Nature’s Aquatic Ballet: The Physics and Synchronization of Schooling Fish 

Anne-Sophie Roy, Emma Warner, Hoi Ching Wat, Lucas Yatcyshyn

Abstract

The schooling of fish is a unique phenomenon that has fascinated people for centuries. The complex interactions between individual fish, their schoolmates, predators, and their environment have been widely studied.  Researchers have explored the dynamics and mechanisms behind the movement of individual fish and moving schools, methods of communication between fish in a school, the evolutionary advantages of schooling, the mechanisms of school formation, and the responses of schools to both attractive and frightening stimuli. This paper elaborates on current knowledge of the physics governing schools of fish and their individual members, highlighting the innovative strategies fish have evolved to thrive in their environment. 

Introduction

Schooling is a form of social behavior in fish, characterized by highly synchronized swimming and mutual coordination in response to environmental stimuli. It includes strategies for space utilization, foraging, predator avoidance, and reproduction.  

While all schools are considered a type of shoal, not all shoals may be considered a school. Shoals, like schools, are an aggregation of fish attracted by certain stimuli, but may form separately from schooling behavior (Pavlov & Kasumyan, 2000). The distribution and orientation of fish in a shoal may or may not be consistent between individuals; however, for a shoal to be considered a school, all members of the group must be oriented parallel to each other and located a certain distance apart (Fig. 1). Furthermore, individuals become a part of a shoal independently of one another, whereas in schools, there is a mutual attraction between fish in the school (Pavlov & Kasumyan, 2000). 

Fig. 1 (A) A school of fish as compared with (B) a shoal of fish (Emma Warner’s own artwork). 

Species of fish exist on a spectrum from those that assemble as a school to those that do not. In fact, even species known for schooling may not do so throughout their entire life. There are fish that cannot survive outside of a school while there are also fish that do not form shoals ever. It was estimated that approximately 25% of fish exhibit schooling throughout their life, while approximately 50% only school during larvae and ontogeny (Shaw, 1978). 

The diversity in schooling behavior highlights its evolutionary significance. The primary driving force for the evolution of schooling behavior is defense against predators, however, schooling is also beneficial for feeding, reproduction, and the migration of fish (Pavlov & Kasumyan, 2000). Among vertebrates, group life as a social behavior is formed and becomes widespread beginning from Teleostei, the largest infraclass of the class Actinopterygii, bony fish characterized by the ability to protrude their jaw bones (Kasumyan & Pavlov, 2018; Patterson & Rosen, 1977). The biology of teleosts is incredibly diverse, indicating a higher correlation between schooling behavior and the ecology and characteristics of life of fish than with their ancestry. For example, most schooling fish are pelagic—inhabiting the upper layers of the ocean away from shore—and populate well-lit areas with minimal visual landmarks (Pavlov & Kasumyan, 2000).  

This ecological context also influences the age at which fish first begin schooling. Schooling behavior is not strictly predetermined by the schooling level of adults but rather depends on the conditions of the fish’s development (Pavlov & Kasumyan, 2000). Fish only begin to show schooling behavior after achieving certain morphological and functional developments required to actively swim and maneuver synchronously with other fish. For example, larvae have functional sensory and visual systems before they begin school formation, however, optomotor responses, rheoreaction, and the chemosensory systems do not fully develop until the beginning of schooling (Kasumyan, 1997). The ability to learn conditioned defensive responses is also developed at the beginning of schooling. Thus, schooling fish typically first exhibit schooling behavior in ontogeny, after the onset of independent feeding. Fish that live in stagnant or slowly moving water, however, begin forming schools more so during the third stage of development due to slower rate of development as a result of their environment. Schooling instincts continue to develop with age, even after reaching adulthood (Pavlov & Kasumyan, 2000). 

Individuals in a school 

The synchronization and hydrodynamics of a school of fish depend largely on the hydrodynamics of the individuals that make it up. 

