The role of lateral optic flow cues in hawkmoth flight control

Animals use a range of sensory cues to navigate their environment. Vision is particularly important for flying animals to monitor their position with respect to their surroundings, especially the apparent image motion, known as optic flow (Koenderink, 1986), which is generated as they move through their environment. Insects are known to use the information that optic flow provides about their self-movement, as well as about the structure of their environment to control multiple aspects of their flight (Collett, 2002). When flying through narrow passages, they use translational optic flow to negotiate the distance to the surrounding surfaces. If the optic flow induced by two lateral features is similar, bees and flies take a centre position between them (Baird et al., 2010; Kern et al., 2012; Kirchner and Srinivasan, 1989). If one of the features induces lower levels of translational optic flow, insects will fly closer to this side (Dyhr and Higgins, 2010; Kirchner and Srinivasan, 1989), apparently positioning themselves within their environment so as to balance the rate of laterally perceived optic flow across their eyes. Moreover, the rate of translational optic flow controls their flight speed (Baird et al., 2010, 2005; David, 1982; Fry et al., 2009), and their height above the ground (Baird et al., 2006) and below confining structures (Portelli et al., 2011).

While a large body of work on the role of optic flow for the control of free flight has been assembled, much of our understanding is based on results from a relatively small number of insect species, belonging to either Apoidea or Diptera. We therefore set out to investigate whether the previously described flight control strategies are also used by insects with a different optical system, flight kinematics and phylogenetic background. We tested the role of lateral visual cues in forward flight control of the diurnal hummingbird hawkmoth Macroglossum stellatarum (Sphingidae, Lepidoptera). Hawkmoths possess optical superposition compound eyes (Warrant et al., 1999), which makes them an interesting complement to Diptera (apposition compound eyes with neural superposition) and Apoidea (apposition compound eyes). Moreover, their flight kinematics, with rather low wing beat frequencies and the ability to hover, sets them apart from the species of flies and bees tested in flight tunnel setups previously. However, hummingbird hawkmoths share much of their habitat and many plant species that they forage on with a variety of bee species (Pittaway, 1993; Stöckl and Kelber, 2019) and thus provide a very interesting ecological comparison species. Moreover, the anatomy and physiology of their visual pathway for wide-field motion computation is well understood and the spatial and temporal features of their visual system are well described (Stöckl et al., 2017b; Theobald et al., 2010; Wicklein and Varjúe, 1999), making them an ideal species to investigate aspects of visual flight control from physiology to behaviour.

While hawkmoths in general and M. stellatarum in particular have been used as a model to investigate visual flight control (Farina et al., 1995, 1994; Kern and Varjú, 1998; Sponberg et al., 2015; Stöckl et al., 2017a), most studies investigating free-flight behaviour focused on the hawkmoth's hovering mode – in part because hawkmoths are uniquely suited as a model system to study hovering flight control but also because it provides a tractable system for behavioural experiments. These experiments demonstrated in particular that M. stellatarum control their position at a flower with respect to translational as well as rotational optic flow information (Farina et al., 1995; Kern and Varjú, 1998), the spatial and temporal features of which are consistent with the physiological characteristics of their wide-field motion system (Kern and Varjú, 1998; Stöckl et al., 2017b). Little is known, however, about how these hawkmoths control their forward flight using visual cues.

What we know about visual forward flight control in moths in general, and in hawkmoths in particular, results mainly from plume-tracking experiments in wind tunnels. Male gypsy moths (Lymantria dispar) seem to use optic flow from ventrally presented visual patterns during plume tracking in a wind tunnel to maintain their approach speed and heading angle (Willis and Carde, 1990). Moreover, male Heliothis virescens moths were shown to improve the orientation of their flights towards an odour source when visual patterns providing both translational and transverse optic flow information were presented in the wind tunnel (Vickers and Baker, 1994). During plume tracking in a wind tunnel, males of the hawkmoth Manduca sexta respond both to physical obstacles and projected looming stimuli with changes in their flight behaviour (Verspui and Gray, 2009). Recent experiments on plume tracking M. sexta males revealed that they require the dorsal half of their visual field to be un-occluded for stable flight, while the ventral hemisphere can be covered without quantifiable impairment (Copley et al., 2018).

While free-flight experiments with plume-tracking hawkmoths were instrumental in demonstrating the importance of optic flow for stable flight in moths, they are not ideally suited to resolving questions of visual flight control. First, moths are presented with directional olfactory and mechanosensory stimuli (an odour stimulus carried by a constant wind stream), which can influence flight control independent of the visual stimulation. Moreover, the female pheromone provides an efficient motivation for male moths to cross the flight tunnel, but it elicits a coordinated motor programme that defines the flight strategy of the moth: a series of counterturns that result in a zigzagging flight pattern (Carde, 2016). There is evidence that during this concerted behavioural programme, the use of vision for course control changes: tethered walking Bombyx mori males only perform a classical optomotor response upon perceiving rotational optic flow while they are not in the zigzagging phase of their tracking behaviour. Their response to optic flow stimuli actually inverses during the zigzagging phase (Pansopha et al., 2014). Thus, in order to study the role of vision in forward flight control, hawkmoths should ideally be tested without olfactory and wind cues.

