University of Konstanz, Department of Physics, Universtaetsstrasse 10, Konstanz, 78464, Germany.
University of Konstanz, Department of Physics, Universtaetsstrasse 10, Konstanz, 78464, Germany; Centre for the Advanced Study of Collective Behaviour, Universtaetsstrasse 10, Konstanz, 78464, Germany.
J Theor Biol. 2023 Apr 7;562:111433. doi: 10.1016/j.jtbi.2023.111433. Epub 2023 Feb 2.
Understanding why animals organize in collective states is a central question of current research in, e.g., biology, physics, and psychology. More than 50 years ago, W.D. Hamilton postulated that the formation of animal herds may simply result from the individual's selfish motivation to minimize their predation risk. The latter is quantified by the domain of danger (DOD) which is given by the Voronoi area around each individual. In fact, simulations show that individuals aiming to reduce their DODs form compact groups similar to what is observed in many living systems. However, despite the apparent simplicity of this problem, it is not clear what motional strategy is required to find an optimal solution. Here, we use the framework of Multi Agent Reinforcement Learning (MARL) which gives the unbiased and optimal strategy of individuals to solve the selfish herd problem. We demonstrate that the motivation of individuals to reduce their predation risk naturally leads to pronounced collective behaviors including the formation of cohesive swirls. We reveal a previously unexplored rather complex intra-group motion which eventually leads to a evenly shared predation risk amongst selfish individuals.
理解为什么动物会以集体状态组织起来，是生物学、物理学和心理学等当前研究的核心问题。50 多年前，W.D.汉密尔顿假设，动物群的形成可能仅仅是由于个体的自私动机，即最小化被捕食的风险。后者由个体周围的 Voronoi 区域给出的危险域（DOD）来量化。事实上，模拟表明，旨在降低 DOD 的个体形成类似许多生命系统中观察到的紧凑群体。然而，尽管这个问题看起来很简单，但还不清楚需要什么样的运动策略来找到最优解。在这里，我们使用多智能体强化学习（MARL）框架，该框架给出了个体解决自私羊群问题的无偏最优策略。我们证明，个体降低被捕食风险的动机自然会导致明显的集体行为，包括形成有凝聚力的漩涡。我们揭示了一种以前未被探索过的相当复杂的群体内运动，最终导致自私个体之间均匀分担捕食风险。
