ABSTRACT

Most animals shift gaze by a ‘fixate and saccade’ strategy, where the fixation phase stabilizes background motion. A logical prerequisite for robust detection and tracking of moving foreground objects, therefore, is to suppress the perception of background motion. In a virtual reality magnetic tether system enabling free yaw movement, Drosophila implemented a fixate and saccade strategy in the presence of a static panorama. When the spatial wavelength of a vertical grating was below the Nyquist wavelength of the compound eyes, flies drifted continuously and gaze could not be maintained at a single location. Because the drift occurs from a motionless stimulus – thus any perceived motion stimuli are generated by the fly itself – it is illusory, driven by perceptual aliasing. Notably, the drift speed was significantly faster than under a uniform panorama, suggesting perceptual enhancement as a result of aliasing. Under the same visual conditions in a rigid-tether paradigm, wing steering responses to the unresolvable static panorama were not distinguishable from those to a resolvable static pattern, suggesting visual aliasing is induced by ego motion. We hypothesized that obstructing the control of gaze fixation also disrupts detection and tracking of objects. Using the illusory motion stimulus, we show that magnetically tethered Drosophila track objects robustly in flight even when gaze is not fixated as flies continuously drift. Taken together, our study provides further support for parallel visual motion processing and reveals the critical influence of body motion on visuomotor processing. Motion illusions can reveal important shared principles of information processing across taxa.

INTRODUCTION

Animals must be able to identify and classify objects rapidly to generate appropriate behavior. For example, a fly must identify and classify potential predators while moving through a background of foliage. Complicating this process is that locomotion itself generates a moving retinal background image. Subject to ego motion, animals should be able to detect foreground objects more easily if the retinal image of the background is stabilized. Complicating gaze stabilization, however, is that the eyes are never truly still: for instance, in Calliphora, the head is in constant motion in free flight (Hateren and Schilstra, 1999) and our own eyes constantly move as a result of microsaccades, drift and tremor (Martinez-Conde and Macknik, 2017). At present, it is not well understood whether an animal can detect and track object motion better when still than when in motion (Land and Nilsson, 2012).

Seminal work in Musca showed that a fly can readily discriminate an object from the background (Egelhaaf, 1985; Reichardt and Poggio, 1979). Later work in Drosophila revealed that object tracking is spatially distinct from background stabilization, implying that the two systems are distinct (Fox et al., 2014). More recent work in magnetically tethered Drosophila free to pivot showed that detection and tracking of a visual object is enabled by rapid switching between the smooth optomotor reflex that stabilizes the background and saccades that track a foreground object (Keleş et al., 2019; Mongeau and Frye, 2017; Mongeau et al., 2019), further supporting that gaze stabilization and object tracking are implemented by distinct controllers. Drosophila rely on a velocity-based controller that reduces retinal slip while simultaneously integrating object position spatiotemporally (Mongeau and Frye, 2017); therefore, it would appear that these two systems not only are distinct but also operate in parallel. With this contention, we would hypothesize that disruption of one controller, say the velocity controller that stabilizes background motion, would not interfere with the position-based or figure-motion (FM)-based controller for object tracking (Aptekar et al., 2012). Walking flies that are motion blind by blocking T4/T5 pathways can track an object, suggesting parallel control systems (Bahl et al., 2013). However, other work suggests that object–ground discrimination in flight does not require parallel processing, but can instead rely on asymmetric processing by horizontal-system (HS)-like cells (Fenk et al., 2014). Therefore, at present, there are two distinct hypotheses: (1) object and ground discrimination are processed by parallel pathways and (2) object and ground discrimination are asymmetrically processed by overlapping pathways.

To distinguish between these two hypotheses, we used a magnetic pivot enabling free rotation in yaw (Fig. 1A,B). We developed a paradigm that visually hindered the gaze stabilization reflex by presenting Drosophila with a grating below the supposed maximum resolvable spatial wavelength of their visual system (spatial wavelength λ=7.5 and 3.75 deg). For the multifaceted, hexagonal lattice eyes of Drosophila, 1/(√3Δφ) is the smallest spatial frequency of a vertical grating that the eye can resolve, where Δφ is the angle between adjacent ommatidia (Fig. 1C) (Snyder, 1979). When λ of a stimulus is less than √3Δφ, the retinal image is under-sampled, resulting in perceptual aliasing. Drosophila have an approximate inter-ommatidial angle range of 4.5–6 deg (mean 4.5 deg) along the horizontal (yaw) axis (Gonzalez-Bellido et al., 2011), and thus theoretically the Nyquist wavelength of Drosophila is ∼9 deg, although the actual cut-off also depends on facet and rhabdomere diameter as well as on retinal noise levels and background luminance. Indeed, dark-adapted eyes experience an increase in acceptance angle and resolving the edges of a high-frequency pattern requires more photons (Gonzalez-Bellido et al., 2011; O'Carroll and Wiederman, 2014). Acuity at high spatial frequencies is further attenuated by diffraction phenomena and rhabdomere geometry, which together define the acceptance angle Δρ (Buchner, 1984). The acceptance angle further limits the effective cut-off frequency of the optical system as 1/Δρ, which for Drosophila is approximately 1/5 deg (Gonzalez-Bellido et al., 2011). For receptors that are diffraction limited, the contrast ratio decreases to nearly zero at the cut-off frequency (Fig. 1D) (Buchner, 1984; Land, 1997), where the contrast ratio is defined as:
formula
(1)
where ν is the spatial frequency and Δρ is the acceptance angle, which is approximately 5 deg for Drosophila (Buchner, 1984). Animal eyes therefore trade-off acuity and contrast sensitivity, as decreasing Δφ increases acuity but concomitantly decreases contrast sensitivity, because contrast sensitivity is itself proportional to the ommatidial diameter (Land and Nilsson, 2012).
Fig. 1.

