DATA-DRIVEN RECOVERY OF TIME-EVOLVING CAUSAL INTERACTION NETWORKS AND STOCHASTIC DYNAMICS IN ZEBRAFISH GROUPS

Abstract

This thesis explores the collective behavior and dynamics of juvenile zebrafish (Danio rerio) shoals of varying group sizes, employing a multifaceted approach grounded in physics, information theory, graph theory, and stochastic analysis. We look at how groups of 4, 10, 60, 80, and 100 zebrafish interact. We examine two key behavioral metrics: rotation and polarization order parameters, and observe that the decay times derived from the autocorrelation functions of these metrics’ time series increase considerably as group size grows. This signals a heightened level of coordination that arises with increased density, with decay rates of the rotation order parameter in the largest group exhibiting a ten-fold difference compared to the smallest group. To learn more about how coordination and density work together, we used the Optimal Causation Entropy principle (oCSE) to build dynamic, time-evolving, causally- weighted networks that show how zebrafish shoals of sizes 4, 10, and 60 interact with each other. By leveraging these networks, and exploring them using graph theory, we relate the increase in coordination within denser systems to a more consistent, and less volatile causal structure. Within the context of network science, we measure the average number of interacting neighbors, then look at the emergence of leadership, provide a way to quantify it, and compare that across the three different groups. In the concluding part of this study, we use the Kramers-Moyal equation to com- bine Kramers-Moyal coefficients with Sparse Regression techniques, also known as equation learning, to derive interpretable, analytical expressions of stochastic differential equations describing the evolution of the rotation and polarization order parameters for the different group sizes, as well as the coupled differential equation that describes the concurrent evolution of these order parameters. Collectively, our findings cast light on the intricate relationships between collective behavior, emergent sustained coordination, information sharing, and stochastic dynamics in animal groups, providing a holistic framework for studying such systems.