Using detailed swimming trajectories of groups of 8 zebrafish each (see Methods), we constructed the mean distributions of the polarization of the group. Polarization distributions were bimodal (Figure 1), implying that groups of zebrafish often form either highly polarized schools or weakly polarized shoals but take intermediate forms less frequently. We explicitly tested each distribution for bimodality (see Methods): of 118 analyzed distributions, all but 21 were bimodal and the peaks of most distributions that were unimodal fell clearly into one or the other behavioral form (Figure S2).

Polarization distributions changed dramatically with repeated exposure to the testing tank (Figure 1; Table S1), becoming increasingly biased towards shoaling. A similar effect was observed across multiple hours of a single extended exposure to the testing tank (Figure 2) and these effects were highly significant (Tables S1, S2). In other words, zebrafish groups spent more time shoaling and less time schooling as they habituated to the testing environment (Figure 3a). The degree of polarization of schools (the position of the peak corresponding to schooling in the distribution) did not change across repeated exposures to the tank (Repeated Measures ANOVA, F(4, 24) = 1.994, p = 0.128) but the degree of polarization of shoals decreased, i.e., shoals became more disorganized (F(4,24) = 2.816, p = 0.048) as fish habituated to the tank (Figure 3b). This result implies that schooling is a fixed behavioral pattern whereas the characteristics of shoals may depend on environmental factors (such as habituation).

Next, we segmented all the trajectories by which mode they fell into: each frame of data was designated either a schooling or shoaling frame by the polarization of the group at that time-point (unimodal distributions were excluded from this analysis). Most segments lasted only a few seconds, reflecting rapid changes in the groups' polarization, but groups spent over a third of their time (36.4%) in schooling or shoaling segments lasting longer than 30 sec. 2.45% of schooling and 8.87% of shoaling segments lasted for more than 1 min. Shoaling segments were longer, on average, than schooling segments (Figure S3; Table S3).

Finally, we compared the two modes of behaviour on other measures of collective motion: for each frame in each behavioral mode we measured the mean Nearest Neighbor Distance (NND), mean Inter-Individual Distance (IID; the mean distance between an individual and all other members of the group), and mean individual speed (Figure 4). Fish were further apart when in schools than when in shoals (paired-sample t-test; NND, t = 8.51, p<0.0001; IID, t = 9.59, p<0.0001) and swam faster (t = 14.92, p<0.0001). The latter distinction, a positive correlation between speed and polarization, has been previously noted in other fish species [10].

We next tested how changes in group size affect which behavioral mode the group inhabits. Some models of collective motion [8] suggest that the polarization of a group depends on its size or density, an effect that has also been observed in some behavioral data [11], [12]. In these situations, both theoretical and empirical, small groups have widely and rapidly varying polarization; as group size increases polarization both increases and becomes more stable, so that large groups are highly polarized and rarely change direction. We tested groups of zebrafish over a range of group sizes (N = 5, 10, 20, 30, and 50) and applied the same analyses to the data as above (sample polarization time-series' are presented in Figure S4). Figure 5 shows the summed polarization distributions for all group sizes. Contrary to our expectations, and the predictions of the models, larger zebrafish groups were significantly less polarized, on average, than smaller groups (Table S4), spending more of their time shoaling and less time schooling. NND did not vary consistently across group sizes (Figure S5A). Larger shoals were somewhat slower on average than smaller shoals (Figure S5B), though this may simply reflect the greater amount of time they spent shoaling. Note that the mean NND of groups in this experiment was lower than that of groups in Experiment 1.

All animal procedures were approved by the University of Toronto at Mississauga Animal Care Committee and followed the guidelines set by the Canadian Council on Animal Care (CCAC).

Subjects were all laboratory-reared sexually mature zebrafish 3–12 months of age and were 3–4 cm long. All fish were bred in-house. In Experiment 1, 24 groups of 8 fish per group were tested for five consecutive days each; In Experiment 2, 8 groups of 8 fish each were tested once each; and in Experiment 3, 4 groups of each size (N = 5, 10, 20, 30, and 50 fish) were tested once each. All groups consisted of approximately equal numbers of males and females. Groups of fish to be tested together were housed together for at least one week prior to the start of each experiment. Fish were housed in 40-litre tanks containing ‘system’ water that was previously reverse osmosis purified and mixed with sea salt (‘Instant Ocean’ sea salt, Aquarium Systems Inc., OH) so that the conductivity of the water was between 900–1200 micro Siemens (576–768 TDS ppm). The water in the tanks was filtered (Aqueon PowerFilter 30, Franklin, WI), aerated, and maintained at a temperature of 26±2°C. Lights in the room in which the fish were kept turned on at 7:00 h and off at 21:00 h. Fish were fed flake food (Tetramin Tropical Flakes, Tetra, USA) ad lib, 30 min before each testing session.

