相关研究成果：

1. Identifying influential neighbors in animal flocking

      集群行为的研究能为人类的社会生产实践提供有益启示。鱼类个体在游动过程中如何与周围环境以及同伴发生交互从而产生集群行为是长期以来的研究热点。本研究提出了一种新的结合行为分析与计算模型的鱼类个体注意力交互模拟机制，揭示了鱼群中的个体如何产生游动、捕食等集群行为的内在机理。本工作对自然界百万年来如何在演化中发展出集群信息协作给出一种解释。本工作还可以为智能系统和人工多主体系统的协同提供解决思路，如在未来可越来越多地应用于搜索和救援行动、环境和野生动物监测的无人机群操控协作。

原文链接：https://pubmed.ncbi.nlm.nih.gov/29161269/

Fig 1. Collective U-turns in groups of two and five fish.

Figure 2. Reconstruction des interactions entre poissons au sein d’un groupe de 5 poissons lors d’un demi-tour collectif. (A) Trajectoires individuelles durant le demi-tour. Les flèches indiquent la direction de déplacement du groupe (B) Visualisation de la dynamique des interactions entre les poissons au cours du même demi-tour. Les flèches dont la couleur est celle du poisson dont le déplacement est influencé, indiquent la direction de propagation de l’information: du poisson influent vers le poisson influencé.

2. Swarming, schooling, milling: phase diagram of a data-driven fish school model 

      We determine the basic phase diagram of the fish school model derived from data by Gautrais et al (2012 PLoS Comput. Biol. 8 e1002678), exploring its parameter space beyond the parameter values determined experimentally on groups of barred flagtails (Kuhlia mugil) swimming in a shallow tank. A modified model is studied alongside the original one, in which an additional frontal preference is introduced in the stimulus/response function to account for the angular weighting of interactions. Our study, mostly limited to groups of moderate size (in the order of 100 individuals), focused not only on the transition to schooling induced by increasing the swimming speed, but also on the conditions under which a school can exhibit milling dynamics and the corresponding behavioural transitions. We show the existence of a transition region between milling and schooling, in which the school exhibits multistability and intermittence between schooling and milling for the same combination of individual parameters. We also show that milling does not occur for arbitrarily large groups, mainly due to a distance dependence interaction of the model and information propagation delays in the school, which cause conflicting reactions for large groups. We finally discuss the biological significance of our findings, especially the dependence of behavioural transitions on social interactions, which were reported by Gautrais et al to be adaptive in the experimental conditions.

原文链接：https://iopscience.iop.org/article/10.1088/1367-2630/16/1/015026

Fish interactions graphical representation used in the model.

 (a) The respective time series of the polarization (red line) and milling parameters (blue line) for the four distinct regions. (b) A representation of figure 3 right panels where three distinct behavioural regions can be identified by representing the mutually exclusive quantities given for the parameters of milling (M), average neighbour distance (D) and polarization (P), through a colour composition for each parameter (red, green and blue respectively). (c) Typical configurations of these states.

Transition between region schooling and milling states for different speeds.