The influence of visual landscape on the free flight behavior of the fruit fly Drosophila melanogaster
1 UCB/UCSF Joint Bioengineering Graduate Group, 3060 Valley Life Science Building and
2 Department of Integrative Biology, University of California at Berkeley, Berkeley, CA 94720, USA
*e-mail: lancet{at}socrates.berkeley.edu
Accepted 12 November 2001
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Summary |
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Key words: visual control, optic flow, saccade, flight, behaviour, Drosophila melanogaster, motion detection.
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Introduction |
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As a fly moves through its environment, images move across its retina and generate complex patterns of optic flow. A fly can use estimates of these flow patterns to provide information about its own motion, to discriminate objects from background and to determine the relative distance of objects (Collett and Land, 1975; Egelhaaf et al., 1988
; Srinivasan, 1993
; Srinivasan et al., 1999
). Previous studies have demonstrated that the flight trajectories of many fly species consist of straight flight sequences interspersed with rapid changes in heading termed saccades (Collett and Land, 1975
; Schilstra and van Hateren, 1999
; Wagner, 1986
). While several sensory control models have been proposed for the straight flight segments (Collett, 1980
; Wolf and Heisenberg, 1990
), the sensory stimuli responsible for initiating saccades are not known.
During straight flight, there is a focus of expansion within the flys visual field where image velocity is zero. Optic flow radiates from this point. Nearer objects move faster across a flys retina than those farther away. Simultaneous rotation and translation create optic flow fields that are more difficult to interpret. Thus, maintaining straight flight and minimizing rotation are important goals of the flight control system (Collett et al., 1993). Tethered flies turn reflexively in the same direction as any perceived large-field rotation of visual space in an attempt to reduce retinal slip (Götz, 1968
, 1975
). Flies are thought to rely upon this so-called optomotor response to correct for horizontal deviations from straight flight. A similar reflex, mediated by the detection of visual motion in the vertical direction, stabilizes altitude (David, 1979
, 1984
; Wehrhahn and Reichardt, 1975
). Both responses are thought to operate via linear negative feedback systems in which motor output is inversely proportional to features of visual input, such as large-field image velocity.
In contrast, the saccades are rapid, intermittent events that presumably cannot be represented by a simple linear transformation of a sensory input. It is more likely that specific features within the flys visual world trigger the all-or-none events. One possibility is that saccades are triggered by looming objects, similar to the stimuli that evoke landing responses (Borst, 1990). By reconstructing the visual inputs and estimating the optic flow experienced by freely flying Drosophila melanogaster, we attempt to identify the visual computations that act to trigger saccades as the animal flies actively through its environment. The results show that classic linear models of flight control based on optomotor equilibrium cannot account for the behavior of freely flying flies under our experimental conditions.
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Materials and methods |
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The location of the centroid of the fly was determined in each frame. To convert from two two-dimensional images to three-dimensional spatial coordinates, a calibration was required. This calibration was performed using a 38 cmx38 cmx62 cm cube with 13 light-emitting diodes (LEDs) whose exact spatial positions were known. A transformation matrix based on the positions of the LEDs in each of the two-dimensional frames and their three-dimensional position was calculated using software written using Matlab (Mathworks). This transformation matrix was used to convert the centroid position in each of the two-dimensional frames to a three-dimensional spatial coordinate. The translational velocity of the fly was determined from the distance the fly covered in the x,y plane between samples. The change in the flys altitude between frames will be referred to as the vertical velocity. Because of the small size of Drosophila melanogaster and the large field of view monitored by the cameras, we were unable to determine the exact angular position of the flys body. Thus, to estimate the heading of the fly and its angular velocity about the yaw axis, we assume that the horizontal projection of the longitudinal axis of the fly is a tangent to the flight path at all times, which is equivalent to assuming no side-slip and no yaw relative to the flight path. While this assumption would be largely invalid under field conditions in the presence of wind, it may serve as a fair approximation under laboratory conditions in still air. Further, while the presence of moderate side-slip and yaw would quantitatively alter some of our analyses, they would not effect the primary conclusions.
