The free-flight response of Drosophila to motion of the visual environment

Insects possess a remarkable repertoire of sophisticated aerobatic behaviours such as centring and escape responses, collision avoidance, and an elaborate landing programme (for a review, see Egelhaaf and Kern, 2002). Previous research has shown that, especially in flies, aerial manoeuvres require elaborate sensory feedback from the gyroscopic halteres, the campaniform sensilla on the wings or the compound eyes(Chan and Dickinson, 1996; Dickinson and Palka, 1987; Fayyazuddin and Dickinson,1996; Hengstenberg,1988; Götz,1980; Nalbach,1994). Over the years, the interplay between sensory stimuli and the formation of motor commands for flight control has been thoroughly investigated on different levels covering electrical recordings from motion-sensitive neurons (Borst and Egelhaaf, 1989; Egelhaaf and Borst, 1993; Franceschini et al., 1989; O'Carroll,1993; Warzecha et al.,1992), the flight musculature under tethered flight conditions(Balint and Dickinson, 2001; Egelhaaf, 1989; Götz, 1983; Heide and Götz, 1996; Heide et al., 1985; Lehmann and Götz, 1996; Tu and Dickinson, 1996), and experiments on flight behaviour in tethered and free flight under a great variety of stimulus conditions (Ennos,1989; Frye and Dickinson,2001; Götz,1987; Heisenberg and Wolf,1988; Heisenberg and Wolf,1993; Tammero and Dickinson,2002a; Wagner,1985; Wolf et al.,1995; Wolf and Heisenberg,1990).

Early studies on flight control (e.g. Blondeau and Heisenberg, 1982; Götz, 1968; Reichardt and Poggio, 1976)demonstrated that tethered flies produce yaw moments around the vertical body axis when stimulated under open-loop feedback conditions with a rotating large-field panorama in a flight simulator (optomotor response). The experiments consistently showed that yaw moments depend on a large variety of stimulus factors including angular velocity, contrast and the spatial wavelength of the rotating pattern. Under closed-loop conditions, optomotor behaviour persists as long as the external visual stimulus produces retinal slip on the animal's compound eye (Wolf and Heisenberg, 1990). Optomotor turning behaviour in an animal is considered to operate via a feedback loop in which an increase in neural activity produced by retinal slip on the ipsilateral eye activates the flight muscular system on the contralateral side of the animal's body. As a consequence, it had been suggested that an animal achieves straight flight when optic flow is similar in the two eyes [optomotor equilibrium(Götz, 1975; Wehner, 1981)]. Recently,researchers successfully implemented the optomotor reflex on robotic platforms and numerical models (Huber et al.,1999; Iida, 2003; Neumann and Bülthoff,2001; Reiser and Dickinson,2003).

In the past, the fundamental concepts on visuo-motor control mechanisms in flies gained from tethered flight studies have also been tested in free-flight experiments on various fly species(Collett and Land, 1975; Wagner, 1986). For example,Collett demonstrated optomotor response in male hoverflies (Syrittapipiens) flying inside a rotating pattern drum(Collett, 1980a; Collett, 1980b). These data show that the animals compensate for retinal slip up to angular pattern velocities of approximately 200°s^–1, employing two behavioural strategies: the flies either turn around their vertical axes while hovering with low forward speed at the centre of the drum, or they perform side-slip manoeuvres in front of the visual pattern. Interestingly, retinal slip compensation via side-slip flight occurred more often than via yaw turning, which was interpreted as a possible consequence of the specialized frontal eye region in male hover flies favouring smooth object tracking (Collett and Land,1975). In contrast to hover flies, similarly sized houseflies(Musca domestica) apparently employ an alternative strategy to achieve optomotor equilibrium during free flight(Wagner, 1986). Although Musca produces continuous yaw moments in response to a rotating visual panorama when flying under tethered flight conditions, the predominant free-flight behaviour in response to a 2.5Hz horizontally oscillating visual panorama consists of rather straight segments interspersed with fast saccades(Wagner, 1986). This behaviour lasts up to an angular slip velocity of approximately 700°s^–1.

The conventional view that optomotor steering response in flies is due to rotational motion cues has recently been questioned by Tammero and colleagues who suggested an alternative concept for turning control in tethered flying Drosophila (Tammero et al.,2004). The authors showed that translational motion cues generated by laterally centred foci of expansion and contraction may fully account for yaw torque response in this species. On the level of visual motion detection this finding implies that steering responses to image rotation might emerge from a visual system organized to detect translation flow fields, rather than from a rotation-sensitive system. This result is also supported by a previous analysis on fruit flies flying freely in a stationary environment(Tammero and Dickinson, 2002a; Tammero and Dickinson, 2002b). In this study, the authors demonstrated that lateral expansion of visual cues may initiate a flight saccade while the asymmetry in the output of the local motion detector prior to the saccade primarily influenced the direction, but not the turning angle, of the saccade. There is also evidence that in a stationary environment freely flying fruit flies gradually turn away from the side experiencing a greater motion stimulus, a response opposite to that predicted from a conventional model based upon optomotor equilibrium. From their experiments the above authors thus concluded that course control primarily results from haltere feedback and is only modified indirectly by visual input. However, despite the recent progress in understanding the various roles of the visual system for saccade initiation, and the halters as the primary sensory organ for flight stabilization and the control of straight flight in the fruit fly, it has remained open to what extent freely flying Drosophila uses visual feedback for controlling its flight path when stimulated under optomotor conditions with a moving visual environment(Tammero and Dickinson, 2002b; Frye, 2007).

Thus, in this study we attempted, first, to determine whether flight behaviour of freely flying Drosophila is consistent with minimizing retinal slip during optomotor stimulation; second, to evaluate the significance of a rotation- and translation-sensitive motion detector network for flight control; and third, to tackle the question of how total aerodynamic force is distributed on the three force components: thrust, upward force and lateral force in the manoeuvring fly. For this purpose, we flew single animals in a flight arena that rotates a large-field panorama at six distinct angular velocities. While the animal responded to the moving panorama, we simultaneously measured the panorama's angular position and the fly's three-dimensional body position including the orientation of the longitudinal body axis. From these measurements we subsequently derived the animal's (i)horizontal and (ii) vertical velocity, (iii) side-slip movement, (iv) turning motion around the vertical body axis, (v) visual gaze and (vi) retinal slip by modelling the output of the `Hassenstein–Reichardt' elementary motion detector (EMD) of both compound eyes. A numerical model for force balance eventually demonstrated a solution that permits the prediction of the minimum flight path radius of a flight trajectory from the animal's flight velocities and locomotor capacity.

All experiments in this study were performed on 3- to 5-day-old female Canton S wild-type fruit flies (Drosophila melanogaster Meigen) from an inbred laboratory stock. The animals were reared at room temperature(22°C) on commercial Drosophila medium (Carolina Biological,Charlotte, NC, USA). Pre-tests showed that a certain percentage of animals within our lab colony did not fly for at least 5 s. To separate flying from non-flying individuals, we thus pre-selected the fruit flies in a 6 cm×6 cm wide and 28 cm high vertical wind tunnel on their ability to actively fly upwind for at least several seconds. The wind tunnel was made from translucent acrylic glass and painted with Fluon GP1 (Whitford GmbH, Diez, Germany)diluted 50% with water to prevent the flies from climbing up the inside walls. At the top of the wind tunnel two 81 ml capturing chambers were attached to the side walls that contained an odour source (vinegar diluted to 70% in water), and a 20 W halogen lamp illuminated the wind tunnel from above. To attract the flies towards the odour source, a fan mounted at the bottom of the wind tunnel accelerated humidified room air downstream at a moderate velocity of less than 0.1 m s^–1. Throughout the pre-selection experiment, we repeatedly reloaded the wind tunnel with flies by placing them on a starting platform (grid) above the fan. The female fruit flies subsequently used for the free-flight arena experiments had a mean body mass(±s.d.) of 1.24±0.21 mg. In total, we tested N=131 flies in the optomotor arena.

