Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish, and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinate their movements is a challenging task. These mechanisms take place at the individual scale and can be described as a combination of interactions between individuals and interactions between these individuals and the physical obstacles in the environment. Thanks to the development of novel tracking techniques that provide large and accurate datasets, the main characteristics of individual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of studies, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummy-nose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio), which both present a burst-and-coast motion. From the detailed quantitative description of individual-level interactions, it is thus possible to develop a quantitative model of the emergent dynamics observed at the group level, whose predictions can be checked against experimental results. This method can be applied to a wide range of biological and social systems.

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

集体迁移的群居生物范围从细胞和细菌到人类群体，包括成群的昆虫、鱼群以及成群的鸟类或有蹄类动物。揭示这些群体协调其运动的行为和认知机制是一项具有挑战性的任务。这些机制发生在个体尺度上，可以描述为个体之间的相互作用以及这些个体与环境中物理障碍之间的相互作用的组合。由于提供大量准确数据集的新型跟踪技术的发展，个人和集体行为模式的主要特征可以以前所未有的精度进行量化。然而，在大量研究中，社会互动通常由力图方法描述，其解释和预测能力有限，很少适合在简洁明了的数学模型中直接实现。在这里，我们提出了一种通用方法来提取参与协调生物体群体集体运动的个体之间的相互作用。然后我们应用这种方法来描述两种浅滩鱼的社会互动特征，拉米鼻四（Hemigrammus rhodostomus）和斑马鱼（Danio rerio），它们都呈现出爆发和海岸运动。因此，从个体层面相互作用的详细定量描述中，可以开发出在群体层面观察到的新兴动态的定量模型，其预测可以根据实验结果进行检查。这种方法可以应用于广泛的生物和社会系统。

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。