Adaptive Network Dynamics and Evolution of Leadership in Collective Migration

TL;DR

This paper presents an adaptive network model for collective migration, analyzing how leadership evolves based on costs, social cues, and network structure, with implications for biological and robotic systems.

Contribution

It introduces a tractable adaptive dynamic network model that explains leadership evolution, hysteresis effects, and the influence of network topology in collective migration.

Findings

Bifurcation analysis explains hysteresis in migration recovery.

A minimum connectivity threshold leads to leader-follower differentiation.

Network topology influences leadership emergence in small populations.

Abstract

The evolution of leadership in migratory populations depends not only on costs and benefits of leadership investments but also on the opportunities for individuals to rely on cues from others through social interactions. We derive an analytically tractable adaptive dynamic network model of collective migration with fast timescale migration dynamics and slow timescale adaptive dynamics of individual leadership investment and social interaction. For large populations, our analysis of bifurcations with respect to investment cost explains the observed hysteretic effect associated with recovery of migration in fragmented environments. Further, we show a minimum connectivity threshold above which there is evolutionary branching into leader and follower populations. For small populations, we show how the topology of the underlying social interaction network influences the emergence and location of leaders in the adaptive system. Our model and analysis can describe other adaptive network dynamics involving collective tracking or collective learning of a noisy, unknown signal, and likewise can inform the design of robotic networks where agents use decentralized strategies that balance direct environmental measurements with agent interactions.