The STARFLAG handbook on collective animal behaviour: 2. Three-dimensional analysis
Section snippets
The Problem of the Border
One of the major problems we face when analysing the 3D structure of a group of animals is that of the border. Whatever species is observed, animals on the border of the group will inevitably introduce a bias into any measurements taken, unless they are properly treated. This problem has been mostly disregarded by previous empirical observations and numerical studies alike. It is only with a very large number of points, say beyond 106 in 3D, that the ratio between surface and volume becomes
What to Measure and How to Do it
In this section we list some useful observables, and illustrate some of the subtle technical pitfalls one may encounter. It is clear, however, that the decision of what to measure depends on the scientific aims of a study. In no way do we wish to suggest here that there is a unique, or a best, way to analyse 3D data.
Conclusions
In all the methods discussed in this work we put the emphasis on mathematical rigour. The reason why we did that is not simply because we are physicists, nor because we think that mathematics, or physics, must be predominant in the study of collective animal behaviour. On the contrary, we believe that in order for the fundamental biological properties of animal groups to emerge in the clearest way, it is necessary first to eliminate the trivial geometric effects. As we explained through several
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G. Parisi and A. Procaccini are at the Dipartimento di Fisica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 2, 00185 Roma, Italy.