Extended Data Fig. 12: Fast representational sequences around turns and echolocation.

a, Top: Example flights with turns, shown in top view. The colour at each position indicates the local 3D curvature. Grey triangles mark the turn point, defined as the location of maximum curvature (Methods). Bottom: Distribution of maximum curvature across flights (n = 1,354 flights from 22 sessions, 6 bats). The vertical line denotes the threshold value of 1 m⁻¹ used to distinguish loops from straight flights. b, Top: Distribution of representational sequence (sweep) occurrence within a [−1, 1] s window around detected turns (n = 122 automatically detected sweeps, 18 flights with turns, 6 sessions, 5 bats; median turn time from start/stop of flight: 1.9 s/1.7 s). Black line shows the kernel density estimation. Bottom: Average echolocation rate, velocity and curvature aligned to the turn point (n = 274 flights with turns from 10 sessions, 4 bats). Thick lines represent the mean; shaded areas denote s.e.m. c, Average echolocation rate across normalized flight phase (%; 0 = take-off, 100 = landing) for straight flights versus loops (n = 880 straight flights from 16 sessions, 4 bats; n = 274 flights with turns from 10 sessions, 4 bats). Each echolocation trace was normalized to its maximum value before averaging. Note the transient increase in echolocation rate near the midpoint of loops. Thick lines indicate mean; shaded areas denote s.e.m. d, Average decoding error (top) and echolocation rate (bottom) across wing-beat cycles from straight flights (n = 591 straight flights from 15 sessions, 4 bats). Traces are aligned to the phase of the wing-beat and split into cycles with (blue, n = 3,451 cycles for whole flight, n = 1,712 for 1st half) versus without (red, n = 6,184 cycles for whole flight, n = 3,166 for 1st half) echolocation. Plots on the right include only wing-beat cycles from the first half of flights. Solid lines indicate mean; shaded areas indicate s.e.m. Note the reduction in decoding error during cycles with echolocation. e, Average echolocation rate in a [−40:40] ms window around observed sweeps versus randomly selected time points (two-sided Wilcoxon sign rank test, n = 1,214 sweeps, 4 bats; Methods). Bars indicate the mean, error bars are s.e.m.