Fish communicate with water flow to enhance a school's social network Free

Schooling offers a number of benefits to social species. A school provides mating opportunities, offers protection from predators, enhances foraging (Day et al., 2001; Godin et al., 1988) and may reduce the energetic cost of swimming through hydrodynamic interactions (Ashraf et al., 2017; Marras et al., 2015; Seo and Mittal, 2022; Hemelrijk et al., 2015; Svendsen et al., 2003). These benefits are realized to an extent that depends on the capacity of a group of fish to form a cohesive social network (Kent et al., 2019; Ward et al., 2018; Crosato et al., 2018; Rosenthal et al., 2015). In a cohesive school, fish respond rapidly to changes in the speed and heading of their neighbors such that the group moves nearly in unison. However, it remains unclear how such cohesive motion depends on the individual sensory modalities of schooling fish.

Schooling depends to a large extent on the visual system. Many species cease to school in the absence of illumination, including sticklebacks (Gasterosteus aculeatus: Ginnaw et al., 2020), freshwater cyprinids (Danionella translucida: Schulze et al., 2018), characids (Astyanax mexicanus, Petitella rhodostomus: Kowalko et al., 2013; McKee et al., 2020) and a number of pelagic marine species (Pseudocaranx dentex, Thunnus orientalis and Scomber scombrus: Hunter, 1968; Torisawa et al., 2007; Ali, 2001). This failure to maintain a cohesive school in the dark may occur because vision is necessary or because the fish lose motivation to school, perhaps as a result of a perceived lack of a predatory threat. Regardless, schooling occurs when fish can see one another. A larger school offers the appearance of more conspecifics, but also presents greater occlusions to the surrounding environment (Davidson et al., 2021; Tunstrøm et al., 2013). Thus, school size may be used to manipulate the visual system in an effort to understand its role in schooling.

The lateral line system potentially offers a sensory complement to vision for schooling. This flow-sensing system includes an array of mechanoreceptors in the skin that allow a fish to sense the velocity and pressure gradient of a flow field (van Netten and McHenry, 2013; Kroese and van Netten, 1989; Kroese and Schellart, 1992). The hair cells that facilitate the transduction of flow cease to function when exposed to aminoglycoside antibiotics at a specific concentration over a particular duration (Wersäll, 1961; Kroese and van den Bercken, 1982; Mekdara et al., 2022). Fish may swim closer together, or further apart, with reduced polarization, greater frequency of collisions and uncoordinated changes in speed when the lateral line system is compromised (Partridge and Pitcher, 1980; McKee et al., 2020; Faucher et al., 2010; Mekdara et al., 2018, 2021, 2022). These effects occur despite the organizing influence of the hydrodynamic interactions between schooling fish. Modeling suggests that these interactions aid in a school's cohesion and can serve to synchronize the swimming of neighboring fish, even in the absence of sensory cues (Filella et al., 2018; Heydari and Kanso, 2021; Li et al., 2020). Although experimental manipulations of the lateral line offer intriguing glimpses into its role in schooling, the capacity of water flow to serve as a channel for communication remains unclear.

Analytical tools from information theory and graph theory offer a framework for understanding the social networks formed between animals. Shannon entropy is a measure of the information content within a signal and additionally indicates the unpredictability of that signal. Entropy is fundamental to information theory (Shannon, 1948; Shannon and Weaver, 1963) and its utility in animal signaling has been debated among behaviorists (Owren et al., 2010; Seyfarth et al., 2010). Entropy has provided a basis for measurements as varied as the vocal complexity of bird songs (Kershenbaum, 2014) and the evasiveness of prey (Moore et al., 2017). Schooling offers a special case for the application of entropy measurements because fish move with coordinated kinematics that depend on an ability to communicate. The similarity in motion between fish may be quantified by mutual information (MI), which is calculated as the difference between the sum of the individual measures of entropy and their joint entropy (Reza, 1994). MI has been instrumental in assessing communication among individuals (Schaerf et al., 2017; Ward et al., 2018; Kent et al., 2019), through pairwise comparisons across all individuals in a school. It should be noted that MI measurements could reflect factors other than communication, such as hydrodynamic interactions, but a reduction in MI by compromising a sensory system may reasonably be interpreted as an effect on communication. Measures of MI can be integrated with graph theory to map information flow within the school. In graph-theoretical terms, each fish is represented as a node in a network, with edges between nodes weighted by the MI values that represent the strength of communication (Niizato et al., 2020).

