Data from: Signatures of optimal control in pairs of schooling zebrafish

Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a cohesively moving unit correctly predicts the characteristics of social interactions in fish. Our methodology explains why social attraction is negatively modulated by self-motion velocity and positively modulated by partner motion velocity, and how the biomechanics of fish swimming can shape the form of social forces. Crucially, the values of all parameters in our model can be estimated from independent experiments that need not relate to measurement of social interactions. We test our theory by showing a good match with experimentally observed social interaction rules in zebrafish. In addition to providing a theoretical rationale for observed decision rules, we suggest that this framework opens new questions about tuning problems and learnability of collective behaviours.

集群运动的动物会通过协调自身动作维持群体凝聚力。目前已有针对多个物种种群运动协调的大量数据与分析，但学界仍缺乏可推导协调规则形式的理论框架。本研究探讨最优控制理论（optimal control theory）能否从第一性原理出发，预测社会互动的内在规则。我们发现，以最小化成对集群鱼类（schooling fish）形成协同运动单元所需时长为目标设计的控制规则，能够准确预测鱼类社会互动的特征。本研究的方法可解释为何社会吸引力会随自身运动速度负向调控、随同伴运动速度正向调控，同时阐明鱼类游泳的生物力学如何塑造社会作用力的形式。至关重要的是，我们模型中所有参数的数值均可通过无需测量社会互动的独立实验进行估算。我们通过证明该理论与斑马鱼（zebrafish）实验中观测到的社会互动规则高度契合，对其进行了验证。本研究不仅为已观测到的决策规则提供了理论依据，同时表明该框架可引出关于集体行为的调谐问题与可学习性的全新研究议题。