Animals
All experiments were performed on 2- to 4-day-old fruit flies, Drosophila melanogaster Meigen, from a laboratory culture descended from 200 wild-caught females. Flies were starved (to motivate longer flight sequences) and adapted to the light level of the flight arena for 6 h prior to each experiment. Experiments with a textured background were performed using 22 females and 18 males. Experiments with a uniform background were performed with 25 females and 21 males. Some flies provided more than one trajectory. We filmed the flies in the flight arena one at a time, with data collection terminating after the fly had landed on either the floor or the walls of the arena.
Visual reconstruction and motion detection calculation
The flys three-dimensional trajectory was smoothed to remove digitization errors using a fifth-order low-pass Butterworth filter with a cut-off set at 15 Hz, half the video sampling rate. The trajectory was then upsampled by a factor of 5 (to 150 Hz) using a cubic spline interpolation. The angle that the walls of the arena would subtend along the flys retina was then calculated assuming (i) that the flys body and head were yaw-stabilized with respect to its flight trajectory, and (ii) that the horizontal plane of the head was aligned parallel to the ground. These assumptions were necessary given the lack of information about the flys body position and the position of the flys head relative to its body. The angle the walls subtended across the flys retina was calculated by projecting the image of the walls onto a sphere, representing both the flys eyes, for each point along the flys trajectory. We generated a 1080x540 pixel image of the walls that represented all 360° of azimuth and 180° of elevation. Thus, each pixel represented the intensity of a square 0.33°x0.33° patch of visual space. The angular spacing () and the angular sensitivity (
) of the flys photoreceptors are both approximately 5° (Buchner et al., 1976
; Götz, 1964
; Heisenberg and Wolf, 1984
). To blur the image such that it would appear as seen through the optics possessed by Drosophila melanogaster, each frame was then smoothed using a 30x30 pixel two-dimensional Gaussian filter with a standard deviation of 5 pixels and then downsampled by a factor of 15 along both dimensions. This created a 72x36 pixel matrix of intensities, with each pixel representing a 5°x5° square of visual space, for each point along the flys trajectory.
For each pixel, the intensity signal was converted to a contrast signal by subtracting the mean intensity of that pixel taken over the flight period. These contrast images were fed into horizontal and vertical motion-detector models. The direction of motion was analyzed using delay and correlate HassensteinReichardt elementary movement detectors (Borst and Egelhaaf, 1989; Reichardt, 1961
). In this motion-detection model, the contrast signals from neighboring photoreceptors are compared by a multiplication after one of the signals has been delayed. A detailed description of the motion-detection algorithm that was used is included in the Appendix. The delay function within the detector model was performed by convolving the contrast signal with a first-order low-pass filter whose impulse response is an exponential decaying with a time constant of 40 ms. To ensure that our results were not affected by processing prior to the motion-detection phase, we also ran the motion-detection model by first processing the input intensities with a first-order high-pass filter (time constant 50 ms) instead of subtracting the mean intensity. The filtered intensities were then summed with the original intensities scaled by a factor of 0.15, in a manner identical to Kern et al. (2000
). In examples using peripheral filtering, the time constant of the low-pass filter in the delay line of the motion detector was increased to 100 ms.
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Results |
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As flies move through their environment, they encounter visual backgrounds that differ in contrast and texture. To determine how a spatially structured background influences the basic flight pattern, we compared the behavior of flies within a textured background with that seen within a uniform background. In the uniform environment, the wall of the circular arena consisted of a homogeneous translucent white surface. This uniform environment was not, however, entirely devoid of visual features because of the presence of two contrast edges, a lower horizon between the dark floor and the white walls of the arena and an upper horizon where the top of the wall met the dark curtain above. For experiments in the textured environment, the wall of the arena was lined with a random checkerboard pattern to provide a richer visual background.
The flight trajectories generated with textured and uniform backgrounds were quite distinct (Fig. 4A). Histograms representing the time spent by the flies in different portions of the arena (Fig. 4B), as well as the spatial distribution of saccades (Fig. 4C), indicate that, when surrounded by a uniform background, flies approached the walls much more closely before saccading and, thus, explored a larger area of the arena. In contrast, the textured background constrained the flies to the center of the arena. Histograms of various flight parameters generated under the two visual conditions are shown in Fig. 5. The uniform background raised the flies horizontal velocity (P<0.0005, t-test) and increased the range of vertical velocities (P<0.01, F-test). The flies also flew at a higher altitude within the uniform background (P<0.0005, t-test), with the mean altitude lying almost exactly at the transition from the uniform white wall to the black curtain. Thus, the presence or absence of a richly textured visual background has a substantial impact on the motor output that emerges from the flight control system.
