Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy.
Laboratoire de mathématiques de Besançon, UMR-CNRS 6623, Université de Bourgogne Franche-Comté, 16 Route de Gray, 25000, Besançon, France.
Bull Math Biol. 2021 May 10;83(6):69. doi: 10.1007/s11538-021-00901-8.
Collective migration of cells and animals often relies on a specialised set of "leaders", whose role is to steer a population of naive followers towards some target. We formulate a continuous model to understand the dynamics and structure of such groups, splitting a population into separate follower and leader types with distinct orientation responses. We incorporate leader influence via three principal mechanisms: a bias in the orientation of leaders towards the destination (orientation-bias), a faster movement of leaders when moving towards the target (speed-bias), and leaders making themselves more clear to followers when moving towards the target (conspicuousness-bias). Analysis and numerical computation are used to assess the extent to which the swarm is successfully shepherded towards the target. We find that successful leadership can occur for each of these three mechanisms across a broad region of parameter space, with conspicuousness-bias emerging as the most robust. However, outside this parameter space we also find various forms of unsuccessful leadership. Forms of excessive influence can result in either swarm-splitting, where the leaders break free and followers are left rudderless, or a loss of swarm cohesion that leads to its eventual dispersal. Forms of low influence, on the other hand, can even generate swarms that move away from the target direction. Leadership must therefore be carefully managed to steer the swarm correctly.
细胞和动物的集体迁移通常依赖于一组专门的“领导者”，它们的作用是引导一群盲从的跟随者朝着某个目标前进。我们提出了一个连续的模型来理解这种群体的动力学和结构，将群体划分为具有不同取向反应的独立的跟随者和领导者类型。我们通过三种主要机制来整合领导者的影响：领导者对目的地的取向的偏差（取向偏差）、领导者在朝着目标移动时更快的移动速度（速度偏差）以及领导者在朝着目标移动时使自己更容易被跟随者发现（显著偏差）。分析和数值计算用于评估群体成功地朝着目标被引导的程度。我们发现，对于这三种机制中的每一种，在广泛的参数空间中都可以成功地实现领导，其中显著偏差是最稳健的。然而，在这个参数空间之外，我们还发现了各种形式的不成功的领导。过度影响的形式可能导致群体分裂，领导者挣脱并使跟随者失去方向，或者群体失去凝聚力，最终导致其分散。另一方面，低影响力的形式甚至可能导致群体远离目标方向移动。因此，领导必须谨慎管理，以正确引导群体。