Magnetic tether paradigm and control framework. (A) Flies were suspended within a magnetic field, surrounded (360 deg) by LED panels, and were free to rotate about the yaw axis. A high-speed camera recorded the fly's bottom position. (B) Closed-loop control diagram of flight in the magnetic tether. With a static panorama, flies produce body motion that generates visual reafference. The difference between motion and reafference generates some error (retinal slip). (C) Left: diagram of compound eye ommatidia mosaic. The separation distance between each ommatidium defines the inter-ommaditial angle Δφ. The distance about the horizontal axis is considered for vertical gratings. Right: grating defined by spatial wavelength λ. (D) Contrast ratio (actual divided by perceived contrast) as a function of spatial wavelength for Drosophila melanogaster. Acceptance angle Δρ=5 deg for the simulation. At λ=7.5 deg, the contrast ratio is ∼1%. (E) Closed-loop control diagram. Inset: proposed parallel visual motion processing pathway for object tracking and background stabilization.

Fig. 1.

Magnetic tether paradigm and control framework. (A) Flies were suspended within a magnetic field, surrounded (360 deg) by LED panels, and were free to rotate about the yaw axis. A high-speed camera recorded the fly's bottom position. (B) Closed-loop control diagram of flight in the magnetic tether. With a static panorama, flies produce body motion that generates visual reafference. The difference between motion and reafference generates some error (retinal slip). (C) Left: diagram of compound eye ommatidia mosaic. The separation distance between each ommatidium defines the inter-ommaditial angle Δφ. The distance about the horizontal axis is considered for vertical gratings. Right: grating defined by spatial wavelength λ. (D) Contrast ratio (actual divided by perceived contrast) as a function of spatial wavelength for Drosophila melanogaster. Acceptance angle Δρ=5 deg for the simulation. At λ=7.5 deg, the contrast ratio is ∼1%. (E) Closed-loop control diagram. Inset: proposed parallel visual motion processing pathway for object tracking and background stabilization.

Behavioral experiments in tethered, walking and flying Drosophila showed that the turning response to a rotating grating decreases near zero at the Nyquist wavelength and curiously reverses below Nyquist wavelength, indicating perceptual aliasing (Buchner, 1976; Gotz, 1965). The same effect was demonstrated in bees (Kunze, 1961). However, at present it is not known how the behavioral results by Buchner (1976) and Gotz (1965) in tethered preparations manifest in more naturalistic closed-loop conditions. Furthermore, a recent study challenges the notion that Drosophila ocular spatial resolution is limited by the inter-ommatidial distance by showing that rapid rhabdomere contraction can generate hyperacute vision below aliasing wavelength, enabling discrimination of a grating with spatial wavelength as low as 1.16 deg (Juusola et al., 2017). Low background luminance levels in Buchner's (1976) work (16 cd m−2) would have generated very low R1–R6 photoreceptor outputs, rendering it difficult to resolve hyperacute visual patterns (Juusola et al., 2017). It is at present unclear whether hyperacuity is observable under more naturalistic flight conditions where animals experience ego motion and hence sensory reafference. Specifically, can flies stabilize a grating below the aliasing limit in closed loop?

Here, we show that when presented with a static grating at or near Nyquist wavelength in a magnetic tether, Drosophila melanogaster could not maintain gaze at a single location: instead, they drifted continuously. Under the same visual conditions in a rigid-tether system, flight responses were not distinguishable from responses to a resolvable pattern, suggesting that in the magnetic tether, self-motion induces a motion illusion driven by perceptual aliasing. We then tested whether the flies could detect and track an object at all when gaze is not fixated as a result of perceptual aliasing of the background. We presented flies with a high contrast, moving object superimposed over a λ=7.5 deg static grating. We show that gaze fixation is not necessary for closed-loop object pursuit, thereby providing further support for the hypothesis that background stabilization and object-tracking controllers operate in parallel (Fig. 1E).

MATERIALS AND METHODS

Animals

A wild-type Drosophila melanogaster strain was maintained at 25°C under a 12 h:12 h light:dark cycle with access to food and water ad libitum. This D. melanogaster strain was reared from a wild-caught iso-female line. All experiments were performed with 3–5 day old adult female flies.

Magnetic tether paradigm

Animals were prepared for each experiment according to a protocol that has been described previously (Bender and Dickinson, 2006a; Duistermars and Frye, 2008). Flies were cold-anesthetized by cooling on a stage maintained at approximately 4°C. For the magnetic tether, stainless steel pins (100 µm diameter; Fine Science Tools, Foster City, CA, USA) were glued onto the thorax by applying UV-activated glue. Flies were allowed at least 1 h to recover before running experiments.

