There is a great diversity of social groupings of fish; within this broad spectrum of social groupings is a so-called school. Notemigonus crysoleucas is a species widely distributed in North America whose "schooling behavior" presents vision as a primary sensory modality and under certain evidence lateral line as a secondary. Numerous models have been proposed, many of which display realistic-looking dynamics, but nonetheless rely on untested assumptions about how individuals integrate information to guide movement. The purpose of this study was to build a model based on experimentally tested assumptions and to determine the most relevant factors that contribute to the formation and maintenance of the golden shiner school structures. A model of the Lagrangian-Newtonian type of school structure was built under the theoretical framework of natural structures (take into account that the school fish is a natural structure), using behavioral rules inferred directly from experimental data (trajectories of golden shiners swimming in two-fish and three-fish schools, positions and velocities). The factors we considered in this model were mostly social, and included the functional form of attraction and repulsion from neighbors (natural structure connection), and scaling of neighbor influence. The model was contrasted with another experimental data
Results/Conclusions
The model was adjusted considerably to the experimental data. It indicated that alignment emerges from attraction and repulsion, and pairwise interactions qualitatively capture the correct structure of spatial interactions in small groups, and this structure persists in larger groups of fish. Our model suggests that speed modulation in response to the positions and velocities of neighbors and the functional form of attraction and repulsion are a dominant component to the formation and maintenance of the structures.