Fish were tested in a circular white plastic tank with a diameter of 91 cm, filled with system water to a depth of 10 cm (Figure S6), located in one corner of the room where they were housed. The temperature of the water in the tank was kept at 26±2°C. A moveable black room divider visually separated the tank from the rest of the room. The tank was lit by two fluorescent light fixtures placed at opposite sides of the tank, ensuring an even level of illumination in all parts of the tank. Experiments were filmed using a Sony Handycam (model HDR-XR-520) attached to the ceiling with the lens of the camera 200 cm above the surface of the water, located so that the entire tank was visible in the frame of the video. Videos, at 1920×1080 pixels and 12 fps, were converted into AVI format using iSkySoft Video Converter (v 2.2).

All testing was performed between 10:00 and 14:00 h each day. Fish were gently netted from their home tank and transferred in a plastic beaker to the testing tank. They were then gently poured into the center of the tank. After the session ended, fish were netted into the beaker and returned to their home tank. Sessions lasted for 30 min in Experiments 1 and 3, and for 4 hours in Experiment 2. The water in the testing tank was replaced after each two groups had been tested to control for possible odor cues left by previous groups. Sample videos of the sessions are in the Supplementary Materials (Videos S1S2, S3, S4, S5, S6, S7, S8, S9, S10).

A custom application (described in [23]) extracted the swim path trajectories of all the fish for a 5 min segment of each trial, starting 5 min after the fish were placed in the testing tank. Briefly, the tracking system identified each fish in each frame of video by subtracting it from a reference image that did not contain the fish and locating ‘clumps’ of pixels that were sufficiently different in the two images. Locations were then stitched together into trajectories assuming that fish did not move very far in the time between consecutive frames (0.08 sec). Occlusions (when two or more fish occupied the same clump) were resolved by assuming that fish turned minimally during the occlusion or, when necessary, manually (see [23] for details). In Experiments 1 and 3 only one 5 min segment per session was coded; in Experiment 2, one 5 min segment was coded for each hour of the session (i.e., mins 5–10, 65–70, 125–130, and 185–190). Raw trajectories were analyzed using Mathematica (v 7.0; Wolfram Research). The trajectories were smoothed with a linear (unweighted) moving average, using a window of 0.5 sec. Any fish that had temporarily left the group, as defined in [24], were excluded from analysis for the duration of their excursion. Individuals or sub-groups of size n were considered to be separate from the main shoal (on an excursion) when their NND_n (i.e., the distance to their nth nearest neighbor) was greater than the mode of the distribution of all NND_n (see [24] for details). Using the data from Experiment 3 we demonstrate, however, that considering only cohesive groups did not change the basic features of the resulting distributions (Figure S1b). However, the data with excursions removed are presented in the main text as this method more accurately reflects the behavior of the shoal [24].

Polarization was defined in 2 different ways, to control for possible boundary effects caused by the curved wall of the testing arena. The data presented in the main text use the standard definition of polarization as the magnitude of the mean movement vector of all members of the group (, where v_i is the movement vector of fish i in a group of size N). However, large groups swimming along the walls of our circular tank might be less polarized than smaller groups simply because they adhere to the curvature of the walls and inhabit a larger arc of the circle. To overcome this difficulty, we recalculated the orientation of each fish in each frame relative to the (tangent to the) wall of the tank at the nearest point to the fish, effectively linearizing the tank walls. We then recalculated the polarization of the group using these relative orientations. We show that the polarization distributions generated using this modified procedure are not qualitatively different from those generated by the standard measure (Figure S1a).

Polarization distributions were individually tested (i.e., the distribution from each session was tested) for bimodality using a Maximum Likelihood Estimation (MLE) method: the best-fit mixed-Gaussian models with one, two, and three components were found for each distribution; likelihood scores were calculated for each model; and the Bayesian Information Criterion (BIC) was used to select the most likely model [25]. For bimodal distributions, pairs of Gaussian distributions were fit to the distribution and the point at which they crossed was used as a threshold to partition the data into its component modes (Figure 1, inset). Note that, as a result, the assignment of frames of data as either schooling or shoaling is session-dependent. All statistical analyses were conducted either in Mathematica or SPSS (v 17.0). A significance level of 0.05 was used for all tests. In Experiment 1, 2 sessions had to be excluded from analysis due to video recording errors.