Generation of stable heading representations in diverse visual scenes.

Nomenclature We follow an abbreviation convention agreed upon by most research groups working in the central complex 51 : For compass neurons 33 , E (Ellipsoid Body) before ‘-’ represents predominantly spiny and putatively postsynaptic processes, and P (Protocerebral Bridge) and G (Gall) after ‘-’ represent predominantly bouton-like and likely presynaptic processes. Fully expanded, E-PG stands for PB G1–8 .b-EBw.s-D/Vgall.b 51 . Similarly, P-EN neurons ( Fig. 1 ), which arborize in the N (noduli), refer to PB G2–9 .s-EBt.b-NO1.b neurons 51 . Terminology In the manuscript, we use the term ‘heading representation’ to describe what the E-PG neurons encode. Note, however, that the representation often persists when a tethered fly is standing still on a ball 3 —that is, when it has no heading in a strict sense. Based on such data, we would define ‘heading’ as the angular orientation of the fly’s body-axis in a visual scene. Future experiments may well determine that E-PG neurons represent the head-direction of the fly, but all E-PG imaging experiments thus far, including those in this study, have been performed on head-fixed flies in tethered preparations, leaving this issue unresolved.

Fly stocks

Fly stocks were described previously 33 , 34 . Briefly, flies with either a codon-optimized UAS-GCaMP6f 52 or a recombinant of UAS-CsChrimson-mCherry-tag 53 and UAS-GCaMP6f or codon-optimized-UAS-GCaMP6f 52 were driven by split-GAL4 54 , 55 SS00096 from the Rubin lab. All experiments were performed with 6–10 day old female flies. Flies were randomly picked from their housing vials for all experiments. All flies were raised from the egg stage on standard cornmeal and soybean–based medium 56 or with additional 0.2 mM all- trans -retinal 53 for flies with CsChrimson. Fly preparation for imaging during head-fixed flight The procedure for fly preparation was described previously 33 . Briefly, flies were anaesthetized on a cold plate at 4°C. The front legs were removed and the proboscis was pressed into its head capsule and immobilized with wax to minimize brain movement. The fly was tethered at the tip of a tungsten wire and positioned under a custom-designed stainless-steel shim as previously described 13 , 57 , 58 . The back of the head capsule was kept nearly vertical to maximize exposure of the fly’s eyes to the surrounding LED arena. UV curable adhesive was used to fix the head under the shim, then the cuticle at the top of the head and fat cells were carefully removed and trachea were carefully pushed to the back of the brain to optically reveal the center brain.

Visual stimulation

Visual arena The hardware was described previously 33 . Briefly, a female fly was placed at the center of the arena and visual stimuli were presented on a vertically placed cylindrical LED display 59 spanning 330° in azimuth and 60° in elevation. The display was covered with multiple layers of color filter to avoid excessive leak into a photon detector and a diffuser to avoid reflection 3 , 13 , 57 . The wingbeat amplitude of each wing was computed online by analyzing images acquired with a camera, using custom-built image analysis software written in MATLAB, similar to a previously described method 58 . The image acquisition rate of the camera was 119.2 Hz, which was slow enough to capture the full shadow of wings to compute the wingbeat amplitude. For closed-loop experiments, the gain was 5.1°/s for each degree of the difference between the left and right wingbeat amplitudes (ΔWBA) 60 . Air was manually puffed at the fly if it stopped flying. The data during this stalled period was excluded from analyses. Stimuli We used various visual stimuli. Natural scenes were derived from panoramic photographs taken at the Janelia Research Campus. Utilizing the full luminance resolution of the arena resulted in excessive leak into a photon detector even after multiple layers of filters, making it impossible to detect bump position, especially with extremely low laser power used for simultaneous imaging and optogenetic stimulation. Further, the level of light at full luminance was enough to activate CsChrimson in most flies. To reduce the light leak and undesired activation of CsChrimson, we downsampled and monochromatized natural scene photographs ( Fig. 1h , i , 4a , and 5a ) to four luminance levels close to a log scale (0, 2, 6, and 15). Other visual stimuli include a bright vertical stripe spanning 60° in elevation and 15° in azimuth ( Fig. 3a , Extended Data Fig. 1b , 3b , 4d , and 4i ), two bright vertical stripes 165° apart ( Extended Data Fig. 3a ), a random dot pattern of which each pixel is either maximum bright or dark, and patterns containing four small horizontal bars each spanning 30° in azimuth and 15° in elevation ( Extended Data Fig. 5a , b ). Note that all the stimuli used in this study were presented on a blue LED arena. We used a gray scale in the figures for visual clarity. To avoid a sudden luminance change that might induce a startle response in flies, the 30° arena gap behind the fly was stitched in all protocols to maintain overall luminance. Thus, when an object crosses the gap, it does not disappear but jumps across it.