The present study aimed to test the extent of information sharing between schooling fish through manipulations of flow sensing and the school size, which additionally alters visual cues. These experiments were performed with Petitella rhodostoma, which is a highly social species that, along with the closely related Petitella bleheri (previously referred to as Hemigrammus bleheri), has emerged as a model for the study of schooling (Ashraf et al., 2016, 2017; McKee et al., 2020; Puckett et al., 2018; Lecheval et al., 2018; Calovi et al., 2018). These species swim with intermittent kinematics (McKee et al., 2020; Calovi et al., 2018), which means that individuals move with periods of acceleration and deceleration that cause the cohesion and motion of a school to vary across time. As both visual and flow cues may be scale dependent, we examined the swimming of schools of varying size (15, 30, 45 and 60 fish) with high-throughput automated kinematics. We assessed the role of flow sensing by comparing conventional measures of kinematics and information sharing in schools of fish with a compromised lateral line with those of schools of fish with an intact lateral line.

We acquired ∼200 adult rummy-nose tetra, Petitella rhodostoma (Ahl 1924), from the aquarium trade. The fish were held in 75 l tanks (in groups of ≤50 fish per tank) within a flow-through system at 27°C on a 14 h:10 h light:dark cycle with daily feeding. The fish were of similar body length, 3.17±0.01 cm (mean±1 s.e.m., N=30, measured from kinematic recordings). All husbandry and experimental protocols were conducted with the approval of the Institutional Animal Care and Use Committee at the University of California, Irvine (IACUC Protocol #AUP-17-012).

At the start of a series of experiments, 60 fish were randomly chosen from the pool of ∼200 fish and sorted into groups of 5, 10 and three groups of 15. Groups of fish were held outside the experimental tank, in 1 l containers within a heated and aerated water bath with recirculating flow, where the fish within sorted groups were free to school with one another. The first group of 5 fish was introduced into the experimental tank and allowed to acclimate (>30 min) prior to video recording. Each experiment consisted of a 3 min recording of spontaneous swimming by a school of fish. After the recording concluded, 10 fish were added (for a total school size of 15) and allowed to acclimate for the remainder of the 12 min interval between recordings. The remaining three groups of 15 fish were introduced into the experimental tank after each subsequent recording, such that the school size for each recording was 30, 45 and 60 fish. Note that we excluded the schools of 5 fish from our analysis because we found their kinematics were highly different from those of the larger schools. Once a full scaling series was complete, the school was randomly returned to the holding tanks. This process was repeated until we succeeded in performing experiments for three replicate schools at each size. Fish exposed to lateral line treatment were not used for more than one experiment following the treatment (described below). Therefore, our replicates of fish schools were composed of a unique combination of randomly selected individuals, though those individuals were shared across schools. It should be noted that this experimental design introduces possible historical effects. For example, a school of 60 fish consists of 15 fish that schooled together for 60 min in a holding tank while the other 45 fish were built up from a school of 5, then 10, then two groups of 15 fish over that same period.

