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Optimal recruitment strategies for groups of interacting walkers with leaders

Ricardo Martínez-García1,2, Cristóbal López1, and Federico Vazquez3

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain
  • 2Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544-1003, USA
  • 3Instituto de Física de Líquidos y Sistemas Biológicos UNLP-CONICET, 1900 La Plata, Argentina

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Phys. Rev. E 91, 022117 – Published 17 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022117

Abstract

We introduce a model of interacting random walkers on a finite one-dimensional chain with absorbing boundaries or targets at the ends. Walkers are of two types: informed particles that move ballistically towards a given target and diffusing uninformed particles that are biased towards close informed individuals. This model mimics the dynamics of hierarchical groups of animals, where an informed individual tries to persuade and lead the movement of its conspecifics. We characterize the success of this persuasion by the first-passage probability of the uninformed particle to the target, and we interpret the speed of the informed particle as a strategic parameter that the particle can tune to maximize its success. We find that the success probability is nonmonotonic, reaching its maximum at an intermediate speed whose value increases with the diffusing rate of the uninformed particle. When two different groups of informed leaders traveling in opposite directions compete, usually the largest group is the most successful. However, the minority can reverse this situation and become the most probable winner by following two different strategies: increasing its attraction strength or adjusting its speed to an optimal value relative to the majority's speed.

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Outline

Information

Phys. Rev. E 91, 022117– Published 17 February, 2015
  • Received 9 September 2014
  • Revised 20 November 2014

©2015 American Physical Society

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