The magnetic tether system has been described elsewhere (Bender and Dickinson, 2006a; Duistermars and Frye, 2008). The display consisted of an array of green (570 nm) 96×16 light emitting diodes (LEDs) that wrap around the fly, subtending 360 deg horizontally and 56 deg vertically (Fig. 1A); therefore, each pixel on the visual horizon subtended 3.75 deg on the eye. Panel LED matrices operated at a wavelength of 570 nm. Flies were suspended between two magnets, allowing free rotation along the vertical (yaw) axis and illuminated from below with an array of eight 940 nm LEDs (not shown). The angular position of the fly within the arena was recorded at 160 frames s−1 with an infrared-sensitive camera placed directly below the fly (A602f, Basler, Ahrendburg, Germany). The LED arena operated at maximum intensity with a mean luminance of approximately 72 cd m−2. We also used a larger LED display system with 192×40 LEDs – twice the diameter of the 96×16 display – with each pixel subtending 1.875 deg on the eye.

After suspending flies within the magnetic field, they were given several minutes to acclimate. We began each experiment by eliciting sustained rotation of the fly by revolving a visual panorama either clockwise or counter-clockwise for 30 s at 120 deg s−1. This stimulus elicited a strong rotatory, smooth co-directional optomotor turning response with occasional saccades. From these data, we estimated the fly's center of rotation by computing the cumulative sum of all camera frames and measuring its centroid. Any fly that could not robustly follow the rotating panorama was not used for experiments. We presented each stimulus for a period of 20–30 s, defining the duration of an individual trial. Between trials, we presented a fixed visual landscape for 25 s for the fly to rest. The procedure to identify saccades from heading data has been described elsewhere (Mongeau and Frye, 2017). We modeled the fly as an ellipsoid and determined the heading by calculating the major axis of the ellipse in each video frame. The asymmetry between head and abdomen along the longitudinal axis was used to determine the direction of the fly heading vector.

Rigid-tether paradigm

After cold-anesthetizing flies at 4°C as above, we affixed a small tungsten pin onto the thorax using UV-activated glue. Flies recovered for at least 1 h prior to experiments. They were then placed in the center of a cylindrical flight arena with the same pixel size and color wavelength as for the magnetic tether paradigm. The arena has been described elsewhere (Reiser and Dickinson, 2008). The display consisted of a cylindrical array of 96×32 LEDs subtending 330 deg horizontally and 94 deg vertically. An infrared diode (940 nm) projected light onto the wings, casting a shadow onto two separate optical sensors. A custom wingbeat analyzer (JFI Electronics, Chicago, IL, USA) transformed the signal from each optical sensor into a signal proportional to the wingbeat amplitude (defined as left minus right wing). Changes in wingbeat amplitude (ΔWBA) signals from the optical wingbeat analyzer were acquired at 1000 Hz. The LED arena operated at maximum intensity with a mean luminance of approximately 72 cd m−2.

Paper grating

To determine the possible effect of the LED arena on the behavioral response in the magnetic tether, we printed a black-and-white grating on white paper using a laser printer with a resolution of 4800×1200 dots per inch. The paper grating had the same overall diameter and height as the magnetic tether LED arena with λ=7.5 deg. Using full room white illumination with flicker frequency above that of the Drosophila visual system (Cosens and Spatz, 1978), we measured the mean luminance inside the paper drum to be ∼80 cd m−2 (Tondaj LX-1330B), which was similar to the LED arena luminance (72 cd m−2). For the trials with a paper pattern and the larger LED arena, we used the fly's observed drift to compute the center of rotation.

Elementary motion detector (EMD) model

Computational model

We implemented an EMD model as previously described for Drosophila visual physiology (Dickson et al., 2008; Tuthill et al., 2011). We modeled the optical, spatial low-pass filter for each ommatidium of a single array of 1×72 ommatidia using a Gaussian function of the form:
formula
(2)
where ζ is the angle from the optical axis of the ommatidium and Δρ is the acceptance angle. Here, we used Δρ=kΔφ where Δφ is the inter-ommatidial angle (fixed at 4.5 deg) and k=1.1, as previously measured (Buchner, 1984). We computed the image by convolving an intensity signal I(ζ,n), where n is the discrete sample time, with the acceptance angle of the modeled ommatidia:
formula
(3)
We used the Hassenstein–Reichardt, delay-and-correlate EMD model such that the output VEMD(n) of adjacent photoreceptors A and B is defined as:
formula
(4)
where VA(n) and VB(n) are the output of the two photoreceptors and V′A(n) and V′B(n) are the delayed outputs of the same photoreceptors by a first-order delay filter of the form:
formula
(5)
where τ is the time constant (set at 40 ms). We computed the EMD response by summing across all simulated ommatidia and taking the mean of the sum at each temporal frequency.

Analytical model

We also simulated an analytical model of the EMD subject to a sinusoidal input signal (Borst et al., 2003). The steady-state response R of the ith detector located at φ is:
formula
(6)
where ΔI is the contrast of the pattern, τ is the time constant of the low-pass, first-order temporal filter, Δφ is the inter-ommatidial angle (spacing of detector), ω is the angular frequency of the stimulus and λ is the spatial wavelength of the pattern. Here, we used ΔI=1 (full contrast), τ=40 ms and Δφ=4.5 deg. This model assumes a sinusoidal grating x(t) of the form:
formula
(7)
where v is the constant angular velocity of the stimulus and Ī is the mean luminance. This model, unlike the computational model described above, does not take into consideration the filtering optics of the compound eye defined by acceptance angle.

