"It turns out that the entire group can respond indirectly to a single individual, as each individual's movement response is a signal to its next neighbour," said Lewis, the Canada Research Chair in Mathematical Biology. "By this method, signals are passed quickly from individual to individual. So for example, one fish turns, causing the next one to turn, then the next one, and so on. This produces the complex collective behaviours--swarm formation, zig-zag group movements--that emerge from the ‘bottom up? simply based on interactions between neighbors."
Until Eftimie’s work, these complex emergent patterns could not be connected clearly to simple rules for the small scale communication between individuals.
People have had some success in proposing rather complex and detailed explanations for how specific species form into groups, says Lewis. "What Raluca's work does is show that very simple and straightforward sets of rules can produce the complex kinds of patterns seen in nature," says Lewis, also from the Department of Biological Sciences. "Her work has stripped out the unnecessary detail to the core elements of communication that give rise to the patterns found in large scale groups."
In particular, the researchers looked at the direction from which animals can receive signals from their neighbors. "For example, some species of birds use directional communication, and therefore, we may assume that in this case the behaviour of an individual will be influenced by the signals received from those con-specifics that face towards this individual," said Eftimie. "Based on these observations, we come up with some simple rules that can describe the different ways animals communicate. Then we incorporate these rules into the mathematical model, and check what kind of movement patterns we get."
The team came up with 10 complex patterns. Some are classical, such as stationary pulses, ripples or traveling trains but they
Source:University of Alberta