We therefore designed a flight tunnel setup for M. stellatarum in which animals were trained to cross a flight tunnel without directional olfactory and wind information. Our results show that in terms of lateral position control, hawkmoths use a similar strategy to that of Apoidea and Diptera, balancing the magnitude of translational optic flow perceived in both eyes. The variability in flight speed across individual hawkmoths was considerably larger than that observed in bees or flies in similarly sized tunnels, and was influenced by the spatial frequency of the lateral cues. Moreover, we observed differences between the flight paths of individual hawkmoths and those of the entire population in lateral tunnel position and flight speed when the presented optic flow was unbalanced.

Adult male and female Macroglossum stellatarum (Linnaeus 1758) were obtained from a colony in Lund, Sweden. Eggs were collected from these starter animals and the caterpillars raised on their native host plant Gallium sp. The eclosed adults (both male and female) were allowed to fly and feed from artificial feeders (Pfaff and Kelber, 2003) in flight cages (60×60×60 cm, length×width×height) on a 14 h:10 h light:dark cycle for at least 1 day before experiments began.

A Perspex flight tunnel (100×30×30 cm, length×width×height) was positioned to connect to the flight cages (Fig. 1A). Each flight cage was illuminated by four fluorescent tubes with a daylight-like spectrum (Osram L 18 W/965 Biolux Tageslicht G13, see Fig. S1A; spectrum measured with Maya2000 Pro, Ocean Optics), resulting in a light intensity of 1450 lx in the middle of the flight cage pointing towards the ceiling (measured using an HT309 digital lux meter, HT Instruments). All fluorescent lights were operated with electrical ballasts (GloMat 2×40 W, Hagen) to minimise flickering at twice the AC carrier frequency. While some flicker at this frequency and harmonic multiples prevailed (Fig. S1B,C), the standard deviation of the light intensity variations was only 2.7% of the mean intensity. Considering that the 50% cut-off frequency of the photoreceptors of M. stellatarum is at around 50 Hz and that of the wide-field motion-sensitive neurons is below 20 Hz (Stöckl et al., 2017b), the light flicker was probably imperceptible to the hawkmoths.

The tunnel was positioned to align with the top of the flight cages, as hummingbird hawkmoths preferred to fly in the upper part of their flight cages. Along the top of the tunnel, in a distance of 30 cm, two fluorescent light tubes of 895 mm length were mounted (Osram L 30 W/965 Biolux Tageslicht G13). To prevent moths from seeing the light tubes or the visual panorama above the tunnel and using them as orientation cues, a piece of white felt serving as a diffuser was placed on top of the tunnel. Gauze (Gazin Verbandmull 8-fach, Lohmann & Rauscher) was placed on the bottom of the tunnel to avoid light reflections from the entrance, as well as inspection of the visual panorama below the tunnel. It was thin enough to allow the camera to film through it.

Screens in the middle of both flight cages (60 cm high, 45 cm wide) prevented animals in the tunnel from seeing into the flight cages and obtaining visual cues that could influence their flight paths. The feeders were hidden behind these screens. ‘Collars’ made from white cardboard (10 cm width) covered the top and sides of each tunnel entrance. They additionally screened the view from within the tunnel into the flight cages and prevented animals from ‘accidentally’ entering the tunnel – which increased the number of animals crossing the tunnel in a directional fashion, rather than entering at random, circling in the tunnel or landing on the tunnel walls.

A camera (Playstation Eye, PS3, Sony) was positioned 1.5 m below the tunnel to film its entire 1 m length. It was controlled by ContaCam 7.9.0 beta7 software (Contaware) in motion detection mode to automatically record a 4 s video when motion was detected in the central 50 cm of the tunnel (recording 2 s before and 2 s after the motion detector was triggered). The camera filmed at a frame rate of 50 Hz and an aspect ratio of 640×480 pixels. We initially tested for potential image distortions caused by the lenses of the camera that could affect the accurate quantification of moth position in the tunnel by measuring the width of the tunnel at 20 cm intervals on the resulting camera videos. We found no evidence of distortion (at an error margin of 2%) and therefore used the raw camera images without further correction for analysis.

