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 behaviors.

集群移动的动物会协调自身运动以维持群体凝聚力。目前学界已在多个物种中获取了大量关于运动协调的实验数据与分析成果，但仍缺乏能够推导协调规则具体形式的理论框架。本研究旨在探究最优控制理论（optimal control theory）能否从第一性原理（first principles）出发，推导出社会互动背后的行为规则。我们发现，以最小化一对群游鱼类（schooling fish）形成具有凝聚力的运动单元所需的时间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。我们的方法解释了为何社会吸引力会随个体自身运动速度呈负向调控，随同伴运动速度呈正向调控，以及鱼类游泳的生物力学（biomechanics）如何塑造社会作用力的具体形式。至关重要的是，模型中所有参数的取值均可通过与社会互动测量无关的独立实验进行估算。我们通过与斑马鱼（zebrafish）实验观测到的社会互动规则高度吻合，验证了该理论的正确性。本研究不仅为已观测到的决策规则提供了理论依据，还表明该框架为群体行为的调谐问题与可学习性研究开辟了新的方向。