Basic fish anatomy 

Most schooling fish share a basic anatomy that allows them to efficiently cut through water in a streamlined manner (Fig. 2). Much of this anatomy, including the skeletal and muscular system, aids in the fish’s swimming ability while other features help them survive in an underwater environment. The gill apparatus, important for respiration in fish, is situated behind the head while the rest of the fish’s vital organs are within the body cavity. The spinal cord and vertebral column run from the head to the caudal fin. Most of the fish’s body is composed of muscular tissue which is optimized for swimming (Weitzman & Parenti, 2024). 

The skeletal system serves as an anchor for the fish’s muscular tissue, contributing to its ability to swim through the water; its main components include the skull bones, vertebral column, and fin rays. Bony fish, which commonly form shoals, have spool-shaped vertebrae with a skeleton composed of only bones. Cartilaginous fish such as sharks have an internal skeleton consisting mostly of cartilage, as opposed to bone, including a cartilaginous vertebral column. These different skeletal structures highlight how each species is adapted to its unique environment (Weitzman & Parenti, 2024). 

Most fish have one to multiple dorsal fins on the midline of their back, providing stability when swimming. Other fins include the tail fin, which helps to generate thrust and propel fish through water along with the anal fins and the paired pelvic and pectoral fins (Weitzman & Parenti, 2024). 

Fig. 2 (Top) Skeleton of a perch (order Perciformes). (Bottom) dissection of a perch (Weitzman & Parenti, 2024). 

Most of the muscle mass of a fish is contained in the trunk of the fish and allows the fish to propel itself through water. Several chevron-segments of body musculature are attached to adjacent vertebrae and vertebral processes. The contraction of these trunk muscle segments results in body undulations, propelling the fish forward. The caudal (tail) fin moves based on the contractions of the trunk muscles and therefore also aids in the fish’s forward motion. Fish primarily use their other fins for stability and changing direction, as opposed to propelling themselves forward, and so fin muscles are relatively small as compared with trunk muscles (Weitzman & Parenti, 2024). 

Hydrodynamics of an individual fish 

The study of fluid motion and the forces acting on solid bodies submerged in fluids and moving in relation to them is known as hydrodynamics (Merriam-Webster). Hydrodynamic efficiency refers to the ability to use less energy to move through fluids with the best possible spatial layouts and movement patterns. For fish, there are different strategies to increase hydrodynamic efficiency such as employing vortices, lowering drag, or coordinating their motions. 

As an object moves through the water, it pushes water aside, creating trailing vortices. Professor Tadashi Tokieda of Stanford University demonstrated this using a ping pong ball in a bathtub (Haran & Tokieda, 2022). If one pushes the ball down just below the surface, it shoots up into the air well above the water. However, as the ball is pushed deeper below the water, it instead rises to the top and stops upon reaching the surface. This intriguing phenomenon is the result of the ball shedding individual vortices as it rises to the surface. As the ball rises, the water is pushed out of the way, moving, and rotating along the side of the ball. The pushing and rotation of water causes multiple vortices to form, using energy as the ball oscillates back and forth to the surface (Fig. 3). This lost energy is responsible for why the ball is unable to shoot up out of the water (Haran & Tokieda, 2022). 

Fig. 3 As the ping pong ball moves to the surface, it pushes aside rotating vortices of water (Haran & Tokieda, 2022). 

Now, picture a submarine moving through the water. Like the ping pong ball, it displaces water as it moves forward horizontally. Similarly, it creates rotating vortices in its trail. The vortices from opposite sides of the submarine spin such that they create a net pull on the submarine (Fig. 4). This takes away from its momentum, creating inefficiency (Haran & Tokieda, 2022). 

Fig. 4 Rotating vortices left by the submarine produce a net pull on the submarine (Haran & Tokieda, 2022). 

A fish, unlike a submarine, is not powered by a nuclear reactor or some other powerful form of energy. Instead, evolutionary pressures have created an ingenious method for fish to swim efficiently through the water. Through the undulations of their body, the vortices are displaced to the opposite sides of the fish. This displacement creates a net push on the fish, propelling it forward (Fig. 5). The jet-engine-like push created by the fish’s unique method of swimming is why fish can swim so effortlessly and quickly whereas Olympic swimmers splash all over the place and hardly move faster than a walking pace (Haran & Tokieda, 2022). 

