Emergence in Collective Animal Behavior

Nature has presented us a wide variety of fascinating collective behaviors in animals – birds flying in flocks, fish swim in shoals and wild horses move in herds. A number of models are proposed in order to understand the origin of collective behavior and reveal the underlining physics. In this paper, two theoretical models are reviewed: the discrete SPP model and the continuum hydrodynamic model. Both model show that long-range ordering arise as a result of local interactions of the system. The results are compared with recent quantitative experimental data and the emergence of ordered collective motion is discussed. In the evening sky of European countryside, thousands of starlings fly in a flock and move cohesively in one direction. The flock keep changing its direction every couples of minutes, and each individual bird flies with seemingly effortless skill to keep up the motion of the entire flock. While in the waters of Atlantic Ocean, the same trick is played by a school of herrings. Fish swim harmonically in the school as through they are programmed and know exactly what to do at any given time. We have all seen such amazing spectacles in real life or on television. Many words are used to describe the phenomenon: flocking, herding, schooling, swamping. These words are essentially the same, namely collective animal behavior. Figure 1: Images of collective behavior. (a) A typical fish school in the ocean [1]. (b) Starlings flocking in the dusk [2]. (c) Traffic flow in Paris [1]. (d) A swamp of fire ants [3]. (e) A Mexican wave in a football stadium [1]. (f) A group of marching locusts [1]. (b)