Swarm Behaviour - Models

Models

The simplest mathematical models of animal swarms generally represent individual animals as following three rules:

1. Move in the same direction as your neighbours
2. Remain close to your neighbours
3. Avoid collisions with your neighbours

The boids computer program, created by Craig Reynolds in 1986, simulates swarm behaviour following the above rules. Many subsequent and current models use variations on these rules, often implementing them by means of concentric "zones" around each animal. In the zone of repulsion, very close to the animal, the focal animal will seek to distance itself from its neighbours to avoid collision. Slightly further away, in the zone of alignment, the focal animal will seek to align its direction of motion with its neighbours. In the outermost zone of attraction, which extends as far away from the focal animal as it is able to sense, the focal animal will seek to move towards a neighbour.

The shape of these zones will necessarily be affected by the sensory capabilities of the given animal. For example the visual field of a bird does not extend behind its body. Fish rely on both vision and on hydrodynamic perceptions relayed through their lateral line, while Antarctic krill rely both on vision and hydrodynamic signals relayed through antennae.

However recent studies of starling flocks have shown that each bird modifies its position, relative to the six or seven animals directly surrounding it, no matter how close or how far away those animals are. Interactions between flocking starlings are thus based on a topological rule rather than a metric rule. It remains to be seen whether this applies to other animals. Another recent study, based on an analysis of high speed camera footage of flocks above Rome and assuming minimal behavioural rules, has convincingly simulated a number of aspects of flock behaviour.