Humans and ants are among the few species that engage in two-way traffic. Maintaining a smooth and efficient traffic flow while avoiding collisions is challenging for humans. Yet ants seem to be masters of traffic management. They can efficiently move back and forth between their nests and food without overtaking or passing each other, forming a steady stream of traffic. Few studies have looked at how ants maintain such a smooth flow even as the number of ants on a path increases.

Now, Poissonnier, Motsch et al. have designed an experiment to investigate whether ants can maintain their steady stream of traffic when their path to food gets more crowded. This involved manipulating the density of ants using a combination of different sized colonies (ranging from 400 to 25,600 Argentine ants) and changing the width of the bridge connecting the ants to their source of food. The experiment was repeated 170 times, and data was collected on traffic flow, speed of the ants, and number of collisions.

For pedestrians and car traffic, the flow of movement will slow down if occupancy levels reach over 40%. Whereas in ants, the flow of traffic showed no signs of declining even when bridge occupancy reached 80%. The experiments revealed that ants do this by adjusting their behavior to their circumstances. They speed up at intermediate densities, avoid collisions at large densities, and avoid entering overcrowded trails.

Studying ant traffic management has been a source of inspiration for scientists working with large groups of interacting particles in many fields. This includes molecular biology, statistical physics, and telecommunications. It may also have relevance for managing human traffic, particularly as scientists develop autonomous vehicles that might be programmed to work together cooperatively as ants do.

Many organisms such as herds of migrating wildebeests, swarms of insects and bacteria, starling flocks, fish shoals or pedestrian crowds take part in flow-like collective movements (Ball, 2004; Berdahl et al., 2013; Berdahl et al., 2018; Buhl et al., 2006; Chowdhury et al., 2005; Fourcassié et al., 2010; Giardina, 2008; John et al., 2009; Moussaïd et al., 2011; Sumpter, 2010; Vicsek and Zafeiris, 2012; Zhou et al., 2008). In most cases, all individuals cruise along the same path in a unique direction, which facilitates coordination. The task of maintaining a smooth and efficient movement becomes more challenging when individuals travel in opposite directions and are bound to collide (Fourcassié et al., 2010). Along with humans (Helbing et al., 2005; Moussaïd et al., 2011), ants are one of the rare animals in which collective movements are bidirectional. Ants are central-place foragers, which entails a succession of journeys between their nest and their foraging site. When exploiting large food sources, many species lay chemical trails along which individuals commute back and forth (Czaczkes et al., 2015; Gordon, 2014). The flow of individuals on these trails can reach several hundred ants per minute (Couzin and Franks, 2003). Yet, ants seem to fare better than us when it comes to traffic management (Burd et al., 2002; Dussutour et al., 2004; Fourcassié et al., 2010; Hönicke et al., 2015). However, we lack direct experimental evidence showing that ants do not get stuck in traffic jam at high density (Burd et al., 2002; Hönicke et al., 2015; John et al., 2009).

In traffic engineering, the relation between the density of individuals k and the flow q (the speed v times the density k) is often described via the fundamental diagrams (Chowdhury, 2000; Greenshields et al., 1935; Helbing, 2009; Helbing, 2001; Helbing and Huberman, 1998; Hoogendoorn and Bovy, 2001; Pipes, 1953; Underwood, 1960) (Figure 1A). The speed-density and flow-density diagrams vary depending on the system under scrutiny but share similar properties. First, the flow q increases with the density k from zero to a maximum value and then decays until it goes back to zero at the so-called maximum jam density k_j. The flow-density curves are usually concave with an optimal value for k on the path at which maximum flow or capacity is reached (Helbing and Huberman, 1998). Second, the speed is maximum when an individual is traveling alone (free flow speed v_f) and decreases with the density k. The speed becomes zero and individuals stop at jam density that is v(k_j)=0 (Nagatani, 2002; Treiber et al., 2000).

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Despite their apparent efficiency in traffic management, few studies have investigated the relation between density, speed and flow in ants (Burd et al., 2002; Gravish et al., 2015; Hönicke et al., 2015; John et al., 2009). In leaf-cutting ants (Burd et al., 2002) and fire ants (Gravish et al., 2015) speed decreases when density increases while for wood ants (Hönicke et al., 2015) and mass raiding ants (John et al., 2009) the speed remains constant when density increases. However, the range of densities tested was large enough to observe traffic jams only in the study conducted with fire ants traveling in tunnels (Gravish et al., 2015). The highest densities as well as the estimated occupancy (fraction of area covered by ants), recorded in leaf-cutting ants (Burd et al., 2002), wood ants (Hönicke et al., 2015) and mass raiding ants (John et al., 2009) were relatively low: 0.8 ants.cm⁻² (occupancy 0.20), 0.6 ants.cm⁻² (0.13) and 0.3 ants.cm⁻² (0.10) and not sufficiently high to generate a traffic jam as ants never exceeded the capacity of the trail, that is the maximum value of the flow allowed by the trail width.

