The Strategy of Predator Evasion in Response to a Visual Looming Stimulus in Zebrafish (Danio rerio)

Synopsis A diversity of animals survive encounters with predators by escaping from a looming visual stimulus. Despite the importance of this behavior, it is generally unclear how visual cues facilitate a prey’s survival from predation. Therefore, the aim of this study was to understand how the visual angle subtended on the eye of the prey by the predator affects the distance of adult zebrafish (Danio rerio) from predators. We performed experiments to measure the threshold visual angle and mathematically modeled the kinematics of predator and prey. We analyzed the responses to the artificial stimulus with a novel approach that calculated relationships between hypothetical values for a threshold-stimulus angle and the latency between stimulus and response. These relationships were verified against the kinematic responses of zebrafish to a live fish predator (Herichthys cyanoguttatus). The predictions of our model suggest that the measured threshold visual angle facilitates escape when the predator’s approach is slower than approximately twice the prey’s escape speed. These results demonstrate the capacity and limits to how the visual angle provides a prey with the means to escape a predator.

In the analysis outlined in Methods, we considered the maximum possible value for a sensory cue to bound the theoretical possibilities. To find the maximum value for the threshold rate of change for the visual-angle, we solved Eqn. 2 where t thresh = −t lat to yield the following relationship: θ thresh max = 4wu w 2 + 4t 2 lat u 2 . (S1) Finding the escape distance for a threshold value of the visual-angle rate required consideration of the timing of the escape. For this, we solved Eqn. 2 for the visual angle as a function of time (θ(t)), zero equal to the time-to-collision, and negative time values on the approach. Using this equation, we found the first-derivative of the visual angle with respect to time to calculate the time at which the threshold-stimulus angle rate was reached: The distance between the predator and prey was calculated (d resp = −u(t thresh + t lat )) for the moment at which the prey initiated their escape at varying threshold values.
As performed for the visual angle (Fig. 3), we determined the threshold values for the latency and visual-angle rate of change in response to an artificial stimulus (Fig. S1). We calculated the visual-angle rate of change discretely from measurements of the visual angle that were smoothed with a spline (the 'spaps' function in MATLAB). This entailed finding the best fit to the unity line over a range of values (15.3 deg s −1 < θ thresh < 27.5 deg s −1 , 17 < N < 26) that corresponded to the average of values for latency (830 ms < t lat < 850 ms) that were about one-tenth of a second longer than obtained for the visual angle.
The behavioral responses to the artificial stimulus was tested against experiments with a live predator. The results for the threshold visual-angle rate of change found variation between quartiles of -481.6 deg s −1 and 511.1 deg s −1 in response to the live predator ( Fig. S2B). This wide range of variation included all the values measured in response to the projected stimulus with a high coefficient of determination (15.3 deg s −1 < θ thresh < 27.5 deg s −1 ). This indicates general agreement between the results of the two types of experiments and is consistent with previous estimates of 24.6 deg s −1 (t lat = 0 ms) (Dill, 1974).
We modeled the kinematics of predator and prey where the prey responds to a threshold value of the rate of change in the visual angle. Simulation results suggested that zebrafish escaped at a minimum distance that shows a low likelihood of escape, regardless of the predator's speed (Fig. S3). This suggests that the visual-angle rate of change does not offer a robust sensory cue for successful evasion, which is unlike what is predicted for the visual angle (Fig. 5). Figure S1: Determination of the threshold visual-angle rate of change for experimental responses to the projected looming stimulus. (A-C) Relationship between the stimulus and response times, assuming three different values for the threshold visual angle rate. As described in the present manuscript (Fig. 3), this relationship should conform to a slope of unity and yintercept equal to the latency predicted for each value of the threshold-stimulus angle rate.
(D) The coefficient of determination for the unity-line fit for each value of the thresholdstimulus angle rate, (E) the corresponding latency, and (F) sample size (blue). We selected values for latency and the threshold visual-angle rate of change where the coefficient of determination was relatively high (gray bar) for comparison with responses to a live predator (Fig.  S2).    (Fig. S2) the horizontal bars (light gray) indicate distance values where the prey have a low probability of escape (d min < 2 cm). Calculations were performed for predators of variable relative speed (K = 0.5, K = 1.5, and K = 3.0). Calculations were performed for a relatively wide predator (w = 5.00 cm, A-C) and a relatively narrow predator (w = 1.25 cm, D-F). (G-H) The minimum distance as a function of relative predator speed at particular values of the thresholdstimulus angle rate (θ thresh = 21 deg s −1 ) for a relatively wide predator (w = 5.00 cm, G) and a relatively narrow predator (w = 1.25 cm, H).