Collective Behavior: Macroscopic versus Kinetic Descriptions

From individual to collective information processing in fish schools

Guy Theraulaz

Université Paul Sabatier

Swarms of insects, schools of fish and flocks of birds display an impressive variety of collective patterns that emerge from local interactions among group members. These puzzling phenomena raise a variety of questions about the interactions rules that govern the coordination of individuals’ motions and the emergence of large-scale patterns. While numerous models have been proposed, there is still a strong need for detailed experimental studies to foster the biological understanding of such collective motion. I will describe the methods that we used to characterize interactions among individuals and build models for animal group motion from data gathered at the individual scale. Using video tracks of fish shoal in a tank, we determined the stimulus/response function governing an individual’s moving decisions from an incremental analysis at the local scale. We found that both attraction and alignment interactions are present and act upon the fish turning speed, yielding a novel schooling model whose parameters are all estimated from data. We also found that the magnitude of these interactions changes as a function of the swimming speed of fish and the group size. The consequence being that groups of fish adopt different shapes and motions: group polarization increases with swimming speed while it decreases as group size increases. The phase diagram of model revealed that the relative weights of the attraction and alignment interactions play a key role in the emergent collective states at the school level. Of particular interest is the existence of a transition region in which the school exhibits multistability and intermittence between schooling and milling for the same combination of individual parameters. In this region the school becomes highly sensitive to any kind of perturbations that can affect the behavior of just a single fish.