Spatio-temporal action field (STAF)

To quantify the bar-tracking effort of flies in the rigid-tether paradigm, we used a previously described STAF technique (Aptekar et al., 2014). We determined the impulse response function of a fly at 24 uniformly spaced azimuthal locations by convolving the fly's steering response (ΔWBA) with a pseudo-random, maximum length shift register sequence (m-sequence) prescribing bar position for each trial (MacWilliams and Sloane, 1976). The m-sequence prescribed positive (+1) and negative (−1) steps controlling bar position, with each step corresponding to one pixel or 3.75 deg angular displacement of the bar. For each fly, the position of the bar was randomized at the prescribed 24 locations. For each test period, we presented three periods of a 127 element (7th order) m-sequence. The visual scene was updated at a frame rate of 25 Hz or every 40 ms such that each update was perceptually instantaneous. The refresh rate of the LED arena was approximately 2.6 MHz (Reiser and Dickinson, 2008). Each trial lasted 15.6 s with a total experimental time for each fly of ∼28 min. To keep the fly motivated after each trial, we presented a bar under virtual closed-loop for 5 s.

Statistical analysis

All statistical analysis was performed using Matlab (Mathworks, Natick, MA, USA) and JMP (SAS, Cary, NC, USA). Unless otherwise specified, we report means±1 s.d. When displaying box plots, the central line is the median, the bottom and top edges of the box are the 25th and 75th percentiles and the whiskers extend to ±2.7 s.d.

RESULTS

We presented static, wide-field panoramas of different spatial wavelengths to flies that were free to rotate in yaw in a magnetic pivot (Fig. 1A). As expected, under these visual conditions, flies generated occasional saccades interspersed by periods of gaze stabilization between saccades (Fig. 2A). We challenged the operation of the gaze stabilization reflex by presenting flies with a grating of light and dark stripes at a spatial wavelength λ of 7.5 deg, near the maximum resolvable spatial wavelength of the Drosophila visual system. At λ=7.5 deg, the perceived contrast ratio for Drosophila is ∼1% as a result of the ommatidial acceptance angle, leaving little-to-no detectable features in the panorama; thus, we hypothesized that the panorama should be ambiguous (Fig. 1D). Curiously, at λ=7.5 deg, flies smoothly drifted whereas flies maintained stable headings when presented with gratings of higher spatial wavelengths (Fig. 2A). To illustrate this peculiar result further, we simulated two-dimensional flight trajectories from angular heading data by prescribing a constant flight speed (30 cm s−1). This simulation illustrates the tortuous fight trajectory at λ=7.5 deg compared with other spatial wavelengths (Fig. 2B). To quantify the amount of drift, we (1) separated the data set into flies that on average turned more clockwise (CW) or counter-clockwise (CCW) against the stationary background grating and (2) removed saccades from the smooth angular heading data using custom algorithms. Across all animals and trials, these data confirmed that the drift is strongly present at λ=7.5 deg but not at other wavelengths (Fig. 2C−E). Animals did not preferentially drift CW or CCW (χ2 test, d.f.=1, P=0.666). In some trials at λ=7.5 deg (16% of all trials), flies spontaneously changed direction.

Fig. 2.

Gratings of spatial wavelength below Nyquistwavelength destabilize the gaze stabilization reflex. (A) Top: example 25 s trials for the same fly presented with a static 7.5 deg (left) and 15 deg (right) spatial wavelength pattern. Bottom: angular speed data. The dashed line is the calculated threshold for saccade detection. The inset shows the drift generated by the 7.5 deg static background. Arrowheads indicate inter-saccade intervals, with marked differences between 7.5 deg (yaw drift) and 15 deg (no yaw drift) spatial wavelengths. (B) Simulation of two-dimensional flight trajectory from fly heading data by prescribing a fixed flight speed (30 cm s−1). For visual clarity, a randomly selected subset of trials is shown (gray lines) and three trials are highlighted in red. (C) Angular heading data (with saccades removed) for six static gratings of different spatial wavelength and a randomly textured and uniform grating. Trials are shown for flies that drifted predominantly in the clockwise (CW, left) and counter-clockwise (CCW, right) direction. (D) Box plot of net heading angles for data in C. (E) Speed of flies for data shown in C and D. (F) Drift speed in magnetic tether with a paper drum of λ=7.5 deg (n=15 flies, 75 trials) and 9 deg (n=12 flies, 60 trials). (G) Drift speed in the magnetic tether with higher spatial resolution (each pixel subtending 1.875 deg; n=5 flies, 25 trials). The drift speed is statistically significant between 3.75 and 7.5 deg (P<0.001). (H) Spontaneous saccade dynamics. For C−E and H, n=36 flies.

Fig. 2.

Gratings of spatial wavelength below Nyquistwavelength destabilize the gaze stabilization reflex. (A) Top: example 25 s trials for the same fly presented with a static 7.5 deg (left) and 15 deg (right) spatial wavelength pattern. Bottom: angular speed data. The dashed line is the calculated threshold for saccade detection. The inset shows the drift generated by the 7.5 deg static background. Arrowheads indicate inter-saccade intervals, with marked differences between 7.5 deg (yaw drift) and 15 deg (no yaw drift) spatial wavelengths. (B) Simulation of two-dimensional flight trajectory from fly heading data by prescribing a fixed flight speed (30 cm s−1). For visual clarity, a randomly selected subset of trials is shown (gray lines) and three trials are highlighted in red. (C) Angular heading data (with saccades removed) for six static gratings of different spatial wavelength and a randomly textured and uniform grating. Trials are shown for flies that drifted predominantly in the clockwise (CW, left) and counter-clockwise (CCW, right) direction. (D) Box plot of net heading angles for data in C. (E) Speed of flies for data shown in C and D. (F) Drift speed in magnetic tether with a paper drum of λ=7.5 deg (n=15 flies, 75 trials) and 9 deg (n=12 flies, 60 trials). (G) Drift speed in the magnetic tether with higher spatial resolution (each pixel subtending 1.875 deg; n=5 flies, 25 trials). The drift speed is statistically significant between 3.75 and 7.5 deg (P<0.001). (H) Spontaneous saccade dynamics. For C−E and H, n=36 flies.

