Experimental validation of an individual-based model for zooplankton swarming

The individual-based model of swarm maintenance proposed by Okubo and Anderson (1984) and Okubo (1986) is tested using data from aggregations of Daphnia magna and Temora longicornis swarming about a light shaft in the laboratory. The form of the model employed here consists of a Newtonian balance between random-flight diffusion (i.e., random excitation and drag) and a simple, linear concentrative force. Three model parameters k, ω, and B, which express the strength of the damping, concentrative, and excitational forces, are calculated from theoretical fits to digitized animal trajectories. These parameters provide a means of assessing the biological and physical forces which balance to maintain zooplankton swarms in a variety of settings: active swarming in turbulent regions, passive aggregation by convergent flows, or combinations of aggregative and dispersive behavior in quiescent environments. The appropriateness of the model to the laboratory swarms is verified using both kinematic criteria (the form of individuals’ velocity autocorrelations) and dynamical ones (velocity distributions and spatial acceleration fields; the ratio of swarm size to swimming speed).