The flies were tested in a cylindrical free-flight arena on their ability to follow moving visual stimuli under optomotor stimulus conditions. The arena consisted of two concentric 20 cm high acrylic cylinders of 14 and 19 cm diameter, respectively. The inner translucent cylinder was immovable and prevented the animals from landing on the second outer cylinder (pattern cylinder) that was equipped with a visual random square pattern. Each pattern square covered an 8°×8° wide area when seen from the centre of the arena and was either black or translucent with 50% probability(Fig. 1A,C). To evaluate any spontaneous preference of the animals for certain parts of the random square pattern, we measured the time with which flies orientated towards eight equally spaced 45° wide sectors of the surrounding panorama and calculated the normalized flight direction probability. A one-way ANOVA test suggested no significant differences in spontaneous preference between the eight sectors(P>0.05). The maximum difference in probability between two neighbouring sectors was 5±10%, and the mean probability difference for all sectors was 2±5% (mean ± s.d.). Relative mean brightness of each sector was 46±0.1% (mean ± s.d., translucent squares 100%and black squares 0% brightness). An infrared diode mounted on the rotating cylinder was used to track the angular position of the panorama during video analysis.

Three surrounding circular fluorescent light tubes illuminated the pattern cylinder from outside while the cylinder's frosted surface established diffusive and rather uniform light conditions within the arena. To avoid flicker responses of the fly's compound eye to changing light intensities produced by the 50 Hz power line, we operated the fluorescent tubes at 20 kHz(Pick, 1974). Mean light intensity inside the arena was 183 cd m^–2, and the entire setup was covered with black cardboard to reduce any further changes in light conditions during the experiments. The bottom of the inner cylinder was covered with white foam rubber containing a small plastic tube (5 mm diameter tubing) in the arena centre. The tubing allowed single flies to enter the arena via a microprocessor-controlled gate that connected the plastic tubing to a small reservoir holding approximately 20 pre-selected flies. An infrared light path that consisted of a 780 nm, 3 mW laser (Roithner, Vienna,Austria) and a photo-detector integrated into the tubing outlet produced a video trigger signal as soon as a fly had entered the arena and started flying. Although the visual system of Drosophila is almost insensitive to light above wavelengths of approximately 620 nm, we switched the laser off immediately after the fly had voluntarily initiated flight(Hardie, 1986). In response to the take-off trigger signal, a high-speed video camera (NEC HI-DcamII, Tokyo,Japan) recorded the position of the fly inside the arena and the azimuth position of the surrounding visual pattern at 125 frames s^–1,4 ms exposure time and at a resolution of 1020×1020 video pixels. For each fly we recorded an 8 s flight sequence using Pixoft video-capturing software (Pixoft v3.0, Pixoft Diagnostic Imaging, Birmingham, UK).

To establish optomotor stimulus conditions while the fly was flying inside the arena, we rotated the pattern cylinder at six different speeds: 0, 100,300, 500, 700 and 900° s^–1 using a conventional electrical gear motor (MFA/Como Drills 919D, Conrad, Hirschau, Germany). To avoid any confounding response of the animals produced during the acceleration phase of the pattern cylinder, we started the pattern motion as soon as a single fly passed the gate and continued walking towards the plastic tubing outlet. We rotated the pattern cylinder counter-clockwise, because previous results did not show any significant differences between the two rotary directions (Student's t-test, P>0.05, N=24 flies, cylinder velocity 500° s^–1). Throughout this paper, the angular velocity of the rotating pattern cylinder is termed `arena velocity'. Under the experimental conditions, the average flight time of each fly inside the arena was 2.5±0.48 s (mean ± s.d.), except for experiments with 500° s^–1 arena velocity(4.6±0.5s, mean ± s.d.). To avoid transient flight behaviours associated with take-off dominating the experimental data, we excluded flight sequences below 1.5 s total flight length from the video analysis. We also eliminated flight data below a minimum flight velocity of 40 mm s^–1, because flight sequences were occasionally interrupted by short periods of landing. Mean ambient temperature during the experiments was 28°C with only small fluctuations of approximately ±2°C(s.d.). In general, compared with previous studies with a larger stationary arena (Tammero and Dickinson,2002a; Tammero and Dickinson,2002b), our smaller flight arena was a compromise between the difficulties of rotating the panorama at up to 900° s^–1angular velocity, the resolution of our video camera required for detecting body orientation from single images using blob analysis (see following paragraph), and the space available for manoeuvring flight.

We analysed the recorded video images using self-written software in Visual C++ and commercial imaging components (Matrox Imaging Library Mil 7.5, Dorval,Canada). From each video frame, we estimated the (i) position of the fly's centre of gravity, (ii) the angular orientation of the longitudinal body axis when possible, and (iii) the size of the fly using blob analysis, which treats the animal's picture as a unified group of neighbouring video pixels(Fig. 1B, Fig. 2). From these data, we derived (i) the translational velocities of the animal (horizontal, vertical and side-slip velocity), (ii) the fly's turning (angular) velocity around the vertical axis, (iii) flight altitude and (iv) the curvature of the flight path, employing custom-written routines in Origin 7.0 (OriginLab, Microcal,Northampton, MA, USA). We interpolated missing data points by linear regression in cases where the imaging software could not automatically detect the fly on the video images, which occurred in approximately 1.0% of all data. Moreover, we reduced data noise due to both small errors in detecting the fly's position and potential errors resulting from the image resolution by performing two-dimensional data averaging (adjacent averaging on the horizontal x- and y-coordinates; running window with five data points or 40 ms). If not stated otherwise, all values given in the text are means ± s.d.

While the animal's horizontal and vertical velocities may easily be derived from the blob's x- and y-positions, estimations of instantaneous turning velocity may vary according to the video analysis algorithm. In 52% of all data we were able to reliably retrieve the fly's yaw orientation from a single video frame, because in these cases the ratio between the lateral (b) and longitudinal (a) extension of the blob ellipse was smaller than 0.8 (Fig. 2B). Blob analysis permits estimation of body orientation (gaze)independent from flight direction as shown in Fig. 2A. In this example, Drosophila follows the rotating pattern by sliding sideways in an attempt to reduce retinal slip. Sideward translational motion without yaw rotation may reduce retinal slip in the frontal visual area of the animal,whereas the lateral eye regions experience retinal slip due to image expansion or contraction. However, since blob shape is susceptible to changes in body posture, we estimated body orientation, gaze and turning velocity from the changes in flight direction (heading) given by two (orientation, gaze) and three (angular velocity) successive data points (centre of blob) throughout our study, and in accordance with previous studies on free flight(Tammero and Dickinson, 2002b)(Fig. 1D,E). A direct comparison between the two methods exhibited a mean correlation coefficient squared (R²) of approximately 0.62±0.12 and a mean slope of 0.99±0.02 (reduced major axis linear regression fit; mean P=0.00015, six arena velocities, 131 flight sequences, Fig. 2B). We found small variations in R² values among the six tested arena velocities, suggesting that side-slip manoeuvres are apparently most frequent at maximum flight speeds in response to 900° s^–1 arena velocity (0° s^–1: 0.99, 0.64; 100°s^–1: 1.01, 0.65; 300° s^–1: 0.98, 0.68;500° s^–1: 0.98, 0.78; 700° s^–1:0.95, 0.57; 900° s^–1: 0.98, 0.43; for arena velocity:model II slope, R² value). On average, the two methods produced similar results (Student's t-test, P>0.05, 131 flight sequences).

