Army ants dynamically adjust living bridges in response to a cost-benefit trade-off

Abstract

The ability of individual animals to create functional structures by joining together is rare and confined to the social insects. Army ants (Eciton) form collective assemblages out of their own bodies to perform a variety of functions that benefit the entire colony. Here we examine ‟bridges" of linked individuals that are constructed to span gaps in the colony's foraging trail. How these living structures adjust themselves to varied and changing conditions remains poorly understood. Our field experiments show that the ants continuously modify their bridges, such that these structures lengthen, widen, and change position in response to traffic levels and environmental geometry. Ants initiate bridges where their path deviates from their incoming direction and move the bridges over time to create shortcuts over large gaps. The final position of the structure depended on the intensity of the traffic and the extent of path deviation and was influenced by a cost-benefit trade-off at the colony level, where the benefit of increased foraging trail efficiency was balanced by the cost of removing workers from the foraging pool to form the structure. To examine this trade-off, we quantified the geometric relationship between costs and benefits revealed by our experiments. We then constructed a model to determine the bridge location that maximized foraging rate, which qualitatively matched the observed movement of bridges. Our results highlight how animal self-assemblages can be dynamically modified in response to a group-level cost-benefit trade-off, without any individual unit's having information on global benefits or costs.

Keywords: collective behavior; optimization; self-assembly; self-organization; swarm intelligence.

Fig. 1.

(A) Experimental apparatus from above, with ant bridge cartoon to show relative size. θ indicates the angle of separation between the platforms, in this case set to 20°. Over 30 min, the bridge has moved the distance d from its initiation point at the intersection of the platforms to its current location. See Materials and Methods for explanations of the empirical measurements d, w, b, and D_max, and the cost–benefit model for descriptions of L_A, L_T, L₁, L₀, and L_E. The position of L_T corresponds to the position of the main trail axis, as described in the text. The width (w_A) and length of each movable platform section was 3.3 cm and 24 cm, respectively. (B) Apparatus with θ set to 12°. Hinges are shown as circles. (C) Apparatus with θ set to 60°. The surface area of a bridge, used to estimate costs, is shown in blue, and the reduction in travel distance is shown with red dashed arrows for the same bridge migration distance (d).

Fig. 2.

Bridge movement as a function of (A) experimental time, (B) angle θ, and (C) traffic intensity. Each dot represents the position of a single bridge for each minute of each experiment. These values are partial residuals computed from a GLM as described in the text: they represent the relationship between a given independent variable and the bridge position, given that the other two independent variables are also in the model. The solid line and its semitransparent envelope represent the best fit of the GLM for each independent variable and its 95% confidence interval.

Fig. S1.

Bridge width as a function of bridge length for each angle θ. Each circle shows the width and length of a single bridge at any point in time. Solid lines are linear regressions for each angle θ. Shaded areas are the 95% confidence region.

Fig. 3.

The relationship between costs and benefits for bridges at certain θ angles. Dashed lines are theoretical cost–benefit relationships as computed from our model (and depicted in Fig. S2). Each circle shows the distance saved and surface area of an individual bridge at any point in time. Solid lines are LOESS curves built from the experimental data for each angle θ that help visualize the general trends in the data.

Fig. S2.

Theoretical costs (A) and benefits (B) as a function of distance moved by the bridge toward the main trail axis for different θ angles. In A, the cost function takes into account the widening of bridges observed as they move toward the main trail axis (Fig. S1).

Fig. 4.

(A) The optimal bridge position d as a function of apparatus angle θ for different ant densities. Other model parameters as described in Materials and Methods. (B) Comparison between the predicted final position of the bridge (solid line) and the experimental observations (dots) as a function of the angle θ. The value of parameter $A$ (the only free parameter of the model) was chosen to best fit the experimental observations. Note that changing its value would only affect the numerical outcome of the model, not the general shape of the relationship. The experimental observations reported in this figure are partial residuals computed from a GLM as described in the text.