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

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