Traveling pulse emerges from coupled intermittent walks: A case study in sheep

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from sync...

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Bibliographic Details
Published in:PloS one 2018-12, Vol.13 (12), p.e0206817-e0206817
Main Authors: Azaïs, Manon, Blanco, Stéphane, Bon, Richard, Fournier, Richard, Pillot, Marie-Hélène, Gautrais, Jacques
Format: Article
Language:English
Subjects:
Analysis
Animal behavior
Animal cognition
Animals
Behavior
Behavior, Animal - physiology
Biology and Life Sciences
Case reports
Case studies
Decision making
Displays (Marketing)
Evolution
Flow-density-speed relationships
Health aspects
Life Sciences
Mathematical models
Models, Biological
Parameters
Physical sciences
Physics
Pulse propagation
Research and analysis methods
Robustness (mathematics)
Sheep
Sheep - physiology
Social Sciences
Walking
Walking Speed - physiology
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Summary:Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0206817