Adaptive network dynamics and evolution of leadership in collective migration

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.

The content and availability of information affects the evolution of social-information gathering strategies

“…We saw this when we looked at greedy optimization processes for fitness based on access to abundant resources or based on both predation and access to scarce resources. Pais and Leonard (2014) also found that heterogeneity in the weight given to social information can persist, both when the trait is determined by adaptive dynamics and when individuals selfishly change their strategies to improve their own fitness. That different models of different types of strategies give rise to heterogeneity suggests that it might be a common feature of strategies for gathering social information and that we might expect to see it in natural populations.…”

“…The flock will eventually reach consensus with every v i = 1, as long as there is a path in the network from every node to at least one node that perceives the cue (Pais and Leonard 2014). In the Appendix A.2, we show that, if bird i does not perceive the cue, then…”

“…A similar framework is used to study noisy opinion dynamics with an environmental cue in Fitch and Leonard (2014) and Pais and Leonard (2014). Now the dynamics of y follow…”

“…While there are many models of the evolution of social-information use, few, to our knowledge, compare information about different facets of the environment (in our case, predators and resources). Additionally, while some models of the evolution of social-information use consider the weight given to social information (as opposed to personal information) (e.g., Pais and Leonard 2014;Shaw and Couzin 2013;Torney et al 2015), none to our knowledge consider the evolution of the number of neighbors in a topological interaction network. Finally, our work considers two group-level properties that have not previously been studied together.…”

On the speed-accuracy tradeoff in collective decision making

“…Collective decision making in ideal human groups using the DDM and the interrogation paradigm is studied in [13]. Related collective decision making models in animal groups are studied in [14]. In this paper, we study collective decision making in ideal groups using the DDM and the free response paradigm.…”