We compromised the ability of the lateral line system to sense flow by exposure to an ototoxin, as previously established (McKee et al., 2020). Fish were exposed to a solution of neomycin sulfate (0.9 g neomycin sulfate per 1 l fish water, pH 6.8, Fisher BioReagents, Fair Lawn, NJ, USA) for a period of 2 h in the dark to avoid bleaching the solution. In the evening prior to an experiment, fish were randomly chosen from the pool of untreated fish and held overnight in a standalone 75 l holding tank filled with 3 l of fresh fish water, a heater and aeration stones. A concentrated solution of neomycin sulfate (2.7 g per 50 ml fish water, pH 6.8, covered to avoid light exposure) was fed into a peristaltic pump with opaque tubing, equipped with an outlet timer. The outlet timer was set so that the peristaltic pump turned on 2.5 h prior to the room lights illuminating the following morning. This allowed the concentrated stock solution to slowly drip into the holding tank over the course of 30 min, prior to the 2 h treatment time. Fish were retrieved 30 min after the room lights were activated and moved to a series of three fresh water rinses, each for 3 min. Fish were sorted into holding tanks, as described above, and held in fresh water until the start of an experiment. Once treated, fish were used only for experiments on that day and were not reused. The treatment was verified by a lack of behavioral responses to the flow generated by pipette. Control fish exhibited an escape response or rapid turn away from this jetting stimulus, whereas the treated fish did not. In addition, treated fish exhibited a diminished fluorescent vital stain DASPEI {2-[4-(dumethylamino)styryl]-nethylpyridinium iodide; Invitrogen, Eugene, OR, USA}, as previously described (McKee et al., 2020).

We designed and constructed an aquarium to generate video recordings for high-throughput kinematic analysis. The rectangular tank (118 cm square and 30 cm tall) was built of clear acrylic (1.7 cm thick) and filled to a shallow water depth (∼3 cm) to constrain swimming to predominately 2D motion and to reduce occlusions by making it less likely for fish to swim above and below one another (Fig. 1A). To maximize the contrast of the fish, the tank was raised on a scaffolding of extruded aluminium so that we could position an infrared light source beneath it. This back-lighting consisted of a custom array of infrared (850 nm) light-emitting diodes (360DigitalSignage, Shenzhen, China). These IR LEDS possessed integrated circuitry with the lights spaced at an interval (3.5 cm) and featured an adhesive backing, which we used to affix strips spaced 2.5 cm apart to a sheet of acrylic. Positioned at some distance (11.5 cm) above the LED array was an additional sheet of acrylic which served to hold two sheets of gel diffuser material (Goshoot). This layer successfully distributed the discrete illumination generated by the IR lights for a nearly uniform field of IR illumination that was positioned 21.5 cm below the floor of the tank. An additional layer of plastic diffuser material was adhered to the floor of the tank with aquarium-grade silicone to prohibit fish from seeing reflections of themselves.

We sought to constrain the swimming of fish in a circular space to avoid the potential effects of the tank's corners. We developed a transparent barrier to avoid high-contrast edges that can appear in the interface between a wall and floor (Fig. 1A). This was composed of an acetate wall that was positioned at an angle with respect to the floor, held in place by a plastic hoop that encircled the barrier's upper circumference (diameter 1.03 m at the water's surface). A canister filter (Fluval 207, Fluval Aquatics, Mansfield, MA, USA) provided low flow circulation around the acetate barrier and water exchange with an external 75 l tank with a heater maintained the experimental tank temperature. Additionally, five small computer fans were installed near the visible light source to induce air flow and maintain a relatively constant water temperature (26 to 28°C).

The tank was illuminated by an array of white LEDs (Taiko 2×1 RGB LED Light Panel, Luxli) directed upwards, towards a reflective photo umbrella. The entire setup was additionally surrounded by reflective mylar, which served to contain and scatter the white light within the setup. To prevent the visible light from generating reflections on the water's surface, we enclosed the space above the tank with diffuser cloth tapered upward with an opening at the top for the lens of our camera (Fig. 1A).

