Prey fish possess a remarkable ability to sense and evade an attack from a larger fish. Despite the importance of these events to the biology of fishes, it remains unclear how sensory cues stimulate an effective evasive maneuver. Here, we show that larval zebrafish (Danio rerio) evade predators using an escape response that is stimulated by the water flow generated by an approaching predator. Measurements of the high-speed responses of larvae in the dark to a robotic predator suggest that larvae respond to the subtle flows in front of the predator using the lateral line system. This flow, known as the bow wave, was visualized and modeled with computational fluid dynamics. According to the predictions of the model, larvae direct their escape away from the side of their body exposed to more rapid flow. This suggests that prey fish use a flow reflex that enables predator evasion by generating a directed maneuver at high speed. These findings demonstrate a sensory-motor mechanism that underlies a behavior that is crucial to the ecology and evolution of fishes.
Predation is fundamental to the biology of fish predators and prey. From the earliest stages of growth, prey fish survive attacks by fish predators with the ‘fast-start’ escape response (Fuiman and Magurran, 1994). Although this maneuver displaces a larval fish by less than a body length (Kimmel et al., 1974), it is effective because of limitations inherent to the predatory strike. Predator fish commonly use suction feeding, where the prey is targeted by low pressure created through the rapid expansion of the mouth cavity. This is effective over a small region directly in front of the mouth for a brief period (Kimmel et al., 1974; Day et al., 2007). Therefore, prey survive by escaping just beyond the limited reach of a predator.
It is unclear how the sensory systems of prey fish operate quickly enough to coordinate an evasive maneuver. The visual system can recognize a predator at a distance (Dill, 1974), but requires substantial neuronal processing that can delay an escape. For example, it takes most zebrafish (Danio rerio) larvae at least 200 ms to react to a visual stimulus (Burgess and Granato, 2007), which is about an order of magnitude longer than the duration of mouth opening during suction feeding (Wainwright et al., 2001; Day et al., 2007). In contrast, prey fish can respond to a flow stimulus in less than 4 ms (Liu and Fetcho, 1999) and thereby escape before the predator opens its jaws (Stewart et al., 2013). Flow sensing is achieved by the lateral line system, which includes mechanoreceptors with hair cells in the skin (Dijkgraaf, 1963). An experimental ablation of these cells causes larval fish to fail to survive predatory attacks, even when the visual system is unimpaired (Stewart et al., 2013). Therefore, the lateral line is necessary for survival, but it remains unclear what role flow sensing plays in coordinating an escape.
Here, we present results that demonstrate how predator evasion is facilitated by the lateral line system. This was determined by behavioral experiments that exposed larval zebrafish in the dark to the controlled flow generated by a predator robot. This flow, known as the bow wave (Holzman and Wainwright, 2009), was measured by flow visualization and modeled with computational fluid dynamics. We examined the three-dimensional high-speed responses of larvae in relation to the bow wave. Furthermore, we compared our observed fast-start responses with the results of several behavioral algorithms that mathematically predicted the direction of fast starts. The results of these approaches suggest that prey survive by evading the predator with a directed reflex that is stimulated by the bow wave.
We exposed larval fish to the flow generated by the motion of a robotic predator. This robot consisted of a motor-driven translation stage that propelled the body of a dead adult zebrafish through the center of a water-filled tank that contained zebrafish larvae in the dark (see the Materials and methods for details). Using infrared illumination, two video cameras recorded the behavioral responses of larvae that were not mediated by vision. Under these conditions, we found the robot provided a mimic of the predator that was sufficient to consistently stimulate a fast start. All larvae along the predator's path (N=202) responded within 2 cm to the predator's approach with a fast start (Fig. 1; supplementary material Movie 1). The approach speed of the predator significantly affected the response distance of the prey (Fig. 2; one-way ANOVA, d.f.=2, N=198, P<<0.01), with larvae approached at high speed (20 cm s–1) responding from slightly greater distances than larvae approached at 2 or 11 cm s–1 (Tukey–Kramer multiple comparison method for unequal sample sizes, P<0.05) (Dunnett, 1980).
