ESM Videos.zip from Applying collective motion models to study discordant individual behaviours within a school of fish

Computational models of collective motion successfully reproduce the most common behaviours of a school of fish, using only a few elementary interactions between individuals. However, their ability to also reproduce individual behaviours that are discordant from those of the group has not yet been adequately investigated. In this paper, a self-propelled particle model using three interaction zones is considered in relation to the counter-rotation of an individual: a phenomenon observable in real schools of fish milling in a torus, when an individual moves in the same torus but in the opposite direction for a certain period of time. This study shows that the interactions of repulsion, orientation and attraction between individuals moving at constant speed in a three-dimensional space, with asynchronous updating, can generate temporary counter-rotations. The analysis of such events sheds light on the mechanisms that start the counter-rotation and those that end it. Although the contribution of the repulsion interaction is often significant to start and terminate the counter-rotation, it does not prove to be decisive. Indeed, it is observed that even when interactions between individuals are limited to attraction alone, temporary counter-rotations of individuals occur, provided the fish density along the circumference is not uniform. Some of these conclusions, deduced from the simulations performed, are visually consistent with what is observed in some underwater video recordings of milling schools of fish.

群体运动的计算模型仅依靠个体间的数种基础交互作用，即可成功复现鱼群最典型的群体行为。然而，此类模型复现与群体行为相悖的个体行为的能力，尚未得到充分研究。本文针对个体反向旋转（counter-rotation）现象，采用了一种包含三类交互区域的自驱动粒子模型（self-propelled particle model）：该现象可在真实环面（torus）内集群盘旋游动的鱼群中观测到，即某一个体在同一环道内沿相反方向游动一段时间。本研究表明，在三维空间中以恒定速度运动的个体间，通过斥力（repulsion）、定向对齐（orientation）与吸引力（attraction）的交互作用，并采用异步更新（asynchronous updating）机制，即可产生暂时性的反向旋转现象。对这类事件的分析，揭示了触发与终止反向旋转的内在机制。尽管斥力交互对于触发与终止反向旋转往往起到重要作用，但并非决定性因素。实际上，观测发现，当个体间的交互仅局限于吸引力作用，且环道圆周方向上的鱼群密度非均匀分布时，同样会出现个体暂时性反向旋转现象。本研究通过模拟实验推导得出的部分结论，与部分环道集群盘旋鱼群的水下视频观测结果在视觉上具有一致性。