A complete account of the behavioral repertoire uncovers principles of larval zebrafish hunting behavior

In goal-directed behavior animals select actions from a diverse repertoire of possible movements. Accurately quantifying the complete behavioral repertoire can uncover the underlying rules that guide such goal-directed behavior. However, these movements are usually complex, high-dimensional, and lead to various outcomes, posing a challenge to fully capture the complete repertoire. By tracking freely hunting zebrafish larvae using a highspeed camera and analyzing their movements, we developed a mathematical model that accurately reproduces the complete repertoire. Using the model, we show that fish position and change in heading angle following a movement are coupled, such that the choice of one of them limits the possibilities of the other. This repertoire structure uncovered fundamental principles of movements, showing that fish rotate around an identified rotation point and then move forward or backward along straight lines. From the uncovered movement principles, we identified a new guiding rule for prey interaction: in each movement, fish turn to face the prey and then move forward or backward. This enables decoupling between orientation and distance selections of the fish during the hunt. These results provide a comprehensive and continuous description of the repertoire of movements, reveal underlying algorithmic rules that govern the behavior, and offer insights into the potential neural implementation of the repertoire.