The light intensity in the tunnel, measured from the centre (width, height and length) of the tunnel, was 1150 lx pointing up, 370 lx pointing down, 750 lx towards the exit of the tunnel and 670 lx towards the sides. This was obtained using a lux meter (HT309 digital lux meter, HT Instruments) with a spectral sensitivity function which closely matches the spectral sensitivity of the hawkmoth's green receptors (Telles et al., 2014), which in insects provide the main (though not exclusive) input to wide-field motion vision (Wardill et al., 2012). This information is probably used by hawkmoths for flight control tasks like the one tested here. We used five different types of visual stimuli lining the lateral walls of the tunnel. (1) Random chequerboard patterns, which induced translational optic flow of a range of spatial frequencies. They were composed of black and white squares of 13.9 mm side length, which was equivalent to a viewing angle of 5.3 deg from the centre of the tunnel. (2) Vertical sinusoidal stripes, inducing translational optic flow at three different spatial frequencies. The default frequency used was 0.105 cycles cm⁻¹, which was equivalent to 0.0285 cycles deg⁻¹ as viewed from the centre of the tunnel; the ‘fine’ spatial pattern was half this wavelength (0.21 cycles cm⁻¹, 0.0556 cycles deg⁻¹) and the ‘coarse’ spatial pattern was double the default wavelength (0.053 cycles cm⁻¹, 0.0155 cycles deg⁻¹). All spatial frequencies were well within the spatial resolution limits of the photoreceptors and wide-field motion neurons of M. stellatarum (Stöckl et al., 2017b). (3) Horizontal sinusoidal stripes of the same spatial frequency as the default vertical stripes. (4) Grey walls made from grey cardboard, which produced an average of 350 lx measured from the centre of the tunnel. (5) White walls made from white cardboard, which reflected an average of 680 lx measured from the centre of the tunnel.

All stimuli with black and white contrast were printed on white paper using a laser printer (C3325i, Canon) at a nominal contrast of 100%. The actual contrast measured in the tunnel was 81% (555 lx on the ‘white’ and 58 lx reflected from the ‘black’ part of the pattern, measured at 3 cm from a 50 cm wide black and white pattern, respectively). The average light intensity reflected from the chequerboards and sinusoidal gratings was 350 lx.

Forty hummingbird hawkmoths were accustomed to the setup for 2 days. During the first day, they were moved to one of the two flight cages connected to the tunnel, while clearly visible feeders were presented at the tunnel exit in the opposite flight cage. The tunnel walls were lined with the chequerboard pattern. Animals were then allowed to cross the tunnel to reach the feeders. Several times a day, all animals that had crossed over were moved back into the starting cage, to encourage them to use the tunnel again to feed. The next day, the feeders were hidden behind a white screen, and animals were allowed to cross the tunnel again, and regularly moved back to their starting cage.

After being familiarised with the setup, the entire population of hawkmoths were kept in the flight cages with two feeders on both sides hidden behind the screens, and were allowed to freely cross the tunnel. The wall patterns were changed daily or every 2 days if too few flights were recorded in the first 24 h period. Flights across the tunnel were filmed continuously, although the first hour after pattern changes was not analysed to allow hawkmoths to adjust to the new visual scenario.

In the first two sets of experiments, we analysed the flight behaviour based on individual flight tracks rather than animal identity. We therefore made sure that the flight tracks we obtained represented a considerable proportion of the hawkmoth population in the flight tunnels. To this end, we performed three consecutive tests on consecutive days in which we counted the number of hawkmoths that crossed the tunnel lined with random chequerboard patterns. Over the course of 3 h, 70%, 68% and 53%, respectively, out of 40 hawkmoths in the flight cages crossed the tunnel. We therefore concluded that the recorded flights were generated by a representative proportion of the hawkmoth population in our experimental approach.

In this sub-experiment, animals were accustomed to the setup as described above. They were then separated into individual holding tubes to keep track of animal identity and placed into the setup one by one. Each hawkmoth was positioned on a platform, which was centred in the right-hand flight cage and aligned with the centre height of the tunnel. Animals would warm up on the platform and take flight, and were allowed to cross the tunnel to access the feeders hidden behind the screen in the opposite flight cage. Animals that did not warm up or did not fly through the tunnel within the first 5 min after warming up were excluded from the experiment. Animals that did fly across the tunnel to the feeders were caught there, moved back into the starting cage, and allowed to cross the tunnel again. This procedure was repeated as long as the animal returned to the feeder. We obtained between 1 and 12 tunnel crossings per individual and condition this way. To obtain a sufficient sample of variation between individual flight tracks, we only included animals crossing the tunnel at least three times per condition in the analysis.

