Extended Data Fig. 5: Supplementary figures and additional evidence that direction sensing is enacted using a correlation-based algorithm.

a, Schematic illustrating calculation of latency \(\Delta T\) between antennae hits for moving edges. Correlation-based models for direction selectivity depend on the latency \(\Delta T\) of the time at which the edge hits the two sensors – in this case, the fly’s two antennae. Measuring \(\Delta T\) does not require resolving the image or stimulus at antennal resolution (~300 \(\mu \)m), rather \(\Delta T\) can be inferred with knowledge of the fly’s orientation relative to the bar direction \(\varphi \), as well as the speeds of the fly and bar – all of which are known. See Methods for details of the calculation and an estimate of the uncertainty. b, Spatiotemporal correlation functions for correlated noise stimuli (Fig. 4c–f). Each type of correlated noise stimulus is characterized by the correlation function \(C(\Delta x,\Delta t)\) computed between all pairs of bars separated spatiotemporally by \(\Delta x\) pixels and \(\Delta t\) frames. Since our stimuli are generated by summing and binarizing Gaussian variables, nonzero correlations off of the origin have magnitude 1/3²⁶. For example, for positively correlated with-wind stimuli (top left plot), \(C\left(1,1\right)=C\left(-1,-1\right)=1/3\), and the remaining correlations are zero, while for negatively correlated with-wind stimuli (bottom left plot), \(C\left(1,1\right)=C\left(-1,-1\right)=-1/3\). c, Snapshots of glider stimulus with correlations along \(+x\) axis, for 3 consecutive frames. In one instance of time, the stimulus is a random pattern of light and dark 1-pixel-wide bars perpendicular to the 150 mm s⁻¹ laminar wind. Each \(x\)-pixel is perfectly correlated with the pixel to its right in the next frame; thus the pattern in the next frame is the same as the pattern in the current frame, but shifted by one pixel. Visually, this would be perceived as a fixed pattern moving coherently to the right in discrete steps. d, Like correlated noise stimuli, gliders are defined by their correlation matrix \(C(\Delta x,\Delta t)\). Unlike correlated noise, the correlations i) have magnitude 1, and ii) exist for many spacetime points. That is, for rightward correlated gliders, a given pixel in a given frame is perfectly correlated with the pixel to its right one frame later, but also with the second pixel to its right 2 frames later, etc. Thus \(C(\Delta x,\Delta t)\) has values +1 along the diagonal. Similarly, \(C(\hspace{-.25mm}-\hspace{-.25mm}\Delta x,\Delta t)\) has values 1 along the anti-diagonal. Since \(+x\) points downwind, we call gliders with correlations to the right “with-wind”, and gliders with correlations to the left “against-wind,” in analogy to the correlated noise stimuli (Fig. 4d). e, Turning bias versus fly orientation for with-wind (blue) and against-wind (red) gliders. Data using pattern update rates of 45 or 60 Hz are pooled. Shaded errors: SEM. Gliders are presented in 4s blocks, interleaved with 4s of no stimulus. Turning bias is defined as the sign of the change in orientation from 200 to 500 ms after the block onset. We only used flies with speeds < 12 mm s⁻¹ for gliders, since long-range correlations can interfere with the intended correlation if fly walking speed is near the glider speed. n = 301, 247 onset events, for with-wind and against-wind, respectively. f, Turning bias averaged over all orientations for different glider speeds. Glider speed is calculated as (pixel width)\(\times \)(pattern update rate) where the pixel width is 290 µm and the pattern rate is some multiple of the inverse frame rate, 1/(180 Hz). n = 141, 163, 138, 190 onset events for with-wind stimuli at glider speeds 25, 16, 12, and 10 mm s⁻¹, respectively; n = 159, 119, 128, 137 onset events for against-wind stimuli at same glider speeds, respectively. g, For correlated stimuli to be sensed in our assay, the bar width (size of \(x\)-pixel, 290 µm), must be on the order of the fly antennal separation (\(\sim \)300 µm⁵⁸). h, Glider stimuli experiments repeated for bars that were double the width, 580 µm. Differences now disappear for with and against-wind correlations, consistent with bilaterally enabled direction sensing, since these bars are too wide to consistently stimulate antennae differentially. Shaded errors: SEM. n = 195, 169 onset events for with-wind and against-wind, respectively.

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