Watch a flock of starlings for a few minutes and it’s easy to see its remarkable behaviour. The birds seem to move in synchrony even though they can be separated by the width of the flock itself. Somehow the movement of birds on opposite sides of the flock must be correlated even though they can only reasonably communicate with their nearest neighbours.
Just how this happens has been the subject of much fascination. One way to tackle this problem is to simulate flocking behaviour on a computer, compare the simulation with the actual flocking behaviour and thereby attempt to explain it.
This has certainly produced some interesting insights but it suffers from a serious lack of detailed measurements of real bird behaviour in large-scale flocks. That has recently changed with the advent of advanced computer vision techniques that can measure the position and velocity of a large number of moving objects in a single frame.
Today, William Bialek at Princeton University and a few pals use this newfound data to build the simplest theoretical model that can reproduce the actual behaviour of real flocks.
Their model produces a remarkable insight. They say flocks of starlings operate in a very special physical state that allows correlations between individual birds to extend more or less infinitely, in this case across the entire width of the flock.
Bialek and co begin by analysing the position and velocity of between 122 and 4268 starlings in 21 distinct flocking events. They use this data to work out the correlations between the movement of individual birds in the flock and the variance of their speeds relative to the average.
These measurements show that the behaviour of the birds is extraordinarily fine-tuned. Individual birds fly at a velocities that are very similar to those of their neighbours. In other words, they match both the speed and direction of birds flying nearby.
This raises an interesting question. Each bird’s behaviour is correlated with its nearest neighbours but under ordinary conditions, this correlation should decay over some characteristic distance scale, usually not much further than the distance between the birds themselves.
So by this way of thinking, only neighbouring birds can be synchronised creating small independent groups.
How then can the entire flock become synchronised? This is where a little physics comes in useful. Physicists have long known of phase changes in systems where a small change in one parameter can lead to a huge change in the bulk properties of the system.
One famous example is a magnet in which a small change in temperature causes the spins in a magnet to suddenly align. Below this temperature the bulk behaviour is as a magnet, below this temperature the material is not a magnet.
The important point, however, is that when this change happens, spins that are separated by great distances become correlated. In fact, the correlation scale becomes infinitely large.
The point at which this occurs in a system is known as a critical point. What seems clear about flocking is that it too can only occur at a critical point where the correlation scale extends across the entire flock. When this happens, all the small groups of neighbouring birds behave as one, which is what creates the characteristic flocking behaviour.
This critical behaviour falls naturally out of the model that Bialek and co have created and which they describe with great clarity as like a system of springs that connect each bird to its nearest neighbours and that can be tuned in a way that changes the influence they have on each other.
At first glance, it seems remarkable that the complex behaviour of such a large number of individual organisms can be so finely balanced to operate at a critical point.
“Biologically, birds may vary their speeds either for individual reasons, or to follow their neighbors, paralleling the competing forces captured in the model. In this language, the critical point is the place where social forces overwhelm individual preferences,” say Bialek and co.
But that implies is that there is something special about the social behaviour of birds that leads to this critical point. Just how birds manage the social interactions isn’t clear but they certainly provides a huge advantage. When a flock operates away from the critical point, a bird on the outskirts of the flock can only influence its nearest neighbours when a predator approaches.
But all that changes when the flock operates at the critical point. In that case, an individual that spots a predator can influence the behaviour of the entire flock. Indeed, there is much evidence that flocks are remarkably immune from predator attacks. “We know that attacks by predators on a flock have very low success rates,” say Bialek and co.
That’s a fascinating insight into the complex physics behind a remarkable and beautiful biological phenomenon. It may also provide insight into how artificial systems can exploit criticality. It’s not hard to imagine how this behaviour might be useful for controlling swarms of robots or even from routing information across networks.
Ref: arxiv.org/abs/1307.5563 Social Interactions Dominate Speed Control In Driving Natural Flocks Toward Criticality