All videos containing flight tracks were sorted before analysis. As the hawkmoths did not all cross the tunnel in a directed fashion, but showed a variety of behaviours (such as turning around at some point in their path and flying back, inspecting the walls or trying to land on them), we defined the following criteria for a flight track to be included in the analysis: animals had to cross the entire length of the tunnel without crashing into parts of it or attempting to land, while the tunnel had to be free of other hawkmoths. These flights were then analysed, while incomplete flights (which fulfilled all criteria except crossing the entire length of the tunnel) and non-directed flights (in which hawkmoths circled in the tunnel, inspected walls or made landing attempts) were excluded from further analysis (Table 1).

Flight tracks were digitised using custom-written software (available from the corresponding author upon request) for Matlab 2017b (The Mathworks), as well as DLTV software for Matlab (Hedrick, 2008). For the custom-written software, the position of the hawkmoth was quantified as the centroid of the animal's body in the image after a background subtraction and thresholding operation (using the function bwlabel). For the DLTV software, we initialised the automatic tracking algorithm by selecting the centroid of the animal's body manually. The digitised tracks were further analysed in the central 80 cm of the tunnel: we quantified the median of the lateral positions of each single flight track in the tunnel, the average flight speed (as the average of all inter-frame velocities) and the variation in in-flight position (as the standard deviation of the lateral position of each flight track). Each flight track was treated as an individual and independent data point in the population flight experiments, while we took animal identity into account for the individual flight experiments.

The statistical analysis was performed in Matlab 2017b (The Mathworks). The median lateral position in the tunnel, average flight speed and in-flight variation of the individual flight tracks were compared across conditions using the non-parametric Kruskal–Wallis test after initial tests confirmed that the data were not normally distributed. If not indicated otherwise, statistical results are shown with a significance level of 5%. The results of the statistical tests, including post hoc comparisons with Bonferroni-corrected P-values are shown in Tables S1–4.

To test whether the variation between consecutive flight paths of an individual hawkmoth differed from that of the entire population of flights, we calculated the standard deviation of the flight parameters used in the previous analysis (median of the lateral position, average speed and in-flight variation) as a measure of the variation between consecutive flights. We did this once within individuals and once across the population. As the number of flights per individual and condition varied, we sub-sampled the population measures to the same number of flights as observed for each individual hawkmoth, to avoid sample bias of the calculated standard deviation. We therefore sampled the same number of flights from the population as were obtained for a given individual and calculated the standard deviation for the three flight parameters from these. We then repeated this procedure for all possible combinations of flight paths out of the population given this particular number of flights and calculated the average of all resulting standard deviations of each flight measure. This average was then compared with the standard deviation of flight measures of the individual hawkmoths using a paired signed-rank test.

The control of forward flight in hawkmoths could readily be tested with the newly established flight tunnel setup (Fig. 1A,B), as the animals quickly explored the tunnel and learned about the new route connecting their two holding cages. Hawkmoths showed a considerable variation of behaviour in the tunnel: while some crossed the tunnel in a smooth, directed movement towards the other exit, others inspected the walls, tried to land or turned around some way along the tunnel to fly back (Table 1). Presenting patterns inducing translational optic flow or patterns that provided a strong contrast resulted in a higher proportion of directed and complete tunnel crossings than under non-optic flow conditions (Fig. 1C,D, Table 1).

Without optic flow or strong contrast on the walls, many animals entered the tunnel, but then turned back or even settled on the tunnel walls rather than exiting on the other side. In the following analysis, we only included flights with complete tunnel crossings in which animals were oriented towards the exit of the tunnel at all times (i.e. did not face towards the walls in an attempt to land there).

We first investigated the flight behaviour of hawkmoths with symmetrically arranged wall patterns. We selected a range of patterns from examples used in previous investigations of flight control in similar tunnels which represent different aspects of visual information: random chequerboard patterns, which induce translational optic flow over a range of spatial frequencies; vertical sinusoidal stripes inducing translational optic flow of one spatial frequency; and horizontal sinusoidal stripes of the same spatial frequency, which provide strong contrast, but induce little translational optic flow. Finally, we tested grey and white walls, which provided neither contrast nor optic flow cues to the hawkmoths (Fig. 2A). Hawkmoths showed a clear centring behaviour with the symmetrically arranged patterns inducing translational optic flow, as has been described in honey bees (Kirchner and Srinivasan, 1989), bumblebees (Baird et al., 2010) and blowflies (Kern et al., 2012). Their flight tracks were concentrated in the centre of the tunnel and avoided areas close to the walls (Fig. 2A). We quantified the strength of the centring response as the variance in the median position of each flight track: the smaller the variance, the stronger the centring response (Fig. 2B, Brown–Forsythe test for pairwise comparison of variance; see Table S2). The medians of the distributions did not differ significantly from each other, except for a significant difference between all conditions and the white wall patterns (see Table S1). The centring response was significantly stronger with the chequerboard pattern and vertically oriented sinusoidal grating, which induced translational optic flow, than with other patterns (Fig. 2B). The horizontal sinusoidal patterns, which provided strong contrast at the tunnel walls, produced a significantly stronger centring response than white or grey tunnel walls. With these last two visual cues, animals used the entire width of the tunnel.