The peculiar result that Drosophila drifts in the presence of a static panorama composed of near-minimum resolvable spatial wavelength demonstrates that the optomotor reflex is perpetually active in closed-loop to stabilize gaze by reducing retinal slip generated by ego-motion. At λ=7.5 deg, flies are generating reafferent optic flow from their own motion (Fig. 3A). One possible explanation is that flies cannot eliminate reafferent optic flow to stabilize gaze because their eyes presumably cannot detect or resolve high-contrast, high-frequency edges. Furthermore, motion of the fly itself due to destabilization of optokinetic reflexes may further exacerbate the detection of high-contrast features as a consequence of motion blur. Motion blur, a result of temporal integration, manifests first as a loss of contrast to the highest spatial frequencies (Snyder, 1979). Taken together, at λ=7.5 deg, the closed-loop gaze stabilization reflex may become effectively an unstable closed-loop control system in which the reafferent and efferent signals are not properly balanced, i.e. a difference in perceived versus actual body velocity, leading to non-zero net body velocity (Fig. 3A). We tested whether flies cannot in fact resolve features of sufficient contrast at λ=7.5 deg by presenting flies with a uniformly lit panorama. Indeed, for a contrast ratio of 1% with a pattern of λ=7.5 deg, we might expect flies to respond no differently than in the presence of a uniform panorama. Although flies drifted significantly more in the presence of a uniform panorama than with panoramas of λ=15–90 deg, the effect was less pronounced than under λ=7.5 deg (Fig. 2C−E). Flies presented with a λ=7.5 deg pattern drifted at a median speed of 8 deg s−1, which was statistically different from the drifting speed in the presence of a uniform background (median=2 deg s−1; t-test, P<0.001), suggesting that aliasing effects enhance the motion illusion (Fig. 2E).

Fig. 3.

Modeling of perceptual aliasing. (A) Proposed interpretation of perceptual aliasing in closed loop. A mismatch between the sign of the perceived motion direction (Vp) and the actual body velocity (Vf) elicits a non-zero body velocity due to a non-zero error, corresponding to the observed drift in the magnetic tether. (B) Hassenstein–Reichardt elementary motion detector (EMD) model with spatial filter (S), first-order, low-pass filter (LP), multiplication non-linearity (×), summation (Σ) and inter-ommatidial distance (Δφ). (C) EMD steady-state response of the analytical model as a function of spatial frequency for a fixed temporal frequency of 2 Hz. Shaded region: aliasing of visual input. (D) EMD steady-state response of the analytical model for distinct spatial wavelengths λ. For visual clarity, the 3.75 and 15 deg EMD responses were offset as they fully overlap. (E) Same as D but for a computational EMD model with a discrete low-pass filter and spatial filter simulating Drosophila optics. For all simulations, we used Δφ=4.5 deg.

Fig. 3.

Modeling of perceptual aliasing. (A) Proposed interpretation of perceptual aliasing in closed loop. A mismatch between the sign of the perceived motion direction (Vp) and the actual body velocity (Vf) elicits a non-zero body velocity due to a non-zero error, corresponding to the observed drift in the magnetic tether. (B) Hassenstein–Reichardt elementary motion detector (EMD) model with spatial filter (S), first-order, low-pass filter (LP), multiplication non-linearity (×), summation (Σ) and inter-ommatidial distance (Δφ). (C) EMD steady-state response of the analytical model as a function of spatial frequency for a fixed temporal frequency of 2 Hz. Shaded region: aliasing of visual input. (D) EMD steady-state response of the analytical model for distinct spatial wavelengths λ. For visual clarity, the 3.75 and 15 deg EMD responses were offset as they fully overlap. (E) Same as D but for a computational EMD model with a discrete low-pass filter and spatial filter simulating Drosophila optics. For all simulations, we used Δφ=4.5 deg.

To verify that yaw drifting at λ=7.5 deg was not an artefact of the visual display (LED arena, see Materials and Methods), we repeated the same experiment under similar mean luminance levels with a black-and-white striped drum printed on white paper. Although flies drifted less on average with a paper drum than in the LED arena, the effect was nonetheless considerable, with a median rotation speed of 2 deg s−1, resembling the effect of the uniform grating (Fig. 2F). Notably, the paper grating was under broadband white light illumination whereas the LED panels operated within a wavelength range centered on 570 nm, slightly above the optimal wavelength for the maximum optomotor response (Heisenberg and Buchner, 1977). The drift speed at λ=7.5 deg on paper was significantly larger than that for λ>7.5 deg in the LED arena (t-test with λ>7.5 deg wavelengths pooled, P<0.001). As another control, we tested flies in a virtual reality arena with twice the diameter, and therefore twice the spatial resolution (subtending 1.875 deg per pixel) but the same mean background luminance. When presented with a λ=7.5 deg static grating (2 pixels ON, 2 pixels OFF repeating), flies generated significant drift (median=5 deg s−1), comparable to the arena with lower resolution (Fig. 2G). The same flies presented with a λ=3.75 deg grating also drifted considerably, although less so than at 7.5 deg (median=2 deg s−1; t-test, P<0.001, n=5 flies, 25 trials; Fig. 2G). The difference in drift between 7.5 deg and 3.75 deg suggests that aliasing near Nyquist wavelength generates larger drift and therefore enhances the motion illusion effect, whereas λ much smaller than the Nyquist wavelength limit appears more like a spatially uniform background. Taken together, these results suggest that drift experienced by flies was robust and largest at λ=7.5 deg, with some effects due to the type of background (LED versus paper) and pixel resolution (1.875 versus 3.75 deg).