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To gain some insight into the features of visual motion that might elicit the saccades, we used the kinematic data to reconstruct the visual world as seen from a flys perspective as it flew within the arena with both the textured (Fig. 9A, top) and the uniform (Fig. 9A, bottom) background. We divided the visual environment into quadrants measuring 90° (azimuth) by 180° (elevation). Fig. 9B represents a snapshot of the flys visual world at the instant the fly was at the positions shown by the red circles in Fig. 9A. The lower panel of Fig. 9B emphasizes that, while visual cues in the uniform background were sparse, the two horizontal edges do provide input to the flys visual system. After reconstructing these images, we then estimated the flys perception of the magnitude and direction of optic flow using an array of vertical and horizontal HassensteinReichardt elementary motion detectors (EMDs) (Reichardt, 1961; Borst and Egelhaaf, 1989
) (for details, see Appendix). The properties of the EMDs were based on a standard model derived from behavioral and physiological experiments in flies (Egelhaaf and Borst, 1989
; Reichardt and Poggio, 1976
).
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According to the optomotor equilibrium model, a fly maintains a flight course by minimizing the net horizontal rotation of its visual surround (Götz, 1964, 1968
). Thus, we first examined the pattern of large-field horizontal motion preceding each saccade. Large-field horizontal image motion results from rotation about the yaw axis as well as from sideways translation. Forward translation also generates image motion with a horizontal component, particularly about the equator of the eye. The large-field horizontal motion experienced in the frontal position of each eye was estimated by summing the output of the horizontal EMDs over each of the two front visual quadrants to generate a time course of the front-to-back motion the fly experiences (Fig. 10A; red arrows indicate the direction of large-field motion; see Appendix for details). The individual large-field horizontal motion traces are then overlaid and aligned such that the initiation of the saccade occurs at time zero (Fig. 10B). The average (shown by the red lines in Fig. 10B) provides a record of the typical large-field horizontal motion experienced on each half of the frontal field of view prior to, during and after each saccade. Ipsilateral refers to the side away from which the fly is turning (generally the side nearest the wall of the arena), and contralateral refers to the opposite side. As expected, the most prominent feature in these traces is a large horizontal motion signal produced when the animal rotates rapidly during the saccade (the peak within the gray shaded region). However, it is the features prior to the initiation of saccades that provide clues as to the stimulus trigger. Preceding each saccade, in the textured background, the fly experiences a steady front-to-back motion on the ipsilateral side that reaches a small peak and then decreases towards zero immediately preceding the saccade. On the contralateral side, the front-to-back motion is smaller, and immediately before the saccade there is a peak in front-to-back motion. Thus, certain features of the large-field horizontal flow might play a role in triggering the rapid turns. Large-field horizontal signals were entirely absent preceding saccades in the uniform background as a result of the absence of vertical edges. This indicated that unidirectional horizontal visual motion could not explain the occurrence of saccades under all visual conditions (Fig. 10B, lower traces).
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A further cue that might initiate saccades is image expansion. To construct a rough measure of horizontal expansion seen by each eye, we summed the rightward horizontal motion over the right half of the frontal quadrant of the eye and the leftward motion within the left half of the frontal quadrant (Fig. 11A). Vertical expansion was determined by summing the upward motion components over the top half of the frontal quadrant and the downward components over the lower half of the frontal quadrant for each eye (see Appendix for exact details). Prior to each saccade, the fly experiences a slow horizontal expansion in its frontolateral visual field followed by an abrupt contraction caused by the rotation during the saccade itself (Fig. 11B, left). Focusing on the period preceding the contraction associated with the saccade, horizontal expansion on the ipsilateral side is relatively constant before each saccade within a textured background. On the contralateral side, the fly experiences much less horizontal expansion. Within the uniform background, the horizontal expansion component is undetectable because of the absence of vertical edges. Vertical expansion, however, is quite prominent because of the presence of the two horizontal edges (Fig. 11D). Prior to each saccade, there is a steady increase in vertical expansion on the ipsilateral side and a small increase on the contralateral side.
