Figure 1.
Random difference produced from random SPP model with respect to the total number of particles.
Figure 2.
Moving average of the collective asymmetry () vs. the total number of escaped ants (
).
The two dashed lines above and below the curve are the s (the standard error of the mean) of the moving average. This curve displays a high profile when the number of ants is small as well as a decrease of
to a low profile when the number of ants is large. The inset shows, within the 291 individual experiments, that the number of experiments in which
,
and
is 151, 134 and 6, respectively.
and
denotes the total number of ants escaping left and right, respectively. This indicates that there are no hidden biased environmental factors affecting the direction of ant movement.
Figure 3.
Percentage of of Vicsek-like model.
is assigned a value of 0.2 (circle or dots), 0.5 (triangle) and 0.8 (square).
is assigned a value of 0.6 (hollow), 2.0 (gray) and 3.75 (black). The black square (
,
) corresponds to parameter values as in Altshuler's model (11). All the points are averaged over 10000 runs of simulation.
Figure 4.
Schematic diagram demonstrating the rules of the alarm pheromone model.
The left and the right panels show the updating rules in the model from time step to
, respectively. The circle denotes one ant, and the black arrows denote its current velocity vector. The numbers on the lattice denote the amount of pheromone, and the gray arrow pointing to 6 denotes the vector from the ant to the lattice where the concentration of pheromone is largest within its detection range. It should be noticed that the pheromone amount value in the simulation is not real world pheromone amount value. In our simulation, the amount of pheromone an ant puts on lattice and the amount of pheromone evaporates each time step are both less than 1. For simplicity, we use integers here.
Figure 5.
The comparison of the alarm pheromone model results and the experiment outcomes from Fig.2.
The solid dots (simulation results) are averaged over 10000 runs with the parameters and
. The model simulation agrees well with the experiment outcomes with the initial increase and then following decrease.
Figure 6.
The simulation result (solid dots) produced by the alarm pheromone model agrees well with the experimental result (circle), and both differ from the random results (gray circle). The solid dots (simulation result) are averaged over 1000 runs.
Figure 7.
The solid dots denote the best-fit simulation result with the following parameters: and
. The others denote 4 combinations of different parameters when
is assigned a value of 1/2 and 1/10, and
is assigned a value of 6 and 60 seconds. This demonstrates that the initial increasing and then decreasing pattern is robust. All the points are averaged over 1000 runs.
Figure 8.
Moving average of the collective asymmetry () vs. the total number of escaped ants (
) when changing the period of the moving average to be 21, 31, 41 and 51.
These data indicate that the initial increasing and then decreasing pattern in the experiment does not depend on parameter values.