The λ=7.5 deg pattern is near the predicted Nyquist wavelength, but for Drosophila it is closer to 9 deg based on the average inter-ommatidial distance along the yaw axis (Gonzalez-Bellido et al., 2011). To test whether there is a difference in fly response between a 7.5 and 9 deg spatial wavelength pattern, we presented flies with a static paper pattern at these two spatial wavelengths. Overall, the drift speed was similar under the two conditions (Kruskal–Wallis, P=0.102; 7.5 deg: n=17 flies; 9 deg: n=12 flies), suggesting similar perceptual aliasing influences at λ=7.5 deg and 9 deg (Fig. 2F).

Interestingly, flies on average generated the same number of spontaneous saccades across all spatial wavelengths (Pearson test, P=0.781, 6546 saccades; median saccade frequency=0.36 deg s−1), suggesting that saccades were generated even when gaze was not maintained at a single location, supporting the notion that some saccades are triggered by spontaneous processes. Overall, the spontaneous saccade rate was consistent with previous studies (Bender and Dickinson, 2006a; Ferris et al., 2018; Mongeau and Frye, 2017) and there was no robust influence of spatial properties of the panorama on saccade dynamics (Fig. 2H).

To test whether the λ=7.5 deg pattern is resolvable, we simulated the computational response of a Hassenstein–Reichardt EMD (Fig. 3B). As predicted from an EMD analytical model subject to a sinusoidal input, aliasing, i.e. negative EMD outputs, should occur within the spatial frequency range 1/Δφ>1/λ>1/2Δφ (Fig. 3C) (Buchner, 1984). For the analytical model, a pattern of λ=7.5 deg generated a comparatively large negative steady-state EMD output when compared with resolvable visual stimuli, corroborating previous results by Buchner (1984) and Gotz (1965) (Fig. 3D,E). In contrast, the computational model, which includes an optical spatial filter, generated a comparatively small negative EMD output for λ=7.5 deg. Therefore, the analytical model, without simulating eye optics, can potentially overestimate the biological motion detector response and therefore also the predicted flight behavioral responses. The analytical EMD model predicted a large positive EMD response at λ=3.75 deg whereas the computational model predicted little-to-no response. Our experimental results showed that flies drift significantly at λ=3.75 deg; therefore, these results do not agree with the EMD model predictions. Taken together, the EMD output can predict visual aliasing near the Nyquist spatial wavelength of the eye, with different predictions in relative magnitude based on the type of EMD model implemented. Whereas a λ=7.5 deg pattern is resolvable to Drosophila, because the drift occurs from a motionless static stimulus, we conclude that it is illusory and driven by perceptual aliasing (Fig. 3A).

If flies cannot maintain a constant gaze at λ=7.5 deg, can they detect and pursue a superimposed moving object? If the gaze stabilization reflex and the object pursuit systems are indeed parallel control systems, then we would expect object pursuit to be intact when the gaze stabilization reflex is obstructed, provided that the object is of sufficient contrast and its motion is not blurred. We previously showed that flies robustly track a moving object superimposed on a counter-rotating ground, enabled by rapid switching between smooth movement gaze stabilization and object detection and saccadic pursuit (Mongeau and Frye, 2017). We repeated this experiment but added one condition in which the object rotated superimposed on a grating of λ=7.5 deg. Under these conditions, we hypothesized that the low-contrast background pattern should elicit weak or no responses because of the presence of a highly salient foreground feature. As previously observed (Mongeau and Frye, 2017), when moving an object on a broadband randomly textured ground, flies switched between bouts of saccadic tracking in pursuit of the object and smooth gaze stabilization between saccades (Fig. 4A). When the object exited the field of view, flies primarily generated smooth turns at rotational body velocity near unity gain (Mongeau and Frye, 2017). From these results, we would predict that gaze stabilization is important for object fixation as gaze is rapidly stabilized between saccades, within as little as 20 ms from the termination of a saccade (Mongeau and Frye, 2017). Therefore, we predicted that flies cannot stabilize an object on a λ=7.5 deg grating. Strikingly, when the object moved on the λ=7.5 deg grating, object pursuit was intact (Fig. 4A, bottom). Flies generated robust bouts of tracking saccades even if they could not maintain a constant gaze, as evidenced by periods of drifting heading between saccades (Fig. 4A, bottom). Flies generated more object-tracking saccades on a static λ=7.5 deg grating than on a rotating background across all background speeds for a balanced experimental design (Fig. 4B). At higher background speeds, we suspect that it was more challenging for flies to switch between gaze stabilization and object pursuit, as evidenced by the decreasing number of tracking saccades (Fig. 4B).

Fig. 4.