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Discussion |
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Effects of experimental limitations and model assumptions
The main experimental limitation of this study was the low spatial and temporal resolution of our visualization system. This low resolution was the consequence of the deliberate choice to maximize the distance over which we could track flies. Current studies using high-speed video indicate that a visualization cube with sides no greater than 1 cm is required to capture wing and body kinematics accurately at 5000 frames s1 (S. Fry and M. H. Dickinson, in preparation). In the present study, flight trajectories were sampled at 30 frames s1 over a 1 m diameter arena, and we estimated saccade durations as brief as 100 ms, or approximately three sample points. This limited temporal resolution did not, however, prevent the detection of saccades, which appeared as clear spikes in recordings of angular velocity. In addition, we estimated saccade amplitude from the change in trajectory heading, a measurement that does not require a high temporal resolution of the saccade itself. The low spatial resolution prevented measurement of the flys body position and the position of the head relative to the body. To reconstruct the flys visual input, we assumed that the horizontal projection of its longitudinal body axis was aligned along the flight trajectory. These assumptions may be reasonable in still air because, unlike larger flies, Drosophila melanogaster display minimal side-slip under laboratory conditions (David, 1978). Drosophila melanogaster may, however, move their head relative to their body during flight, and the impact of such movements is absent from our estimation of optic flow. However, because our visual processing model included large-field spatial summation, its predictions should be robust with respect to the precise orientation of the flys head. Further, if the head stabilization reflex functions in flight to stabilize gaze in the face of body rotation (Land, 1999
; van Hateren and Schilstra, 1999
), this reflex would serve to dampen the motion of the eye and render the free flight conditions closer to those of our model.
A second critical set of assumptions relates to the filter values used in our modeling of the movement detector array. However, changing the filters upstream of the motion detector (from simple subtraction of the direct current signal to a high-pass filter with a time constant of 50 ms) and in the delay line of the detectors themselves (from 50 to 100 ms) did not alter the salient result of the analysis. Even with different filter settings, the output of total expansion followed a similar time course preceding saccades in both the uniform and textured backgrounds. Thus, our central conclusions that total expansion is currently the most parsimonious explanation for the saccade trigger is robust to the assumptions of our basic modeling methods.
Translational velocity in free flight
The mean horizontal flight speed measured in this study (30 cm s1) is substantially slower than that reported in a recent study of the free flight of Drosophila melanogaster by Marden et al. (1997) (4670 cm s1). These authors compared the free flight trajectories of two control lines of flies with those of two lines selected for their ability to fly through a baffled wind tunnel. While the maximum flight speed did not differ among the control and selected lines, the tunnel-selected flies were more likely to fly near peak performance. Given the results of the present study (Fig. 5), this large discrepancy in flight performance is probably due to differences in the visual environment. Marden et al. (1997
) used a cubic arena with a side length of 0.5 m lined with white translucent Plexiglas which was back-illuminated with bright fluorescent lights. Thus, this environment would have provided little or no contrast input to expansion detectors and other motion-sensitive circuitry within the visual system. The absence of such input might explain the elevated flight velocity. Alternatively, the phototactic reflexes that were activated by the use of an ultraviolet light source might have elicited near-maximal flight speed. In either event, the differences in both mean and peak flight speed measured under different visual conditions suggest that the sensory environment exerts a strong influence on flight performance. It is even possible that the performance difference noted among control and tunnel-selected lines might result from a disparity in visual processing circuitry or some other sensory system involved in flight control.