Protocols

Optogenetic bump offset shift

An experiment (14 flies, Extended Data Fig. 1b – d , i , and m ) began with a 1 min exposure to a closed-loop random dot stimulus (Trial 1). It was followed by three 1 min closed-loop single stripe trials (Trials 2–4), a 5 min optogenetic manipulation trial that imposes a fixed 90° offset between the bump and a scene (Trial 5), three 1 min closed-loop single stripe trials (Trial 6–8), another 5 min optogenetics trial with −90° offset (Trial 9), and two 1 min closed-loop single stripe trials (Trials 10–11). Each trial was followed by a 15 s dark trial before the next trial started. During optogenetic manipulation trials, eight positions in the EB, separated by 45° (with a visual stimulus of a corresponding offset), were sequentially stimulated, each of which took approximately 2–2.5 s. The initial position of the visual stimulus during closed-loop trials was random. Trial 2 was used for flies to establish a stable offset. Trials 3–4 and trials 7–8 were used to measure the baseline variability of the bump offset within a single fly before optogenetic manipulation. Trials 6–7 and Trials 10–11 were used to measure the baseline variability after optogenetic manipulation. Trials 4 and 6 were used to measure the effect of optogenetic manipulation in trial 5 (90° offset). Trials 8 and 10 were used to measure the effect of optogenetic manipulation in trial 9 (−90° offset). Control experiments (10 flies each) used the same order of trials except that either CsChrimson was not expressed ( Extended Data Fig. 1j and n ) or the stripe was not presented ( Extended Data Fig. 1k , o ) during manipulation trials. A natural scene was also tested ( Fig. 2a – d , Extended Data Fig. 1f , h , and l ). To increase statistical power, all data collected before or after the −90° protocol were rotated 180° and pooled with 90° protocol during analyses. Bump offset shift with two vertical stripes The order of trials was identical to optogenetic bump offset shift experiments, but, during manipulation trials, two stripes at opposite sides of the visual field (165° apart in the 330° arena) were presented under closed-loop control ( Extended Data Fig. 3d – i ). Trials 6 and 10 were used to measure the number of bumps and the bump offset variance for the initial 15 seconds after manipulation trials, and Trials 7 and 11 were used as control trials. 10 flies were tested.