It is well known that insects [honey bees (Baird et al., 2005), bumblebees (Baird et al., 2010), sweat bees (Baird et al., 2011), blowflies (Kern et al., 2012) and fruit flies (David, 1982; Fry et al., 2009)] control their flight speed by the amount of translational optic flow they perceive. These insects all fly slower with strong translational optic flow cues versus weak or absent cues. We therefore quantified the average flight speed of the hawkmoths in the tunnel to investigate whether they adjusted their speed according to the perceived translational optic flow. In general, hawkmoths displayed a large variety of flight speeds in the tunnels. The wide range of flight speeds observed in hawkmoths was probably due to their ability to modulate their flight speed from 0 (performing stationary hovering) up to 250 cm s⁻¹, the fastest speed we observed in the tunnel (Fig. S2). Despite this variety, we did observe an effect of translational optic flow on the flight speed of hawkmoths: the average flight speed was significantly lower with vertical sinusoidal patterns than with horizontal ones or with grey walls in the tunnel (Fig. 2C; Table S1). Interestingly, the average speed was lower with white walls compared with the other non-optic flow conditions, which might have been caused by the lack of orientation cues in this condition, causing the moths to slow down.

Moreover, the average flight speed of hawkmoths was also high with the random chequerboard pattern and was not significantly different from that with horizontal stripes or grey walls (Fig. 2C). This observation was unexpected, as the chequerboard patterns also provide strong translational optic flow. However, their spatial structure differs from the vertical sinusoids, which resulted in much lower flight speeds, suggesting that the spatial content of the translational optic flow affected the flight speed of hawkmoths. This hypothesis was supported by further experiments with vertical stripe patterns with different spatial frequencies (one double and one half the initial spatial frequency used in Fig. 2), which showed that the average flight speed of hawkmoths significantly increased when patterns with lower spatial frequencies were presented (Fig. 3B), while there was no effect on the centring response (Fig. 3A).

The chequerboard patterns resulted in distinct differences to the vertical patterns not just in flight speed but also in the straightness of flight path through the tunnel, potentially caused by differences in their spatial content. Animals showed less lateral variation in their flight path (quantified as the standard deviation of lateral positions of each flight path; Fig. 2D; Table S1) with the chequerboard than with the vertical stripe pattern, suggesting that animals can control the straightness of their flight path better if a wider range of spatial frequencies is provided. To exclude that the particular spatial frequency we chose for these experiments caused the increased variability in lateral position, we quantified the in-flight variation with two additional spatial frequencies (one double and one half the initial frequency used) and did not observe a significant difference between any of the spatial frequencies used (Fig. 3C). In line with their impact on the centring response, the white and grey patterns also resulted in distinctly larger variation in lateral position (Fig. 2D).

As has been described in the pioneering experiments by Kirchner and Srinivasan (1989), when presented with an imbalanced optic flow scenario, honeybees fly towards the side with lower levels of translational optic flow. The same flight strategy has since been observed in most apoidean species investigated (e.g. Chakravarthi et al., 2018), though not in sweat bees (Baird et al., 2011). Hawkmoths showed a very similar strategy when presented with one tunnel wall showing horizontally oriented sinusoidal stripes and one with vertically oriented ones (Fig. 4A). Their avoidance of the wall inducing strong translational optic flow was apparent from the median lateral position of the flight tracks, which shifted significantly closer to the wall on which horizontally oriented stripes were presented (Fig. 4B; Table S4). We also observed a significantly increased in-flight variation for asymmetrical optic flow conditions as compared with symmetrical ones (Fig. 4D; Table S4). Moreover, the average flight speed increased for asymmetrical optic flow conditions to an intermediate level between the symmetrical high and low optic flow conditions (Fig. 4C; Table S4), suggesting that hawkmoths integrated information from both eyes to control their flight speed.