Saccades as fixed motor patterns
These free flight experiments demonstrate that flies produce fixed-amplitude saccades of approximately ±90° within the horizontal plane (Fig. 7). Free flight experiments in other species have shown that the saccade angles in larger flies are typically smaller than those seen in Drosophila melanogaster, although the saccades exhibited by small houseflies (Fannia canicularis) are also approximately 90° (Zeil, 1986). One possible explanation for the constancy of saccade amplitude within each species is that the saccade motor program is terminated by visual feedback. However, our observation that saccades are of constant amplitude in a uniform visual background, from which no cues are available for orientation about the yaw axis, argues strongly against this possibility. Further, the additional visual information present during flight within the textured background does not alter the distribution of saccade amplitudes (Fig. 7). These data are consistent with tethered flight experiments in which the magnitude of torque spikes (thought to be the tethered flight equivalents of saccades) was unaffected by imposed motions of a stripe upon which the animal was fixating (Heisenberg and Wolf, 1979
). Further, freely flying hoverflies, Syritta pipiens, make substantial errors when generating saccades towards targets and show no evidence of correcting the saccade once it has been initiated (Collett and Land, 1975
).
Another possible explanation for the consistency of saccade amplitude is that saccades might represent the feedforward output of a stereotyped motor program performed without any sensory feedback. However, while the experiments described above appear to rule out a role for visual feedback, other modalities might still function to regulate saccade amplitude. For example, the observation that torque spikes are shorter when flies are tethered loosely, allowing them to rotate more freely about their yaw axis, suggests that haltere feedback may play a role in terminating the saccade motor program (Mayer et al., 1988).
Image expansion and saccade initiation
Changing the flys visual environment altered its saccade rate, demonstrating that an internal clock mechanism is not responsible for the timing of saccades. Because the absence of large-field rotation signals during flight within a uniform background did not prevent the generation of saccades, it is unlikely that flies perform saccades in response to rotation cues. Similarly, the absence of large-field vertical motion before saccades eliminates the possibility that saccades are generated as a result of a flys perception that it is rising or falling. The noise inherent in our simple estimates of expansion preceding individual saccades (see Fig. 11) suggests that our model for calculating total expansion is a simplification of the calculations that might be performed by the fly. For example, the spatial integration performed on the dendrites of lobular plate cells functionally removes temporal noise, causing the cells membrane potential to vary smoothly with image velocity (Single and Borst, 1998). However, the fact that the average sum of horizontal and vertical expansion rises along a similar time course before saccades within both textured and uniform backgrounds (see Fig. 12), despite differences in flight speed and approach distance under these two visual conditions, suggests that image expansion plays a role in the initiation of saccades. The presence of vertical edges that can provide horizontal expansion cues, which are absent during flight within a uniform background, explains why the flies generate saccades more frequently within a textured background.
If flies use image expansion cues for their initiation, saccades may represent a reflexive response to avoid rapidly approaching objects. Neurons sensitive to small objects approaching from any orientation have been identified in locusts (Gabbiani et al., 1999, 2001
; Rind and Simmons, 1992
). These neurons fire at a peak rate when a small-field stimulus exceeds a threshold angle subtended on the locusts eye (Gabbiani et al., 1999
). Although it is possible that saccades occur as a result of the fly performing a similar calculation, it is more likely that neurons sensitive to large-field expansion stimuli are responsible. It has been suggested that neurons that spatially sum the output of multiple local motion detectors underlie the initiation of the expansion-dependent landing response (Borst, 1986
; Borst and Bahde, 1986
), and similar computations may underlie the triggering of saccades. In Calliphora erythrocephala, recordings from neurons descending through the central connective have detected descending cells that are sensitive to image expansion directly in front of the fly (Borst, 1991
). Of the two classes of expansion-sensitive cells within the optic lobes of the hawkmoth Manduca sexta, the class 2 cells have properties that are consistent with our behavioral results (Wicklein and Strausfeld, 2000
).
Sensory integration for the control of saccades and straight flight
The optomotor response refers to a flys tendency to turn in the same direction as a large-field motion in order to minimize image motion across the retina (Götz, 1975; Heisenberg and Wolf, 1984
). The fly is thought to use this response to correct deviations from straight flight that may arise from external disturbances, such as the presence of a strong crosswind, or internal asymmetries, such as damage to one wing. In our experiments, asymmetries in visual motion are generated whenever a fly moves along a path that does not intersect the center of the arena. Our data show that, when faced with such asymmetries, Drosophila melanogaster turn away from the side experiencing the greater amount of visual motion, a response opposite to that expected if the flies were to fly according to a simple optomotor equilibrium model. Thus, while we did not impose a perturbation in image rotation, our results suggest that freely flying flies move straight in the face of bilateral asymmetries in visual motion. These results are similar to those of experiments with monocularly blinded freely flying blowflies (Lucilia sp.), which show little difference in their free flight behavior compared with control animals (Kern and Egelhaaf, 2000
). The same monocular flies did, however, show a tendency to turn in the direction of the non-occluded eye when walking (Kern and Egelhaaf, 2000
; Kern et al., 2000
). By rotating in this fashion, the walking flies might be shifting the focus of expansion laterally such that the sum of all the horizontal components of the optic flow would be zero, thereby restoring optomotor equilibrium.