Nevertheless, despite the strong coincidence between the two estimates for body orientation, the fly's actual gaze may still differ from these values due to head movements during flight (Hateren and Schilstra, 1999; Hengstenberg, 1988; Hengstenberg, 1991; Hengstenberg and Sandeman,1986; Kern et al.,2005). A recent study on head motion in freely flying blow flies during straight flight, for example, yielded saccadic head movements at angular velocities in the range of ±100° s^–1(Hateren and Schilstra, 1999). Due to the limited resolution of the high-speed video camera, we could not address this issue in the present study.

Despite the use of a single video camera, blob analysis also allowed us to estimate the height of the flying fly inside the arena. The pictograms in Fig. 1B show that with increasing flight altitude the oval fly blob becomes increasingly circular and also larger on the video image due to a decrease in image focus. We estimated the absolute height of the animal by comparing blob size with previous measurements in which we had moved a tethered fly by hand up and down in the middle of the arena (linear regression fit, y=75+0.84x,R²=0.94, P<0.0001, N=14 measurements, Fig. 1B). Since perspective distortion produced by the camera lens (50 mm, Nikon, AF Nikkor,Düsseldorf, Germany) was negligibly small, amounting to less than one image pixel difference between the centre and the wall of the inner cylinder,we did not expect a significant change in blob size with increasing distance from the arena centre. Thus, the altitude estimates for a fly flying in the centre and the periphery of the arena should be widely identical. We confirmed this hypothesis by experiments in which we mapped the geometry of a calibration grid displayed at the arena bottom on the recorded video image. To remove data noise produced by local changes in brightness due to the rotating pattern cylinder and alteration of the fly's body posture such as body swings during flight saccades, we applied a digital low-pass filter with a cut-off frequency of 12.5 Hz on the vertical z-coordinate.

We also used flight altitude to correct our x/y position estimates in order to obtain exact velocity estimates for the animal. Without this correction, for example, we would record an approximately 18.5% larger horizontal velocity for a fly flying at 150mm flight altitude, and thus closer to the camera lens, than for an animal flying with the same speed but close to the arena bottom. The accuracy of this approach, however, depends on the robustness of our blob estimates that may potentially change due to image blur. Severe image blur of a fast cruising fly produces potentially larger blobs that would cause an overestimation of flight altitude. We considered this problem as follows. In our video image, each millimetre of the arena is represented on average by 6.1 video pixels. An animal that moves with an elevated forward velocity of 0.6ms^–1 and close to the arena bottom would thus move 2.4 pixels within a single video frame (exposure time 4ms). At an average blob size between approximately 100 and 200 video pixels(Fig. 1B), however, an additional 2.4 pixel offset would increase blob size by only 1.2% (200pixels)and 2.4% (100pixels). These values correspond to a potential error in flight altitude estimation of 1.2 and 2.4mm, which is less than one wing length in Drosophila (2.5mm, Fig. 1B). Even more extreme forward velocities of 1.0ms^–1 would produce errors well below the measured behavioural effects. Consequently, the analysis above suggests that motion blur may not considerably change our position estimates in the vertical due to short image exposure time.

A major goal of this study was to examine optomotor behaviour in freely flying Drosophila. We thus estimated the response of the fly's visual motion system during flight by modelling the output of the Hassenstein–Reichardt EMD for horizontal motion on both complex eyes,assuming a 360° horizontal by 80° vertical field of view. This was achieved by projecting the visual environment of the pattern cylinder on the fly's spherical complex eyes at each moment of time according to the position and orientation of the animal inside the visual panorama. Due to the limits of our experimental setup, however, we simplified this approach as follows. First, the spatial resolution of the video image did not permit recording of the position of the fly's head and concomitant estimation of the orientation of the eyes with respect to the visual environment, as mentioned above(Kern et al., 2005). We circumvented this restriction by determining gaze from the direction in which the fly was heading. Second, we ignored roll `banking' moments around the longitudinal body axis of the animal, because these movements could not be measured from the video images. The modelled EMD output thus solely depended on changes in the angular position around the fly's vertical axis, horizontal velocity and the distance to the surrounding panorama.

We simulated the azimuth response of the two-dimensional EMD detector system according to conventional assumptions as described previously(Borst and Egelhaaf, 1989; Borst and Egelhaaf, 1990; Tammero and Dickinson, 2002b). The spherical projection of the pattern was mapped onto the eye with a spatial resolution of 0.1° and subsequently smoothed with a Gaussian filter. The width of the Gaussian filter at 50% half-peak height was 3.8°, and its total effective range was limited to 7.6°, centred on each data point. The value of 3.8° is slightly higher than the width of angular sensitivity of each photoreceptor in Drosophila, which is approximately 3.5°(Götz, 1964), for the following reason. In the fruit fly, the angular spacing of the visual axes between two adjacent ommatidia is 4.6°. During simulation, however, we divided the 360° horizontal field of view into four units (I–IV)each (45° visual field in the horizontal) with 5° spacing. To maintain the ratio of 0.76 between the spacing of visual axes (4.6°) and the angular sensitivity (3.5°) in the analytical model, we slightly raised the width of the Gaussian filter to 3.8°. We calculated the response of the EMDs by convolving the Gaussian-filtered signal with the impulse response of a first-order high-pass and low-pass filter with a time constant of 50 ms(Kern and Egelhaaf, 2000) and 40 ms (Borst and Egelhaaf,1989) and for a time period of 150 and 120 ms, respectively. In a separate pathway, the Gaussian-filtered signal was attenuated by a factor of 0.15, and bypassed the high-pass filter response during peripheral filtering(see Appendix). Subsequently, the signals of adjacent EMDs were spatially integrated within each 45° horizontal section and averaged within an 80° range in the vertical direction (40° below and above the horizontal) that was considered to be approximately similar to the expected spatial integration process of neural activity in the fly's large field neurons of the lobula plate (Haag et al.,1992). In our analytical framework, all eight EMD units of the two simulated eyes produced a positive EMD output in response to front-to-back visual motion. With these outputs, we simulated two system configurations: a rotation- and an expansion-sensitive system with a lateral focus of expansion by summing up the responses of all units for one eye or by taking the difference between the sums of the two frontal (I+II) and two caudal units(III+IV) of each compound eye, respectively. See Appendix for a more detailed explanation of the equations used in the simulation.

While flying inside the optomotor free-flight arena, the flies reliably responded to the rotating visual panorama by systematically altering (i) their positions inside the arena (Fig. 3A–F and Fig. 4), (ii) their horizontal, vertical and turning velocities(Fig. 5) and (iii) their flight style (Figs 6 and 7, and supplementary materialFigs S1 and S2). The probability plots in Fig. 3 show the temporal probability and thus the time the flies spent in a certain region of the arena. At stationary pattern (Fig. 3A) and low arena velocities (100–300°s^–1, Fig. 3B,C), the flies apparently did not explore the entire arena space but rather spent most of their time flying near the arena centre. By contrast,at the maximum arena velocity of 900° s^–1, we measured highest probabilities near the wall of the inner translucent cylinder(Fig. 3F). To analyse these changes in greater detail, we re-plotted the underlying data distributions as histograms and as a function of the distance (d) between the arena centre and the inner arena cylinder (Fig. 4A). The data show that in a stationary environment the flies cruise at a distance of 25 mm, on average (median, white dotted line, Fig. 4A). With increasing arena velocity the peak of the histograms moves towards the inner cylinder wall yielding medians ranging from 30 mm at 200° s^–1 to 50 mm at 900° s^–1 arena velocity, respectively. This result in conjunction with the geometry of the flight path suggests that fruit flies obviously prefer to move on distinct, differently sized concentric trajectories around the arena centre. The distance of these trajectories from the arena centre significantly increases with both increasing arena velocity(linear regression fit, y=0.02x+32, R²=0.97, P<0.001, N=6 data points)and increasing forward velocity (linear regression fit, y=0.02x+38.8, R²=0.88, P<0.001, N=13 data points, Fig. 4B).

