A flock of starlings. At certain times of the year we can observe so many unique, large black bodies circling in breathtaking descents and ascents in the sky, creating spectacular choreographies. In reality, hundreds, thousands of birds - starlings to be precise- synchronise their movement to keep the group cohesive and react collectively to predator attacks and external stimuli.

An imitative mechanism generates this collective phenomenon. Each bird adapts its flight direction and speed to that of a dozen birds nearby. In this way, when one bird changes its motion, its neighbours imitate it, and, by a sort of word of mouth, the change spreads throughout the group.

The fundamental necessity for this spectacular phenomenon called flocking is that the individuals remain within the group, moving in a coordinated manner, between braking and accelerating, having to submit to a series of mechanical and physiological constraints required by the complex flight dynamics. How birds regulate their speed within the group is not yet well understood.

In a recent paper published in Nature Communications, the Cobbs group (Collective behaviour in biological systems), which brings together researchers from Sapienza University of Rome and the CNR Institute for Complex Systems in Rome, suggests a new mathematical model that explains precisely how individuals within a flock of birds regulate their speed.

"Imagine that we experience on ourselves a mechanism similar to the flight of starlings when we are in traffic or on the motorway and adjust our gait according to the cars in front of us. When a car brakes, those in its immediate vicinity imitate it. The change in speed then propagates to the whole line of cars, which collectively slow down", says Antonio Culla, a  Physics PhD student at Sapienza University, and Irena Giardina, a member of the group and first author of the article.

"But there is another element to consider," Culla continues. "The speed of a car is limited by its engine: a hatchback cannot reach the speed of a sports car. Similarly, because of its physiological structure, a starling cannot fly as fast as a hawk".

But how is this speed control modelled?

Starlings have a preferred value of flight speed (about 43 km/h), called reference speed, due to their physiological structure. When they are in flight within a group of their peers, it is almost effortless to move at a speed slightly different from the reference speed, while it is challenging to move much faster or much slower.

In the proposed theoretical model, the individual element of the flock regulates its speed within the group dynamic, as long as it remains within reasonable values, like a kind of limiter on a car, which allows the driver to deviate from the reference value, but not to exceed a set limit.

The unique database of flocks of starlings built by the Cobbs group over the past 15 years, unique in that it includes the three-dimensional trajectories of 45 flocks of various sizes (from 10 to 3000 birds), has made it possible to prove the effectiveness of the study. The new model allows the elements within the flock to coordinate their movements and be highly correlated with each other while maintaining a speed close to the reference speed, just as in flocks observed in the field.

The Cobbs research group's study opens up new avenues towards understanding biological systems also in robotics and engineering.

References: 

Marginal speed confinement resolves the conflict between correlation and control in collective behaviour - Andrea Cavagna, Antonio Culla, Xiao Feng, Irene Giardina, Tomas S. Grigera, Willow Kion-Crosby, Stefania Melillo, Giulia Pisegna, Lorena Postiglione & Pablo Villegas - Nature Communications (2022) DOI https://doi.org/10.1038/s41467-022-29883-4

Further Information

Irene Giardina 
Department of Physics 
irene.giardina@uniroma1.it