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The study of collective animal behaviour must progress through a comparisonbetween the theoretical predictions of numerical models and data coming fromempirical observations. To this aim it is important to develop methods ofthree-dimensional (3D) analysis that are at the same time informative about thestructure of the group and suitable to empirical data. In fact, empirical dataare considerably noisier than numerical data, and they are subject to severalconstraints. We review here the tools of analysis used by the STARFLAG projectto characterise the 3D structure of large flocks of starlings in the field. Weshow how to avoid the most common pitfalls i the quantitative analysis of 3Danimal groups, with particular attention to the problem of the bias introducedby the border of the group. By means of practical examples, we demonstrate thatneglecting border effects gives rise to artefacts when studying the 3Dstructure of a group. Moreover, we show that mathematical rigour is essentialto distinguish important biological properties from trivial geometric featuresof animal groups.

The STARFLAG handbook on collective animal behaviour: Part II, three-dimensional analysis