In animal groups, individual decisions are best characterized by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so-called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise. Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects owing to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterize the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives and the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature.

This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.

在动物群体中，个体决策的最佳特征是概率规则。此外，许多物种的动物生活在小群体中。少数个体之间的概率交互会导致所谓的群体层面的内在噪声。理论预测，内在噪声的强度不是一个常数，而是常常取决于群体的集体状态；因此，它也被称为状态相关噪声或乘法噪声. 令人惊讶的是，这种噪音可能会产生集体秩序。然而，由于缺乏使我们能够将数据与理论联系起来的方法，只有少数关于集体行为的实证研究关注了这种影响。在这里，我们展示了一种直接从集体动力学的高分辨率时间序列数据中表征随机性作用的方法。我们通过采用两个经过充分研究的基于个人的集体行为玩具模型来做到这一点。我们认为，群体级别的噪声可能会在个体尺度上编码有关潜在过程的重要信息。总之，我们描述了一种方法，使我们能够在动物（或细胞）集体的经验数据与噪声诱导状态现象之间建立联系，否则该领域在很大程度上仅限于理论文献。

本文是主题问题“生物系统中集体迁移的多尺度分析和建模”的一部分。