# Birds of a feather… use marginal speed confinement to flock together

We’ve all experienced the stunning sight of a flock of birds soaring overhead, engaged in a magical, synchronous dance. How birds regulate their speed – keeping the flock from splitting – has eluded scientists. Even less well understood is how an individual bird’s change of speed affects others in the flock, even over large distances, such as in murmurations.

New modelling published in a paper in Nature Communications might have cracked the underlying mathematics.

Earlier models for flocking were based on each bird mimicking the behaviour of its neighbours and, the paper’s authors write, “assumed that all individuals within the group moved with the same constant speed”. But in nature – and even in artificial systems that exhibit flocking – the speeds of individuals fluctuate. Other earlier models also didn’t do a good job of making sure the theoretical birds couldn’t reach unreasonable speeds which the biomechanics of real birds simply couldn’t attain.

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Focusing on starlings (Sturnus vulgaris), the scientists tweaked their models until the behaviour of their computerised birds matched that of real birds. Starlings fly at 8 to 18 metres a second, but average flock speed is always 12 metres per second. Startlingly, “no matter how large the flock, individual speed changes are correlated to each other”, the authors write.

The statisticians argue that the key is “marginal speed confinement”. They write that there is a “natural” speed dictated by the physical limitations of the bird (or other flocker). Fluctuations around this velocity in this new model are restricted by marginal speed confinement which “ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations”.

Comparing their numerical results with footage from real-life starling swarms, the team’s model reproduced the observed traits of flocks ranging in size from 10 to 3,000 individuals.

While noting that marginal speed confinement may not be the only statistical reason for the observed behaviour in flocking, the researchers note that similar strategies may be used in other bird flocks. They also suggest that it may play a role in an array of biological collective behaviour such as the movement of bacteria, clusters of cells, insect swarms, or in sheep.

This new model is a step toward increasing our knowledge of collective behaviour in biology and could have practical applications in robotics to enhance correlation and reduce large speed fluctuations in drone swarms, the authors argue. The team notes that the subject of their research is not restricted to an understanding of “starling flocks, and not even only of natural systems, but of all instances, biological and artificial, of self-organised collective behaviour. Speed control is therefore a crucial issue in both biology and engineering.”