Fig. 5 The rotating vortices are exchanged to opposite sides by the fish, creating a push on the fish similar to a jet engine (Haran & Tokieda, 2022). 

In the field of flow dynamics, experts refer to this unique flow pattern as the reverse Kármán vortex street (Fig. 6) (Wolfgang et al., 1999). 

Fig. 6 An example of the beautiful patterns known as the Kármán vortex street (Wikipedia contributors, n.d.). [Link: https://en.wikipedia.org/wiki/File:Vortex-street-animation.gif] 

The role of pectoral fins in swimming 

Fish in schools can perform a variety of complex movements which allow them to remain part of the school as the school transitions from moving, to feeding, resting, or threat response.  

Located posterior to the fish head are bilateral pectoral fins. Pectoral fins are relatively small compared to caudal fins and generate minimal thrust. This raises the important question: what function do these body parts serve? Looking at the function of pectoral fins in rainbow trout helps to illustrate their importance and evolutionary advantage. 

The rainbow trout, known as Oncorhynchus mykiss, is a bony fish that shares the common, streamline fish shape. Using a combination of kinematic analysis and quantitative flow visualization, scientists were able to pinpoint the exact function of these fins: Instead, pectoral fins are important for stability and quick maneuvering while fish swim and allow straight-ahead swimming, hovering, low speed turning maneuvers, and braking (Drucker & Lauder, 2003). Rainbow trout swim with their pectoral fins adducted against their body. Doing so also maximizes the undulation of the muscular caudal fin to produce maximum thrust (Drucker & Lauder, 2003). 

Pectoral fins also allow fish to “hover” and remain stationary in water. Hovering is maintained through the fine movements of the pectoral fins, performing a sculling motion. The pectoral fin is “depressed and twisted along its axis so that the surface which before the maneuver faced medially becomes posteriorly oriented” (Fig. 7) (Drucker & Lauder, 2003). Through this movement, the fish can generate just enough lift to maintain its depth as well as to remain stationary and stable in the water. 

Fig. 7 Illustration of the force vectors generated from Oncorhynchus mykiss (Rainbow Trout) braking (Drucker & Lauder, 2003). 

Low speed turning maneuvers require a similar rotation as in hovering; however, the pectoral fin moves in the opposite direction above the ventral body margin rather than below it (Drucker & Lauder, 2003). 

When making sudden maneuvers, fish create a cupped shape with their pectoral fins to minimize drag. Extending the cupped pectoral fins bilaterally produces a retarding drag force which rapidly slows the fish. Typically, breaking ahead of the center of mass causes a somersaulting motion due to Newton’s Third Law of Motion, however, fish can brake without somersaulting forward. Breder’s Hypothesis explains this phenomenon: Elongated fish with the pectoral fins low on the body create braking forces oriented horizontally without a vertically oriented lift component, leading to a force that would lead to substantial pitching without an opposing force (Fig. 8) (Drucker & Lauder, 2003). 

Fig. 8 A representation of Breder’s Hypothesis as it applies to Oncorhynchus mykiss. The arrows represent the velocity of the fish while the broken lines show the angle of inclination of the center of mass of the fish above the horizontal. An angle of inclination of 22.3 degrees supports Breder’s hypothesis (Drucker & Lauder, 2003). 

The mobility of the fin base allows for the kinematic versatility pectoral fin; this increased maneuverability helps fish evade predators, catch prey, and form complex shoals, providing an evolutionary advantage (Drucker & Lauder, 2003). 

Shoal structure and composition 

Shoals are typically three-dimensional structures that vary greatly in shape and size over time, even among the same species. They are highly homogenous—the fish that make them up are often of the same species or very similar in appearance and swimming abilities. Shoals may split into smaller groups and then may join other groups to form a larger group, remaining constant for very short periods—never exceeding one day, and typically limited to only for a few minutes or hours (Pavlov & Kasumyan, 2000).  