Horizontal and turning velocity in an insect that achieves optomotor equilibrium in a rotating visual environment depend on two factors: the distance of the animal from the arena centre and the angular velocity of the visual panorama. Potentially, the animal may limit horizontal speed independently of arena velocity by flying closer to the arena centre. The data in Fig. 3A–F and Fig. 4A, however, show a systematic increase in distance between the flies and the arena centre with both increasing arena velocity and increasing horizontal velocity. Thus,horizontal velocity of the animals increases from approximately 0.26±0.08 m s^–1 in a stationary environment to a maximum of 0.5±0.09 m s^–1 at 700°s^–1 arena velocity (Fig. 5, black circles). Maximum forward velocity apparently saturates at this level, suggesting that the fly has either reached its maximum locomotor capacity or is constrained by the walls of the inner cylinder as suggested by the asymmetrical distribution of the histograms at 500–900° s^–1 arena velocity(Fig. 4A). A mean distance between the fly and the cylinder of 20–30 mm corresponds to approximately 10 wing lengths.

At the level of mean angular velocity, Drosophila widely compensates for the rotational stimulus by exactly matching turning to arena velocity. This behaviour is maintained for arena velocities ranging from 100 to 500° s^–1 and indicated by small and less than±6° s^–1 differences between the fly's turning rate and the blue line that indicates the required turning rate for optomotor equilibrium (Fig. 5, blue). In general, this result is not opposite to the assumption that retinal slip drives optomotor responses, because the mean values ignore the temporal substructure of the data set. We show later in this paper that the fly slightly oscillates its turning velocity and that the elementary motion detector system thus produces sensory feedback for flight control, even though the mean retinal slip on each compound eye is close to zero. The fly may achieve zero retinal slip on both compound eyes flying at any point of the arena, regardless of its distance to the centre: the only prerequisite is that turning velocity matches arena velocity and the fly's horizontal velocity is equal to the translational velocity of the arena at this location. Under these conditions, the fly would be virtually tethered inside the arena while rotating together with the pattern drum. At an arena velocity above 500°s^–1, turning velocity decreases with increasing arena velocity, producing a mismatch between turning rate and angular velocity of the arena of approximately –154° s^–1 at 700°s^–1 arena velocity and –617° s^–1at 900° s^–1 arena velocity.

In the flying insect, total flight force is the vector sum of three translational forces: upward force, thrust and side slip. Depending on body mass (in the case of upward force) and the friction between the surrounding air and the moving body including the flapping wings, these forces determine the animal's upward, forward and sideward velocities. Side slip seems to be negligible under our experimental conditions (see Materials and methods), but vertical velocity distinctly varies, depending on stimulus strength and the fly's own horizontal velocity. The dynamics of vertical flight velocity can be characterized by two major components: an initial steep gain in flight altitude immediately after take-off lasting approximately 0.4 s (linear regression fit, mean slope=0.66±0.02 m s^–1, N=6 sequences), followed by a more moderate increase in vertical velocity that depends on stimulus conditions (linear regression fit, model I slopes at 0° s^–1 arena velocity: 0.26 m s^–1; 100 s^–1 arena velocity: 0.20 m s^–1; 300 s^–1 arena velocity: 0.20 m s^–1; 500 s^–1 arena velocity: 0.23 m s^–1; 700° s^–1 arena velocity: 0.47 m s^–1). We calculated maximum vertical flight performance of the fly as the mean of all data points within a recording that fell within the top 1% of velocities in each distribution. These data differ only slightly between the six stimulus conditions and range from approximately 0.38±0.05 m s^–1 (N=101 sample points)measured at 500° s^–1 arena velocity to approximately 0.48±0.02 m s^–1 (N=37 sample points) during flight in a stationary visual environment. Mean climbing velocities of an entire flight sequence are shown in Fig. 5 (red). These data suggest only moderate vertical velocities compared with horizontal velocity ranging from values close to zero[3.7(±40.5)×10^–3 ms^–1, 700°s^–1] to a small maximum value of 69.2(±69.1)×10^–3 ms^–1 at 100° s^–1 arena velocity (N=131 animals).

As reported previously, fruit flies exhibit stereotypical flight saccades when flying inside a stationary environment(Tammero and Dickinson,2002b). We distinguished saccadic turning from other forms of turning, employing a minimum threshold for peak angular velocity inside the saccade of 1000° s^–1. Fig. 6A–C shows flight trajectories from three flies flying inside the flight arena with a stationary random-dot environment, all exhibiting saccadic turning at a mean horizontal velocity of approximately 0.26 m s^–1 (colour coded). Although turning velocity prior to and after the saccades changes with changing arena velocity (base line of colour plots in Fig. 6D), we measured approximately the same maximum turning velocity(0° s^–1 arena velocity, 1542° s^–1turning velocity; 100° s^–1 arena velocity, 1521°s^–1 turning velocity; 300° s^–1 arena velocity, 1470° s^–1 turning velocity; 500°s^–1 arena velocity, 1477° s^–1 turning velocity; 700° s^–1 arena velocity, 1520°s^–1 turning velocity; and 900° s^–1 arena velocity, 1650° s^–1 turning velocity) and saccadic length of approximately 130 ms under all experimental conditions(Fig. 6D). As a consequence,angular accelerations during turning are highest when the animal flies sufficiently straight before initiating the saccade(Fig. 6; 0°s^–1 arena velocity, black; 100° s^–1arena velocity, red). We also found a distinct increase in forward velocity between 0.06 and 0.25 m s^–1 (0.124±0.076 m s^–1, mean ± s.d., N=6 traces, Fig. 6E) starting approximately 140 ms prior to the saccade. These data suggest that the flies first begin to turn when they achieve peak velocity during horizontal acceleration, i.e. approximately 70–80 ms or 15 stroke cycles prior to the turn. We evaluate this increase in horizontal velocity prior to turning as a potential artefact of the small flight arena later in the Discussion. During angular acceleration, horizontal velocity transiently decreases by approximately 0.12±0.007 m s^–1 (0° s^–1 arena velocity, 0.12 m s^–1 forward velocity;100°s^–1 arena velocity, 0.11ms^–1 forward velocity; 300° s^–1 arena velocity, 0.11 m s^–1 forward velocity; 500° s^–1 arena velocity, 0.13 m s^–1 forward velocity; 700°s^–1 arena velocity, 0.13 m s^–1 forward velocity; and 900° s^–1 arena velocity, 0.13 m s^–1 forward velocity) while mean saccade frequency slightly increases by 23%, from approximately 2.7 to 3.5 Hz, with increasing mean horizontal velocity measured between two saccades (intersaccade velocity,linear regression fit, y=0.13x+2.6, R²=0.04, P=0.024, N=131 flies, Fig. 6F).

Fig. 4C shows that in our 140 mm diameter optomotor free-flight arena, the fly's mean turning angle in a stationary environment amounted to 120±26° (N=131 flies),which is higher than the 90° reported previously. With the increasing need to turn faster in response to the angular velocity of the optomotor stimulus,saccadic turning angle increases to a mean maximum value of 145±15°, which was obtained at 700°s^–1 arena velocity. However, Fig. 4C also shows that most of the increase in total turning velocity is due to an increase in smooth turning manoeuvres with turning rates below 1000°s^–1 (for flight path see Fig. 7F) and not predominantly to an increase in saccadic turning angle. We found that the turning angle of smooth turns steeply increases from 56±32° at 0°s^–1 arena velocity to 115±38° at 500°s^–1 arena velocity. At flight conditions(700–900°s^–1 arena velocity) in which the animal may not stabilize its gaze as required for retinal slip compensation(Fig. 5, blue), however, smooth turning angle decreases again towards a value obtained at low arena velocity(100° s^–1, Fig. 4C). This change in ratio between saccadic and smooth turning angles is shown in Fig. 4D,assuming a mean saccadic length of 100 ms duration. Smooth turning time, the time between two saccades, decreases significantly with increasing arena velocity by –21(±5.6)×10³ s²deg.^–1 (linear regression fit, y=–0.02x+0.39, R²=0.77, P=0.02, N=6 data points) yielding times of 0.36±0.14 s (0° s^–1 arena velocity), 0.35±0.08 s (100°s^–1 arena velocity), 0.33±0.13 s (300°s^–1 arena velocity), 0.33±0.07 s (500°s^–1 arena velocity), 0.25±0.04 s (700°s^–1 arena velocity) and 0.27±0.0.07 s (900°s^–1 arena velocity).

