Starlings in flight: understanding the patterns of animal group movement
The earliest hypotheses formulated about collective animal behaviour were based on qualitative observations. Due to the absence of any quantitative empirical insight these hypotheses turned out to be purely speculative. It is from 1960s that the first empirical studies of collective animal behaviour in three dimensions were attempted that led to some quantitative results. These 3D studies of collective animal behaviour gave a first realistic perception of the structure of animal groups and their dynamic properties and the experimental techniques employed were sound. Yet these earlier studies were not satisfactory. The number of animals in all these studies was very low compared to natural conditions, where groups can range up to thousands, or even hundreds of thousands of individuals. Also these studies needed to be refined and developed, in order to produce more substantial results.
Keeping this in mind a consortium of ornithologists, physicists and biologists in Italy and other European countries begun studying birds under STARFLAG (Starlings in flight: understanding the patterns of animal group movement), a project financed by the European Commission. Their goal was to study collective animal behaviour, both with an empirical and with a theoretical approach.
Starlings in flight
Using statistical physics, optimization theory and computer vision techniques these researchers were able to produce quantitative and systematic data on the two main attributes of starlings in flight: global properties (shape, size, orientation and movement) and internal structure (density profile and neighbours distributions). In doing so their aim was two-fold:
i) To provide a detailed analysis of the mechanistic laws of flocking, at the global and structural level. This would enable them to set a new empirical benchmark for testing existing models of self-organized collective behaviour.
ii) They wished to characterize the attributes of flocks as emergent properties of the grouping phenomenon. To this end, they attempt to place their results in the context of the biological function of grouping, individual fitness consequences, interaction with the environment and mutual interaction between individuals.
Basically in their project the researchers collected three-dimensional data on large aggregations—thousands, rather than tens, of birds and then tried to analyze the data to determine the fundamental laws of collective behavior and self-organization of these bird aggregations in three dimensions.
Data Collection
Data were taken from the roof of Palazzo Massimo, Museo Nazionale Romano, in the city center of Rome, in front of one of the major roosting sites used by starlings during winter. Birds spend the day feeding in the countryside and come back to the roost in the evening, ∼1 h before sunset. Before settling on the trees for the night, starlings gather in flocks of various sizes and perform what is called “aerial display,” namely an apparently purposeless dance where flocks move and swirl in a remarkable way. By using stereometric digital photogrammetry and computer vision techniques they reconstructed for the first time the individual 3D positions and 3D velocities in 24 flocking events. A flocking event is a series of consecutive shots of a flock at a rate of 10 frames/s. Analyzed flocks had different numbers of birds (from 122 to 4,268 individuals) and different linear sizes (from 9.1 to 85.7 m).
Matching problem
The key to achieving the STARFLAG results was the solution of the correspondence, or matching, problem. When using any 3D technique, one must place into correspondence different images of the same animal. For example, in stereometry, one has two images of the group taken from two different points of view. In order to perform a 3D reconstruction, one must take a given animal’s image on one photograph, and identify the corresponding image on the other photograph. The matching problem is particularly severe when there are many similar animals positioned very close to each other, which, unfortunately, is typical in natural flocks. Until now, no computer algorithm has been able to do this automatically, and thus the matching was performed by hand. Clearly, this severely limited the number of animals and the density of the groups that could be studied. The researchers at STARFLAG solved this problem by using a blend of statistical physics, computer vision and mathematics.
Results
The researchers found that flocks are relatively thin, with variable sizes, but constant proportions. They tend to slide parallel to the ground and, during turns, their orientation changes with respect to the direction of motion. Individual birds keep a minimum distance from each other that is comparable to their wingspan. The density within the aggregations is non-homogeneous, as birds are packed more tightly at the border compared to the centre of the flock.
They also found that a given bird interacts not with all birds within a certain distance, as most models had assumed, but rather with a fixed number of neighboring birds, independent of how far apart they may be.
According to the researchers the most exotic feature they observed of the bird flocks was their strong correlation. The correlation did not decaying with the distance. This means a bird flock behaved like a biological system that had gone critical. This means the system is always ready to optimally respond to an external perturbation, such as a predator attack as in the case of flocks. That is why, explain the researchers, in flocking, any external perturbation, and in particular predation, is likely to directly cause a change of velocity (direction, modulus, or both) of a small subset of birds that first detect the perturbation. Such localized change must transmit to the whole flock to produce a collective response.
Conclusion
In all the methods they have used in their work the researchers have put emphasis on the mathematical rigour. They believe that in order for the fundamental biological properties of animal groups to emerge in the clearest way, it is necessary to wipe out a measurement from the trivial geometrical effects that can lead to erroneous conclusions. According to the researchers empirical data are rough, noisy, scarce, and very difficult to obtain. In fact, empirical data are pure gold in the field of collective animal behaviour. Mathematical rigour is necessary to extract from such data the maximum amount of biological information.
Source: http://www.pnas.org/content/early/2010/06/11/1005766107.full.pdf+html
July 7, 2010