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Computational exploration of treadmilling and protrusion growth observed in fire ant rafts
Fig 6
Ant Activity Phases.
(A) Snapshots of initially circular, simulated rafts are shown after 1.5 hours of simulation time. Here, η = 0.2, R = 0.9 ℓ and 
. (B) Snapshots of protrusions, each representing the minimum observed radius of tip curvature from its raft at final simulation time, are depicted for each of the respective values of 
. The black line cropping each snapshot at its bottom is an open border to the remainder of the raft. The values of 
yielding each morphology for (A-B) are denoted beneath each snapshot in (B). (C) Mean freely active agent packing fraction, ⟨ϕ⟩, (blue) and maximum surface excess, Smax, (red) are plotted with respect to 
, and averaged over 5 simulations at each value of 
, with error bars presenting standard error of the mean. Horizontal dotted lines in (C) represent the experimentally measured values of ϕ = 0.24 and Smax≈1.8. The bounds of the parameter space that matches experiments are marked where these respective lines intersect the numerical data (see “Exp. Match Zone” between 
and 1.47). There exists a zone between roughly 
and 2.0 of continuous phase transition between rafts with minimal-to-no growth whatsoever (ϕ≈1 and S~1.2) at low activity levels and frequent protrusion growth (low ϕ and S>2) at high activity levels. (D) Mean protrusion tip radius (Rκ) is plotted with respect to 
. Anywhere from four (in the case of no growth) to forty-one observations were ensemble averaged depending on protrusion frequency. Where no protrusions were available (
) the mean convex edge radius is reported instead. The top dotted line represents the initial raft diameter of 10 ℓ, while the bottom dotted line represents the limit of Rκ→0.5 ℓ, corresponding to the radius of one agent. (C-D) share a horizontal axis. (E-G) Three chronological snapshots of an experimental ant raft exhibiting different phases of protrusion growth are compared to (H-J) three chronological snapshots of a simulated raft when 
was modulated between 1.1 and 1.6. (K) The time evolution of surface excess as measured from one experiment (red circles) and ensemble averaged over 28 numerical simulations (black curve with a negligible shaded region representing standard error of the mean) are displayed. Note that the simulations start close to S = 1 given the initially circular raft shape. Time, t*, is normalized by the experiment duration for a more direct comparison. Structural agents are depicted in cyan, while dispersed free agents are depicted in red. All scale bars represent 10 ℓ. All simulated rafts displayed were initiated as circles such that protrusions emerged stochastically.
doi: https://doi.org/10.1371/journal.pcbi.1009869.g006