Table 1.
The relationship between meshedness and colony size in ants.
Figure 1.
Typical evolution of a tunnelling network dug by A(0) = 200 ants, at 5, 9 and 72 hours after T0.
The outer circle represents the periphery of the sand disk (radius mm). Plain disks represent chambers, and lines represent tunnels. Open disks denote active fronts (F), progressing from a peripheral node (P), from an existing gallery (L1) or from an existing node (L2).
Table 2.
Parameters of the model.
Figure 2.
Quantification of the parameters of the digging dynamics from experimental data with A(0) = 200 workers.
(a) Ant activity parameters ( and
) are retrieved from the evolution of the dug length
: three typical experimental cases are shown as solid lines and their corresponding predictions by the model as dashed lines (see also fig. S1 for all experimental results). (b, c) The rates of initiation of new peripheral nodes
and of new lateral nodes
are retrieved respectively from (b) the regression slope of the number of peripheral nodes
as a function of
and (c) the number of lateral nodes
as a function of
(each symbols corresponds to each of the three experiments shown in (a)). Regressions for all cases can be found in fig. S2 and S3. (d) The rates of initiation of new lateral
and peripheral
nodes converge to a common value (one symbol per experiment, dashed line:
).
Figure 3.
The structural properties of the observed networks at the end of experiments after three days (one symbol per experiment) are well predicted by the model for (a) the length , (b) the number of nodes
, (c) the number of tunnels
and (d) the mean degree
.
In each plot, vertical bars indicate 95% confidence interval predicted by the model and were numerically estimated using simulations (N = 2000 simulations per experiment using the corresponding set of behavioural parameters). Horizontal bars indicate the predicted median. Note that experiments have been ordered by increasing ordinate values.
Figure 4.
Examples of experimental networks dug by the ants in 72 hours depending on the number of workers (a) , (b)
, (c)
.
The corresponding values of the meshedness are respectively 0.0, 0.092 and 0.194.
Figure 5.
The impact of colony size on the final topology is shown by the meshedness as a function of the number of workers
.
Symbols: experimental values for the three group sizes (green: A = 50, red: A = 100, blue: A = 200, same colours as in Fig. S4). Orange boxes: means and 95% CI predicted by the model using the complete collection of parameters sets. Blue boxes: means and 95% CI predicted by the model using the set of averaged parameters. Brown boxes: means and 95% CI predicted by the model using averaged branching rates, and activity parameters corresponding to the average activity. Gray boxes: 95% CI predicted by the simplified model using the same parameters.
Figure 6.
Meshedness at the end of experiments as a function of the number of workers, predicted by the simplified model in a space with no boundary, either using the set of median values of parameters (brown line), picking randomly a parameter set among the experimental ones (black line), or using the set of median values but with the highest lateral nodes formation rate value (red line) or the lowest one (blue line).
The number of workers was repeatedly picked uniformly between A = 1 and A = 7,000 for each condition and the lines report the corresponding tendency obtained by a lowess procedure (see Fig. S5). The meshedness increases as the number of workers increases, from tree-like structures () towards triangular networks (
) up to a saturation value. The predictions including the experimental variance of parameter estimations (black lines) show that the transition of
induced by the increase of
is robust to behavioural noise.