Therefore, we tested whether the hawkmoths' average lateral position in the tunnel affected the average flight speed in the asymmetrical optic flow condition. If the average flight speed was the result of the linear integration of the translational optic flow perceived by both eyes, then hawkmoths that flew closer to the wall presenting weaker optic flow cues should fly faster, as this wall would take up a larger part of their visual field, and thus should have a greater influence on the linear integration operation. We therefore quantified whether there was a correlation between the average lateral position in the tunnel and the hawkmoth's flight speed in the asymmetrical optic flow condition. If our hypothesis of a linear integration based on the proportion that each wall occupied in the animal's field of view was true, then we would expect a positive correlation between lateral position in the tunnel and average flight speed (when positive values of lateral position in the tunnel represent the wall with low translational optic flow). We did indeed observe a weak, yet significant, correlation between average lateral position and average flight speed (Fig. 5A); however, the correlation was negative, indicating that animals which flew very close to the wall with the horizontally oriented stripes flew slower compared with animals crossing the tunnel at a greater distance from the wall. We did not observe a significant correlation for other symmetrical pattern conditions (Fig. 5B–D), indicating that the observed effect was truly caused by the asymmetrically presented optic flow. Our finding suggests that flight speed was not simply adjusted as a linear integration of the perceived optic flow over both eyes. Rather, the animals seemed to take into consideration other factors – for instance, that they were flying very close to a potential obstacle (as they clearly perceived the wall with the horizontally oriented stripes, which, though not inducing strong translational optic flow, still provided a very strong contrasting surface).

As we observed a considerable variation in our three flight summary measures (medium lateral position in the tunnel, average flight speed and in-flight variation), we wondered whether this was due to inter-individual variation or variation between consecutive flights of an individual hawkmoth (intra-individual variation). Studies using marked bumblebees found that intra-individual variation between flights did not differ from inter-individual variation (Dyhr and Higgins, 2010; Linander et al., 2015). To resolve this question in hawkmoths, we let individual hawkmoths fly from a starting position in the right-hand flight cage through the tunnel to feeders hidden behind a screen in the left-hand cage (Fig. 6A). By transporting the moths back to their starting position after a short feeding session, we obtained 3–10 successive tunnel crossings from individually identified animals.

We then tested whether the variation (quantified as standard deviation) in the three flight parameters between consecutive flights of an individual hawkmoth was different from that of flights from the whole population of hawkmoths. If individuals followed consistent flight strategies – for example, if one individual preferred one side of the tunnel or flew at a consistent speed – the variation in these parameters should be smaller between individual's flights than across the population. For symmetrical optic flow patterns (Fig. 6C), we observed no significant difference between the variation in flight parameters of one individual and that across the entire hawkmoth population (Fig. 6D; Table S5). However, for asymmetrical optic flow conditions (Fig. 6C), the variation in both the median position in the tunnel and the average flight speed was significantly lower within flight tracks from an individual hawkmoth than across the population (Fig. 6E; Table S5). There was a trend but no significant difference in the in-flight variation as well. This suggests that individual hawkmoths showed distinguishable flight preferences with respect to position in the tunnel and flight speed when faced with asymmetrical optic flow cues. It is possible that such individual preferences also exist in the symmetrical optic flow conditions, but are masked in the statistical comparisons by the persisting variance in individual flight tracks. Only when moths are forced into more ‘extreme’ flight manoeuvres do these individual strategies become apparent.

We designed a flight tunnel setup in which the role of visual cues for forward flight control could be tested in the hawkmoth M. stellatarum. Our results show general similarities between the flight control strategies of hawkmoths and those of several species of bees and flies tested in similar flight tunnel setups, specifically with respect to position control. However, we also observed some interesting differences, particularly in speed control and individual variance.

From work in Diptera [blowflies (Kern et al., 2012)] and Apoidea [honeybees (Chakravarthi et al., 2018; Kirchner and Srinivasan, 1989) and bumblebees (Baird et al., 2010; Dyhr and Higgins, 2010)], we have a good understanding of the role of translational optic flow for position control during forward flight (Kern et al., 2012; Chakravarthi et al., 2018; Kirchner and Srinivasan, 1989; Baird et al., 2010; Dyhr and Higgins, 2010). Our results in the hawkmoth M. stellatarum extend the range of species in which these control strategies were tested to Lepidoptera, and to insects with different eyes (optical superposition) and flight kinematics (low wing beat frequencies and the ability to hover) than previously investigated species. The fact that we observed a very similar use of translational optic flow cues for position control in flight tunnels suggests that the simple strategy of balancing optic flow to negotiate gaps and cluttered environments might be universally used across insect orders.