As already mentioned, Fig. 5suggests that the fruit flies try to match their turning speed to the angular velocity of the rotating arena in an attempt to reduce the difference in retinal slip on both compound eyes. Direct evidence for the assumption that Drosophila tries to achieve retinal slip compensation in free flight similar to the response measured in tethered flies, however, requires simulation of the optic flow during flight. We thus simulated a Hassenstein–Reichardt EMD array for horizontal motion as described above. Typical time traces for (i) the EMD response of a rotation-sensitive system simulated for both compound eyes in free flight, (ii) the fly's gaze towards the pattern and (iii) its body motion are shown in Fig. 7 for two different experimental conditions: flight in a stationary environment(Fig. 7A–E, Fig. 8) and flight with an outer panorama rotating counter-clockwise at 500° s^–1(Fig. 7F–J).

Despite the smaller arena size compared with previous research(Tammero and Dickinson,2002b), the data superficially show the same typical properties of flight behaviour, such as regular saccades. In the stationary environment the simulated EMD response is approximately similar in magnitude for the two eyes,because the flies typically remained close to the arena centre(Fig. 7A, red cross). Fig. 7D,E shows the relationship between turning and left-minus-right eye EMD response, and between horizontal velocity and left-plus-right eye EMD output. The difference in EMD response is also plotted in pseudo-colour for each sample point of the flight paths in Fig. 7A,F. A common feature of all flight sequences and at all stimulus conditions is that turning and horizontal velocities typically change out of phase, often producing regular large oscillations of the rotation-sensitive EMD array(left-minus-right eye). These oscillations are shown in Fig. 7I during optomotor stimulation with a rotating pattern cylinder at 500° s^–1. In this example, the fly stabilizes its gaze (black) towards the pattern(red), since the two curves in Fig. 7G run in parallel, while flight saccades are almost absent (grey dots).

To further assess the mean response of the rotation-sensitive EMD detector system under the various stimulus conditions, we plotted the EMD outputs as normalized histograms for both left-minus-right(Fig. 9A) and left-plus-right eye (Fig. 9B). We derived the histogram peak and the width of the distribution by fitting Gaussian curves(Fig. 9, red) and plotted both measurements as a function of arena velocity in Fig. 10B (left-minus-right eye) and Fig. 10C(left-plus-right eye). The data show that in a stationary environment, the difference in EMD output of the two eyes is close to zero. This finding suggests that there is no preferred direction of turning behaviour and/or the time ratio between turning and straight flight is relatively small. During optomotor stimulation, the flies apparently minimize both the difference and the sum in retinal velocity between the two eyes because the EMD responses of the rotation-sensitive array remain close to zero over a wide range of arena velocities (linear regression fit, y=–0.12+1.16×10^–4x,R²=0.05, P=0.66, N=6 data points, Fig. 10B; y=–0.12+1.44×10^–4x,R²=0.30, P=0.26, N=6 data points, Fig. 10C, respectively).

Due to the previous finding that steering in response to image rotation might emerge from a visual system organized to detect expanding flow fields rather than a rotation-sensitive system (see Introduction), we also simulated the EMD response of an expansion-sensitive system(Fig. 10A, lower pictogram). The left-minus-right eye difference of this detector system is plotted in Fig. 10D and suggests that this detector consistently produces a mean response close to zero and without a significant slope (linear regression fit, y=7.40×10^–3–2.4×10^–6x,R²=0.01, P=0.85, N=6 data points, Fig. 10D). To highlight the relationship between turning velocity and the two different types of EMD system, we plotted the EMD response for two flies flying in a stationary environment and under optomotor stimulation (300° s^–1) in Fig. 10E and F, respectively. The linear regression analysis fit suggests that in these animals the output of the rotation-sensitive system (black) significantly decreases with increasing turning velocity by a slope of–2.8×10^–3 deg.^–1 s in a stationary environment (P<0.0001, R²=0.44, N=319 sample points) and by –4.0×10^–3deg.^–1 s at 300° s^–1 arena velocity(P<0.0001, R²=0.55, N=794). In contrast, the left-minus-right eye response of the expansion-sensitive system(red) exhibits much smaller regression coefficients (R²values) of 0.19 (0° s^–1) and 0.01 (300°s^–1 arena velocity), and without a significant slope during optomotor stimulation (P>0.05, R²=0.01, N=794). Mean regression statistics for the six arena velocities and all 131 flies is shown in Table 1. In general, the rotation-sensitive EMD system produced significant slopes in most of the experimental conditions (100–700°s^–1 arena velocity), whereas none of the slopes calculated for the expansion-sensitive system were significantly different from zero(0–900° s^–1 arena velocity).

The relationship between arena velocity and horizontal/turning velocity suggests that the curvature of the flight path might be constrained by at least two factors: first, the fly's locomotor performance and/or, second, the relatively small size of our flight arena. Both hypotheses are driven by the results in Fig. 11, which show how path curvature depends on horizontal(Fig. 11A) and turning velocity (Fig. 11B). In this figure we have plotted the relative frequency of all tested flies in pseudo-colour to highlight the most frequent locomotor states and the boundaries of the data distributions. Due to the counter-clockwise rotation of the visual panorama, most data points are scattered around positive curvatures as indicated in red. Moreover, the data show a decrease in variance of path curvature with increasing horizontal velocity(Fig. 11A). At maximum flight velocities of approximately 1.04 m s^–1 for single flies,curvature is constrained to a single value of approximately 0.015 mm^–1 or a path radius of 67 mm, which is close to the arena radius of 70 mm. This result suggests that at maximum horizontal velocity,turning behaviour might be limited by the radius of our optomotor arena because Fig. 3 and Fig. 4B show that under these conditions the flies commonly remain near the cylinder walls. By contrast,flight curvature may vary distinctly by approximately ±0.2 mm^–1 at low horizontal velocities around 0.04 m s^–1. For comparison, the relationship between angular velocity and path curvature is shown in Fig. 11B in which positive(negative) values indicate left (right) flight turns.

The relative frequency of the various combinations between horizontal and turning velocity during Drosophila flight is shown in Fig. 11C. Due to both the saturation value for horizontal velocities at approximately 0.49 m s^–1 and the apparent break point in turning velocity at 500° s^–1, both shown in Fig. 5, we split the data set into a lower and higher velocity subset (vertical line, Fig. 11C). This splitting appears to be justified by the apparent change in slope at the break point,which we confirmed by linear regression analysis on 12 (10), 0.04 m s^–1 wide velocity bins derived from the left (right) half of the distribution (left-hand distribution: y=312+0.42x,R²=0.90, P<0.0001, N=12 data points;right: y=58+0.96x, R²=0.87, P<0.0001, N=10 data points, Fig. 11C). The smaller slope (equal to mean path curvature) at high horizontal velocities suggests that the angular velocity of Drosophila is increasingly compromised with increasing forward velocity. As mentioned above, these changes might be due to size constraints of the arena that increasingly limit path radii with decreasing distance from the cylinder wall or by the maximum locomotor capacity of the fly's flight apparatus. The latter hypothesis is tackled in the following section.