Gaze fixation is not necessary for object detection and pursuit. (A) Sample 25 s trials for (top) a bar moving counter-directionally over a randomly textured background and (bottom) a bar moving over a λ=7.5 deg static background for the same fly. Top: flies generate bouts of smooth gaze stabilization (black arrowhead) interspersed with object-tracking saccades (green arrowhead). As a wide-field stimulus, the background absolute angle is arbitrary but is shown here for reference. Bottom: flies drifted in the presence of a static background and generated tracking between bouts of drifting. (B) Left: tracking saccade count for a textured bar moving counter-directionally to a randomly textured ground. Right: tracking saccade count for a textured bar moving on a λ=7.5 deg ground. n=32 flies, 18,189 saccades total, 3,195 tracking saccades total.

Fig. 4.

Gaze fixation is not necessary for object detection and pursuit. (A) Sample 25 s trials for (top) a bar moving counter-directionally over a randomly textured background and (bottom) a bar moving over a λ=7.5 deg static background for the same fly. Top: flies generate bouts of smooth gaze stabilization (black arrowhead) interspersed with object-tracking saccades (green arrowhead). As a wide-field stimulus, the background absolute angle is arbitrary but is shown here for reference. Bottom: flies drifted in the presence of a static background and generated tracking between bouts of drifting. (B) Left: tracking saccade count for a textured bar moving counter-directionally to a randomly textured ground. Right: tracking saccade count for a textured bar moving on a λ=7.5 deg ground. n=32 flies, 18,189 saccades total, 3,195 tracking saccades total.

We showed that drift is generated by a static grating near Nyquist frequency, but are these effects manifest in an open-loop, rigid-tether paradigm where sensory reafference is less natural? Under the same visual conditions in a rigid-tether arena restricting body movement but not head movement, we tested whether ΔWBA signals might be biased in the presence of a 7.5 deg background (Fig. 5A,B), where ΔWBA provides an indirect measurement of steering torque (Tammero et al., 2004). WBA signals in the presence of a 7.5 deg grating were not distinguishable from WBA signals in the presence of a resolvable static pattern (paired t-test, P=0.900, n=13 flies), suggesting body motion-induced visual drift in more natural conditions (magnetic tether), which cannot be captured in an open-loop paradigm (rigid tether) (Fig. 5C; Fig. S1). Without fictive drift in an open-loop, rigid-tether paradigm, it would follow that object fixation should remain intact. In particular, is intact object detection and fixation under an illusory background dependent on sensory reafference due to ego motion? To test this, we used the STAF paradigm with rigidly tethered flies that were free to move their head, thereby generating much less ego motion than in the magnetic tether (Aptekar et al., 2012, 2014). A bar superimposed on a λ=7.5 deg static background moved pseudo-randomly, centered on distinct locations in azimuth, from which spatially distinct impulse response functions relating bar motion and wing steering response can be computed (Fig. 5D,E). Measuring impulse responses at 24 distinct locations along the azimuth generates the STAF profile, which, as expected, exhibited a stereotyped spatial tuning for bar-steering responses (Fig. 5F) similar to those generated for random background patterns in our previous work (Fox et al., 2014). Therefore, in the presence of the λ=7.5 deg static background, flies robustly tracked the bar.

Fig. 5.

Rigid-tether paradigm indicatesthat aliasing effects are induced by body motion. (A) A fly is suspended within a virtual reality arena and wing motion is tracked to infer steering effort via changes in wing-beat amplitude (ΔWBA). (B) Open-loop control diagram of the rigid-tether paradigm. (C) Wing steering responses (ΔWBA) to the static random (left) and λ=7.5 deg grating (right). The thick black line and gray area indicate mean±1 s.d. Colored lines represent the mean for each individual fly. (D) Top: pseudo-random sequence of object position. Bottom: wing steering response of one fly to the sequence. (E) Example impulse response function between visual stimulus and steering for one fly tested at one azimuthal location. The unit of response amplitude on the scale bar is uncalibrated ΔWBA (volt degree second or V deg s). (F) Impulse responses to pseudo-random object motion measured at 24 azimuthal locations and assembled into a spatio-temporal action field (STAF) for n=12 flies.

Fig. 5.

Rigid-tether paradigm indicatesthat aliasing effects are induced by body motion. (A) A fly is suspended within a virtual reality arena and wing motion is tracked to infer steering effort via changes in wing-beat amplitude (ΔWBA). (B) Open-loop control diagram of the rigid-tether paradigm. (C) Wing steering responses (ΔWBA) to the static random (left) and λ=7.5 deg grating (right). The thick black line and gray area indicate mean±1 s.d. Colored lines represent the mean for each individual fly. (D) Top: pseudo-random sequence of object position. Bottom: wing steering response of one fly to the sequence. (E) Example impulse response function between visual stimulus and steering for one fly tested at one azimuthal location. The unit of response amplitude on the scale bar is uncalibrated ΔWBA (volt degree second or V deg s). (F) Impulse responses to pseudo-random object motion measured at 24 azimuthal locations and assembled into a spatio-temporal action field (STAF) for n=12 flies.

