Modeling zebrafish geotaxis as a feedback control process

Developing mathematical models of the feedback control process underlying animal behavior is of critical importance to understand their interactions with the environment and emotional responses. For instance, fish geotaxis (the tendency to swim at the bottom of the tank) is known to be a highly sensitive measure of anxiety, but how and why animals tend to display such a complex response is yet to be fully clarified. Leveraging the theory of stochastic differential equations, we develop a data-driven model of geotaxis in the form of a feedback control loop where fish use information about the hydrostatic pressure to dive towards the bottom of the tank. The proposed framework extends open-loop models by incorporating a simple, yet effective, control mechanism to explain geotaxis. We focus on the zebrafish animal model, which is a species of choice in the study of anxiety disorders. We calibrate the model using available experimental data on acute ethanol treatment of adult zebrafish, and demonstrate its effectiveness across a wide range of comparisons between theoretical predictions and empirical observations.