Shape  

The shape of a school is one of the parameters that may vary greatly over a period of time as the fish redistribute to transition between the different shapes of schools (Pavlov & Kasumyan, 2000). Moving or “polarized” schools are highly coordinated. All fish in a polarized school face the same direction and move parallel to each other, resulting in curved or arching movement. When a school stops moving to feed, it becomes a “foraging” school. Fish in a foraging school disperse and the school becomes rounded. When fish are at rest, they disperse further than when in a foraging school to form a “resting” school and hang inactively in midwater. In the presence of a predator, schools form a rounded “defensive” or “look-around” school, similar in shape to foraging schools, but are denser (ie. fish are closer together). Fish face different directions, usually towards the outside of the school (Fig. 9) (Pavlov & Kasumyan, 2000). 

Fig 9. (1) Polarized moving school, (2) resting school, (3) feeding school, (4 and 5) side view of feeding schools of pelagic predators, (6) look-around school, (7 and 8) defensive schools evading a predator (Pavlov & Kasumyan, 2000). 

Size

The number of fish in a school at a given time is extremely variable as schools frequently split and rejoin. Depending on the species of fish, the average number of fish in the school also differs; large predators and young freshwater fish tend to form smaller schools (Pavlov & Kasumyan, 2000). Typically, school size is measured by its length, width, and depth, rather than by the number of individual fish. School size can range from a few meters, and up to several hundred. For example, the European anchovy Engraulis encrasicolus, can from schools up to 400,000 square meters in area (Fig. 10, Fig. 11) (Pavlov & Kasumyan, 2000).  

Fig. 10 Shoals of anchovies forming a “dark shadow” as seen from above (Popular Science Team, 2014).  

Fig. 11 Shoals of anchovies (Popular Science Team, 2014).  

Composition 

The composition of schools is often highly homogenous in species, size, and shape of individuals, and activity. For example, the sizes of fish in a school do not typically differ more than 50% of the average body length of fish in the school (Shaw, 1962). This is because fish that are phenotypically different from the rest of the school—for example in appearance or swimming ability—are more likely to be attacked by predators. The greater the physical similarities are between fish, the higher the survival rate of fish under immediate predation threat.  

There are, however, some cases of mixed-species schools. Schools of young fish tend to be less homogenous and have a lesser ability to retain unity at rapid maneuvers, mainly due to the presence of many different-aged fish. The lesser homogeneity in young-fish schools allows mixed-species schools to form and explains why mixed-species schools are more common among young fish than among adults (Pavlov & Kasumyan, 2000). 

Factors that impact shoaling 

There are several biotic and abiotic factors that impact shoaling including food-availability, predators, light, and sound. For example, the degree of hunger and level of food motivation modify schooling behavior. Fish show higher locomotion under food deficit, and in non-moving schools, food deprivation leads to dispersion and lower school density. The presence of a predator or other frightening stimuli causes significant changes in the behavior of a school. For example, the movement speed and density of the school increase, and the school takes a more spherical shape (Pavlov & Kasumyan, 2000). 

Temperature, current, and density of visual landmarks also impact the formation of schools. For example, school behavior is heavily influenced by noise and light, particularly in smaller groups where the effect is stronger (Jhawar et al., 2020). These sensory cues are essential for fish to school which is crucial for their survival. 

Vision is the sensory basis of schooling fish, and so when there is not adequate light, fish are less able or no longer able to imitate their neighbors which significantly increases the risk of predation (Pavlov & Kasumyan, 2000). The greater risk to fish in low light explains why many schooling fish disperse in the evening and become less active, as this makes the fish less conspicuous to predators and therefore increases the survival rate of the fish. 

