Daphnia swarms: From single agent dynamics to collective vortex formation

Swarm theories have become fashionable in theoretical physics over the last decade. They span the range of interactions from individual agents moving in a mean field to coherent collective motions of large agent populations, such as vortex-swarming. But controlled laboratory tests of these theories using real biological agents have been problematic due primarily to poorly known agent-agent interactions (in the case of e.g. bacteria and slime molds) or the large swarm size (e.g. for flocks of birds and schools of fish). Moreover, the entire range of behaviors from single agent interactions to collective vortex motions of the swarm have here-to-fore not been observed with a single animal. We present the results of well defined experiments with the zooplankton Daphnia in light fields showing this range of behaviors. We interpret our results with a theory of the motions of self-propelled agents in a field.