Aerial photographs of migrating wildebeest herds reveal striking distributional patterns, including wavy fronts. These patterns vary over scales that are much larger than the individual’s perceptual range, and thus cannot be explained simply as random fluctuations on uniformity. Furthermore, since the individual is only aware of its immediate surroundings, broad-range patterns must be explained in terms of local decisions. This paper suggests a model for the dynamics of large herds and a mechanism for their self-organizing pattern formation. We overcome the problem of modeling a two-dimensional distribution of a large population by considering only the leading layer. The conditions under which uniform fronts are stable (or unstable) are analyzed. In the latter case, small perturbations on uniformity evolve to large-scale patterns, as we demonstrate by computer simulations. We suggest this as a possible mechanism for spontaneous generation of long-range patterns.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics