Figure 3.

Turning modulation around light transitions. (A) Value map of “lock-index” for correlation matrices (B,E,F,I,J). For a pair of consecutive turns, “locked” turns (2 turns in the same direction) populate the white diagonal (correlation), and “flipped” turns (2 turns in opposite directions) the black diagonal (anti-correlation). The lock-index ranges from −1 to 1, −1 being “flipped” (with identical turning magnitudes) and 1 being “locked.” (B) Correlation matrices for consecutive turns, data pooled from all 32 fish. Left panel: all pairs of consecutive turns in light. Most are small angle turns, and fish have a small bias for “lock.” Right panel: all pairs of consecutive turns in dark. Most large angle turns are “locked” in the same direction. Above each matrix: corresponding histograms of average lock-indices for each fish, calculated with (A). (C) Sample trajectory of Virtual Circle experiment. Traces after the fish reached the edge of the arena and before it returned to within the virtual borders are colored in light gray. (D) Distribution of duration of stimuli (Dark intervals or Light intervals, respectively), pooled from all fish. (E,F) Correlation matrices with corresponding histograms similar to (B), but for different specific categories of turns. (E) For 2 groups of turns around Light-to-Dark transitions, as indicated on axes. Note that the pair of turns surrounding the transition is “flipped,” and the pair immediately afterward is “locked.” (F) Similar to (E), but for turns around Dark-to-Light transitions. (G,H) Playback experiment: visual stimuli from VC assay (Dark Flashes) played-back to naïve fish (see text). (G) Sample trajectory of the playback experiment. (H) Actual distribution of stimuli duration of the playback experiment, from 27 fish. (I,J) Compare to (E,F), but from the playback experiment. The similarity to (E,F) indicates that the lock-flip tendencies do not depend on a specific geometry of the virtual border. (K) Illustration of a model in which both “lock” and “flip” turns tend to lead the fish back toward the virtual border. (L) Example session from a simulation (displayed as in Figure 2D) that implements both Algorithm I [Angle] (from Figure 2B) and Algorithm II [Lock/Flip] (from B,E,F). (M) The average probability of returning to light within 3 bouts (expansion of Figure 2E). Compared between real fish (n = 32) and the two simulations (n = 100 each). Simulations are labeled by the algorithms implemented: “A” = Algorithm I [Angle], “LF” = Algorithm II [Lock/Flip]. [Mean ± s.e.m, ^*p < 0.001 (paired t-test) for all pairs.]. (N) Probability that a fish returns to light within n bouts, mean ± s.e.m plotted as a function of n, color-coded as in (M).