Such an interpretation is unlikely in our experiments because the flies tended to deviate from a straight course by turning away from the nearer wall, the direction opposite to that which would restore optomotor equilibrium. Further, the slope relating approach angle and deviation angle was significantly larger during flight within a textured background, indicating that deviation increased with the amount of visual information. The direction of the deviations from straight flight in our experiments is reminiscent of the centering response seen in honeybees attempting to balance the image velocity on either side (Srinivasan et al., 1991).
During the straight flight segments between saccades, a fly could make use of both mechanosensory and visual cues to maintain a stable course. The flys haltere system is capable of sensing rotations about all three axes (Dickinson, 1999; Nalbach, 1993
; Nalbach and Hengstenberg, 1994
) and could use such information to correct course deviations. Our experiments also demonstrate that flies possess a visually mediated centering response that directs their flight path away from the side perceiving the greater amount of visual motion. Further, flies possess fixation behaviors in which they track small visual targets. Thus, within the flight control system, there are potential conflicts between a mechanosensory equilibrium system (the halteres) that attempts to maintain straight flight and a visual system that directs the fly away from obstacles and towards objects. Given that these two modalities may often act at crossed purposes, it is of interest to note that pathways exist through which each of these two modalities might alter the gain of the other. In Calliphora vicina, the muscles controlling the halteres receive input from the visual system (Chan et al., 1998
). Thus, the visual system has the ability to either amplify or decrease the flys sensitivity to angular velocities. Evidence for the reciprocal pathway is also present. The haltere sensory cells can influence head position and, thus, visual motion sensitivity through their connections with neck muscle motor neurons (Gilbert and Bauer, 1998
; Sandeman, 1980
).
Previous models for flight control in large flies suggest that lobula plate tangential cells (LPTCs) sensitive to large-field horizontal motion (HS cells) are necessary for yaw stabilization and, thus, for straight flight (Hausen and Egelhaaf, 1989; Hausen and Wehrhahn, 1990
). During the periods in which these horizontal cells would be active, the flies in our experiments do not respond in a way that would minimize asymmetries in optic flow by rotation, as would be predicted by the optomotor equilibrium model. Thus, the HS cells that respond strongly during tethered flight recordings do not appear to play an analogous role during free flight. If straight flight is maintained largely by feedback from the haltere system, the role of the HS cells in free flight must be re-evaluated. One hypothesis is that the HS cells correct low-frequency slow drifts that the halteres cannot detect. In addition, the LPTCs of the vertical system (VS cells) might approximate matched filters sensitive to optic flow patterns for various combinations of rotation about the pitch and roll axes (Franz and Krapp, 2000
; Krapp and Hengstenberg, 1996
). While the fly may rely more heavily upon halteres for flight stabilization about its yaw axis, visual feedback is important in stabilizing pitch and roll. Halteres do, however, provide feedback to stabilize pitch and roll as well (Dickinson, 1999
).
