Observação experimental de transição de fase schools-shoals em peixe-zebra (Danio rerio)

Abstract

The collective behavior of active matter encompasses a wide diversity of existing living organisms, ranging from microscopic systems to large-scale systems. Such systems are recognized by their individuals having the ability to transform internal or environmental energy into movement, characterizing them as out-of-equilibrium physical systems. An interesting example to observe is groups of fish that make use of information exchange between the individuals that make up the group to develop energetic, anti-predatory, and food-seeking benefits. From individual decisions, collective patterns of large-scale structures emerge that can be quantitatively analyzed. However, most of the definitions that address the emergence of these patterns, such as the structures of schools and shoals, are based on conceptual criteria of sociability. In this work, we analyze the phase transition of zebrafish groups, through the variation of density. To do so, we used video cameras to capture the position and velocity of zebrafish in a controlled environment. We considered a circular container with a diameter of 50 cm and a water depth of 5 cm, tracking the trajectories of zebrafish, varying the number of individuals N. Then, we investigated the correlation measures of the derivatives of the polarization, aggregation, and Dcentroid parameters used in this work, between the time series for groups of N = 2, 13, and 30 individuals, using the q-gaussian parameter that served to reinforce schools-shoals phase transitions of zebrafish. Thus, we are able to characterize a phase transition between fish groups through the average values of the time series of polarization, aggregation, and D-centroid parameters, influenced by density variation. In addition, we observed variation in the correlation between fish through the fluctuations of these same parameters. With the experimental data of these parameters, we were able to quantify the behavior of schools and shoals during our analyses.