Forced optogenetic inverse mapping

There were two 1-minute single stripe closed-loop trials followed by 10 minutes of an optogenetic inverse mapping trial and 2 minutes of a probe trial ( Fig. 3 ). Consecutive trials were separated by a 3 s dark trial. Natural scene protocols Two 2 min closed-loop trials with a downsampled and monochromatized forest scene were presented (Trials 1–2). They were followed by two 2 min closed-loop trials with an open-space scene (Trials 3–4), and all 4 trials were repeated (Trials 5–8). All consecutive trials were separated by a 5 s dark trial. The initial scene orientation of each trial was random. Trials 2 and 5 were used to measure the offset shift between two forest scene trials separated by open-space scene trials. Trials 4 and 7 were used to measure the offset shift between two open-space scene trials separated by forest scene trials. Trials 2 and 3 were used to measure the offset shift during the transition from a forest scene to an open-space scene. Trials 4 and 5 were used to measure the offset shift during the transition from an open-space scene to a forest scene. 10 flies were tested ( Fig. 1h , i , 5b and d ). The whole protocol was repeated for another pair of less reliable natural scenes (‘dense forest’ and ‘bush’, Fig. 5a , b , and d ). Finally, to address the relevance of 2D organization of the visual scene to the bump position computation, the same protocol was repeated with two scenes of 4 artificial objects: in each scene, four horizontal objects were presented with equal azimuthal separation and either the same or different elevations ( Fig. 5a , c and e ). Bump offset shift with limited optogenetic manipulation An experiment ( Fig. 4 , Extended Data Fig. 4 ) began with a 1 min closed-loop trial with a single stripe (Trial 1). It was followed by a 2 min closed-loop single stripe trial (Trial 2), a 30 s open-loop probe trial (Trial 3), a 5 min open-loop manipulation trial (Trial 4), a 30 s open-loop probe trial (Trial 5), a 2 min closed-loop trial (Trial 6), a 30 s open-loop probe trial (Trial 7), a 5 min open-loop manipulation trial (Trial 8), a 30 s open-loop probe trial (Trial 9), a 2 min closed-loop trial (Trial 10). All consecutive trials (except the probe trials following manipulation trials) were separated by a 3 s dark trial. The initial scene orientation of closed-loop trials was random. During Trial 2, the bump offset was roughly determined by visual inspection. Then a target offset was determined to be 180° away from this baseline offset and optogenetically imposed during manipulation trials. Three manipulation protocols were used (10 flies each). The first protocol (local protocol 1) spanned 60° of the EB, in which three positions separated by 30° were optogenetically stimulated. Each position was stimulated for 1.5 s-2.5 s in sequence. The probe trials were composed of the same visual stimuli used during optogenetics trials to measure the effectiveness of the optogenetic manipulation. The position of a stripe in closed-loop probe trials began at the middle of the range of stripe positions used during manipulation. The second protocol (local protocol 2) spanned 60° of the EB, in which three positions separated by 30° were optogenetically stimulated. Each position was stimulated for 1.5s-2.5s in sequence. During probe trials, two stripe positions (one at the center of the manipulated area and another 180° away from it) were repeatedly presented (each for 3 s) to probe the global effect of local manipulations. The position of a stripe in closed-loop probe trials was random. For further analysis, flies from the two protocols (1 and 2) were pooled ( Extended Data Fig. 4j and k ) and regrouped depending on the position of the bump and the stripe at the beginning of the probe trial. The last protocol (local protocol 3) spanned 180° of the EB ( Extended Data Fig. 4d ), in which eight positions separated by 22.5° were optogenetically stimulated. The same probe stimuli as local protocol 2 were used in addition to eight stripe positions separated by 45° to cover all orientations. The offset during probe trials was measured over the last 5 seconds. The last protocol was repeated with a natural scene ( Fig. 4 ). The position of the pattern, wingbeat amplitudes, air-puffing signal, and two-photon frame trigger were all simultaneously collected using custom software written in MATLAB that utilized National Instrument data acquisition hardware.

Two-photon calcium imaging

Calcium imaging was performed using a custom built two-photon microscope 61 . We used a 40x objective (NA 1.0, 2.8mm WD) and a GaAsP photomultiplier tube (PMT). A Chameleon Ultra II laser tuned to 930 nm with a custom-built pulse compressor was used as the excitation source with a maximum power of 8 mW at the sample. We used the same saline as in previous studies 3 with adjusted calcium concentration at 2.0 mM. We imaged the EB over 6-plane volumes using a fast remote focusing technique 62 , which was modified in-house, at a rate of 9.8 Hz volume rate (256×256 resolution, 58.8 Hz frame rate) with an equal spacing of 3–6 μm between individual scanning planes. The objective was tilted by 30° to enable imaging of the ellipsoid body with the fly’s head at a natural, vertical angle.

Two-photon optogenetic stimulation

The protocol used was largely along previously described lines 33 , but differed in a few details. A single two-photon laser source was used for both imaging and optogenetic stimulation, by temporally modulating the laser power, which was implemented using the PowerBox feature in ScanImage 61 replacing the custom MATLAB software described in previous work 33 ( Extended Data Fig. 1a ). Increased two-photon efficiency due to a pulse compressor allowed a lower laser power for imaging and optogenetic stimulation than previously described 33 . For the calcium-imaging-only period, a maximum laser power of 2 mW was used for both forward and backward scanning phases. During optogenetic stimulation of CsChrimson, the laser power was kept the same except for the defined stimulation area only during the forward scanning phase, where a maximum laser power of 30 mW (typically 20 mW) was used. To prevent tissue damage, this laser power was manually adjusted during each trial to a minimal power that was sufficient to develop a bump at the site of stimulation. On average, the optogenetically induced GCaMP signal measured during backward scanning phase was 13.3% greater than the normal condition across flies (one-tailed paired-ttest, p=0.022) in the optogenetic bump-shifting experiment with a natural scene. This higher than natural activity was required to inhibit the naturally generated bump. However, two vertical-stripe protocol results indicate that plasticity can be induced at the natural activity level.

Data analysis

We used MATLAB for data analysis. To avoid bias, no statistical methods were used to predetermine the power and the sample size. The fixed-offset optogenetic experiment used 14 flies, and the forced optogenetic inverse mapping experiments relied on 8 flies. All other experiments were performed until data from 10 flies was collected.

