The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource—such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins—while urging for an optimal resource value. Notably, this model can be approximated by an attraction–repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared “resource field,” the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field–based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.

寻求如何集体自组织以最大化社会群体成员的生存机会，需要在个人福祉最大化和群体福祉最大化之间找到最佳折衷方案。在这里，我们开发了一个最小模型，描述消耗或生产的活跃个体，并对共享资源做出反应——例如飞行细菌的氧气浓度或企鹅的温度场——同时敦促最佳资源价值。值得注意的是，该模型可以通过吸引-排斥模型来近似，但一般来说，它的特点是多体相互作用。虽然前者阻止一些个体接近共享“资源场”的最优值，但集体的多体交互会产生非周期性模式，从而使群体能够集体自我优化。可以说，所提出的基于场的最佳集体相互作用代表了活性物质物理、集体行为和微生物趋化性界面上的通用概念。这一概念可能作为优化合成活性剂整体的有用成分，或帮助揭示某些社会群体用来最大化其生存机会的通信规则的各个方面。