While the general centring response to right–left symmetrical optic flow cues (Fig. 2) and the avoidance of the stronger translational optic flow side of asymmetrical stimuli (Fig. 4) was similar to previous results, we also noticed some interesting differences in the behaviour of the hawkmoths, which might be attributable to the species-specific lifestyle. Different insect species seem to have different ‘safety margins’ for the lateral walls inducing translational optic flow. Hawkmoths had a distinctly smaller safety margin from lateral tunnel walls compared with blowflies, honeybees and bumblebees presented with high contrast random chequerboard patterns. Blowfly flight tracks were all centred in the central 50% of the tunnel, for tunnels of comparable width (36 cm) to those used here, as well as for narrower ones (Kern et al., 2012). In other words, their safety margin to the lateral walls in the 36 cm wide tunnel was at least 7.5 cm. Bumble bees showed a similar behaviour: all flight tracks were within the core 30% of a 30 cm wide tunnel and the averages of lateral flight track positions remained within the central 5 cm of the tunnel (Linander et al., 2015), thus keeping the tunnel walls at a minimum distance of about 10 cm. The safety margin of the hawkmoths was much smaller: despite showing a clear centring response compared with conditions of low or non-existent translational optic flow (Fig. 2), there was still a substantial proportion of flight tracks between 5 and 7.5 cm from the wall, and a small fraction at less than 5 cm distance. The averages of lateral flight positions spread across the central 10 cm of the tunnel, thus extending twice as wide as those of bumblebees in a very similar setup (Linander et al., 2015). This is surprising considering that M. stellatarum is more than twice as large as a blowfly, and slightly bigger than a bumblebee, with a considerably larger wingspan. Thus, in relative terms, the animals had to negotiate the narrowest tunnel in relation to their size.

It is unlikely that hawkmoths approach the walls inducing strong translational optic flow more closely than bumblebees or flies because they perceive the patterns less clearly. The Michelson contrast of the patterns in our study was slightly higher than that used with bumblebees (Linander et al., 2015) and we know that the motion-sensitive neurons of M. stellatarum are highly contrast sensitive down to a threshold of 5% (Stöckl et al., 2017b). This is comparable to the behaviourally determined motion contrast sensitivity of bumblebees (Chakravarthi et al., 2017; Dyhr and Higgins, 2010). Moreover, the spatial sampling base of the eyes of M. stellatarum ranges between 1 and 2 deg of visual angle (Warrant, 1999), similar to that of bumblebee eyes (Taylor et al., 2019). The spatial cut-off frequency of the wide-field motion-sensitive neurons of M. stellatarum (Stöckl et al., 2017b) is slightly higher than the behaviourally measured cut-off frequency of bumblebees (Chakravarthi et al., 2017). The 50% temporal cut-off frequency of M. stellatarum motion neurons, however, is distinctly lower than that of Bombus lapidarius (O'Carroll et al., 1996). While the temporal frequencies generated by the presented patterns in our study were still within the temporal response limits of the hawkmoth's motion-sensitive neurons (8 cycles s⁻¹ with the vertical sinusoidal gratings of 0.1 cycles cm⁻¹ at an average flight speed of 80 cm s⁻¹; Fig. 2C), it would be interesting for future research to explore how the relatively low temporal tuning of the hummingbird hawkmoth's motion vision system affects the effective stimulus strength, and whether this is related to the small distance they keep from the lateral walls. It is also possible that M. stellatarum generally keeps a smaller safety distance to obstacles than blowflies or bumblebees irrespective of the perceived strength of the translational optic flow. This might be related to their ability to hover, and thus to potentially stop and change course more easily. This hypothesis is supported by results from plume-tracking M. sexta in wind tunnels, which cleared the obstacles in their flight paths also at just a few centimetres distance (Verspui and Gray, 2009). However, whether this would be similar in a course control scenario without olfactory cues remains to be tested.

The median flight speed we observed in our experiments (ranging from 80 to 110 cm s⁻¹ in the different optic flow conditions; Fig. 2C) was in good agreement with forward flight speed measured previously in two individuals of M. stellatarum (150 cm s⁻¹ in a large flight arena without optic flow cues; Henningsson and Bomphrey, 2013). The variation in flight speed (ranging from 50 to 250 cm s⁻¹) we observed in M. stellatarum was distinctly larger than the flight speed variation observed in the hawkmoth M. sexta when flying in wind tunnels (Willis and Arbas, 1991). However, the low variation in flight speed observed in M. sexta might have been caused by the constant headwind present in the tunnel, to which the animals might have adjusted. It is also possible that the special flight motor programme (Carde, 2016) induced upon pheromone tracking tightly regulates flight speed in male hawkmoths.

However, the variation in flight speed observed in M. stellatarum was also distinctly larger than that of bees (Chakravarthi et al., 2018) and bumblebees (Linander et al., 2015) in similarly sized tunnels, yet similar to that of flies (Kern et al., 2012). In flies, the large variation in flight speed could be correlated with individual flight speed characteristics related to animal size (Kern et al., 2012). However, our experiments on the variation of flight performance within identified individuals does not suggest a similar relationship in hawkmoths: in the symmetrical optic flow conditions, consecutive flight tracks of individual hawkmoths did not show a lower variation in average flight speed than flight tracks across the population (Fig. 6D).