Here, we investigated if ants succeed in maintaining a smooth traffic flow and avoid traffic congestion under the widest possible range of densities. We used the European supercolony of Argentine ants Linepithema humile, which is a major pest around the world and the largest recorded society of multicellular organisms (Giraud et al., 2002). In our experiment, a colony was connected to a food source using a bridge (Figure 1B). To manipulate density, we used a combination of bridges of different widths (5, 10 and 20 mm) and experimental colonies of different sizes (from 400 to 25,600 ants). We conducted a total of 170 experiments. The flow q and the density k were recorded on each experiment every second for one hour giving us 612,000 flow/density (non-independent) observations pairs. We succeeded in generating large variations of density (from 0 to 18 ants.cm⁻²) and occupancy (from 0 to 0.8).

Before pooling the data of all the 170 experiments to analyze the fundamental diagrams, we assessed the reliability of our experimental protocol with regard to foraging behavior. First, we verified that feeding behavior was not affected by the number of ants reaching the food (Figure 1—figure supplement 1). Most ants ate once at the food source, precluding the existence of a negative feedback caused by crowding at the feeding site that could affect food exploitation and recruitment behavior (Grüter et al., 2012). Second, we controlled that the bridge width itself did not affect ant speed. In absence of interactions and when ants were traveling alone, their speed was similar regardless of the bridge width (Figure 1—figure supplement 2).

Macroscopic traffic dynamics in ants

We first studied ant traffic at a macroscopic level. The flow of ants q heading in both directions was plotted as a function of density in Figure 2A. The flow q increased with the density k to a certain point and then it remained constant. We analyzed the relationship between k and q using three different macroscopic traffic functions (Greenshields et al., 1935; Pipes, 1953; Underwood, 1960) (Figure 2B). All the parameters of the functions were fitted using a nonlinear least squares fit procedure (Figure 2B, Supplementary file 1). All the statistical models performed similarly well but failed at predicting the data at intermediate and large densities. Thus, based on experimental data, we introduced a two-phase flow function to describe the relationship q-k as a piecewise linear function, with first a linear increase of the flow, followed by a constant value when the jamming density was reached.

(1) ${\displaystyle \mathrm{T}\mathrm{w}\mathrm{o}-\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}:q(k)=k\cdot vifk\le k_{j}andq(k)=k_j\cdot v=q_{j}ifk>k_j}$

Figure 2 with 1 supplement see all

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Then, we conducted a model selection analysis using Akaike weights to assign conditional probabilities to all statistical models. Thanks to our large dataset, the result was unequivocal: the two-phase statistical model was selected (Figure 2C, Figure 2—figure supplement 1, Supplementary file 1).

Why did the ants not jam or clog, as one would expect in usual traffic situations? This could result from a spatiotemporal organization of the flow at high density (Fourcassié et al., 2010). The traffic is considered as spatially organized when the flows of inbound and outbound ants are not completely intermingled and lane segregation occurs (Couzin and Franks, 2003; Fourcassié et al., 2010). Temporal organization arises when oscillatory changes in the flow direction are observed and the traffic becomes intermittently unidirectional that is alternating clusters of inbound and outbound ants occurs (Fourcassié et al., 2010). Both type of organizations limits the rate of time-consuming contacts (collisions) and allows ants to maintain a smooth traffic (Fourcassié et al., 2010). However, in our experiments, no clear evidence of such organizations was observed. In contrast, when ant density reached a critical threshold, inbound and outbound flows became intermingled temporally (Figure 3—figure supplement 1) and spatially (Figure 3A, Figure 3—figure supplement 2, Video 1 and Video 2). In addition, contrary to pedestrian traffic (Helbing et al., 2005; Moussaïd et al., 2011), the relationship between density k and flow q was only marginally influenced by the degree of asymmetry in the flows (Figure 3B, Figure 3—figure supplement 3). Simply put, it did not increase faster with the density k when traffic was mostly unidirectional (i.e. proportion of outbound flow q_o close to 1 or 0, traffic considered as asymmetric) than when it was entirely bidirectional (i.e. proportion of outbound flow q_o close to 0.5, traffic considered as symmetric). This is illustrated in Figure 3B by the tendency for the isoclines to run parallel to the y-axis (Figure 3B). Therefore, we focused our next analyses on individual behavior to understand how ants maintained a constant flow despite the increasing density.

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Video 1

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Video 2

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Microscopic traffic dynamics in ants

From an individual behavior perspective, most traffic-flow functions (Greenshields et al., 1935; Pipes, 1953; Underwood, 1960) suggest that individual speed decreases non-linearly with the density due to friction between individuals. However, the two-phase flow traffic function suggested that there was no evidence of such friction between ants when the density was below eight ants.cm⁻² that is the flow increased linearly, whereas above eight ants.cm⁻² frictions appeared but increased only linearly with the density that is the flow remained constant over a wide range of densities. How can we quantify such friction at the individual level?