We recorded the kinematics of swimming with a single mirrorless digital camera (Sony Alpha, A7III, Sony Electronics Inc., San Diego, CA, USA). The camera was positioned at the center of the tank, at a considerable height above the water's surface (1.8 m) to minimize parallax distortion. The video signal from the camera was captured to disk with a video recorder (Atomos Sumo19, ATOMOS Global Pty Ltd, Los Angeles, CA, USA) at 4K (3840×2160 pixels) resolution at a standard frame rate (29.97 frames s⁻¹). To maximize sensitivity to the IR LEDs, we had the camera's IR filter removed by a third party (LifePixel, Mukilteo, WA, USA). In pilot experiments, we found that the camera would fail to record over long durations because of overheating. We therefore affixed a Peltier cooler (model TEC1-12706, HiLetgo, Shenzhen, China) with a heat sink and built-in fan (model CM4-FAN-3007-B-12V, Waveshare, Shenzhen, China) to the back of the camera with a thermal pad to permit long-duration recordings. We controlled the duration of recordings by the video recorder with a computer (iMac with an Intel i9 processor and a Radeon Pro 580X graphics card, macOS Ventura 13.0.1, Apple Inc., Cupertino, CA, USA) by playing a timecode audio signal from the computer's headphone jack to the recorder's SDI input. As a consequence of this arrangement, we were able to perform our recordings on a schedule that was controlled with custom software, which we programmed in the Python scripting language (v.3.10).

Video recordings of schooling were analyzed with a combination of custom and open-source software scripted in Python and MATLAB. We preprocessed the recordings to enhance their contrast and to remove imperfections in the uniformity of background illumination. This included steps to manually select the region of interest, just inside the water's edge, and to generate a mean image. The mean image found the average intensity for each pixel from 150 video frames captured across experiments, performed upon a particular school of fish. This preprocessing software used the open-source package OpenCV (v.4.6.0) to generate a video file that (1) masked the area outside of the region of interest, (2) cropped to the region of interest, (3) subtracted the mean image from each frame and (4) performed thresholding of dark blobs (for the fish) within a manually specified range of area and pixel intensities. These video files were then passed into TRex (Walter and Couzin, 2021), which is open-source tracking software that we executed with Python code. TRex generated kinematic data, with some capacity to correct for occlusions. We exported TRex's measurements of the body centroid coordinates of each fish, their speed and heading to Matlab (v2022a, MathWorks, Natick, MA, USA) for kinematic analysis. This stage of the processing first used outlier identification of speed measurements to identify periods of occlusion in the data and then performed linear interpolation of the coordinates to fill in these gaps in the measurements. After this, the raw kinematic data (x- and y-coordinates, velocity and heading) were smoothed with a cubic spline-fit interpolation.

We additionally measured the approximate shape of the school. For each video frame, we found a best-fit ellipse by least-squares to the positions of fish using a toolbox in Matlab (‘fit_ellipse’, v.1.0). We found the aspect ratio of the ellipse as the major axis in the direction of the mean heading, divided by the minor axis, in the perpendicular direction. The best-fit ellipse additionally provided a measure of the approximate area encompassed by the school.

We used generalized estimating equations (GEE) analysis to evaluate the effects of school size and flow sensing on schooling kinematics. This modification of a generalized linear model is suitable for the present experimental design because of its ability to account for correlations among repeated measures and clustered data (Liang and Zeger, 1986). Unlike traditional regression methods, GEE provides robust standard errors and unbiased parameter estimates even when the within-group correlation structure is unspecified. These features make GEE ideal for handling shared individuals across replicates (Zeger and Liang, 1986). By incorporating the correlation structure of the data, GEE enhances the validity of inferential statistics, thus ensuring that the effects of the predictors on the outcomes are accurately assessed in the presence of within-group dependencies (Hubbard et al., 2010). These statistical analyses were performed with the R scripting language using the ‘geeglm’ function (http://www.R-project.org/;https://CRAN.R-project.org/package=geepack).

We used information theory to quantify information sharing between fish in a school. We calculated MI based on comparisons of measurements for the speed and heading between all pairwise combinations of school members. These calculations were performed over each kinematic recording in 2 s intervals of time (Fig. 2A,B), with a 0.25 s overlap between successive intervals. For each interval, we first discretized the speed measurements for all fish into eight bins, with the bin widths adjusted such that each bin contained an equal number of measurements among all fish. The heading was similarly discretized, which together yielded 64 kinematic bins (Fig. 2C) that were found to be sufficient to reflect the distributions of speed and heading.