Calculation of fluorescence changes

The background noise level was predetermined by measuring the oscillatory noise from the PMT. This level was then subtracted from all imaging data, and the data was half-rectified before further analysis. A running average intensity projection of a volume (6 planes) at a given time was computed for each pixel. Then, 16 ROIs were manually assigned, as previously described 33 . Next, time series for each ROI were obtained by taking the average of the fluorescence signal within the ROI at each point in time. For calcium imaging experiments without optogenetics, ΔF/F0 was computed using F0 as the mean of the lowest 10% of signals in each ROI. No further temporal smoothing was applied. Population vector average (PVA) of a bump and its amplitude As a simple measure of the bump position and strength, the PVA was computed as the weighted vector average across EB wedges, with the weight determined by the fluorescence level (ΔF/F0), and the vector determined by the position of each ROI in the EB. The amplitude of the PVA was determined as the length of the average vector. We used brewermap (S. Cobeldick, MathWorks file exchange) with a color scheme ‘blue’ from http://colorbrewer2.org/ to depict all PVA plots.

Calculation of the number of bumps

For each frame, a bump was defined as any contiguous set of ROIs with ΔF/F0 greater than a threshold value (defined in each frame to be the mean ΔF/F0 across ROIs + 1 s.d.) 3 ( Extended Data Fig. 3h ). Offset between the estimated bump position and the pattern position, and offset deviation For a given trial, the first 15 seconds were discarded, as were time points when the fly did not fly, which were determined by the wingbeat amplitude. The offset between the absolute scene orientation (to the experimenter) and the PVA estimate was calculated as the mean angular difference for the remaining time. The deviation was calculated as the circular variance. Note that the visual arena, covering 330°, was mapped to 360°, as was the position of the scene.

Analysis of optogenetic offset manipulation trials

The exact artificial offset imposed by optogenetic stimulation during manipulation trials was determined by the mean angular difference between the scene orientation and the PVA during optogenetic stimulation.

Circular linearity test

For the optogenetic manipulation protocol, the expected amount of offset shift was assumed to be the same as the artificially imposed amount of shift. The sum of absolute angular difference between these two values across flies was used as a test statistic. To obtain the null distribution, the observed amounts of shift were randomized across flies and the sum of absolute angular differences was calculated, all of which was repeated 10,000 times. The p-value was calculated by counting the number of outcomes from randomization that were smaller than the test statistic ( Extended Data Fig. 1h – k ). Circular unimodality or circular asymmetricity test We used this test to determine if a set of directional data was significantly unimodal or asymmetric. The circular variance of the data was used as a test statistic. Each data point was assigned a random direction sampled from a circularly uniform distribution, after which the circular variance was calculated. This random assignment procedure was repeated 10,000 times to generate a null distribution. The p-value was determined by the number of times when the circular variance was smaller than the test statistic ( Fig. 1j , Extended Data Fig. 5c ). Note that this method only reliably works for unimodal data and may generate false negative results for multi-modal data. Bootstrap test of the mean difference This test was used to establish the difference of means of two datasets when they did not satisfy the assumption of Gaussian distributions. The difference of means of two data sets was used as a test statistic. Two sets of data were pooled, random samples were assigned to each group either with (bootstrap) or without (randomization) replacement, and the difference of means of two groups were calculated. This process was repeated 10,000 times to generate the null distribution. The p-value was computed by counting the number of events whose outcome was greater than the test statistic ( Extended Data Fig. 1l – o ). Note that random sampling both with and without replacement generated similar p-values in all tests in our study. Circular variance of pinning offset The variance in pinning offset relative to each scene ( Fig. 5b and c ) was computed as the circular variance of the instantaneous pinning offset along the time of a single trial. Each fly experienced 4 repetitions of two scenes. For each scene, all trials were pooled across flies (total 40 trials each). Circular variance of inverse map The circular variance (CV) of the bump offset during the probe trial was calculated for both normally arranged EB ROIs and inversely arranged EB ROIs. If the CV of the latter was smaller than the former, the mapping from the visual scene orientation to compass neurons was determined to be inverted ( Fig. 3d ). Binomial exact test For Extended Data Fig. 4j ; Baseline probability of flies shifting offsets by more than 90° is one out of seven if stripe starts outside manipulated positions (red dots). Assuming binomial sampling from this distribution, chance of six or more flies out of 13 shifting their offsets by more than 90° (blue dots) is p=0.0059. For Extended Data Fig. 4k ; Baseline probability of flies shifting offsets by more than 90° is three out of sixteen if stripe or bump starts outside manipulated positions (red dots). Chance of all four flies shifting offsets by more than 90° (blue dots) assuming binomial sampling with a probability of 3/16 is p=0.0012.

