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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. 

Invasive alien species threaten natural ecosystems worldwide, prey on native species, and deplete their food sources. Mosquitofish is one of the most invasive freshwater fish worldwide and its negative impacts on the native fauna are alarming. Despite the urgency of contrasting the mosquitofish invasion, we have access to very few methods to combat them. Even when successful, these methods can be excessively labor-intensive or dangerous to native species. Robotic predators may constitute a promising tool in combating mosquitofish. Our group has recently proposed the use of a robotic predator that can perform targeted attacks against mosquitofish. The robotic predator consists of three operational parts: a two-dimensional robotic platform, a magnetically connected replica of a native mosquitofish predator, and an in-house developed live tracking software. The robotic replica was programmed to swim along a predetermined trajectory and randomly target mosquitofish in real time through a dedicated tracking software. Building on available experimental results, we put forward a comprehensive mathematical toolbox based on symbolic dynamics, recurrence quantification, and information theory to detail the behavioral interaction between the robotic predator and mosquitofish. 

Invasive alien species threaten biodiversity worldwide and contribute to biotic homogenization, especially in freshwaters, where the ability of native animals to disperse is limited. Robotics may offer a promising tool to address this compelling problem, but whether and how invasive species can be negatively affected by robotic stimuli is an open question. Here, we explore the possibility of modulating behavioural and life-history responses of mosquitofish by varying the degree of biomimicry of a robotic predator, whose appearance and locomotion are inspired by natural mosquitofish predators. Our results support the prediction that real-time interactions at varying swimming speeds evoke a more robust antipredator response in mosquitofish than simpler movement patterns by the robot, especially in individuals with better body conditions that are less prone to take risks. Through an information-theoretic analysis of animal–robot interactions, we offer evidence in favour of a causal link between the motion of the robotic predator and a fish antipredator response. Remarkably, we observe that even a brief exposure to the robotic predator of 15 min per week is sufficient to erode energy reserves and compromise the body condition of mosquitofish, opening the door for future endeavours to control mosquitofish in the wild.