The vast majority of fast-start responses were directed away from the robotic predator. We found that the fast start increased distance from the initial position of the predator in 96% of larvae (N=202). Larvae positioned to the side of the predator robot generally moved laterally, irrespective of approach speed. This was indicated by larvae positioned at least 0.5 cm lateral to the body axis of the predator exhibiting a median azimuth (±1 median deviation) of 59.2±48.8 deg (N=14), 69.2±30.6 deg (N=16) and 47.5±35.8 deg (N=20), respectively, for approach speeds of 2, 11 and 20 cm s–1 (Fig. 1C). Similarly, larvae positioned ventral to the predator directed the fast start downward, irrespective of the predator's approach speed (Fig. 1D). Therefore, responses were directed in both azimuth and elevation. Larvae positioned directly in front of (Fig. 1C), or dorsal to (Fig. 1D), the predator swam away in a variety of directions.
The lateral line system was manipulated to determine whether these responses were mediated by flow sensing. We found that larvae with a compromised lateral line system failed to respond to an encounter with our robot. In particular, 30 larvae positioned directly on the path of the robot's motion were swept aside without exhibiting any swimming in response (e.g. supplementary material Movie 2). This suggests that the fast start of untreated fish (Fig. 1) was mediated by the lateral line system.
Computational fluid dynamics
We developed a computational fluid dynamics (CFD) model of the flow generated by the predator's motion (Fig. 3A) to understand the flow stimulus to which larvae were exposed in our behavioral experiments. We tested this model by comparing its flow field predictions against flow visualization measurements by particle image velocimetry (PIV). Because of limitations in the sensitivity of the PIV measurements, we focused this comparison on regions in the flow field that exceeded 0.5 cm s–1 in the bow wave and where larvae responded to the predator (Fig. 1). We found that the PIV and CFD flow fields agreed in the qualitative spatial pattern of flow (Fig. 3B) and that the values for flow speed were similar. The average difference between the PIV and CFD speeds at each position was less than 7% for all approach speeds. Therefore, there was good agreement between the model and flow visualization.
Our examination of the bow wave predicted by CFD found that flow speed was roughly proportional to the speed of a predator's approach. Therefore, the ratio of flow speed to approach speed was similar for all approaches (Fig. 3E) with a spatial pattern characterized by rapid attenuation of speed with distance ahead of the predator. To examine the dependency of the bow wave on Reynolds number, we conducted simulations with an ideal (i.e. inviscid) fluid. This condition yielded a wake behind the body that contrasted what was predicted for realistic Reynolds numbers due to viscous effects (Fig. 3C,D). Despite this difference, the bow wave flow was largely similar (Fig. 3E). The only substantial deviation between viscous and inviscid simulations was apparent within 2 mm of the predator's rostrum, where the boundary layer influences the profile of the bow wave. Larvae rarely responded to flow in this close proximity (Fig. 1). Therefore, the bow wave flow field is largely independent of Reynolds number for the range of values presently considered (Re>450).
We combined the results of CFD simulations and our behavioral experiments to consider how larvae use spatial cues in the bow wave to direct a fast start. The azimuth angle of the mean flow velocity along the length of a larval body was not found to be significantly correlated with the azimuth of the fast start (Fig. 4, P=0.29, N=203). Therefore, larvae did not align their response with respect to flow velocity. However, we did find that larvae consistently directed their fast start away from rapid flow when we transformed the flow field with respect to the larva's local frame of reference (Fig. 5A,B). By this transformation, all positive azimuth angles indicated responses away from the side of the body exposed to flow of higher velocity for approach speeds of 2 cm s–1 (109.0±55.8 deg, N=45), 11 cm s–1 (98.7±54.7 deg, N=60) and 20 cm s–1 (87.8±36.6 deg, N=44). These values indicate that the median response was directed at an approximate right angle in azimuth with respect to the initial orientation of the body for the approach for the two faster approach speeds (Fig. 5C). The consistency of this response occurred despite large differences in the flow encountered by larvae in different positions and orientations. A more subtle directional response was measured in elevation. Larvae did not direct responses in elevation when the ventral surface of the body was exposed to more rapid flow (Fig. 6A). However, more rapid flow on the dorsal surface directed responses slightly downwards (Fig. 6B) for approach speeds of 2 cm s–1 (–11.2±15.2 deg, N=25), 11 cm s–1 (–14.1±20.9 deg, N=28) and 20 cm s–1 (–24.0±20.7 deg, N=18).
