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”，其作用是引导一群幼稚的追随者朝着某个目标前进。我们制定了一个连续模型来理解这些群体的动态和结构，将一个群体分成具有不同方向反应的单独的追随者和领导者类型。我们融入领导者的影响力通过三个主要机制：领导者朝向目的地的方向偏差（方向偏差），领导者在朝着目标移动时更快地移动（速度偏差），以及领导者在朝着目标移动时让下属更清楚自己（显着性偏见）。分析和数值计算用于评估蜂群成功引导到目标的程度。我们发现，这三种机制中的每一种都可以在参数空间的广泛区域中产生成功的领导力，而显着性偏差则是最稳健的。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，追随者束手无策，或者群体凝聚力的丧失导致其最终分散。另一方面，低影响形式甚至可以产生远离目标方向的群体。因此，必须谨慎管理领导才能正确引导群体。