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The evolution of leadership in migratory populations depends not only oncosts and benefits of leadership investments but also on the opportunities forindividuals to rely on cues from others through social interactions. We derivean analytically tractable adaptive dynamic network model of collectivemigration with fast timescale migration dynamics and slow timescale adaptivedynamics of individual leadership investment and social interaction. For largepopulations, our analysis of bifurcations with respect to investment costexplains the observed hysteretic effect associated with recovery of migrationin fragmented environments. Further, we show a minimum connectivity thresholdabove which there is evolutionary branching into leader and followerpopulations. For small populations, we show how the topology of the underlyingsocial interaction network influences the emergence and location of leaders inthe adaptive system. Our model and analysis can describe other adaptive networkdynamics involving collective tracking or collective learning of a noisy,unknown signal, and likewise can inform the design of robotic networks whereagents use decentralized strategies that balance direct environmentalmeasurements with agent interactions.

Adaptive Network Dynamics and Evolution of Leadership in Collective Migration