Chapter 5: Moving Together
Picture by Dora Biro
Some of the most mesmerizing examples of collective animal behaviour are seen overhead every day. V-shaped formations of migrating geese, starlings dancing in the evening sky and hungry seagulls swarming over a fish market, are just some of the wide variety of shapes formed by bird flocks. Fish schools also come in many different shapes and sizes: stationary swarms; predator avoiding vacuoles and flash expansions; hourglasses and vortices; highly aligned cruising parabolas, herds and balls. This chapter investigates these moving schools and flocks and other collectives. The main modelling tool I will use in describing the dynamics of flocking are self-propelled particle (SPP) models. In SPP models ‘particles’ move in a one, two or three dimensional space. Each particle has a local interaction zone within which they respond to other particles. These models allow us to investigate the conditions under which collective patterns are produced by spatially local interactions. As we shall see, remarkably complex flocking patterns can emerge from only simple rules for between individual interactions.
Key ideas covered in this chapter: attraction and aggregation; alignment; propogation of directional information; self-propelled particle models; phase transitions; locust marching; rules of interaction between animals; starling flocks; complex moving patterns; milling behaviour; decisions on the move; many wrongs vs leadership; homing pigeons; evolution of flocking;confusion effects.
Links
Iain Couzin's homepage
Danny Grunbaum's homepage
Julia Parrish 's homepage
Starflag project
Tamas Vicsek's homepage
References
Biro, D., Sumpter, D. J. T., Meade, J. & Guilford, T. 2006. From compromise to leadership in pigeon homing. Current Biology, 16, 2123-2128.
Buhl, J., Sumpter, D. J. T., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. R. & Simpson, S. J. 2006. From disorder to order in marching locusts. Science, 312, 1402-1406.
Couzin, I. D., Krause, J., James, R., Ruxton, G. D. & Franks, N. R. 2002. Collective memory and spatial sorting in animal groups. Journal Of Theoretical Biology, 218, 1-11.
Hamilton, W. D. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
Niwa, H. S. 2004. Space-irrelevant scaling law for fish school sizes. Journal of Theoretical Biology, 228, 347-357.
Okubo, A. 1986. Dynamical aspects of animal grouping. Advances in Biophysics, 22, 1-94.
Parrish, J. K., Viscido, S. V. & Grunbaum, D. 2002. Self-organized fish schools: An examination of emergent properties. Biological Bulletin, 202, 296-305.
Radakov, D. V. 1973. Schooling in the ecology of fish. New York: John Wiley & Sons.
Vicsek, T., Czirok, A., Benjacob, E., Cohen, I. & Shochet, O. 1995. Novel Type Of Phase-Transition In A System Of Self-Driven Particles. Physical Review Letters, 75, 1226-1229.
Picture by Iain Couzin
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