Behavioral algorithm modeling
We tested whether our measurements were consistent with the predictions of particular behavioral algorithms. Predictions were determined for each measured position and orientation for the bodies of larvae that responded to the robotic predator (Fig. 1A,B). We modeled the flow reflex as a response directed normal to the initial orientation of the body, away from the side of the body exposed to the faster maximum flow speed (Fig. 7B). This algorithm predicted responses that were statistically indistinguishable (P>0.05, N=117 for medial, N=76 for lateral positions) from our measurements, according to the non-parametric Kuiper test (Batschelet, 1981). Another algorithm found to be indistinguishable from our measurements also directed the fast start away from the side of the body exposed to rapid flow, but at a random angle with respect to the initial body orientation (Fig. 7C). In contrast, we found highly significant differences (P≤0.001) when the response was directed toward the side of the body exposed to rapid flow and a right angle (Fig. 7D) or in a completely random direction (Fig. 7E).
Our results suggest that prey fish evade predators by executing a directed fast start in response to the flow generated by the predator. These responses appear to be mediated by the lateral line because compromising this system in our experiments extinguished responses to a robotic predator's approach. In addition, the direction of the fast start (Fig. 1) was oriented away from high flow (Figs 5, 6) in a pattern that was consistent with responses to flow stimuli. These results support earlier findings that flow sensing plays a major role in the survival of larval zebrafish prey (Stewart et al., 2013) and offers a basis for understanding a sensory-motor mechanism of predator evasion.
The direction of a fast start can influence its effectiveness in predator evasion. We found that larvae moved away from a predator's heading most successfully when positioned lateral (Fig. 1A,C) and ventral (Fig. 1B,D) to the predator. These responses are consistent with optimal evasion strategies predicted by differential game theory modeling (Isaacs, 1965). A previous application of this theory to fish demonstrated how prey that move much faster or much slower than a predator should execute a fast start at a right angle from the predator's heading to maximally increase their distance from the predator (Weihs and Webb, 1984). Consistent with this prediction, we found that larvae positioned lateral to the predator moved in a lateral direction (Fig. 1C). However, larvae also exhibited a wide range of responses, most of which were not clustered around this optimum. It is therefore possible that the flow created by a slow approach presents a relatively weak directional signal that fails to accurately inform the prey about the predator's heading.
Faster approach speeds by the robotic predator elicited responses that were more consistent with optimal strategy (Fig. 1C), which predicts that the azimuth angle decreases with approach speed (Weihs and Webb, 1984). In addition, larvae exposed to the two faster approaches moved with elevation angles that were more directed downwards than the slow approach (Fig. 1D). Therefore, larvae more effectively moved to evade the robotic predator when approached at a faster speed. This result may be due to a more intense lateral line stimulus generated by a faster approach (Fig. 3). According to this argument, faster flow serves to more effectively alert a prey to the predator's heading and thereby stimulates a consistently directed response. However, these patterns did not emerge for larvae positioned dorsal to (Fig. 1D), and in front of (Fig. 1C), the approaching predator.
Despite these consistencies with optimal strategy, our measurements do indicate some strategic limitations. Escape responses are most effective when unpredictable (Humphries and Driver, 1970; Weihs and Webb, 1984; Domenici et al., 2011) whereas we found the responses of larvae positioned lateral to a fast approaching predator to be consistent and therefore predictable (Fig. 1C). Furthermore, prey positioned in front of the predator consistently moved in the direction of a fast-approaching predator, where the predator might more easily overtake them (Fig. 1C,D).
The bow wave
Our results are consistent with idea that prey evade predators by initiating an escape in response to the flow generated by a predator's approach (Viitasalo et al., 1998; Kiørboe and Visser, 1999; Visser, 2001; Heuch et al., 2007; Casas et al., 2008; Holzman and Wainwright, 2009; Gemmell et al., 2014; Seamone et al., 2014). This flow field is commonly referred to as a ‘bow wave’, although it does not exhibit the oscillations that are typical of a wave and it is a distinct phenomenon from the surface waves of the same name. The submerged body of a predator does not produce the gravitational surface waves generated by a ship, but rather creates a flow disturbance as it moves forward (Fig. 3). In addition, the flow generated by a predator does not propagate freely like a wave, but instead dissipates quickly after the predator stops moving. Despite these potential complications, we know of no better term than ‘bow wave’ and therefore presently adopt this phrase.
We examined the bow wave for differences due to the Reynolds number of the predator. When normalized by approach speed, the flow velocity of the bow wave exhibited a similar monotonic decay with distance (Fig. 3E). Furthermore, a simulation with an inviscid fluid exhibited the same general pattern, despite differences in the wake posterior to the predator's body (Fig. 3C,D). The main discrepancy in the bow wave between viscous versus inviscid simulations was apparent within a millimeter of the predator's rostrum, where the viscous boundary layer was apparent. However, we found that the vast majority of prey responded to the bow wave outside this region (Fig. 1B), which suggests that the relevant stimuli may be attributed to a phenomenon that is essentially independent of the predator's Reynolds number. The bow wave therefore could be represented by a potential flow model that is easier to implement than the CFD model that we developed.
The flow reflex
We used the results of our CFD simulations to examine the flow conditions that succeeded in stimulating a fast start in prey fish. By the end of the fast start (i.e. completion of stage 2), larvae traversed about 90 deg from their starting orientation (Fig. 5C). The azimuth of this ultimate direction did not correlate well with the azimuth of flow velocity (Fig. 4), but larvae consistently moved away from the side of the body exposed to faster flow. Therefore, the ability of larval fish to move away from the predator (Fig. 1) appears to be a consequence of deciding to move to the left or right at an angle that does not depend on the flow stimulus. We will refer to this behavior as the ‘flow reflex’ (Fig. 8), which is a behavior that is consistent with previous reports of the escape response stimulated in larval fish by water flow (Blaxter and Fuiman, 1989; Liu and Fetcho, 1999; McHenry et al., 2009). The binary directionality of this behavior may explain its strategic failures discussed above. Therefore, the minimal sensory processing that facilitates the high-speed response might limit the ability of the flow reflex to direct an optimal escape.
We modeled behavioral algorithms to test whether our measurements agree with the flow reflex. In separate algorithms, the response direction was calculated at a right angle (Fig. 7B) or random angle (Fig. 7C) with respect to the body. Both models replicated the observed patterns of directional responses (Fig. 1A,C; Fig. 7A), but only when the responses were directed away from the side of the body exposed to rapid flow (Fig. 7D,E). Therefore, larvae move in a manner that is consistent with the flow reflex. However, responding at any particular angle with respect to the prey's body is not important in determining the overall direction of the response.
The flow reflex is consistent with our understanding of the neurophysiology of zebrafish larvae. Lateral line hair cells are innervated by a population of neurons that transmit encoded flow stimuli to command neurons for the escape circuit on the contralateral side of the body (Liao, 2014). This circuit accounts for the ability of flow on one side of the body to stimulate motion on the opposite side (Liu and Fetcho, 1999). Therefore, neurophysiological research on the escape circuit may aid our understanding of the mechanistic basis of predator–prey interactions.
In summary, the flow reflex offers a basis for understanding how interactions between predators and prey are mediated between fishes. It shows how a prey's survival depends on the hydrodynamics of flow stimuli, the sensitivity of the lateral line, the processing of flow cues by the nervous system and the motor control of the fast start. Future research in these areas of neuroscience and biomechanics will offer exciting perspectives for understanding what facilitates and constrains predator–prey interactions. These dynamics have the potential to play major roles in the ecology and evolution of a broad diversity of fishes.
MATERIALS AND METHODS
Zebrafish (Danio rerio Hamilton 1922) larvae served as the prey and adults as predators, as in previous experiments (Stewart et al., 2013). All zebrafish were bred from wild-type (AB line) colonies housed in a flow-through tank system (Aquatic Habitats, Apopka, FL, USA) that was maintained at 28.5°C on a 14 h:10 h light:dark cycle. The fertilized eggs from randomized mating were cultured according to standard techniques (Westerfield, 1993) and larvae were raised in an incubator in E3 embryo media (Brand et al., 2002). Only larvae that were 5 days post-fertilization were used in experiments, which included a total of 268 larvae (body length=0.40±0.038 cm, mean ± 1 s.d.).
