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Abstract Fish schooling has attracted the interest of the scientific community for centuries. Energy savings have been long posited to be a key determinant for the emergence of schooling patterns. Yet, current methodologies do not allow the precise quantification of the metabolic rate of specific individuals within the school, typically leaving researchers with only a single, global measurement of metabolic rate for the collective. In this paper, we demonstrate the feasibility of inferring metabolic rate of swimming fish using the mouth‐opening frequency, a simple proxy that can be scored utilizing video recordings in the laboratory or in the field, even for small fish. The mouth‐opening frequency is independent of hydrodynamic interactions within the school, thereby mitigating potential confounding factors that arise when using locomotory measures associated with tail‐beat motion. We assessed the reliability of mouth‐opening frequency as a proxy for metabolic rate by conducting experiments on zebrafish (Danio rerio) using swimming respirometry. We varied the flow speed from 0.8 to 3.2 body lengths per second and extracted tail‐beat motion and mouth opening from video recordings. Our results revealed a strong correlation between oxygen uptake and mouth‐opening frequency for nonzero flow speeds but not in quiescent water. Contrary to our expectations, we did not find evidence in favor of the use of tail‐beat frequency as a proxy for metabolic rate. Overall, our results open the door to the study of individual metabolic rates in fish schools without confounding factors related to hydrodynamic interactions. 

The phenomenon of fish schooling - coordinated swimming of fish in polarized groups of specific spatial formations- is commonly observed in several species of fish. Fish schooling may even provide hydrodynamic advantages reducing the overall swimming cost of the group. To date, the role of hydrodynamics in coordinated swimming is not completely understood as it is difficult to separately study the role of hydrodynamic interaction from other forms of interaction between the fish. Here, we propose a statistical methodology based on information theoretic tools and flow velocity measurements, that can potentially tease out the hydrodynamic interaction pathways from visual and tactile ones. To avoid experimental confounds from bidirectional interactions and objectively understand cause-and-effect relationships, we design a robotic platform that mimics the behavior of two fish swimming in-line in a controlled setup inside a water channel. We examine the response of a flag to the fish-like unsteady wake generated by an actively pitching airfoil located upstream. We systematically quantify the passive hydrodynamic effect by studying the flapping motion of the flag located downstream of the airfoil in response to both periodic pitching and less predictable, random startling motion of the upstream airfoil. The study integrates experimental biomimetics with information theory to establish a deeper understanding of hydrodynamics in fish schooling. 

Fish often swim in crystallized group formations (schooling) and orient themselves against the incoming flow (rheotaxis). At the intersection of these two phenomena, we investigate the emergence of unique schooling patterns through passive hydrodynamic mechanisms in a fish pair, the simplest subsystem of a school. First, we develop a fluid dynamics-based mathematical model for the positions and orientations of two fish swimming against a flow in an infinite channel, modelling the effect of the self-propelling motion of each fish as a point-dipole. The resulting system of equations is studied to gain an understanding of the properties of the dynamical system, its equilibria and their stability. The system is found to have five types of equilibria, out of which only upstream swimming in in-line and staggered formations can be stable. A stable near-wall configuration is observed only in limiting cases. It is shown that the stability of these equilibria depends on the flow curvature and streamwise interfish distance, below critical values of which, the system may not have a stable equilibrium. The study reveals that simply through passive fluid dynamics, in the absence of any other feedback/sensing, we can justify rheotaxis and the existence of stable in-line and staggered schooling configurations. 

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory. 

Mathematical models promise new insights into the mechanisms underlying the emergence of collective behaviour in fish. Here, we establish a mathematical model to examine collective behaviour of zebrafish, a popular animal species in preclinical research. The model accounts for social and hydrodynamic interactions between individuals, along with the burst-and-coast swimming style of zebrafish. Each fish is described as a system of coupled stochastic differential equations, which govern the time evolution of their speed and turn rate. Model parameters are calibrated using experimental observations of zebrafish pairs swimming in a shallow water tank. The model successfully captures the main features of the collective response of the animals, by predicting their preference to swim in-line, with one fish leading and the other trailing. During in-line swimming, the animals share the same orientation and keep a distance from each other, owing to hydrodynamic repulsion. Hydrodynamic interaction is also responsible for an increase in the speed of the pair swimming in-line. By linearizing the equations of motion, we demonstrate local stability of in-line swimming to small perturbations for a wide range of model parameters. Mathematically backed results presented herein support the application of dynamical systems theory to unveil the inner workings of fish collective behaviour.