Adaptive network dynamics and evolution of leadership in collective migration
Darren Pais and Naomi E. Leonard
(2014), Physica D: Nonlinear Phenomena, Volume 267, Pages 81-93.
Paper at Physica D
Paper at arXiv:1303.2242 [nlin.AO]
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.
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