Robotic predator experiments
A robot allowed us to replicate the hydrodynamics of a predator's approach toward prey fish with controlled motion (Fig. 9). The body of a formalin-fixed dead adult zebrafish served as the stimulus source, which was translated through the center of a water-filled tank (length×height× width=36×8×9 cm) that contained numerous larvae. The predator was held in place by a sting that was anchored to a sled that was free to glide along a rail system (high-speed 23 mm needle-roller carriages on 64 mm guide rails, McMaster-Carr, Santa Fe Springs, CA, USA) and was pushed by a magnetic-drive linear servo motor (model P01-23×160, LinMot Inc., Elkhorn, WI, USA) at constant speed. The sled additionally carried two high-speed video cameras (Photon Focus DR1, Norpix Inc., Montreal, CA, recording at 500 frames s–1 with 640×480 pixel resolution) that focused on the predator's head and region anterior to the predator (an area of 3.00×2.25 cm) from lateral (with the aid of a 45 deg mirror) and dorsal perspectives. The cameras recorded the motion of larvae contained within the tank as they encountered the robot. To remove the possibility of a visual response by larvae, experiments were performed in the dark under infrared (940 nm) illumination. This allowed larvae to be viewed using the IR-sensitivity of the cameras.
Larvae were acclimated to the tank prior to an experiment. We placed between 100 and 200 zebrafish larvae in the tank, which contained water held at 27°C. The preserved predator was positioned in the center of the tank at one end of the chamber. After a 20 min acclimation period, the predator was translated through the tank at one of three randomly selected approach speeds. The three speeds (2, 11 or 20 cm s–1) spanned the range of measured values for adult zebrafish when preying on larval zebrafish (Stewart et al., 2013). This process was repeated after returning the predator to its starting position, where it remained stationary for 5 min before another experiment commenced. Any prey within view of both the lateral and dorsal cameras was considered to be ‘approached’ by the predator. Preliminary experiments established that prey located outside the field of view of the cameras were positioned at least 1.25 cm away from the axis coincident with the predator midline and did not exhibit any response to the robot. To minimize repeated measures from the same larva, experiments on a group of prey ceased once the number of recorded escape responses tallied 15% of the total number of prey within the chamber. Prey responses were excluded if they occurred during the brief duration (<0.25 s) when the predator was changing speed at the start or end of translation. For this study, we included a total of 82, 80 and 76 recordings of prey that were respectively approached at 2, 11 and 20 cm s–1.
We conducted an additional set of behavioral experiments to test the role of flow sensing in prey responses. This was achieved by compromising the lateral line in a group of larvae by exposure to a 250 μmol l–1 solution of neomycin sulphate for a 30 min period, followed by a 1 h recovery prior to experiments. This technique was developed in previous studies (Harris et al., 2003; McHenry et al., 2009), where it was shown to induce cell death in lateral line hair cells while leaving inner ear hair cells intact. In total, 200 prey with an ablated lateral line system were placed in the chamber for experiments, which resulted in 30 recordings of the robotic predator approaching treated prey.
We measured the location and direction of the fast start of larvae from our video recordings as a basis for determining the flow stimulus that triggers and directs this behavior. We used custom software developed in Matlab (v.2012b, with the image processing toolbox, MathWorks, Natick, MA, USA) to digitize three points along the prey body (rostrum tip, center of mass, tail tip) from both the dorsal and lateral images (Matlab datasets are available on request from M.J.M.). The body's center of mass was estimated as the midpoint between the prey's rostrum and the posterior margin of the swim bladder, which is consistent with prior work (Stewart and McHenry, 2010). A fast start was identified by the body rapidly (<15 ms) curling into a C shape, which is characteristic of stage 1 of this behavior (Weihs, 1972; Kimmel et al., 1974). We obtained body coordinates for the video frame prior to the initiation of stage 1 (i.e. the initial position). These coordinates were additionally recorded for the frame at which larvae completed stage 2 (when the body unfurls from a C shape) of the fast start, which was interpreted as the time at which the maneuver was completed. This frame was identified as when the tail reversed back to the direction of bending in stage 1. These landmark positions were transformed with respect to a coordinate system that was defined relative to the predator. Its origin was located at the anterior margin of the predator's rostrum, the x-axis was defined by the approach heading, and the z-axis as the opposite direction from gravity. Following the convention for a right-handed system, the y-axis coordinates were positive to the left of the predator and negative to the right. The response direction was characterized by the azimuth and elevation angles of the center of mass at the end of stage 2, relative to the initial position and accounting for the translation of the cameras. We verified that the direction established by the end of stage 2 was indicative of subsequent swimming in pilot experiments on 15 larvae where we recorded the direction of swimming over a wider field of view.