We found that schools of P. rhodostoma swam intermittently, irrespective of the school size. Periodic changes in speed were characterized by groups of fish accelerating and decelerating across numerous tail beats (Fig. 3A). The school would generally traverse the middle of the tank until encountering a wall, which would prompt a change in heading. Therefore, changes in heading generally occurred during periods of relatively slow speed (Fig. 3B), when high variance was reflected in declines in the polarization parameter (Fig. 3C). The school tended to change direction, as shown by increases in the rotation parameter, at moments when the school was relatively less polarized. Therefore, the polarization and rotation parameters tended to vary out of phase with one another across time. The temporal changes in speed and heading provided the basis for measurements of MI shared between fish. The pairwise calculations of MI, like the polarization and rotation parameters, periodically varied across time as the fish exhibited changes in their degree of coordination (Fig. 3D–F).

We tested how swimming kinematics varied with school size and the ability to sense flow. The mean NND for a school of 15 untreated fish was about 2 body lengths (6.20±0.60 cm, mean±1 s.e.m., N=3), a distance that decreased slightly, but significantly (P=0.007, N=3, Table 1), with increasing school size (Fig. 4A–C). In particular, NND decreased by ∼13% between schools of 15 and 60 fish. Fish with a compromised lateral line system were found to swim with about 15% greater NND than fish with an intact lateral line, a significant difference (P=0.001, Fig. 4C). Untreated fish in a school of 15 moved at a speed of about 3.5 body lengths s⁻¹ (11.62±2.00 cm s⁻¹, N=3). This declined by 26% between schools of 15 and 60 fish, which was highly significant (P=0.003, N=3) and may at least partially be explained by the significant trend in intermittency (P=0.050; Table 1, Fig. 4E). Fish with a compromised lateral line tended to swim more slowly (P=0.046), despite no significant difference in intermittency (P=0.067). As detailed in Supplemental Materials and Methods, we used GEE to test whether the reduction in NND and speed with school size may have resulted from more interactions with the tank walls. In contrast with the trend with respect to school size, we found that fish in the periphery of the tank exhibited larger NND. We additionally found no significant interactive effects between the tank position and school size for NND and speed (Table S1, Fig. S1A–B). Therefore, the effects of school size on NND and speed may not be attributed to wall effects.

We additionally evaluated the effects of our treatments on the area and shape of schools. For each frame of a recording, we found a best-fit ellipse (Fig. 1C) to the body positions of fish in the school. The area encompassed by this ellipse was proportional to the number of fish in the school (P<0.001; Fig. 5A–C, Table 1). However, the wider spacing between fish having a compromised lateral line (Fig. 4C) caused the schools to span a greater area (P<0.001). For example, schools of 60 fish encompassed about one-third greater area when flow sensing was compromised (3900±58 cm²), compared with untreated fish (2920±387 cm²; Fig. 5C). Flow sensing did not affect the shape of schools (P=0.716), which were greater in length than width, as indicated by an aspect ratio of greater than one (Fig. 5A,B,D). However, this elongated shape became progressively less prominent with the size of the school (P<0.001; Table 1), to the extent that a school of 60 fish approximated a circular shape. We did not devise a test for whether the school shape was influenced by interactions with the walls and so that remains a possibility.

