Fig. S1

Positional homeostasis, extended characterization, related to Figure 1

(A) Positional homeostasis example, in which an example fish approximately stabilizes its location in a stochastic virtual water current.

(B) Positional homeostasis assay with a 30-s swim period in an example fish.

(C) Centered trajectories for N = 13 fish showing persistent convergence.

(D) Triple forward pre-displacement/backward pre-displacement assay. Example fish, showing converging trajectories, indicating successful integration across three consecutive pre-displacements. (Shaded regions: SEM in all panels.)

(E) Population data (14 fish) showing near-complete correction for earlier pre-displacement. (One-sample t test, ^∗∗∗p < 0.001, p = 9.7e−10 for forward pre-displacements, p = 1.9e−10 for backward pre-displacement. Error bars: SEM in all panels.)

(F) Assay to test integration over varying durations. An example fish successfully integrates pre-displacement and corrects for it in the swim period.

(G) Population data (4 fish) showing accurate correction, i.e., path integration. (Two-tailed paired t test, ^∗∗∗p < 0.001, p = 1.08e−7 for all forward pre-displacements.)

(H) Animals respond faster (slower) after a backward (forward) pre-displacement, consistent with Figure 1F. (Two-tailed paired t test, ^∗∗p < 0.01, p = 1.76e−3 for backward pre-displacement, ^∗∗∗p < 0.001, p = 3.1e−4 for forward pre-displacement.)

(I) Animals respond more vigorously after a backyard pre-displacement, consistent with Figure 1F. (Two-tailed paired t test, ^∗p < 0.05, p = 0.0151 for backward pre-displacement, n.s. p > 0.05, p = 0.115 for forward pre-displacement.)

(J) Total swim distance (normalized) corresponds to the earlier pre-displacement, consistent with Figure 1F. (Two-tailed paired t test, ^∗p < 0.05, p = 0.031 for backward pre-displacements, and p = 0.012 for forward pre-displacements.)

(K) After motosensory gain changes (high: ×1.5, low: ×0.5), animals still integrate position. Dashed lines: position of model fish performing gain adaptation (linear adjustment of vigor over 5 s) but no path integration. Solid lines: position of real fish.

(L) Swim vigor during low or high motosensory gain shows gain adaptation. (Two-tailed paired t test, ^∗∗∗p < 0.001, p = 1.6e−5.)

(M) Average fish position in low versus high gain trails initially diverges, then converges. Dashed lines: normalization to model fish performing gain adaptation but no path integration.

(N) Example trials during high and low motosensory gain (data from K–M) showing accurate positional homeostasis in both cases.