Do fish swimming in schools or birds flying in flocks have a collective spirit that enables them to move as one? Are they animals with highly developed cognition, a complex instinct or a telepathic gift? A recent study conducted by the research group led by Prof. Charlotte Hemelrijk of the University of Groningen points in another direction. Mathematical models of self-organization show that complicated collective behaviour can be the consequence of a few simple behavioural rules.
In an article in scientific journal PloS ONE (4 August 2011), Hemelrijk and scientific programmer Hanno Hildenbrandt use the StarDisplay computer model to describe the causes of the miraculous variety of shapes in flocks of starlings.
Schools of fish
Previously, Hemelrijk and her collaborators used a comparable computer model to investigate schools of fish. Observations in nature showed that these are always elongated. ‘Our models showed that the elongated shape of schools of fish were the automatic result of self-organization’, Hemelrijk says. In addition to the usual grouping and coordination, no extra rules are needed to achieve this. A fish swimming behind another one will slow down to avoid bumping into the one ahead of it and its former neighbours then move inwards to fill the gap that has opened up. This results in an elongated school.
Flocks of starlings, however, produce a much richer variety of shapes. Video footage of flocks of starlings flying around in search of a place to roost show fantastic variation all over the world. Round, broad, elongated, flocks that shift shape from funnels to hourglasses, thickening, thinning; these are all existing variations. People have wondered for ages how all these different shapes are able to be created. In the 1930s, British ornithologist Edmund Selous – also fascinated by flocks – even attributed the tremendous variety to telepathy.
‘We wanted to find out whether self-organization could provide an adequate explanation’, Hemelrijk states. The new StarDisplay model was once again based on a limited number of principles: birds are attracted to each other, they move in the same direction and they try to avoid bumping into one another. In addition, the model contains mathematical functions describing the flying behaviour using simplified aerodynamics. The simulated starlings experience a lifting force, drag and gravity, and bank when turning.
The program was used to simulate how flocks of starlings circle above a roosting place. Whenever starlings in the model left the area above the sleeping site they were made to turn back.
The turning probably happens differently in birds and in fish. According to the models and empirical research conducted by Hemelrijk’s group, individual fish on the outside of a turning group are able to accelerate slightly, while those on the inside slow down. This enables fish to maintain their original spot in the group and keeps the school elongated.
Birds in a flock, however, turn individually, as is shown in observations of circling rock pigeons published by American biologists Harold Pomeroy and Frank Heppner in 1992 (see illustration). This means that the positions of birds relative to one another change after making a 90-degree turn. Birds that were flying abreast are now flying one behind the other. And if yet another turn is made, the birds that were flying starboard are now suddenly flying portside.
Little variation in speed
This way of turning is one of the major factors leading to the variation in shapes. A flock that is flat and wide becomes long and narrow after a 90-degree turn. ‘StarDisplay shows us that this way of turning is a consequence of the fact that birds do not vary their speed very much’, Hemelrijk says. ‘If we figure more variation in speed into our model, the shapes become more elongated in the direction of the movement. In that case, the result that we had earlier for fish – where shapes remain elongated – also holds true for birds. ’
‘In the PloS ONE article we can only discuss a few of the causes of the variation in shapes of flocks of starlings’, Hemelrijk explains. In addition to the speed which can hardly be varied, other factors are the large number of individuals in the flock, the small number of partners – just seven – that each bird interacts with, making curves and banking in curves.
What has not been modelled is feeding behaviour and behaviour related to avoiding predatory birds. Air as medium, with factors such as wind and turbulence, has not been included in the model either. Hemelrijk: ‘Despite these restrictions, the model has given us quite a few hypotheses to test. This is invaluable, as researching such behaviour in the wild is extremely difficult without a good model to base yourself on.’