Furthermore, a fish’s capacity to maintain orderly and cohesive group behavior may be seriously disrupted by noise (Jhawar et al., 2020). Marine ecosystems are heavily subjected to noise pollution from human activities like ships, industrial processes, and underwater building. This noise may have a detrimental impact on fish schools’ behavior, making it more difficult for them to move, obtain food, and avoid predators. The degree of disturbance in the fish school is determined by the intensity of the noise. Higher noise levels interfere with a fish’s ability to communicate, leading to chaotic and disorderly movement, preventing schooling. Lower noise levels, however, still allow the fish to maintain some degree of synchronization (Jhawar et al., 2020).  

Synchronization and communication between fish in a school  

While vision is the main sensory mechanism for synchronization in schools, the ability of fish to detect changes in water pressure and communicate using electrical signals also contributes to the unity of a school. For example, a blinded Anchoviella, despite being unable to see, is still able to swim with a school (Gray & Denton, 1991). Especially as the speed of a school increases, other senses can become just as important as vision (Gray & Denton, 1991). 

Sound and pressure waves 

The octavo-lateralis system is composed of the lateral line organ and the inner ear and allows fish to detect the acceleration associated with changes in pressure generated by sounds or the movement of things in their environment (Braun & Coombs, 2000). The lateral line system is composed of neuromasts, a type of mechanoreceptors, which are stimulated by water movement (Fig. 12) (Webb, 2011). While these two systems serve similar functions, they operate  over different spatial ranges (Gray & Denton, 1991). 

Fig. 12 The Octavo-lateralis system of fish. The upper diagram shows the inner ear structure while on the lower diagram the lateral line system composed of different neuromasts is shown (Coombs & Van Netten, 2005). 

Since water is effectively incompressible, even slight movements produce measurable pressure differentials. These pressure differences propagate as water waves and are used by fish to communicate, similar to how many land organisms use sound waves to communicate (Braun & Coombs, 2000; Gray & Denton, 1991; Larsson, 2024). As fish move, they produce fast pressure pulses followed by slower pulses. The fast pressure pulses last from 3.5 to 7 milliseconds. It was hypothesized that these fast pressure pulses are produced by muscle movements on the swim bladder. After the fast pressure pulses, the fish produce some slow pressure pulses, which coincide with the fish’s movement (Gray & Denton, 1991). 

The amplitude of the pressure pulses, and whether the pressure compresses or decompresses are important information generated by a fish. The fast pressure pulses are distributed around a fish (Fig.13).  

Fig. 13 Distribution of fast pulse pressure along the horizontal plane of herring. The filled black box shows compression, and the open ones represent decompression. The area of the box represents different pressures (in Pascals) (Gray & Denton, 1991). 

Based on the direction of pulses, a fish is able to identify changes in the movement of its neighbors so that it may rapidly adjust their movements to maintain school synchronization (Gray & Denton, 1991). However, it requires the distance between fish to be smaller than a fish’s length for the fish to be able to detect the fast pulses. Thus, when fish are closer than a fish’s length, they actively school, further providing evidence for the use of fast pulses for fish communication in a school (Gray & Denton, 1991). 

Moreover, as fish move, they produce some movement sounds that can be detected by other fish in the school. As sound travels five times faster in water than in air, these movement sounds can also be important for fish to achieve synchronization (Gray & Denton, 1991).   

The signals generated by the movement of fish in water also help individuals or schools find another school. The signals that individual fish generate depend on their size and shape (Larsson, 2024). Fish with a larger size produce waves with larger pressure (Gray & Denton, 1991). To form a shoal with similar size of fish, they detect the signals generated by other fish (Larsson, 2024). 

Electrical Signals

Some shoals, such as the mormyrids, are mainly active during nighttime and in turbid water where the fish cannot solely rely on their vision or octavo-lateralis system. (Moller, 1976) To perform coordinated movements in such environment, the fish use the electric field. Some fish generate their own electric dipole field through their electric organ. Their electric organ is composed of cells called the electrocytes. These cells have some resting potential, and as they are excited, sodium ions flow into the cells, making the inside more positive. This is followed by the exit of potassium out of the cells. These flows of ions generate electric currents and thus, an electric field. By arranging the electrocyte in series and in parallel, different species of fish generate different electric field signals that allow for species-specific communication. While some electric fish discharge strong and intermittent currents for catching or stunning prey, others discharge their organ continuously for communication (Bennett, 1988). 