Natural scene analysis

Each scene was smoothed with a 2D Gaussian filter with a standard deviation of 4 pixels ( Extended Data Fig. 5e ). Then the 2D autocorrelation of each scene was calculated ( Fig. 5d ). Each scene was tiled horizontally (three copies) and the top and the bottom were padded with zeros. Then, Matlab function xcorr2 was applied to this tiled scene and another scene representing the center of this tiled scene. The middle range of azimuth values of the outcome (corresponding to the azimuthal range of one scene within the tiled image) was finally normalized by the maximum value to obtain 2D autocorrelation. The 1D autocorrelation was obtained by first taking the average intensity of the smoothed scene over elevation, then applying xcorr between this 1D trace and a concatenated version of this trace, and finally normalizing by the maximum value. 2D cross-correlation was computed in the same way except xcorr2 was applied to two tiled scenes: one scene with three horizontal copies of itself padded at the top and bottom, and another scene without horizontal copies but padded at the top and bottom.

Protocols

Optogenetic bump offset shift

An experiment (14 flies, Extended Data Fig. 1b – d , i , and m ) began with a 1 min exposure to a closed-loop random dot stimulus (Trial 1). It was followed by three 1 min closed-loop single stripe trials (Trials 2–4), a 5 min optogenetic manipulation trial that imposes a fixed 90° offset between the bump and a scene (Trial 5), three 1 min closed-loop single stripe trials (Trial 6–8), another 5 min optogenetics trial with −90° offset (Trial 9), and two 1 min closed-loop single stripe trials (Trials 10–11). Each trial was followed by a 15 s dark trial before the next trial started. During optogenetic manipulation trials, eight positions in the EB, separated by 45° (with a visual stimulus of a corresponding offset), were sequentially stimulated, each of which took approximately 2–2.5 s. The initial position of the visual stimulus during closed-loop trials was random. Trial 2 was used for flies to establish a stable offset. Trials 3–4 and trials 7–8 were used to measure the baseline variability of the bump offset within a single fly before optogenetic manipulation. Trials 6–7 and Trials 10–11 were used to measure the baseline variability after optogenetic manipulation. Trials 4 and 6 were used to measure the effect of optogenetic manipulation in trial 5 (90° offset). Trials 8 and 10 were used to measure the effect of optogenetic manipulation in trial 9 (−90° offset). Control experiments (10 flies each) used the same order of trials except that either CsChrimson was not expressed ( Extended Data Fig. 1j and n ) or the stripe was not presented ( Extended Data Fig. 1k , o ) during manipulation trials. A natural scene was also tested ( Fig. 2a – d , Extended Data Fig. 1f , h , and l ). To increase statistical power, all data collected before or after the −90° protocol were rotated 180° and pooled with 90° protocol during analyses. Bump offset shift with two vertical stripes The order of trials was identical to optogenetic bump offset shift experiments, but, during manipulation trials, two stripes at opposite sides of the visual field (165° apart in the 330° arena) were presented under closed-loop control ( Extended Data Fig. 3d – i ). Trials 6 and 10 were used to measure the number of bumps and the bump offset variance for the initial 15 seconds after manipulation trials, and Trials 7 and 11 were used as control trials. 10 flies were tested.