The heading of fish provided a basis for measuring the polarization and rotation parameters of the school. The rotation parameter (Eqn 2) varied significantly (P<0.001) with the number of fish, with values that more than doubled (2.11×) between schools of 15 and 60 fish (Fig. 6A,B). Compromising the lateral line additionally increased the rotation parameter by 78% (P<0.001; Table 1). Polarization did not significantly change with the lateral line treatment (P=0.089, N=24; Table 1), but did significantly decrease with school size (P<0.001; Fig. 6C). In particular, the polarization parameter decreased by ∼30% between schools of 15 and 60 fish (Table 1). As detailed in Supplemental Materials and Methods, we found evidence to support the idea that the scaling of polarization and rotation may at least partially be attributed to interactions with the walls. In particular, we found a significant (P=0.003) interaction between the tank position and school size for the polarization parameter. This indicates that fish in the periphery shared a less common heading than at central positions, which could be a contributing factor to the positive scaling of the rotation parameter (Fig. 6).

We tested how school size and the ability to sense flow affected information sharing between fish. As detailed above, MI (Eqn 4) indicates the information shared between individuals within a school. We found the average measure of MI for individuals to vary significantly with school size (P<0.001, N=24; Table 1, Fig. 7). On average, MI declined by ∼22% between schools of 15 and 60 fish, suggesting that individuals were less responsive to the motion of surrounding fish when the school was larger. MI was significantly affected by compromising the lateral line system. On average, fish shared 13% less MI when they could not sense flow, compared with untreated fish (P=0.003, N=24; Table 1).

As a consequence of their influence on information sharing, the number of fish and flow sensing affected the network properties of schools. We found that the degree, which reflects the number of individuals with which each fish shares information, increased significantly with school size (P<0.001, N=24; Table 1). This amounted to a 68% increase from 15 to 60 fish (Fig. 8A,B). That increase did not outpace the rise in school size, as reflected by a decline in degree centrality (Eqn 5, P<0.001; Fig. 8C). The reduction in degree centrality was likely a contributing factor to the increase in network heterogeneity by 2.5× in schools from 15 to 60 fish (P<0.001; Fig. 8E). Compromising the lateral line system resulted in substantial disruption of network cohesion in the schools. The treatment reduced degree by ∼52%, degree centrality by ∼39% and connectivity by ∼56%, and increased network heterogeneity (Eqn 7) by ∼52%, all of which are highly significant effects (N=24, Table 1).

Our manipulations of school size and the lateral line offer insight into the sensory basis of schooling. Using conventional measures of schooling kinematics (Figs 4–6), these manipulations provide insight into the role of vision and flow sensing that are consistent with current understanding. However, our methods for evaluating communication through measurements of MI (Figs 7 and 8) reveal a more fundamental role for flow sensing than what has previously been appreciated.

The network properties of schools indicate a role for the lateral line system in schooling. Although compromising the lateral line reduced the MI between individuals by only 13% (Fig. 7B, Table 1), the associated decline in communication showed propagating effects throughout the school. Mean values for degree and network connectivity were about twice as large for fish that could sense flow than for those that could not (Fig. 8B,D). By these metrics, one could argue that flow sensing accounts for half of the communication that determines coordination in speed and heading among schooling fish. We additionally found that network heterogeneity in treated fish was twice as large and network connectivity was less than half compared with those of untreated fish (Table 1, Fig. 8D,E). Therefore, flow sensing plays a critical role in the cohesion of a school's social network that is not well reflected by conventional kinematic measurements (Figs 4–6).

The role of the lateral line varied with the size of a school. We found little difference in information sharing and network properties in our schools of 15 fish (Figs 7 and 8), which is consistent with previous work on smaller schools (McKee et al., 2020). This scaling effect is perhaps surprising given the rapid spatial attenuation in flow signals that may be generated by a swimming fish (Hanke et al., 2000). The increase in visual stimuli associated with a larger school size may overwhelm the capacity for school coordination through vision alone, leading to increased reliance on flow sensing as a compensatory source of information from neighboring fish. It is therefore possible that the lateral line system increases the information throughput for fish to respond to neighbors in larger schools. Alternatively, the interactions between the wakes of swimming fish in a school may collectively offer stronger sensory cues for coordination. An additional possibility is that flow cues become more prominent in larger schools merely as a consequence of the tendency for fish to swim closer together (Fig. 4C). Whatever the case, it appears that the role of flow sensing may best be demonstrated in schools of greater size.

