Dynamical aspects of animal grouping: swarms, schools, flocks, and herds.

Grouping of animals is a natural phenomenon in which a number of animal individuals are involved in movement as forming a group. Examples are insect swarms and fish schools. In this article an attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes. Also presented is dynamical modeling for the group size distribution as a result of amalgamation and splitting processes of groups. Examples of animal grouping are described in detail. They are insect swarms, zooplankton swarms, fish schools, bird flocks, and mammal herds. The presented mathematical models are compared with data of these animal groupings.