< Back to Article

Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

Fig 2

Agent-based Model Schematic.

(A) Two free ants of interest (red) are schematically illustrated on a structural section of raft (shaded cyan) in continuous space. Other free ants are shaded grey. The direction of motion () of the ant far from the edge of the raft (left) is predicted entirely by the Vicsek model. In contrast, whether the ant encountering the edge of the raft (right) moves into the water, depends not only on , but also on the competition between active force and the effective edge repulsion force . Each of these forces is governed by the motion of free ants and relative position of water within detection distance R of the ants. (B) A corresponding schematic envisions how these continuous scenarios are coarse-grained into the lattice-based framework of the numerical model. The motion of the free agents of interest (red) remains governed by the direction of travel (white arrows) of neighboring free agents, and effective pairwise repulsion (black arrows) from neighboring water nodes within distance R. However, free agent movement is updated by stepping the free agents to the adjacent structural agents (cyan) or water nodes (white) whose relative direction most closely matches the preferred direction, θ_i. Nodes are displayed in a hexagonal, close-packed lattice for illustrative purposes only, but are initially offset in both directions of the horizontal plane by some amount in the rangeζ and are further randomized by stochastic structural unbinding events as the simulation progresses. (C-E) The shape evolution of a simulated raft over a duration of 20 min (of virtual time), illustrates the implementation of the lattice-based conceptualization from (B) into the numerical model. Shape change is governed by the transition of free agents (red) into the structural network (cyan) at the raft’s edge. The raft depicted was initiated as a circle and all scale bars represent ℓ. (F-G) Agents encountering water in regions of (F) high and (G) low edge curvature are depicted. These respective agents experience high and low values of F^Γ due to the pairwise contributions of repulsion force from detected water nodes (black arrows). The agent in (F) has no freely active neighbors such that the only contribution to its value of F^a is its own self-propulsion force (white arrow), whereas the agent in (G) has many freely active neighbors moving in similar directions towards the water such that it has a high value of F^a oriented off the raft. (F-G) Insets display the vectorial sums that define the effective forces F^a (red) and F^Γ (blue) for the respective agent configurations, thus illustrating how the agent in (G) is more likely to edge-deposit based on Inequality 2.

doi: https://doi.org/10.1371/journal.pcbi.1009869.g002