Supplementary Figure 2: Summary of responses in the horizontal plane with the animal upright

Of 95 cells tested with upright (Fig. 1a) and tilted (Fig. 1b,c) yaw rotations, 5 and 48 cells, respectively, exhibited significant tuning (at p = 0.01, permutation test on the resultant vector length). The 5 cells that responded significantly to rotations around an upright yaw axis, both in light and in darkness (permutation test on the resultant vector, p<0.01) and are classified as azimuth-tuned cells (filled symbols). (a) Resultant (R) vector length during rotation around an upright versus 30° tilted axis. Azimuth responses were weaker (mean R = 0.17 ±0.09 CI for these 5 cells) than responses during rotations around a tilted axis (mean R = 0.37 ± 0.06 CI, n=48, Wilcoxon rank sum test, p = 0.01) (b) Comparison between the resultant vector length during upright rotation in light and darkness. The R vector lengths are not significantly different (Wilcoxon signed rank test, p = 0.8, mean R = 0.15 ± 0.09). (c) Comparison between the Preferred Direction (PD) of cell responses during rotation around an upright versus a 30° tilted axis (computed relative to the visual reference frame). The difference in PD of azimuth-tuned cells was distributed uniformly during CCW (red) and CW rotations (blue) (circular R test p = 0.05 across both directions), indicating that tuning during upright and tilted yaw rotations were independent. (d) Comparison between PD during upright rotation in light and darkness. The difference in PD clusters around 0° (circular mean 0° ± 25° CI).

Using a less stringent criterion (at p = 0.05 on the Rayleigh vector, in either the CW or CCW direction), 34 cells passed the horizontal modulation criterion, 54 cells passed the gravity modulation criterion, and 31 had both. We also recomputed the histograms in c with the larger number (n=34) of cells that would be obtained with less strict criterion for Raleigh vector upright yaw tuning and found that they were not different from uniform (Chi square test, p>0.5 for both directions). Because responses during upright yaw rotation in the horizontal plane were comparatively weak, they have not been further considered here.