Data from: Body size affects the strength of social interactions and spatial organization of a schooling fish (Pseudomugil signifer)

While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible enough to capture changes in the collective behaviour of animal groups at their different developmental stages and group sizes. Here, we analyse the statistical properties of schooling fish (Pseudomugil signifer) through a combination of experiments and simulations. We make novel use of a Boltzmann inversion method, usually applied in molecular dynamics, to identify the effective potential of the mean force of fish interactions. Specifically, we show that larger fish have a larger repulsion zone, but stronger attraction, resulting in greater alignment in their collective motion. We model the collective dynamics of schools using a self-propelled particle model, modified to include varying particle speed and a local repulsion rule. We demonstrate that the statistical properties of the fish schools are reproduced by our model, thereby capturing a number of features of the behaviour and development of schooling fish.

尽管已有大量丰富的自驱动粒子模型（self-propelled particle models）试图解释鱼类及其他动物的集体运动行为，但在模型与实测数据之间开展严谨的统计对比仍颇具挑战。合理的模型应当具备足够的灵活性，以捕捉动物群体在不同发育阶段与群体规模下的集体行为变化。本文结合实验与模拟手段，对鱼群（以似鲻银汉鱼（Pseudomugil signifer）为例）的统计特性展开分析。我们创新性地采用了通常应用于分子动力学（molecular dynamics）领域的玻尔兹曼反演方法（Boltzmann inversion method），以识别鱼类交互的平均力有效势（effective potential of the mean force）。具体而言，我们发现体型更大的个体拥有更大的排斥作用区域，但同时具备更强的吸引作用，这使得它们的集体运动对齐程度更高。我们通过修改自驱动粒子模型，引入可变的粒子运动速度与局部排斥规则，对鱼群的集体动力学行为进行建模。我们证实所提模型能够复现鱼群的统计特性，从而捕捉到鱼群行为与发育过程中的多项关键特征。