We scored the effectiveness of each fast start by whether it moved a larva away from the predator's heading. Responses directed ‘away’ from the predator occurred when the prey increased the distance separating the prey center of mass and the axis of the predator's heading between the start of the response and the end of stage 2. Conversely, responses were scored as being directed ‘toward’ the predator if the distance to the heading decreased during this time span. We additionally calculated the median values for azimuth and elevation, implemented the Circular Statistics Toolbox for Matlab (Berens, 2009). We also calculated the mean deviation, which is a metric of variation about a median value in circular statistics (Fisher, 1993).
We investigated whether the prey's position relative to the predator influenced the direction of a response. The elevation angles for responses were determined for prey that responded at positions dorsal to the heading axis of the predator (i.e. z>0) and those ventral to this axis (i.e. z<0). We considered the azimuth angles of responses by rectifying the y-values of response positions, which effectively created a mirror image of points that were to the right of the predator. We then divided these values by those that were lateral (y>0.5 cm) and medial (0 cm<y<0.5 cm) to the predator.
Computational fluid dynamics
We modeled the three-dimensional flow field around the body of our robotic predator with computational fluid dynamics (CFD) to investigate the flow that stimulates a directed fast start in prey. This model numerically solved the Navier–Stokes equations that govern fluid motion under boundary conditions for a Newtonian and incompressible fluid. These simulations were performed with a general-purpose commercial solver within ANSYS FLUENT (version 13.0.0; ANSYS Inc., Canonsburg, PA, USA) using the finite volume approach.
We measured the shape of the predator to define the boundaries of our fluid mesh. The surface of the predator was measured from digital photographs (1388×1040 pixels) of our preserved adult fish taken under a stereomicroscope (Zeiss Discovery V.20 and an AxioCam HRc camera, Carl Zeiss, Thornwood, NY, USA) from lateral and dorsal perspectives. Using custom software in Matlab, we traced the peripheral shape of the body to define the width and height of the body at 100 equally spaced positions along its length. We defined the volume of the body by approximating the transverse shape at each position with an ellipse of equivalent dimensions. The fins were excluded from our measurements and were thereby assumed to make a negligible contribution to the flow field.
The fluid volume surrounding the body (70×30×30 cm) was constructed using mesh generation software (GAMBIT, Lebanon, NH, USA). The surface of the predator was discretized into triangular meshes with ∼0.4 mm edge lengths. The volume between the predator body surface and the surfaces of the fluid volume was discretized into tetrahedral control volumes. A no-slip boundary condition was prescribed at the body surface of the predator. A velocity-inlet boundary condition was prescribed at the surface facing the head of the predator fish and a pressure-outlet boundary condition was prescribed at the surface facing the tail of the predator. The remaining four outer boundary surfaces were prescribed with a symmetry boundary condition. The inlet velocity was set equal and opposite to the approach velocity for the same steady speeds used in our behavioral experiments (2, 11 and 20 cm s–1). An additional series of simulations were conducted with zero viscosity to evaluate its influence on the predicted flow fields.
We analyzed the flow fields predicted by CFD to determine the flow around larvae at the time of their response. We accounted for the latency between a flow stimulus and escape response by calculating the 3D position of larvae relative to the predator 4 ms prior to the time at which we observed a response (Liu and Fetcho, 1999). However, a sensitivity analysis revealed that latencies of 0, 10 and 20 ms all yielded equal results. Using a Matlab script, we interpolated the flow velocities around the position at which each larva responded to the predator robot in our behavioral experiments (described above). In particular, we solved for velocity at 50 positions along the body, between our measured coordinates for the head and posterior margin of the tail. We additionally calculated the flows at 0.1 body lengths to the left, right, dorsal and ventral to the body along its length to determine the conditions around the body.
