Ants were subdivided into 35 experimental colonies of different sizes by weighing the ants: 400, 800, 1600, 3200, 6400, 12800 and 25600 ants. A few thousand workers were kept into ‘stock colonies’ in order to maintain a stable number of ants in the experimental colonies throughout the duration of the experiment. The experimental colonies were installed in test tube nests placed in a rearing box (L x W x H: 25 × 10×9 cm for the small colony sizes 400, 800, 1600 and 3200 ants and 29 × 27.5×9 cm for the larger colony sizes 6400, 12800 and 25600) with walls coated with Fluon to prevent ants from escaping. The experimental colonies were kept at room temperature (25 ± 1°C) with a 12:12 L:D photoperiod. We supplied each experimental colony with water and a mixed diet of vitamin-enriched food twice a week (Dussutour and Simpson, 2008). Before each experiment, the experimental colonies were starved for five days, and the experiment started when the ants were given access to a food source placed on a platform (120 × 120 mm for small colonies - up to 3200, or 230 × 230 mm for the larger colonies) at the other end of a plastic bridge. The total length of the bridge was 170 mm, and the bridge width was either 5 mm (narrow bridge), 10 mm (medium bridge), or 20 mm (large bridge). The food consisted of a 1M sucrose solution contained in small grooves (100 mm long for small colonies and 185 mm for large colonies) carved in a block of Plexiglas. To prevent crowding effects at the food source, the grooves were numerous enough (nine for small colonies, and 16 for large colonies) to give food access to a very large number of ants. The whole experimental set-up was isolated from any sources of disturbance by surrounding it with white paper walls. Throughout the experiments the traffic on the bridge was filmed from above for 60 min starting as soon as the first ant crossed the middle of the bridge. The number of replicates for each bridge width and each colony size ranged between 4 and 10 leading to a total of 170 experiments. Replicates on the same experimental colony were run at three weeks intervals. The temperature of the experimental room was 25°C.

For the sake of a comparison, we estimated occupancy (fraction of area covered by ants) obtained in previous studies (Burd et al., 2002; Gravish et al., 2015; Hönicke et al., 2015; John et al., 2009) based on density and ant size. We approximated the surface of an ant to a rectangle (body length x head width) and multiplied this area by 1.25 (ratio found in our experiment when dividing the area without legs and antennas by the area with legs and antennas) to include legs and antenna. We found that one ant cover a surface of 25 mm² in leaf-cutting ants (ant size: 8–12 mm, head width: 1.4–2.6 mm; Burd et al., 2002; Nichols-Orians and Schultz, 1989), 4.8 mm² in fire ants (ant size: 2.6–6.1 mm, mean 3.8 mm; head width: 0.6–1.4 mm; Tschinkel, 2013; Tschinkel et al., 2003), 22.25 mm² in wood ants (ant size: 7.7 mm, head width 2.3 mm; Hönicke et al., 2015), and 33.75 mm² in mass raiding ants (ant size: 18 mm, head width: 1.5 mm; John et al., 2009) giving us occupancy level of 0.20, 0.48, 0.13 and 0.10 corresponding to the densities: 0.8 ants.cm⁻², 10 ants.cm⁻², 0.6 ants.cm⁻² and 0.3 ants.cm⁻² respectively.

To ensure that ants did not experience overcrowding at the food source which could affect the recruitment dynamic (Grüter et al., 2012), we measured the probability of feeding when an ant reached the food. In other words, we recorded if the ants fed before leaving the platform to return to the nest. This was done by following 4200 ants arriving at the food source (100 ants for two replicates for each experimental colony size and each bridge width).

To check that the ant traveling time was not affected by the experimental set-ups (i.e. the bridge width itself), we followed a total of 2133 ants that did not experience any collision while traveling on the bridge (706, 693 and 734 ants followed for the 5 mm, 10 mm and 20 mm bridges respectively on 34 different experiments; Figure 1—figure supplement 2).

All individual behaviors were observed on a 20 mm section at the center of the bridge. The measurements began 10·min after the beginning of the experiment, when the outbound and nestbound flows of ants were at equilibrium. To test if the density affected the traveling time on the bridge, we recorded the travel duration T and the number of physical contacts C incurred while traveling. A contact was the result of either a head-on collision or a rear-end collision (when the head of an ant enters in contact with the gaster of the ant preceding it). Once the ant followed had crossed the 20 mm section of the bridge, we followed the next ant entering the section and so on. We followed 98 to 364 ants for each direction, each experimental group size and each bridge width, leading to total number of 7980 ants, of which 80 made a U-turn. Data were issued from 38 experiments in total. Head-on collisions and rear-on collisions were pooled together, as the time lost in each physical contact did not differ significantly (Figure 4—figure supplement 1). A physical contact lasted between 0.1 and 3.2·s (mean ± SD 0.18 ± 0.14 s). Automatic tracking was impossible due to high ant density, so all data were recorded semi-manually by two different persons using a homemade software AntEthoc-Combe-CRCA-CNRS (available upon request). We pressed various keys on a keyboard when an ant 1) entered or left the observation zone, 2) contacted another ant and 3) made a U-turn. Thus for each ant followed, the software gave us the travel time and the number of contacts.