith and Jason Lim for technical assistance with the VLR calibration, and to two referees for constructive feedback on our manuscript.