Bernardi Sara, Painter Kevin J
Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy.
Institute of Atmospheric Sciences and Climate, National Research Council of Italy, Corso Fiume 4, 10133, Turin, Italy.
Bull Math Biol. 2025 Apr 7;87(5):64. doi: 10.1007/s11538-025-01435-z.
In both animal and cell populations, the presence of leaders often underlies the success of collective migration processes, which we characterise by a group maintaining a cohesive configuration that consistently moves toward a target. We extend a recent non-local hyperbolic model for follower-leader systems to investigate different degrees of leadership. Specifically, we consider three levels of leadership: indifferent leaders, who do not alter their movement according to followers; observant leaders, who attempt to remain connected with the followers, but do not allow followers to affect their desired alignment; and persuadable leaders, who integrate their attempt to reach some target with the alignment of all neighbours, both followers and leaders. A combination of analysis and numerical simulations is used to investigate under which conditions each degree of leadership allows successful collective movement to a destination. We find that the indifferent leaders' strategy can result in a cohesive and target-directed migration only for short times. Observant and persuadable leaders instead provide robust guidance, showing that the optimal leader behavior depends on the connection between the migrating individuals: if alignment is low, greater follower influence on leaders is beneficial for successful guidance; otherwise, it can be detrimental and may generate various unsuccessful swarming dynamics.
在动物群体和细胞群体中，领导者的存在往往是集体迁移过程成功的基础，我们将集体迁移过程定义为一个群体保持凝聚形态并持续朝着目标移动。我们扩展了最近用于跟随者 - 领导者系统的非局部双曲模型，以研究不同程度的领导力。具体而言，我们考虑三种领导力水平：冷漠型领导者，即不根据跟随者改变自身运动的领导者；观察型领导者，即试图与跟随者保持联系，但不允许跟随者影响其期望排列方向的领导者；可说服型领导者，即把自身朝着某个目标移动的尝试与所有邻居（包括跟随者和领导者）的排列方向结合起来的领导者。我们运用分析和数值模拟相结合的方法，研究在何种条件下每种领导力水平能使集体成功迁移至目的地。我们发现，冷漠型领导者的策略仅在短时间内可导致凝聚且目标导向的迁移。相反，观察型和可说服型领导者能提供有力的引导，这表明最优的领导者行为取决于迁移个体之间的联系：如果排列一致性较低，跟随者对领导者的更大影响有利于成功引导；否则，可能有害并可能产生各种不成功的群体动态。