Velocity and thus flight direction of a flying insect depend on the ratio between vertical (upward force), horizontal (thrust) and lateral forces (side slip) multiplied by normalized friction, and on the moments around these vectors: yaw (vertical axis), roll (horizontal axis) and pitch (lateral axis, Fig. 12A). The data distribution in Fig. 11Csuggests that angular velocity around the vertical axis is increasingly constrained with increasing horizontal velocity and during flight at elevated locomotor performance the two measurements are inversely correlated, producing almost 180° shifts in phase angle (Fig. 8B). To further discuss these dependencies between biomechanical measurements and measured flight behaviour, we developed a numerical model that predicts the outer boundaries of flight velocity distributions (maximum estimates) from total locomotor capacity and also allows predictions of the relationship between flight path curvature, turning and the animal's horizontal velocity. Although the analytical model makes some inherent assumptions on flight mechanics, we found a marked agreement between experimental data and the data produced by the simulation.

The analytical model is based on the simple assumption that minimum curvature of a flight trajectory is constrained by the fly's maximum locomotor capacity and thus by the limits of total aerodynamic force production. We further assume that the production of moments around the three body axes requires only negligible aerodynamic force and that total force balance can thus be reduced to the vector sum of upward force, thrust and side slip. This assumption is fostered by results obtained during object orientation behaviour of tethered flying fruit flies that modulate their yaw moments within a range of approximately ±1.0 nN m peak to peak(Heisenberg and Wolf, 1984),using graduated alterations in the bilateral difference in wing stroke amplitude (Götz, 1983). We approximated the mean length of the moment arm for yaw turning between the fly's centre of gravity and the aerodynamic force vector to be 2.1 mm,assuming that the chord-wise aerodynamic circulation is at maximum close to a span-wise location of 65% wing length [wing length, 2.5 mm(Lehmann, 1994; Birch and Dickinson, 2001; Lehmann and Pick, 2007; Ramamurti and Sandberg,2001)]. Consequently, the production of a yaw turning moment of 1.0 nN m would require an aerodynamic force of approximately 0.47 μN, which is only approximately 3% of the flight force Drosophila produces at maximum locomotor performance (Lehmann,2004; Lehmann and Dickinson,1997). The numerical model also requires that the fly produces lateral forces during turning due either to banking (roll turn) towards the inner curve side or to modification of wing kinematics without large changes in body posture, similar to those observed in hover flies(Collett 1980a; Collett, 1980b). We moreover ignored body inertia during translational acceleration and the mass moment of inertia during rotational accelerations of the animal because a recent study showed that yaw turning is dominated by drag on the wings and not body inertia(Hesselberg and Lehmann,2007).

In Fig. 12C we illustrate how the minimum flight path radius of an animal increases with increasing horizontal velocity, assuming level flight. The model data also show that with increasing total force production, the animals may fly yaw turns at smaller path radii. At a horizontal velocity of 1.0 m s^–1, for example, a moderate 22% increase in maximum flight force production (from 16.3 to 21.0 μN) allows the animal to decrease its minimum turning radius by 66%from 0.13 to 0.04 mm radius. Assuming a total flight force production F_t in Drosophila of 16.3 μN (see following paragraphs), the force balance model predicts a minimum path radius of 47 mm that a fruit fly may achieve at a mean horizontal velocity of 0.6 m s^–1. At this radius, vertical force production approaches body weight. Consequently, a fly flying at 0.6 m s^–1 may only achieve level or climbing flight at flight path radii larger than 47 mm, which is shown by the blue line in Fig. 12D. Higher horizontal velocities at this path radius entail a loss in flight altitude (Fig. 12D, grey area).

Based on Eqns 3, 4, 5 of our force balance model, we calculated the three force components: horizontal, vertical and lateral force including total force for freely flying Drosophila (stationary environment, Fig. 13A–E;500°s^–1 arena velocity, Fig. 13F–J). Flight in a stationary environment is dominated by saccades that produce pronounced lateral forces of up to 25 μN or approximately 2.5 times the body weight of the animal (Fig. 13D, black),and turning velocities of up to 2800° s^–1(Fig. 13D, red). Interestingly, the fly sinusoidally varied vertical force symmetrically around body weight, producing regular alterations between climbing and descending flight (Fig. 13C). Vertical force modulates at a lower frequency compared with saccadic turning frequency(approximately 3.5 vs 5.5 Hz, respectively) suggesting that vertical velocity control is independent of saccadic turning(Fig. 13C,D). Total flight force varies between approximately body weight (12.2 μN) and 24 μN; a maximum force peak yielded approximately 30 μN in the example. By contrast,flight in response to a 500° s^–1 optomotor stimulus is quite different from the behaviour recorded in a stationary environment(Fig. 13F–J). The example shows that mean horizontal force decreases with decreasing distance between the concentric flight path and the arena centre as required for retinal slip compensation (Fig. 13F,G). Compared with flight in the stationary environment, the changes in vertical force are minimal and total force production stays in a narrow band of force values between approximately 13 and 21 μN(Fig. 13H,J). Fig. 12B summarizes the means of the upper 10% total flight force within a flight sequence of each fly(black) and how these forces are split into the three force components at the six stimulus conditions.

As suggested earlier, the animals may achieve retinal slip compensation for each of the compound eyes when matching both turning rate around the vertical axis to arena velocity and horizontal flight velocity to the translation velocity of the arena at a given distance from the arena centre. Thus, we expect that both horizontal velocity and centrifugal force acting on the fly body should increase linearly with increasing flight path radius because Fig. 4B shows that the distance between the animal and the arena centre linearly increases with increasing horizontal velocity. This relationship is also shown for all 131 tested flies in Fig. 14C, while the underlying data distributions including their relative frequencies are plotted in Fig. 14A,B. A linear regression fit to the mean data shows a significant increase in both horizontal velocity and centrifugal force with increasing path radius yielding slopes of 3.37×10^–3 s^–1 and 0.10μNmm^–1, respectively (horizontal velocity, y=3.37×10^–3x+0.25, R²=0.81, P<0.0001, N=14 data bins;centrifugal force, y=0.10x+0.84, R²=0.97, P<0.0001, N=14 data bins).

We eventually tested to what degree our numerical model may predict maximum velocity and minimum flight path radius for a freely cruising fruit fly by plotting the model results for various assumptions of maximum total flight force production. Due to the comparatively small mean climbing velocities in our experiments (Fig. 5),vertical force was set equal to body weight. We tested four different combinations between force and friction: (1) the maximum force estimate of 13.1 μN (maximum thrust 4.86 μN) derived from tethered flight(Lehmann and Dickinson, 1997)at a normalized friction of 4×10^–6 kg s^–1, (2) 16.3 μN (maximum thrust 10.7 μN) derived from load lifting experiments in which 80% of the tested Drosophilahovered for at least 1 s in an arena, at 9×10^–6 kg s^–1 (Lehmann,1999), (3) a value of 21 μN (maximum thrust 16.8 μN)achieved by 20% of the flies during load lifting, at 14×10^–6 kg s^–1(Lehmann, 1999) and (4) a maximum of 32.4 μN (maximum thrust 30.0 μN at level flight), at 25×10^–6 kg s^–1 that best matched the outer boundary of the experimental data.