It is interesting to note that bumblebees, when flying in very wide tunnels lined with patterns inducing strong translational optic flow (120 and 240 cm width), also display a large variation in flight speed (Linander et al., 2016) – even larger than that observed in hawkmoths. Thus, the regulation of flight speed by lateral optic flow cues might depend on the perceived relative proximity of the environment – and this might differ for different insect species. Thus, for hawkmoths, a 30 cm wide tunnel might not be perceived as a very narrow passage, and hence might not induce a very tight regulation of their flight speed by lateral optic flow cues, whereas it is perceived as such by bumblebees and bees, which only display a similar flight speed range in four times wider tunnels. This hypothesis would also be in line with the observation that hawkmoths did not keep the same safety margin from the lateral walls as flies, bees and bumblebees did (see above). Further investigations with tunnels of different width would shed light on this theory, and provide interesting insight into potential evolutionary and ecological differences in how insects perceive the proximity of surrounding spaces.

Another cause of the large variability in flight speed across the tunnel might be brief hovering bouts during the tunnel crossing. Varying proportions of hovering and forward flight in different flight tracks could then result in a range of average flight speeds, even if all animals kept a relatively constant forward speed. However, if this were the case, one would expect to see two distinct peaks in the distribution of incremental flight speeds, representing the hovering and forward flight phases. The fact that we observed a wide single-peaked distribution of incremental flight speeds across the population of flight tracks (Fig. S2C) suggests that hovering phases were not the (sole) cause of the large variation in flight speed. This is further supported by the large range of maximum speeds of the individual flights: if the animals displayed a constant forward speed, which was interspersed by hovering bouts, the maximum flight speed should be less variable across flight paths. However, a similar range in maximum (Fig. S3) and average (Figs 2C and 3B) flight speed was observed.

We also observed interesting differences between hawkmoths and previously investigated insect species in the regulation of flight speed by translational optic flow. While hawkmoths showed an increase in flight speed with horizontally versus vertically oriented sinusoidal patterns (Fig. 2C), as previously described in flies (Fry et al., 2009; Kern et al., 2012), honeybees (Baird et al., 2005), sweat bees (Baird et al., 2011) and bumblebees (Baird et al., 2010; Dyhr and Higgins, 2010), their flight speed control was not independent of the spatial frequency of the patterns. Hawkmoths showed significantly higher speeds with chequerboard patterns than with vertical sinusoids (Fig. 2C), which induce similar flight speeds in bumblebees (Baird and Dacke, 2012). Generally, flight speed control has been shown to be independent of the spatial structure of the presented stimuli in honeybees (Baird et al., 2005; Srinivasan et al., 1991, 1996) and flies (David, 1982; Fry et al., 2009). However, our results suggest that the spatial structure does play a role in speed tuning in hawkmoths. This is further supported by the observation that hawkmoths adjust their flight speed inversely to the spatial frequency of symmetrically presented vertical sinusoids (Fig. 3B). It will be very interesting to further investigate the role of spatial pattern structure on flight speed control in hawkmoths to understand whether they might use a different neural strategy from that of flies and honeybees for flight speed control from optic flow information.

It has been reported in bumblebees that flight paths resulting from a single individual bee show a similar variation in lateral position and speed to flight paths randomly sampled across the population of bees (Dyhr and Higgins, 2010), suggesting that individual identity can be neglected when studying bumblebee flight performance in tunnels. We observed a similar result when testing hawkmoths under symmetrical optic flow conditions, during which they performed a centring response (Fig. 6D). However, upon presenting asymmetrical translational optic flow cues in which the animal has to perform flight manoeuvres deviating from the centre position of the tunnel, we did observe distinct similarities in the flight paths of individual animals, which resulted in a lower intra- than inter-individual variation in lateral position and flight speed (Fig. 6E). To our knowledge, individual differences in bumblebees were tested under conditions of symmetrical optic flow (Dyhr and Higgins, 2010); thus, it is possible that a similar finding would be made in bumblebees when tested with unbalanced optic flow. In blowflies, individual differences were observed in flight speed even under balanced translational optic flow conditions (Kern et al., 2012). Thus, future flight experiments in hawkmoths that induce more advanced flight manoeuvres than centring would benefit from registering individual identity.

In conclusion, we here present a simple behavioural method to quantify the role of visual cues in forward flight control in hawkmoths, which expands the role of insect models for studies of visual flight control. Our results suggest that the use of translational optic flow information for position control in confined spaces is a strategy shared by all insect orders investigated so far. However, differences in the strength of the centring response, as well as the control of average flight speed, between hawkmoths, bees and flies suggest that the visual flight control is adapted to each insect species' specific anatomical prerequisites and ecological needs.

We thank Emily Baird and Almut Kelber for valuable input and discussions on the experimental paradigm and Johannes Spaethe for lending us his light measurement equipment. We would also like to thank Oliver Pfister from Contaware for the reliable support and custom-adjustments to the camera software.