Modeling Vortex Swarming In Daphnia
  Based on experimental observations in \textit{Daphnia}, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for \textit{Daphnia}, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single \textit{Daphnia}. To simulate vortex swarming of many \textit{Daphnia}, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance - as a special form of asymmetric repulsion between animals - leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in \textit{Daphnia} is provided by comparing experimental and simulation results for two animals. 
Robert Mach, Frank Schweitzer