Decision versus compromise for animal groups in motion

Naomi Ehrich Leonard, Tian Shen, Benjamin Nabet, Luca Scardovi, Iain D. Couzin, Simon Asher Levin

Research output: Contribution to journalArticlepeer-review

64 Scopus citations

Abstract

Previously, we showed using a computational agent-based model that a group of animals moving together can make a collective decision on direction of motion, even if there is a conflict between the directional preferences of two small subgroups of "informed" individuals and the remaining "uninformed" individuals have no directional preference. The model requires no explicit signaling or identification of informed individuals; individuals merely adjust their steering in response to socially acquired information on relativemotion of neighbors. In this paper, we show how the dynamics of this system can be modeled analytically, and we derive a testable result that adding uninformed individuals improves stability of collective decision making. We first present a continuous-time dynamic model and prove a necessary and sufficient condition for stable convergence to a collective decision in this model. The stability of the decision, which corresponds to most of the group moving in one of two alternative preferred directions, depends explicitly on the magnitude of the difference in preferred directions; for a difference above a threshold the decision is stable and below that same threshold the decision is unstable. Given qualitative agreement with the results of the previous simulation study, we proceed to explore analytically the subtle but important role of the uninformed individuals in the continuous-time model. Significantly, we show that the likelihood of a collective decision increases with increasing numbers of uninformed individuals.

Original languageEnglish (US)
Pages (from-to)227-232
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume109
Issue number1
DOIs
StatePublished - Jan 3 2012

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Collective behavior
  • Coordinated movement
  • Kuramoto

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