  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.