DISCUSSION

Visual illusions have been demonstrated in a number of vertebrate and invertebrate animals, illustrating common visual-processing principles across taxa (Srinivasan, 1993). For instance, flies respond robustly to the reverse-φ motion illusion (Tuthill et al., 2011), contrast illusion (Bahl et al., 2015) and even the waterfall illusion (Srinivasan, 1993). Here, we describe a motion illusion in insects for ambiguous static gratings driven by ego motion, which appears analogous to static motion illusions reported in vertebrates. For instance, static motion illusions have been described in a number of human psychophysics studies, perhaps the most famous being the rotating snake illusion reported by Akiyoshy Kitaoka (2002). Such static motion illusions have been linked to microsaccade production in humans (Otero-Millan et al., 2012; Troncoso et al., 2008). Our results support the notion that, just as in humans, as long as the body is mobile, fly eyes are never still, and thus ego motion can generate visual illusions not observable in open-loop, rigid-tether paradigms even if the head is mobile (Fig. 5). Indeed, flies in a magnetic tether are never fully still during inter-saccade intervals, as would be predicted for free flight (Fig. 2) (Bender and Dickinson, 2006a). Our results are consistent with visual feedback being critical during periods of straight flight (Bender and Dickinson, 2006b).

In previous work, Buchner (1976) observed perceptual aliasing in tethered, walking flies when presented with moving gratings with spacing below the Nyquist wavelength. Specifically, in the range φ<λ<2φ, flies turned in the direction opposite to the direction of motion. Buchner (1976) also showed that the turning response is attenuated below Nyquist wavelength as a result of a decrease in contrast ratio. However, recent work (Juusola et al., 2016) challenged Buchner's classic work, showing that perceptual aliasing is absent down to a spatial wavelength of 1.16 deg. Juusola et al. (2016) argued that the mean stimulus light intensity was low in Buchner's work (16 cd m−2), causing R1–R6 photoreceptors to be unable to resolve fine patterns. Our LED arena pattern has approximately five times the mean luminance reported in Buchner's work, thereby rendering it difficult to predict results in our magnetic tether in light of work by Buchner. Notably, Buchner's work predicts that flies would respond no differently to a stationary grating near Nyquist than to a uniform panorama, but we found that this is not the case (Fig. 2). Thus, a main novelty with regards to the presentation of high-frequency gratings in the magnetic tether is that a static stimulus causes significant and robust illusory motion.

Here, we show that a motion illusion supports the hypothesis that object detection and tracking operate in parallel with ground stabilization, suggesting two distinct control systems (Fig. 1E). Our results corroborate open-loop flight studies showing that flies can track an object in a virtual reality closed-loop superimposed on a background with opposite gain (Fox et al., 2014) – thereby lending support to the parallel control system hypothesis – but it remained unclear whether these results extended to more natural flight where flies move their body and therefore generate ego motion. Notably, in the magnetic tether apparatus, behavior operates under closed-loop feedback conditions – rather than simulated closed-loop feedback conditions in rigidly tethered flight – so flies experience naturalistic mechanosensory and visual reafference signals and prescribe their own optomotor gains. Indeed, studying flight in closed-loop conditions made possible our discovery that a pattern of λ=7.5 deg disrupts gaze fixation, i.e. the same experiment in open-loop generates no fictive drift (Fig. 5). This finding extends our previous results, which showed that flies can robustly track an object on a counter-rotating background, because under these conditions flies operated near a gain of 1 and therefore experienced little retinal slip (Mongeau and Frye, 2017), whereas under the motion illusion, flies could not stabilize retinal slip and instead drifted continuously (Figs 2A and 4A). This study adds to a growing body of evidence that parallel visual processing enables robust object detection and pursuit in insect flight (Aptekar et al., 2012; Bahl et al., 2013; Fox et al., 2014).

A recent study showed that microsaccadic sampling via rhabdomere contraction confers Drosophila hyperacuity, whereby tethered flies generate an open-loop optomotor response with a grating as small as 1.16 deg in spatial wavelength, well below aliasing limits (Juusola et al., 2017). Pixels in our LED arena subtend a maximum angle of 3.75 deg onto the fly's retina (and 1.875 deg in the larger arena), previously thought to be below acuity as determined by the inter-ommatidial distance (Gonzalez-Bellido et al., 2011; Reiser and Dickinson, 2008). Even with a paper grating and higher resolution display, flies drifted considerably (Fig. 2F,G), demonstrating that the motion illusion is robust rather than an artefact of the LED arena. For hyperacuity to manifest in the magnetic tether, we would have expected flies to stabilize gaze for gratings below the aliasing limit, but instead flies drifted continuously. We speculate that the drift is driven by visual processes and that mechanosensory information from halteres likely cannot sense the drift as the angular body velocity is well below haltere sensitivity about the yaw axis (Sherman and Dickinson, 2003). Taken together, we show that hyperacuity is not manifest under more natural closed-loop conditions where the body can pivot about yaw and thus continuously generate small ego motion.

Acknowledgements

We thank undergraduates Allie Solomon and Farhaad Khan for laboratory assistance.

Footnotes

Author contributions

Conceptualization: M.A.F., J.-M.M.; Methodology: W.S., B.C., M.A.F., J.-M.M.; Software: W.S., B.C., J.-M.M.; Validation: J.-M.M.; Formal analysis: W.S., J.-M.M.; Investigation: W.S., J.-M.M.; Resources: M.A.F., J.-M.M.; Data curation: J.-M.M.; Writing - original draft: M.A.F., J.-M.M.; Writing - review & editing: M.A.F., J.-M.M.; Visualization: B.C., M.A.F., J.-M.M.; Supervision: M.A.F., J.-M.M.; Project administration: M.A.F., J.-M.M.; Funding acquisition: M.A.F., J.-M.M.

Funding

This work was funded by the National Institutes of Health [R01EY026031 to M.A.F.]. Deposited in PMC for release after 12 months.

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Competing interests

The authors declare no competing or financial interests.

Supplementary information