Forced optogenetic inverse mapping

There were two 1-minute single stripe closed-loop trials followed by 10 minutes of an optogenetic inverse mapping trial and 2 minutes of a probe trial ( Fig. 3 ). Consecutive trials were separated by a 3 s dark trial. Natural scene protocols Two 2 min closed-loop trials with a downsampled and monochromatized forest scene were presented (Trials 1–2). They were followed by two 2 min closed-loop trials with an open-space scene (Trials 3–4), and all 4 trials were repeated (Trials 5–8). All consecutive trials were separated by a 5 s dark trial. The initial scene orientation of each trial was random. Trials 2 and 5 were used to measure the offset shift between two forest scene trials separated by open-space scene trials. Trials 4 and 7 were used to measure the offset shift between two open-space scene trials separated by forest scene trials. Trials 2 and 3 were used to measure the offset shift during the transition from a forest scene to an open-space scene. Trials 4 and 5 were used to measure the offset shift during the transition from an open-space scene to a forest scene. 10 flies were tested ( Fig. 1h , i , 5b and d ). The whole protocol was repeated for another pair of less reliable natural scenes (‘dense forest’ and ‘bush’, Fig. 5a , b , and d ). Finally, to address the relevance of 2D organization of the visual scene to the bump position computation, the same protocol was repeated with two scenes of 4 artificial objects: in each scene, four horizontal objects were presented with equal azimuthal separation and either the same or different elevations ( Fig. 5a , c and e ). Bump offset shift with limited optogenetic manipulation An experiment ( Fig. 4 , Extended Data Fig. 4 ) began with a 1 min closed-loop trial with a single stripe (Trial 1). It was followed by a 2 min closed-loop single stripe trial (Trial 2), a 30 s open-loop probe trial (Trial 3), a 5 min open-loop manipulation trial (Trial 4), a 30 s open-loop probe trial (Trial 5), a 2 min closed-loop trial (Trial 6), a 30 s open-loop probe trial (Trial 7), a 5 min open-loop manipulation trial (Trial 8), a 30 s open-loop probe trial (Trial 9), a 2 min closed-loop trial (Trial 10). All consecutive trials (except the probe trials following manipulation trials) were separated by a 3 s dark trial. The initial scene orientation of closed-loop trials was random. During Trial 2, the bump offset was roughly determined by visual inspection. Then a target offset was determined to be 180° away from this baseline offset and optogenetically imposed during manipulation trials. Three manipulation protocols were used (10 flies each). The first protocol (local protocol 1) spanned 60° of the EB, in which three positions separated by 30° were optogenetically stimulated. Each position was stimulated for 1.5 s-2.5 s in sequence. The probe trials were composed of the same visual stimuli used during optogenetics trials to measure the effectiveness of the optogenetic manipulation. The position of a stripe in closed-loop probe trials began at the middle of the range of stripe positions used during manipulation. The second protocol (local protocol 2) spanned 60° of the EB, in which three positions separated by 30° were optogenetically stimulated. Each position was stimulated for 1.5s-2.5s in sequence. During probe trials, two stripe positions (one at the center of the manipulated area and another 180° away from it) were repeatedly presented (each for 3 s) to probe the global effect of local manipulations. The position of a stripe in closed-loop probe trials was random. For further analysis, flies from the two protocols (1 and 2) were pooled ( Extended Data Fig. 4j and k ) and regrouped depending on the position of the bump and the stripe at the beginning of the probe trial. The last protocol (local protocol 3) spanned 180° of the EB ( Extended Data Fig. 4d ), in which eight positions separated by 22.5° were optogenetically stimulated. The same probe stimuli as local protocol 2 were used in addition to eight stripe positions separated by 45° to cover all orientations. The offset during probe trials was measured over the last 5 seconds. The last protocol was repeated with a natural scene ( Fig. 4 ). The position of the pattern, wingbeat amplitudes, air-puffing signal, and two-photon frame trigger were all simultaneously collected using custom software written in MATLAB that utilized National Instrument data acquisition hardware.

Natural scene protocols Two 2 min closed-loop trials with a downsampled and monochromatized forest scene were presented (Trials 1–2). They were followed by two 2 min closed-loop trials with an open-space scene (Trials 3–4), and all 4 trials were repeated (Trials 5–8). All consecutive trials were separated by a 5 s dark trial. The initial scene orientation of each trial was random. Trials 2 and 5 were used to measure the offset shift between two forest scene trials separated by open-space scene trials. Trials 4 and 7 were used to measure the offset shift between two open-space scene trials separated by forest scene trials. Trials 2 and 3 were used to measure the offset shift during the transition from a forest scene to an open-space scene. Trials 4 and 5 were used to measure the offset shift during the transition from an open-space scene to a forest scene. 10 flies were tested ( Fig. 1h , i , 5b and d ). The whole protocol was repeated for another pair of less reliable natural scenes (‘dense forest’ and ‘bush’, Fig. 5a , b , and d ). Finally, to address the relevance of 2D organization of the visual scene to the bump position computation, the same protocol was repeated with two scenes of 4 artificial objects: in each scene, four horizontal objects were presented with equal azimuthal separation and either the same or different elevations ( Fig. 5a , c and e ).

Supplementary Material 1 2 3 4 5 6 7 8 1541072_vdo1 1541072_vdo2 1541072_vdo3 1541072_vdo4