STARFLAG动物集体行为手册：第II部分，三维分析
The STARFLAG handbook on collective animal behaviour: Part II, three-dimensional analysis
摘要：
动物集体行为的研究必须通过数值模型的理论预测和来自经验观察的数据之间的比较来取得进展。为此目的，重要的是开发三维（3D）分析方法，同时提供有关群体结构的信息，并适合于经验数据。事实上，经验数据比数值数据噪音大得多，而且它们受到几个限制。在这里，我们回顾了分析工具所使用的STARFLAG项目，在该领域的大型椋鸟群的三维结构。我们展示了如何避免最常见的陷阱中的3D动物群体的定量分析，特别注意的问题，由该组的边界引入的偏见。通过实际的例子，我们表明，忽略边界效应会产生文物时，研究一个组的三维结构。此外，我们表明，数学的严谨性是必不可少的，以区分重要的生物学特性从平凡的几何特征的动物群体。
英文摘要：
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.
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