We found that compromising the lateral line system caused fish to school with greater nearest-neighbor distance (Fig. 4A–C). Fish with compromised flow sensing swam about one-third of a body length further apart (Table 1), and the school spanned a greater area (Fig. 5C), than fish with an intact lateral line. Our results offer a more subtle difference between treated and control fish compared with what was previously measured in other tetras (Petitella sp.) for 5-fish schools (1.94 body lengths; McKee et al., 2020) and for 10-fish schools (1.25 body lengths; Faucher et al., 2010), and schools of 10 yellow-eyed mullet (Aldrichetta forsteri, 2.35 body lengths; Middlemiss et al., 2017). However, previous work on schools of 5 and 8 giant danios (Devario aequipinnatus) showed no immediate effect on NND and the frequency of schooling (Mekdara et al., 2018; Tidswell et al., 2024). Therefore, the present results fall within the range of results for NND in previous studies that adopted similar methodology. In contrast, a nerve ablation applied to individual pollock (Pollachius virens) placed in schools of 20–30 untreated fish was shown to decrease NND (Partridge and Pitcher, 1980), raising the potential of a distinct role of flow sensing in this species from what has been observed in others.

Previous studies on schooling that have ablated the lateral line system highlight a variety of effects that help inform our findings. In particular, changes in behavior that potentially alter the speed and heading of a fish should be reflected in calculations of MI (Eqn 4, Figs 2–7). For example, ablating the trunk lateral line in pollock reduced correlations in speed between neighboring fish (Partridge and Pitcher, 1980) and a similar treatment removed the ability of neighboring fish to synchronize with one another in giant danios (Mekdara et al., 2021). Giant danios tend not to direct their swimming towards neighboring fish as much and tetras collide with their neighbors and distribute randomly without the aid of flow sensing (Tidswell et al., 2024; Faucher et al., 2010). Therefore, previous observations reflect a similar reduction in network cohesion following lateral line ablation to what we found in the present study (Fig. 8).

Our results support the notion that vision is fundamental to schooling. As detailed in the Introduction, a diversity of fishes have been shown to be incapable of, or unwilling to, school in the dark (Schulze et al., 2018; McKee et al., 2020; Hunter, 1968; Torisawa et al., 2007; Ali, 2001), whereas the behavior still remains possible when the visual system is functional and the lateral line system is compromised (Partridge and Pitcher, 1980; McKee et al., 2020; Mekdara et al., 2018). Beyond enabling the formation of a school, vision plays a modulating role in how the school moves, as indicated by kinematic parameters that vary with school size. We found that fish swim closer to their neighbors in larger schools, as previously shown (Davidson et al., 2021), and they move more slowly and with greater intermittency (Fig. 4). These trends are not due to the greater frequency of interaction with the tank's walls, but rather are effects of the interactions between the fish within the school (Table S1, Fig. S1A,B). Although the effects of school size are subtle, they do indicate that fish respond to visual cues beyond their immediate neighbors. In contrast, trends in the polarization and rotation parameters (Fig. 6) may partially be explained by a tendency for larger schools to cause fish close to the walls to adopt a dissimilar heading (Table S1, Fig. S1C). Visual cues may provide additional motivation for the trends in polarization and rotation, as previously indicated (Tunstrøm et al., 2013), but it is difficult to differentiate this effect from wall interactions.

Our results indicate a major role for flow sensing in the social networking of schooling fish. This finding emerges from the substantial disruption in degree, network connectivity and heterogeneity (Fig. 8) created by compromising the lateral line system. These results underscore flow sensing as a supplement to the essential role of vision in facilitating schooling. The decreases in NND and speed, and an increase in intermittency with school size that we found suggest that fish respond to visual cues beyond their nearest neighbors.

This project received valuable input from E. Kanso and D. Paley. C. Huang and H. Hang provided valuable input on our data analysis and two anonymous reviewers provided valuable feedback.