We used the flow visualization technique of Particle Image Velocimetry (PIV) to test the predictions of our CFD model. PIV measurements were made by modifying the robotic predator setup used for our behavioral experiments (Fig. 10). The sled carrying the preserved predator also transported a single high-speed camera (Photron Fastcam 1024, Photron USA, San Diego, CA, USA) and the optics to project a sheet of laser light that illuminated particles suspended in the water around the predator. By this arrangement, the camera and light sheet translated in unison with the preserved predator to permit recordings of the motion of the particles around the predator's body. The video camera recorded at high resolution (1024×1024 pixels) and high speed (1000 frames s–1) a 2.5 cm square region anterior and lateral to the predator's head using a macro lens (Nikkor 35-70mm, Nikon Corp., Tokyo, Japan). The laser beam (2 W, 532 nm wavelength, Laser Quantum, San Jose, CA, USA) was transmitted through a series of optics and mirrors to produce a horizontal light sheet that bisected the head of the predator. The particles illuminated by this light source consisted of reflective diamond powder (<1 μm diameter, Lasco Diamond Products, Inc., Chatsworth, CA, USA), dispersed at a density of 0.073 g l–1. Video recordings were collected from dorsal and lateral perspectives of the predator by rotating its body around its longitudinal axis prior to recording. We performed these recordings for each of the approach speeds used in our behavioral experiments (2, 11 and 20 cm s–1).
Software was used to calculate the velocity field from the video recordings. This software, OSIV (Open Source Image Velocimetry, osiv.sourceforge.net), used a fast, direct least-squares algorithm to track the two-dimensional displacement of particles between frames in a video recording. Each frame was divided into a 32×32 grid of cells (each cell had dimensions of 32×32 pixels), with the algorithm determining displacement for each cell to yield a regular grid for each pair of video frames. The corresponding velocity was calculated by multiplying displacements by the frame rate. After rejecting outliers, we found the mean value of the velocity of each cell over a recording of 200 frames. The software then offset the cells in both dimensions by 16 pixels and repeated the analysis in order to yield a 64×64 grid of vectors. We calculated flow in the global frame of reference by adding the approach velocity to all measured flow fields.
We compared the velocity fields calculated by PIV to the flow predicted by CFD using custom software within Matlab. This program interpolated the flow field predicted by CFD to determine the predicted flow velocity on the sagittal and frontal planes at the positions for which we measured flow by PIV. Differences between the PIV and CFD flow fields for the frontal and sagittal planes were quantified as the percentage difference in flow speed between corresponding locations. We found that the average difference between the PIV and CFD flow fields for all approach speeds was less than 7%. This suggests that our CFD simulations yielded a good approximation of the measured flow field around the robotic predator.
Behavioral algorithm modeling
We compared the fast-start direction expected for different behavioral algorithms. At each position and orientation for which we measured a response (Fig. 1A,B), we calculated a prediction for the azimuth of the fast-start direction using a Matlab script. Based on preliminary results, we modeled the flow reflex as a response that was directed normal to the initial orientation, away from the side of the body exposed to more rapid flow. Similarly, an algorithm modeled the response away from flow, but at a random angle with respect to the body. As a contrast, we modeled the responses predicted when directed toward the side of the body exposed to a faster flow velocity and responses that were entirely random. We tested whether the predictions of each algorithm were significantly different from our measurements using a non-parametric test known as a Kuiper test (Batschelet, 1981), as implemented in the Circular Statistics Toolbox for Matlab (Berens, 2009). This is analogous to a Kolmogorov–Smirnov test for circular statistics that also does not assume a particular distribution for the data. This appeared to be necessary when our preliminary analysis revealed that some of our measurements failed to conform to a von Mises distribution (Fisher, 1993).
This work was supported by the National Science Foundation [grant numbers IOS-0952344 and IOS-1354842 to M.J.M.; OCE-1129496 to H.J.].
We would like to thank K. Changsing for help with data analysis.
The authors declare no competing financial interests.