This electric organ discharge is one of the main forces contributing to the cohesion of a shoal of fish. It is shown through experiments that without electric organ discharges, mormyrid fish can no longer perform parallel lineup and single file swimming which occurs when fishes swim one behind another and regroup without colliding into one another (Fig. 14) (Moller, 1976). This demonstrates that fish use multiple systems, from vision to electric signals sensing, to form a shoal of fish (Larsson, 2024). 

Fig. 14 Electric field emitted by two mormyrid fish through their relative electric organ discharge (EOD) for group coherence (Worm et al., 2021).  

Advantages of shoaling

Shoaling and schooling behaviors are advantageous for fish as it allows them to learn from schoolmates, achieve greater swimming efficiency, higher defense, better eating, and safer migration.  

Learned Reflexes

Fish develop conditioned reflexes relatively fast, based on both individual and social learning (Leshcheva and Zhuikov, 1989). For example, the tendency of fish to form schools is reflexive, is independent of the individual experience of the fish, and often dominates other innate behaviors. In most cases, a school’s response to stimuli is driven by individual responses, such as changes in posture, which are then rapidly imitated by other fish in the school. The responses of individuals are learned very quickly as group reflexes. However, in the case that conditioned responses are maladaptive or unimportant, the school loses these responses due to the lack of reinforcement (Pavlov & Kasumyan, 2000). The ability of schooling fish to rely on both individual experiences and that of schoolmates to rapidly create a pool of useful conditioned reflexes “is a most important function of schooling behavior” (Pavlov & Kasumyan, 2000). 

Eating

Schooling is also beneficial in that it facilitates eating. Due to the larger number of fish in a school as compared with a solitary fish, schools can locate food more quickly, and feed more efficiently and intensely (Pitcher 1986). The greater the school size, the greater the length and frequency of time that fish can feed. Schooling also results in increased food competition, which in turn increases intensity of feeding and food availability as competition drives the exploration of new food and spatial resources. Furthermore, competition within schools’ results in fish consuming more food, and resuming normal feeding behavior more quickly after stress (Pavlov & Kasumyan, 2000). 

Migration

Moving in schools facilitates migration as it makes fish less vulnerable to predators, more successful in passing dangerous regions, reduces energy expenditure, and allows fish to determine the correct direction of migration faster (Pavlov & Kasumyan, 2000). 

Defence and Anti-Predator Strategies

One of the most important advantages of a shoal is its anti-predator effects. Schooling fish can detect danger at a much greater distance than solitary fish as being in a group allows them to better distinguish the environmental noises. As previously mentioned, fish of similar size generate similar noises since the amplitude of their movements is alike. The similarity of noise makes it easier for them to recognize environmental noises generated by sources other than the school (Larsson, 2024). Fish’s pectoral fins allow for fish to hover (Drucker & Lauder, 2003), allowing a school of fish to synchronously stop their movements for some short intervals. These synchronized stops allow for the fish to listen to signals generated by outside sources (Larsson, 2024). 

While a large group of fish might seem to be a feast for a predator, the school is an attempt to threaten the predator away. Under increasing threat, greater numbers of fish begin to dart back and forth, making it difficult for the predator to target and successfully attack a fish (Pavlov & Kasumyan, 2000). Furthermore, due to the symmetrical organization of fish in a school, the pressure waves of individual fish form interfere constructively or destructively with each other, forming larger wave signals similar to the ones emitted by a large animal (Larsson, 2024). 

Some fish can generate their own electric field, some predators use this to their advantage and detect the location of the fish by sensing the electric field radiated by their prey. However, to generate a clear image of their prey, they need to be at least five body widths away from their prey. As they move closer to a shoal of fish, they cannot distinguish the electric field of the individual fish and produce a clear image of the individual fish (Fig. 15) (Larsson, 2024). 

