Treadmilling and dynamic protrusions in fire ant rafts

Abstract

Fire ants ( Solenopsis invicta ) are exemplary for their formation of cohered, buoyant and dynamic structures composed entirely of their own bodies when exposed to flooded environments. Here, we observe tether-like protrusions that emerge from aggregated fire ant rafts when docked to stationary, vertical rods. Ant rafts comprise a floating, structural network of interconnected ants on which a layer of freely active ants walk. We show here that sustained shape evolution is permitted by the competing mechanisms of perpetual raft contraction aided by the transition of bulk structural ants to the free active layer and outward raft expansion owing to the deposition of free ants into the structural network at the edges, culminating in global treadmilling. Furthermore, we see that protrusions emerge as a result of asymmetries in the edge deposition rate of free ants. Employing both experimental characterization and a model for self-propelled particles in strong confinement, we interpret that these asymmetries are likely to occur stochastically owing to wall accumulation effects and directional motion of active ants when strongly confined by the protrusions' relatively narrow boundaries. Together, these effects may realize the cooperative, yet spontaneous formation of protrusions that fire ants sometimes use for functional exploration and to escape flooded environments.

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

“…To match experiments, this threshold was set to 1 agent per z 2 , where z 2 is the area occupied by one experimental, structural ant (z ¼ r À 0:5 r ¼ 1:81 � 0:30 mm, where ρ r is the planar structural network density). Consequently, a numerical rate of structural unbinding, min −1 , naturally emerged and matched experimental estimates (Fig 3F) [14], suggesting that 2% of structural agents convert to freely active agents every minute. Thus, through this pairwise contraction, both global network contraction and flux of ants from the structural network to the freely active layer were achieved.…”

“…However, the movement of free agents is constrained to the lattice defined by the structural agents, thus naturally ensuring that free agents can only occupy the spatial domain of the raft. An illustrative schematic of two hypothetical free ants in continuous space is depicted in Fig 2A , while the corresponding conception of free agents in the lattice-based model is shown in Fig 2B . Although the respective states of structural and free ants may consist of multiple layers distributed in the z-axis (depending on the time of inspection) [12,14], we here choose to model each as a single layer of agents based on the experimental observation that during phases of protrusion growth, the structural network generally spread into a monolayer (with a planar density of 0.304 ants mm −1 ) and the freely active layer was-on average-dispersed with a mean packing fraction of approximately 0.24 free ants per structural ant [14]. Fig 2C-2E depicts snapshots of a simulated raft in which the monolayered structural network is represented by cyan lattice sites, and the dispersed active layer on top is depicted by red free agents.…”

“…Naturally, the model must still replicate the global treadmilling dynamics that are prerequisite to sustained shape change and for which global contraction is an essential mechanism. We found previously that the structural layer contracts uniformly throughout the network and that its density is roughly conserved even over long time frames [14]. To capture this uniform global contraction without introducing mechanisms that would require long-range cooperation, we introduce spatially continuous pairwise contraction 1 Each of these forces is governed by the motion of free ants and relative position of water within detection distance R of the ants.…”

“…Note that the initial drops in both α and δ for the simulation data occur since the raft was not initiated at steady state, whereas experimental data was only sampled at pseudo-steady state. (A,C,D,F) Experimental results are courtesy of [14]. All simulated rafts were initiated as circles and shape was allowed to evolve stochastically.…”

“…where hθ j (t)i i is the average orientation, θ, of all neighboring freely active agents (including agent i) at time t. Neighboring agents are denoted by the index j and defined as free agents residing within some detection distance, R, of agent i. , and which depends on just three parameters: particle density, the radius of influence (R) and noise (η) [26]. Therefore, it is favored for its versatility, simplicity and is applied here given the experimental evidence that there exists mutual interactions between free ants, albeit only at the contact length scale [14]. Although this model is commonly used to capture collective motion driven by non-local interactions between self-propelled particles, it is not exclusive to collision-avoiding particles, and we here set R such that only neighbors in contact may directly influence one another.…”