Traveling pulse emerges from coupled intermittent walks: A case study in sheep
Authored by Jacques Gautrais, Manon Azais, Stephane Blanco, Richard Bon, Richard Fournier, Marie-Helene Pillot
Date Published: 2018
DOI: 10.1371/journal.pone.0206817
Sponsors:
French National Research Agency (ANR)
Platforms:
Fortran
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
https://doi.org/10.1371/journal.pone.0206817.s004
Abstract
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.
Tags
movement
collective motion
Model
Pattern-formation
Speed control
Natural flocks