Fig. 15 The red fish represents the predator. In A, it can easily detect an individual fish. In B, as it encounters a shoal of fish, it cannot use its electrosensory system to distinguish individual fish (Larsson, 2024). 

Furthermore, each fish in the shoal generates its own pressure wave, these signals combine to form a complex pattern, preventing the predator from knowing the precise location of an individual fish. (Larsson, 2024) Thus, some predators attack through dissembling the structure of a shoal and eat the individual fishes that are being isolated (Larsson, 2012). 

Other than pressure waves the fish generate, a shoal of fish also actively creates waves at water surface for anti-predator’s purposes. At first, while fish undergo birds‘ attack, some of them dive into water and hit the water surface with their fins. Taking that diving response as a cue, other neighboring fish dive into water as well. This evolved into synchronized diving behavior (Doran et al., 2022). This synchronized diving behavior can even be performed by a multispecies group of fish. For instance, sulphur molly and gambusia dive together under the attacks of birds. (Lukas et al., 2023) These waves create a visual effect that the fish are moving away from the predator and confuse the birds. These waves are shown to be able to double the time interval between the birds’ attack, to decrease the capture probability and to even drive birds to attack elsewhere (Doran et al., 2022). 

Movement and hydrodynamic efficiency in fish schools 

The positioning of fish within a school reduces the energy expenditure of individuals. By synchronizing their movements and taking advantage of the vortices and wake flows generated by their neighbors, fish can swim more efficiently, allowing them to swim greater distances, improve endurance, and increase their chances of survival in the wild (Zhang et al., 2023).  

There are two main hypotheses that describe the hydrodynamic efficiency of coordinated swimming. The vortex hypothesis describes how neighbors situated behind one another engage with the vortices created by the fish in front of them, allowing them to efficiently ‘ride’ in the fluid and thus swimming with less effort (Pan & Dong, 2020; Wei et al., 2022; Zhang et al., 2023). The channelling effect hypothesis describes how fish swimming next to each other creates a channel that eases water flow and reduces drag. Specifically, the turbulence generated between two leading fish helps reduce the water resistance experienced by the fish behind, allowing trailing fish to reduce their tail-beat frequency. Individuals within the school experience save a significant amount of energy because of the combination of vortex exploitation and channelling (Pan & Dong, 2020; Wei et al., 2022; Zhang et al., 2023). 

The vortex and channelling hypotheses can be further described in terms of phase synchronization and the spatial arrangement of fish in a school. 

Phase synchronization  

The wake generated by fish within schools enhances both hydrodynamic efficiency and individual thrust (Zhang et al., 2023). The wake patterns produced are crucial in predicting the overall hydrodynamic performance of fish in the school (Pan & Dong, 2022). These patterns are controlled by the phase difference between individual fish (Wei et al., 2022). Fish alternate their tail-beat phase to match that of their neighbors (Fig. 16). By fine-tuning the phase of their tail movements,’ fish enhance their thrust and swimming efficiency. This phase synchronization allows the school to function as a cohesive unit, with each fish contributing to the overall efficiency of the group (Zhang et al., 2023). The performance of the training fish is highly influenced by the phase difference between itself and the leading fish. This phase difference affects the timing at which the vortices shed by the leading fish reach the head of the trailing fish (Pan & Dong, 2022).  

Fig. 16 (a-e) Velocity vector diagrams of 5 fish silhouettes in different phase. f) diagram of fish body tail amplitude (Zhang, Pang, Wu, Liu & Zhong, 2023). 

Phase synchronization refers to the coordinated timing of tail movements within the school. The phase differences vary from 0° to 360°. Studies have shown that the highest net thrust and swimming efficiency occur when fish in a school keep a phase difference of 180° (Pan & Dong, 2022). This synchronization allows trailing fish to maximize the benefit of the vortices generated by the leader and the neighboring fish, further improving hydrodynamic efficiency. Interestingly, when the phase difference is 90°, trailing fish achieve the greatest propulsive efficiency, with energy savings of up to 58% compared to swimming alone (Pan & Dong, 2022). However, the thrust production is maximized at 0° phase difference, where a leading fish’s vortices provide direct energy-saving benefits to the trailing fish.  

