From agent-based dynamics to a kinetic theory of jellyfish swarms
Massive jellyfish swarms observed at sea can extend over tens of kilometres and contain millions of individuals, yet the mechanisms governing their formation and large-scale dynamics remain poorly understood. Agent-based models provide a framework for describing this dynamics based on jellyfish responses to ocean currents and environmental cues, but become computationally prohibitive when extended to large populations and spatial scales relevant to ocean circulation. Here we derive a continuous kinetic theory from an active-particle model of jellyfish motion. The resulting Fokker-Planck framework incorporates transport by prescribed currents, stochastic reorientation, direct interactions and stimulated steering, allowing chemical signalling to be represented through a coupled field. We further derive a hydrodynamic closure for large swarms by exploiting the separation between fast orientational and slow spatial dynamics, yielding a reduced density equation suitable for implementation in ocean-current models. This framework provides a route from individual behavioural mechanisms to continuum descriptions of jellyfish populations and establishes a basis for constraining model parameters using observations and in-situ measurements. This approach offers a theoretical foundation for future numerical prediction of large jellyfish swarm formation and evolution in realistic ocean flows.