DOI: 10.5061/dryad.prr4xgxw0
title: Data from: Experimental investigation of ant traffic under crowded conditions.

description: Efficient transportation is crucial for urban mobility, cell function, and
 the survival of animal groups. From humans driving on the highway, to ants
 running on a trail, the main challenge faced by all collective systems is
 how to prevent traffic jams in crowded environments. Here, we show that
 ants, despite their behavioral simplicity, have managed the tour de force
 of avoiding the formation of traffic jams at high density. At the
 macroscopic level, we demonstrated that ant traffic is best described by a
 two-phase flow function. At low densities, there is a clear linear
 relationship between ant density and the flow, while at large density, the
 flow remains constant, and no congestion occurs. From a microscopic
 perspective, the individual tracking of ants under varying densities
 revealed that ants adjust their speed and avoid time-consuming
 interactions at large densities. Our results point to strategies by which
 ant colonies solve the main challenge of transportation by self-regulating
 their behavior.
description: 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. <strong>Data collection – Collective level</strong> <em>Flow q</em> The flow represents the number of ants crossing a line per unit of time. The ant flow on the bridge was counted over a 1·sec period during 1·h for all the experiments. Counting began as soon as the first ant crossed a line drawn in the middle of the bridge. Ants seldom climbed on top of each other that is the flow remained two-dimensional in all experiments. <em>Density K</em> The density represents the number of ants per unit of surface. The number of ants over a one cm<sup>2</sup> section encompassing the line drawn in the middle of the bridge was measured with ImageJ using the Analyze/Analyze Particles command, every half a second for one hour. Images were converted in binary images. Ants appeared black while the bridge appeared white. When the ant density was too high for the Analyze Particles command to discriminate the ants from one another, we divided the total area covered by black pixels by the mean area of a single ant. The mean area covered by a single ant on the bridge was measured on a total of 60 isolated ants on 10 experiments picked randomly. Ants covered on average 3.5 mm<sup>2</sup> excluding legs and antennae and 4.4 mm<sup>2</sup> with legs and antennae. For high densities (<em>k</em> &gt; 8) we also analyzed visually a sample of 5000 pictures (<em>i.e.</em> by counting each ant) and compared it with automatically analyzed pictures. We found a good agreement although automatic analysis had a slight tendency to underestimate densities but only when density was higher than six ant.cm<sup>−2</sup> (difference between manual and automatic −0.36 ant.cm<sup>−2</sup>+ /- IC95 0.02). <em>Occupancy</em> 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 mm<sup>2</sup> 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 mm<sup>2</sup> 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 mm<sup>2</sup> in wood ants (ant size: 7.7 mm, head width 2.3 mm; Hönicke et al., 2015), and 33.75 mm<sup>2</sup> 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<sup>−2</sup>, 10 ants.cm<sup>−2</sup>, 0.6 ants.cm<sup>−2</sup> and 0.3 ants.cm<sup>−2</sup> respectively. <strong>Data collection – Individual level</strong> <em>Experimental design assessment</em> 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 (<em>i.e.</em> 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). Traveling time <em>T</em> and number of contacts <em>C</em> 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 <em>T</em> and the number of physical contacts <em>C</em> 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.
description: # Data from: Experimental investigation of ant traffic under crowded
 conditions.
 [https://doi.org/10.5061/dryad.prr4xgxw0](https://doi.org/10.5061/dryad.prr4xgxw0) ## Description of the data and file structure ### Files and variables #### File: Figure2-SourceData.txt **Description:**  Data used to build figure 2 ##### Variables : * D for Density (ants/cm2) (The number of ants over a one cm2 section encompassing the line drawn in the middle of the bridge was measured every half a second for one hour for all the experiments) * F for flow (ant/cm/sec) (The ant flow on the bridge was counted over a 1·sec period during 1·h for all the experiments) #### File: Figure3-SourceData.txt **Description:** Data used to build figure 3 ##### Variables * D for Density (ants/cm2) (The number of ants over a one cm2 section encompassing the line drawn in the middle of the bridge was measured every half a second for one hour for all the experiments) * F for flow (ant/cm/sec) (The ant flow on the bridge was counted over a 1·sec period during 1·h for all the experiments) * Asym : Level of Asymmetry (between 0 and 1). Traffic asymmetry was computed as the number of ants going to the food source per second (outbound flow) divided by the total number of ants traveling on the bridge (total flow *q*). #### File: Figure4-SourceData.txt **Description:** Data figure 4 ##### Variables * travel_time : Individual traveling time in sec (measured on a 20mm section of the bridge) * direction : direction of the ants (1 = going to the food, 2= going to the nest) * speed: distance in mm (20mm) / Individual traveling time T in sec * contact : Number of contacts an ant incurred during the crossing of the bridge (measured on a 20mm section of the bridge) * Av_Density:  average density during traveling time * Av_Flow: average density during traveling time #### File: src\_fig5\_velocity.r **Description:**  code R to build Figure 5 #### File: src\_fig6\_flux\_prediction.r **Description:** code R to build Figure 6 #### File: src\_fig2\_flux\_tableS2.r **Description:**  code R to build Figure 2 #### File: src\_fig4\_contact\_travel.r **Description:** code R to build Figure 4 ## Code/software All the statistical analysis were done using R version R 3.5.0 ([Crawley, 2012](https://elifesciences.org/articles/48945#bib15)). All the parameters of the fundamental diagrams were fitted using a nonlinear least squares fit procedure (command nls; [Baty et al., 2015](https://elifesciences.org/articles/48945#bib4)). This procedure used Gauss-Newton algorithm to find the parameters that minimize the mean square error between the experimental data and the model prediction. The results of the estimations for the four functions are given in [Supplementary file 1](https://elifesciences.org/articles/48945/figures#supp1). A model selection using the Akaike weights (AW) has been conducted to assign a conditional probability for each statistical model. Source codes are available ([Poissonnier et al., 2019](https://elifesciences.org/articles/48945#bib47)).