Fig. 4. Tracking of heading angle does not depend on visual feedback but may incorporate eye gaze direction.

a, Slope of the regression between estimated heading and network phase in closed-loop and open-loop epochs (closed-loop median = −0.579, Q₁ = −1.34, Q₃ = −0.257 versus open-loop median = −0.595, Q₁ = −1.1, Q₃ = −0.37; P = 1.00, two-sided Wilcoxon signed-rank test, n = 8 fish). Colored marks indicate median and the Q₁–Q₃ range. b, Slope of the regression between heading and network phase in different gain conditions; comparison was not significant between any of the conditions (two-sided uncorrected Wilcoxon signed-rank test, n = 5 fish). Colored marks indicate median and the Q₁–Q₃ range. c, Distribution of directional swim-related ROIs (n = 31 fish). All ROIs from all fish are shown in gray, r1π neurons are shown in pink, neurons showing high correlation (more than 0.7) with left and right turning are shown in blue and orange, respectively. d, Example of a recording showing the contribution of gaze direction to the network signal when the fish is not swimming. Network phase (green) represented with the (inverted) heading direction (golden) and gaze direction (orange). The arrow highlights a period of no swimming and large saccades.