Fig 1.
Average scoring of three behavioral metrics for real experiments.
(A-B) Rheotactic metrics taking values between −1 and 1 corresponding to biased headings downstream and upstream, respectively. (C) Spatial entropy, measuring the exploratory behavior across the test section. The average was taken over the entire time series of 9, 000 points for each experimental subject. The gray bar in each violin plot details median (white dot), first and third quartiles, and lower and upper adjacent values. The colored area of a violin plot corresponds to the probability density of the data. Symbols *, ** and *** indicate significant differences from zero with p < 0.050, p < 0.010, and p < 0.001, respectively. Symbol $$$ indicates significant difference between conditions with p < 0.001.
Fig 2.
Modeling zebrafish swimming in a flow as a finite-dipole.
is the profile of the uniaxial background flow. The black dot and arrow denote the fish centroid position (x(t), y(t)) and heading angle θ(t), with respect to the global reference frame (
). The green and red dots represent the left and right location of the vortices of circulation strengths Γl(t) and Γr(t), respectively.
Fig 3.
Hydromechanical feedback mechanism.
(A) Example of rotation induced by a parabolic flow; the red circle of radius r is the approximation used for the fish perimeter in the computation of the local circulation of the background flow. (B) Block diagram describing the feedback mechanism to orient in the flow and perform rheotaxis.
Fig 4.
Calibrated model parameters for conditions Bright and Dark.
(A) Linear rate of decay of the vortex strengths. (B) Baseline value of the vortex strengths. (C) Intensity of the noise added to the time-evolution of vortex strengths. (D) Coupling gain between vortex strengths associated with the ability of a fish to resume straight swimming after a maneuver. (E) Hydrodynamic feedback gain. (F-G) Rates of transitioning from dismissing to using information about the local circulation and vice versa. The gray bar in each violin plot details median (white dot), first and third quartiles, and lower and upper adjacent values. The colored area of a violin plot corresponds to the probability density of the data. Symbol $$ indicates a significant difference between conditions with p < 0.010.
Fig 5.
Average scoring of three behavioral metrics for in-silico experiments.
(A-B) Rheotactic metrics taking values between −1 and 1 corresponding to biased headings downstream and upstream, respectively. (C) Spatial entropy, measuring the exploratory behavior across the test section. The average was taken over synthetic time series of 9, 000 points for each experimental subject. The gray bar in each violin plot details median (white dot), first and third quartiles, and lower and upper adjacent values. The colored area of a violin plot corresponds to the probability density of the data. Symbol $$$ indicate significant difference between conditions p < 0.010, respectively.
Fig 6.
(A) Overview of the experimental apparatus. (B,C) U shape-like honeycomb grids for straightening the flow in the water channel. (D) Measurements of the flow velocity profile (black circles) and parabolic fit (black dash line) at the mid-span using laser Doppler velocimetry, along with the parabolic fit of flow profile from fish locomotion (solid red line).
Fig 7.
Illustration of the wall calibration process.
(A) Two-dimensional projection of the difference of vortex strengths Γl − Γr, as a function of the projected distance, d, and angle to collision, φ, for one trial from Bright. The black curve is a normal function utilized to select relevant values of (φ, d) associated with those instances when the fish turns according to the angle to collision ϕ. (B) Example of calibration of the wall function. Black dots correspond to Gϕ and green dots correspond to the filtered output of |Gϕ|. The red line is the fitted wall function.
Table 1.
Calibrated wall parameters for the 12 fish tested in standard illumination (condition Bright).
For experiments in the dark, KW is set to zero and this form of interaction is absent.