Our data suggest a model of how free flight behavior might emerge from an interaction between a flys motor control system and its visual environment (Fig. 13). While flying along a trajectory, the fly uses an array of delay and correlate motion detectors (Borst and Egelhaaf, 1989; Reichardt, 1961
) to estimate optic flow. However, as it moves, the fly relies on its mechanosensory equilibrium system (halteres) to maintain a straight course. Over short distances, at least, the halteres alone appear sufficient to maintain straight flight. While dominated by feedback from the halteres, tonic feedback from the visual system directs the fly away from large obstacles via a centering response. In addition, the fly is continuously integrating the sum of the horizontal and vertical expansion, which has the effect of removing some of the noise in the expansion signal. If saccades are discrete ballistic events, they are likely to be triggered when some neural signal exceeds a threshold. The expansion signals rise gradually over the 700 ms preceding the saccade (Figs 11, 12) and are laden with rapid fluctuations as a result of the output of local elementary motion detectors. Thus, it is likely that the nervous system conditions the instantaneous signal prior to saccade initiation. For example, temporal integration performed on the expansion signal, in addition to removing noise, would also result in a signal that rises more rapidly, making a more precise trigger for each saccade. When the accumulated sum of horizontal and vertical expansion exceeds a threshold level on either side, the saccade causes the fly to rotate 90° away from the side on which expansion was greatest. Because of the variation in the estimate of total expansion preceding individual saccades, it is difficult to determine the latency of the collision avoidance response. Measurements of responses to visual stimuli indicate latencies of 50 ms during free flight (David, 1984
) and 100 ms during tethered flight (Heisenberg and Wolf, 1988
). Preliminary tethered flight experiments in which flies are stimulated with expanding squares suggest a collision avoidance latency of 50 ms (L. F. Tammero and M. H. Dickinson, unpublished results). Thus, the time-integrated function of total expansion is likely to exceed threshold within that time frame. As with many other escape responses, a saccade in one direction inhibits a saccade in the opposite direction, preventing the fly from attempting to turn in both directions at once. Following the saccade, the accumulated expansion will be cleared, and the fly will continue to fly along a straight trajectory, until total expansion increases again to a level at which another saccade is triggered. In this way, complex free flight patterns of behavior might emerge from a rather simple control algorithm.
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Appendix |
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![]() | (A1) |
where
| (A2) |
A time constant, , of 40 ms was selected on the basis of data from experiments involving larger flies (Borst and Bahde, 1986
; Harris et al., 1999
; OCarroll et al., 1997
). To ensure that our results are not dependent on the time constant in the delay line, simulations were repeated using different values of
. The outputs of horizontal and vertical local motion detectors, hi,j and vi,j, are calculated as:
![]() | (A3) |
and
![]() | (A4) |
These equations show that the outputs of each of the two half-detectors are fed into the subtraction stage with equal weight. As defined, the horizontal local motion detector responds positively to rightward motion and the vertical motion detector responds positively to upward motion. The vector fields plotted in Fig. 9C represent the output of these local motion detectors.
To determine the large-field motion signals, the outputs of the local motion detectors are pooled spatially by linear summation. Large-field horizontal motion signals on the left and right, HL(t) and HR(t) are calculated as the sum taken over all rows for the columns that make up the frontal 180° of the flys field of the view:
| (A5) |
and
| (A6) |
The row and column indices (q1, q2, ... q4.; p1, p2,... p8) represent the indices of the hi,j matrix, as described by the following:
![]() | (A7) |
and
![]() | (A8) |
The locations of the edges of each 5° pixel can be calculated from the matrix indices according to:
![]() | (A9) |
and
![]() | (A10) |
with all values in degrees. Thus, the column with a j index of 54 would correspond to the area of visual space between 85° and 90° of azimuth.
To compute the reverse correlations, the points where the fly initiated each saccade (t0) and the direction of the saccade (left or right) are first determined. For each saccade, a row vector representing the time course of the horizontal expansion from the 0.67 s before the initiation point to 0.33 s after the initiation point is formed.
HLrk is used to symbolize horizontal expansion on the left side preceding and following the kth saccade to the right:
![]() | (A11) |
If a fly were to saccade to the right m times and to the left n times, these row vectors would be assembled into ipsilateral and contralateral large-field horizontal motion matrices, HIps and HCont according to:
| (A12) |
and
| (A13) |
The individual traces shown in Fig. 10B are the rows of the HIps and the HCont matrices. This procedure is repeated for the large-field vertical motion signals, VIps and VCont, which are plotted in Fig. 10D. Measures of horizontal and vertical expansion are calculated according to the following:
| (A14) |
| (A15) |
| (A16) |
and
| (A17) |
HExp,Ips, HExp,Cont, VExp,Ips and VExp,Cont are assembled in the same manner as HIps and HCont. HExp,Ips and HExp,Cont are plotted in Fig. 11B, while VExp,Ips and VExp,R(t) are plotted in Fig. 11D.
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Acknowledgments |
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References |
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