Spatial arrangement  

The density and shape of the school are key factors influencing how fish interact with the flow fields generated by their neighbors (Pan & Dong, 2020). A commonly observed formation is the diamond configuration (Fig. 17), in which the snout of one fish is ahead of the tail of the fish in front of it, allowing the trailing fish to take full advantage of the vortices shed by the leader (Deng & Shao, 2006). The wake vortex produced by the leader is a slender low-pressure area, and the follower uses that area to optimize their swimming efforts (Zhang et al., 2023). This interaction helps the follower fish conserve energy through more efficient movements. 

In Figure 17, fish A generates vortices that move in the opposite direction of its swimming direction. A fish swimming directly behind fish A must expend additional energy to maintain the same speed, as these counteracting vortices create resistance. Fish B, however, requires a less effort vortices align with its swimming direction, acting as additional propulsion. Studies have determined that the best position is midway laterally between the two fish of the preceding row. Fish in the best positions can swim up to 30% higher than fish in the worst positions with equal thrust (Zhang, Pang, Wu, Liu & Zhong, 2023). 

Fig. 17 A horizontal layer of fish in a school in a diamond configuration as seen by the dotted line. Arrows show direction of forces produces by the vortices generated by the three fish in the middle (Zhang et al. 2023). 

The combination of vortices, pressure zones, and synchronized movements enables the school to maximize overall hydrodynamic efficiency. 

Case study: Atlantic Mackerel 

Mackerel schools are excellent examples of how phase synchronization can improve efficiency, allowing the group to support high speeds over long distances with reduced energy expenditure. The Atlantic Mackerel are fast-swimming fish that often form large schools of many thousands in the open sea (Jordan & Evermann, 2012). They can swim up to 50 meters in 10 seconds (Parker, 2023). This is partially due to them adapting over time and now using vortices and synchronizing tail movements to swim more efficiently (Fig. 18) (Zhang et al., 2023). 

Fig. 18 Graph illustrating the difference between synchronized and unsynchronized tail movements in fish. In the top graph, there is a phase shift of 0° (or 180°), meaning their tail movements are synchronized. In the bottom graph, both fish swim unsynchronized creating a phase shift of 90° (Anne-Sophie Roy’s own artwork). 

An Atlantic Mackerel will align itself to create a phase shift of 180° with the fish in front of it by synchronizing its tail movements (Zhang et al., 2023). This optimal arrangement allows the Mackerel to achieve high speeds efficiently.  

Conclusion

Evolution has driven the creation of some of the most intriguing and adaptable species and physical structures on Earth as solutions to surviving different environments. It has created more than just individual organisms and structures. It has created groups and communities to ensure survival. Among all the animals living in groups, schools of fish moving in coordinated manners is one of the most fascinating examples of an organism’s adaptations to its environment.  

Due to their physical structures, fish acquired flexibility in water, allowing them to rapidly adjust their movements to coordinate with their neighbors without colliding with one another. For instance, contractions of the trunk muscles generate body undulations that displace vortices in the water, propelling the fish efficiently. Sculling motions of the pectoral fins create lift and enable hovering, while their cupped shape reduces drag and helps regulate swimming speed. 

To coordinate with their neighbors in differing environments, fish rely not only on vision, but on other sensory inputs including pressure waves and electrical signals. The rapid information exchange between neighboring fish in a school allow them to synchronize even in dark and in turbid water and contributing to their ability to confuse their predators and enhance hydrodynamic efficiency.  

Our current understanding of schools is in its infancy. Further properties and formation of the shoal remain to be investigated. Fully understanding the advanced and complex nature of this phenomenon will only elucidate the intricate and remarkable components of the adaptation of fish to its environment over time. 

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