Effects of environmental features on flocking behavior

Social animals or insects in nature often exhibit a form of emergent collective behavior known as flocking. Animal flocks are strongly affected by the spatial heterogeneity representing static environmental factors, such as landscape. To investigate how this heterogeneity affects flocking behavior, I constructed a two-dimensional, lattice-based environment, in which the spatial heterogeneity was generated using a neutral landscape model. A value ranging from 0.0 to 1.0 was assigned to each lattice site. High values represent favorable environmental conditions, and thus, individuals tend to be attracted to the area with the highest values. The value H controlled the degree of heterogeneity and the value h represented the amplitude of the heterogeneity. To characterize the effect of the spatial heterogeneity, I introduced the order parameter, ?, defined as the absolute value of the average unit velocity. When all individuals move in the same direction, the value of ? is 1, while the value of ? becomes 0 in the case where all individuals move randomly. In this simulation, the flock size, N, has the values of 20, 40, 60, 80 and 100. I investigated the average value of ? and ?_s, for 1500 < t < 2000. The simulation results showed that the value of ?_s increased with an increase in H, regardless of N, until becoming saturated. When the value of h was higher, the value of ?_s became lower.