For a better comparison between the analytical model and experimental data we re-plotted the data distributions for horizontal and turning velocity shown in Fig. 11A and B,respectively, as a function of path radius(Fig. 15). We restricted the data set to positive measurements, because positive path radii indicate left turns (same rotational direction as the visual environment) and thus instances at which the animal is potentially able to achieve optomotor equilibrium (see Materials and methods). Fig. 15A,B shows that the upper boundary of the horizontal and angular velocity distribution can fairly be described by the 95% quantile (blue) of the median (red). While the model (F_t=32.4 μN, Fig. 15D) matches the 95%quantile of angular velocity over a wide range of path radii from 0 to 200 mm,a fair match for horizontal velocities was limited to a range of path radii between approximately 0 and 70 mm (vertical line, Fig. 15C). However, the latter value indicates the radius of the free-flight arena and represents an upper limit to which the fly may fully reduce retinal slip during optomotor stimulation. The apparent saturation of horizontal velocities at 0.9 m s^–1 can thus be seen as a physical constraint of our experimental conditions (diameter of arena) and does not necessarily determine the upper limit for flight path curvatures per se.

Superficially, our best force estimate clearly outscores previous estimations of maximum flight performance, but we should consider that a maximum force value of 2.7 times body weight (32.4 μN) is only 19% higher than 2.1 times the animal's body weight (21 μN) derived from load-lifting experiments. Part of this difference might simply be due to our pre-selection procedure used to increase the number of successful flights. Moreover, since Fig. 15 shows non-averaged flight samples, the outer boundary of the data distribution might result from the combined performance of all 131 flies rather than represent the average among all tested animals. The larger difference in maximum force production between tethered and free-flight studies, in turn, may result from the vast different experimental conditions and the difficulty of measuring transient force peaks in tethered animals using a laser balance [30 Hz signal cut-off frequency (Lehmann and Dickinson,1997)].

In the present study we have investigated the behavioural response and underlying mechanisms with which freely flying fruit flies control their flight paths during visual stimulation in a rotating optomotor free-flight arena. The most prominent findings can be summarized as follows. (i) In a stationary visual environment, flight is characterized by a saccadic flight style. Thus, on average, saccades contribute more to the total turning angle of the animal than smooth turning, which is similar to previous findings (Figs 4, 6). (ii) Horizontal velocity is typically modulated during the saccade and exhibits a transient minimum, while the fly turns at a maximum rate of approximately 1600°s^–1 (Fig. 6D,E). (iii) In response to a rotating visual environment, Drosophila continuously turns on concentric flight paths around the arena centre. Turning velocity matches angular velocity of the rotating panorama up to 500° s^–1 arena velocity (Figs 3, 4, 5, 9). (iv) With increasing angular velocity of the optomotor stimulus, the radius of the circular flight paths increases likewise, and the animal is increasingly displaced from the centre of the visual environment (Figs 3, 4). (v) EMD simulation of both a rotation- and an expansion-sensitive system shows that the difference in EMD signal between the two eyes does not significantly change with increasing arena velocity (Fig. 10B–D). However, the response of the rotation-sensitive system seems to be more tightly correlated with the fly's turning rate than that of the expansion-sensitive system(Fig. 10E,F; Table 1). (vi) A force balance model describing the forces acting on the fly's body suggests that the minimum flight path radius depends on forward velocity during turning flight (Figs 12, 13, 14, 15).

In a stationary environment, the recorded flight traces are similar to those measured previously under free-flight conditions(Tammero and Dickinson,2002b). However, in the previous study, the animals were allowed to cruise in a much larger arena with a diameter of approximately 1.0 m compared with our 0.14 m optomotor arena. The size of our arena is similar to small standard tethered flight arenas, but was a compromise between the ability to rotate the panorama at high angular velocity, to estimate the fly's body orientation from single video images, and the space available for flight. In general, it is difficult to judge which arena size corresponds to a more natural visual environment, because fruit flies probably cruise through open space (equal to the large arena) just as through more dense vegetation (equal to the small arena). The major difference between the two differently sized arenas might be that in a small arena the flies should experience more visual expansion/contraction flows on their retina due to the higher number of approaches towards nearby walls.

The main differences between our study and that of Tammero and Dickinson(Tammero and Dickinson, 2002b)are as follows. (i) We consistently measured a peak turning rate of 1600°s^–1 within a saccade that was independent of the fly's forward velocity (Fig. 6D). In a larger arena, peak turning rate was approximately 38% less and only amounted to approximately 1000° s^–1. (ii) Mean turning angle within a saccade in the smaller arena amounted to 120° with only small variance (Fig. 4C) compared with approximately 90° in the larger arena. The larger turning angle in the present study might be due not only to a higher angular velocity but also to the longer duration of the saccade of approximately 130 ms, compared with 100 ms for fruit flies cruising in the larger arena. For the reasons above, we hypothesize that flight saccades in Drosophila are adjusted by the input of the visual system and do not result from a fixed-action motor pattern produced by the fly's neuro-muscular system. (iii) In the two arenas horizontal velocity between saccades is similar and amounts to approximately 0.25 m s^–1 in the large and 0.28 m s^–1 in our smaller arena.

Moreover, within a saccade, the flies in both arenas decreased their horizontal velocity during yaw acceleration and increased velocity in the second part of the saccade during angular deceleration. We offer two alternative explanations for this finding. First, the increase in horizontal velocity might simply be an artefact of the flight conditions in our small arena. Fig. 6F shows that saccade frequency amounts to approximately 3.0 Hz on average, and at an intermediate intersaccade velocity of 0.4 m s^–1 the path distance between two saccades should thus be scattered around 12 cm – a value that is close to the dimension of the inner arena cylinder. In this respect, the apparent increase (decrease) in horizontal velocity prior to(after) the saccade would solely reflect the modulation of the horizontal velocity of neighbouring saccades occurring approximately every 0.3 s(Fig. 6E). The second, though less likely, explanation is that the distinct increase in horizontal velocity results from an adjustment in flight energetics. In this stage, the increase in horizontal velocity prior to turning reflects a strategy in which the fly increases muscle mechanical power output in the expectation of additional power requirements for the production of centripetal force within the next 20–30 wing strokes. The time window is consistent with the moderate neural activation frequency of the indirect flight muscles between approximately 3 and 7 Hz, or one spike in 28–66 wing strokes, assuming that these frequencies permit only relatively slow changes in mechanical power output of the indirect flight muscles due to changes in intracellular calcium(Gordon and Dickinson, 2006). Thus, the increase in horizontal velocity prior to a saccade might result from the timing of the underlying neural system to boost muscle power output rather than from a specific flight manoeuvre of the animal. Nevertheless, even if this mechanism held true, its benefit is doubtful, because an increase in horizontal velocity causes an increase in centrifugal force, which in turn would require even higher aerodynamic forces for turning.

A major result of the present study is that mean flight path curvature(path radius) linearly decreases (increases) with increasing arena velocity(Fig. 4A). Although the numerical model in Fig. 12 may predict the outer boundaries of the data sets, it may not explain why fruit flies prefer to fly on distinct flight path radii(Fig. 7F, Fig. 13F). As already mentioned in the Results, Drosophila may achieve retinal slip compensation for each of its compound eyes and for a given arena velocity(100–900° s^–1) at any position inside the arena by appropriately adjusting horizontal and turning velocity. In the extreme case,the animal might even rotate at the arena centre without forward motion to achieve retinal slip compensation similar to that found in hover flies(Collet, 1980a; Collet, 1980b; Collet and Land, 1975). Under these conditions,the limits for this behaviour would only result from the animal's maximum angular velocity during continuous turning that is below 1000°s^–1 (Tammero and Dickinson, 2002b). Since side-slip movements are almost absent in our experiments, the flies adjust both turning and horizontal velocity according to their distance from the arena centre. The data in Fig. 10 and Table 1 suggest that this behaviour might result from a rotation-sensitive detector array similar to the system described for tethered flying fruit flies during optomotor stimulation(Wolf and Heisenberg, 1980; Götz, 1983). However,even if our EMD simulation provides evidence that the left-minus-right eye EMD response determines the fly's turning velocity, it may not explain why flies fly at distinct distances from the arena walls. Thus, we suggest that following concentric circular flight paths reflects a state in which the responses due to three distinct, yet interacting mechanisms are dynamically balanced: first, power output of the flight musculature that places constraints on manoeuvrability; second, centrifugal forces during yaw turning that pull the animal towards the arena wall; and third, expansion response due to an expansion-sensitive EMD system that elicits turning moments away from the arena walls.

