A flock of starlings flying over Rome. Credit: COBBS/CNR.
A new mathematical model explains how individual birds within a flock regulate their speed1. The model, developed by researchers at Italy’s National Research Council Institute of Complex Systems, is based on several years of experimental data collected by observing starling flocks in Rome.
Like many other birds, starlings synchronize their movements during flight so that they can respond collectively to the attack of a predator. This phenomenon, called flocking or murmuration, is based on imitation. Each bird adapts its direction of flight and speed to those of about a dozen birds that fly closest to it. When one bird changes its motion, its neighbours imitate it and the change spreads throughout the group. But until now, it was not well understood how individual birds regulated their own speed within the group.
The Collective Behaviour in Biological Systems (COBBS) group at CNR in Rome has built a database of flight trajectory for birds and midges, by compiling video footage from years of field observations. For birds, the researchers operated a sophisticated three-camera system from elevated locations in Rome, such as the roofs where starlings make their nests, to capture high-resolution footage of flocks as they move through the sky.
By applying statistical methods to the flight trajectories data, the researchers discovered that the flocking behaviour of starlings can be explained by a simple model where each bird flies at a preferential speed of about 43 km/h, the one that best fits their body structure. Small variations around this speed are allowed by the model, but larger variations are prevented so that no bird can fly much faster or much slower than the reference speed. The team used this rule to model the flock in simulation, and then verified that the results were similar to what was observed in footage of actual birds.
“In the near future, the research group could introduce in the model a description of the dynamics more faithful to reality, because for now a simplified description has been used and this model can reproduce only static quantities,” explains Antonio Culla, a COBBS PhD student in physics at the Sapienza University of Rome and one of the article’s authors. The model could also be applied to the collective behaviour of fish or insects, or could be used to help program drone coordination in robotics, adds Culla.