The first mechanism relies on the assumption that at elevated flight velocities, curvature is constrained by the animal's steering capacity. For example, a previous study on the limits of locomotor performance highlighted that the fly's kinematic envelope decreases with increasing force production(Lehmann and Dickinson, 2001). At maximum force production, there is a unique combination between stroke amplitude and frequency at which yaw steering performance completely collapses under tethered flight conditions. Assuming that curvature is related to manoeuvrability, a reduction in yaw control might explain some of the decrease in path curvature when the animal increases force production in response to higher arena velocities.

The second mechanism relies on two results: first, on the outcome of our numerical model for force balance as shown in Figs 12, 13, 14, 15 and, second, on the observation that fruit flies typically rotate around their vertical axes through the animal's centre of mass instead of side slipping in front of the rotating arena. Let us consider the following situation: during the initial phase of take-off in which fly typically tumbles for several wing strokes, the animals mostly move away from the release point in the middle of the arena. After this initial time, the animal tries to achieve optomotor equilibrium by minimizing retinal slip on both compound eyes. Thus, the fly accelerates in the horizontal direction in an attempt to match its horizontal velocity to the tangential velocity of the rotating drum and also starts rotating within the direction of the rotating arena to match its turning rate to the arena velocity. This view would be consistent with the mean values of both a rotation- and an expansion-sensitive EMD system, because Fig. 10B–D illustrates that mean EMD responses remain close to zero over a wide range of different arena velocities. Duistermars and colleagues showed that rotation and expansion reside in two separate control systems and thus high-gain optomotor responses may be potentially triggered by laterally centred visual expansions(Duistermars et al., 2007). Table 1, however, indicates that the output of the expansion-sensitive system is significantly independent of the fly's turning velocity and may thus not provide an adequate error signal during continuous yaw turning. Even when assuming that a mean value near zero of the expansion-sensitive system(Fig. 10D) indicates perfect control of yaw turning due to image expansion/contraction, we would expect a significant negative slope in our regression analysis between the left-minus-right eye expansion response and turning velocity. Nevertheless,the expansion-sensitive system may provide information to keep the animal centred while turning, which is discussed in the following paragraph.

In contrast to expansion, the rotation-sensitive system produces a decreasing negative output when the fly's turning velocity increases and approaches zero (optomotor equilibrium), when the turning rate matches angular velocity (counter-clockwise rotation, Fig. 10F, Table 1). In other words, a fly that turns faster counter-clockwise than is required for optomotor equilibrium would turn away from the arena wall but would experience a clockwise rotation of the visual panorama on its compound eyes. Since EMD output is modelled to be positive for front-to-back motion on each eye, this EMD signal consequently would correct for the mismatch and elicit a clockwise rotation of the animal towards the visual pattern, thus providing direction stability. By contrast, turning rates below the arena velocity required for optomotor equilibrium potentially guide the animal towards the arena walls. Under these conditions, however, the rotation-sensitive system would experience an increasing positive left-minus-right eye output that turns the animal counter-clockwise and thus away from the walls. In any case, while flying outside the arena centre, yaw moments result in centrifugal forces that pull the animal away from the arena centre towards the outer wall of the optomotor arena, even if the fly achieves optomotor equilibrium. The expansion-sensitive EMD system described in previous studies(Tammero and Dickinson, 2002a; Tammero and Dickinson, 2002b; Tammero et al., 2004; Duistermars et al., 2007)elicits smooth turning away from nearby walls due to the expanding flow field on the outer eye and contracting flow on the inner compound eye. This mechanism is independent of the animal's actual turning velocity and thus independent of whether the animal experiences counter-clockwise rational flow of the visual environment in cases in which turning rate is smaller than arena velocity, or clockwise rotation in cases in which turning rate is larger than arena velocity. As a consequence, the system produces sensory feedback for centring response that potentially forces the animal to stay away from the wall and, in our case, to move on distinct concentric flight trajectories(Fig. 7F).

The present study demonstrates the complexity of flight behaviour during visual stimulation with large-field patterns in unrestrained flying fruit flies. Visual reflexes based on both rotation- and expansion-sensitive EMD arrays potentially are the driving forces for the measured locomotor changes. Two points should be emphasized: firstly, the preference of the fruit fly to follow concentric circular flight paths, which requires a precise adjustment of both turning and horizontal flight velocity to minimize retinal slip and,secondly, the complex dependencies between horizontal, vertical and turning velocity due to force balance and locomotor capacity for flight. Although the present experiments were originally intended to visually elicit deviations from the fly's flight course, they inherently differ from natural displacements of the animal due to cross-wind or turbulent air. Thus, we cannot exclude the possibility that flight behaviour in response to the optomotor stimulus is shaped by the potential conflict between the lack of mechanosensory stimulation of the halters (signalling no changes in body position) and visual information providing evidence for body rotation due to the rotating environment. The morphology and function of halteres have been well investigated, and there is good evidence in Drosophila that the flight control system uses information coming from these sensory structures to stabilize straight flight while visual information triggers saccades for collision avoidance and permits visual object tracking(Bender and Dickinson, 2006a; Bender and Dickinson, 2006b; Chan et al., 1998; Dickinson, 1999; Fayyazuddin et al., 1994; Nalbach, 1994; Sandeman, 1980; Sherman and Dickinson, 2003; Sherman and Dickinson, 2004; Tammero and Dickinson, 2002b; Tracey, 1974; Wigglesworth, 1946).

In this respect, the experimental approach in this study might represent a more artificial condition during flight compared with flight in a stationary visual environment. Nevertheless, we should expect a driving force for the evolution of motor systems relying on visually mediated optomotor stimuli because particularly insects without halteres, which represent the majority of all flying insects, should rely more strongly on visually mediated optomotor behaviours. Moreover, we should be aware of the finding that other sensory structures, such as the antennae, are also able to control flight behaviour(Frye et al., 2003). In the hawk moth the antennae may even function as gyroscopic organs helping to stabilize the freely flying animal (Sane et al., 2007). Altogether, our results combined with recent findings on flight control in the tiny fruit fly might be particularly valuable for understanding animal locomotion from an organismic perspective and thus for the construction of biomimetic robots that mimic the biomechanics and behavioural rules found in flying insects.

LIST OF ABBREVIATIONS AND SYMBOLS

 
• d

  distance between fly and arena centre

 
• EMD

  elementary motion detector

 
• F_h

  horizontal force (thrust)

 
• F_l

  lateral force (centripetal force)

 
• F_t

  total aerodynamic force of both wings

 
• F_v

  vertical force (upward force)

 
• g

  gravitational constant

 
• H

  impulse response of the EMD high-pass filter

 
• I

  light intensity in EMD model

 
• HP

  high-pass filter

 
• k

  normalized friction on body and wings

 
• L

  impulsive response of the EMD low-pass filter

 
• LP

  low-pass filter

 
• m_b

  body mass of the fly

 
• r

  radius of a flight path

 
• t

  time

 
• u_h

  horizontal velocity

 
• u_l

  lateral (side-slip) velocity

 
• u_v

  vertical velocity

 
• W

  EMD weight function

 
• α

  change in body orientation

 
• τ

  time constant of EMD filter

 
• ω

  turning (angular) velocity

We would like to acknowledge Simon Pick for his help with the numerical model; Jochen Dambacher and Nicole Heymann for their help in conducting the experiments; Ursula Seifert for critically reading the manuscript and the two anonymous referees for the fruitful comments. This work was funded by the Biofuture grant 0311885 of the German Federal Ministry for Education and Research to F.O.L.