A key factor determining ant speed is the number of contacts (i.e. collisions) experienced with nestmates, which makes ants stop and thus decays their overall speed (Burd and Aranwela, 2003; Dussutour et al., 2005; Gravish et al., 2015; Wang et al., 2018). To test if the number of contacts played the role of a hidden variable linking density and speed, we measured the number of contacts C, the density k and the traveling time T for a sample of 7900 ants individually tracked on a 2 cm section of the bridge. As density k grew, the number of contacts C increased linearly (C = 0. 61 k Figure 4A) that is the larger the density, the higher the number of contacts. We observed a linear effect of the number of contacts C on traveling time T, that is each contact slowed down the ants. (T = T₀ + C · ∆T with T₀ = 0.95 s and ∆T = 0.24 s, Figure 4B). T₀ can be interpreted as the traveling time to cross the bridge without contacts (free flow traveling time), whereas ∆T is the time lost per contact.

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So far, density k only had a negative impact on the speed v: it increased the number of contacts C which in return increased traveling time T. However, in our two-phase diagram, density k had no or minor effect on speed v in the phase 1. Therefore, there had to be a positive effect of density k on speed v in this regime. Thus, the interplay between T, k and C had to be more subtle. To combine multiple effects, we estimated the expected traveling time T depending on both density k and number of contacts C. For a given number of contacts C, we visualized the average traveling time T (see Figure 5A) for various values of density k, using local regression fitting. The vertical distance between two neighbors’ curves was given by ∆T. As expected, traveling time T increased with the number of contacts C, but the key information is that density k actually made traveling time T decay initially (up to k ≈ 5). For a given number of contacts C, ants moved faster on the bridge at intermediate density k (i.e. k ≈ 5). To further visualize this positive effect of the density, we estimated the free flow speed v_f, that is speed without contact v_f = L/(T-C·ΔT), where L=2cm is the length of the recording section on the bridge (Figure 5B). v_f is first increasing with density k up to k≈5 ants.cm⁻² and then decays back to its initial value. This phenomenon might be explained by a pheromone effect. It is well known that Argentine ants deposit pheromones both when leaving and when returning to the nest and travel faster on a well-marked trail (Deneubourg et al., 1990).

Figure 5

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To incorporate both effects of the density, we proposed the following formula for the speed:

(2) $v\left(k\right)=\frac{L}{T_0+\Delta T\cdot C\left(k\right)}\cdot \left(\alpha +\beta \cdot k\cdot e^{-\gamma \cdot k}\right)$

where C(k)=0.61·k is the average number of collisions, the three other parameters α, β and γ model the pheromone effect: α corresponds to the intrinsic attractiveness of the unmarked bridge, β represents the positive effect of k and γ measures the range where the pheromone effect might occur. These three parameters were estimated using a non-linear regression algorithm (α=0.812 ± .009, β=0.160 ± .010, γ=0.156 ± .007). We observed a decay of the speed v when k increased (Figure 6A). From this estimation of the speed, we deduced the following formula for the flow:

(3) $q\left(k\right)=k\cdot v\left(k\right)$

We plotted in Figure 6B the predicted flow q and the experimental observations of the sub-sample dataset (N = 7900 observations) used for the estimation. We noticed a clear agreement between the data and the model predictions. The plateau reached was q ≈ 10 ants.cm⁻¹.s⁻¹. Thus, even though increasing density k generated more contacts impacting negatively the flow q through their effect on traveling time T, when k < 5 ant.cm⁻² ants moved faster, which positively impacted the flow q. These two effects counterbalanced, leading to a linear increase of the flow q with density k (phase 1). For k > 8 ants.cm⁻², despite the crowdedness of the trail, ants maintained a constant flow q. The speed v(k) continued to decay due to the increase of contacts, but this negative effect on the flow q(k) was offset by the increase of k. We recovered this phenomenon from our model by estimating the limit flow q as the density k increases:

(4) $\underset{k\to \infty }{\mathit{lim}}q\left(k\right)=\frac{L}{\Delta T\cdot 0.61}\cdot \alpha \approx 11.09$

In other words, the flow in Figure 6B would merely increase for larger values of density k. However, experimentally the flow would have to decay eventually as the ant occupancy on the bridge cannot increase indefinitely. Given that the unoccupied portion of the bridge decayed with the density, it is remarkable that the number of contacts increased only linearly with the density according to Figure 4A (or one could argue even sub-linearly for k > 10 ants.cm⁻²). Interestingly, we also observed that ants restrained themselves from leaving the nest to prevent overcrowding as k never exceeded 18 ant.cm⁻² even though we increased colony size and reduced bridge width (number of ants entering the bridge for the largest colonies ± CI95: 2.69 ± 0.04, 4.34 ± 0.03 and 5.05 ± 0.03 ants.sec⁻¹ for the 5, 10 and 20 mm bridges). Furthermore, U-turns were seldom once the ants were traveling on the bridge (probability of turning back once on the bridge = 0.01).

Figure 6

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Traffic jams are ubiquitous in human society where individuals are pursuing their own personal objective (Youn et al., 2008). In contrast, ants share a common goal: the survival of the colony, thus they are expected to act cooperatively to optimize food return. In pedestrian and car traffic (Banks, 1999; Helbing et al., 2005), at occupancy levels above 0.4 the flow starts to decline, while in ants, the flow showed no sign of declining even when occupancy reached 0.8. Here, by investigating traffic dynamics on a large range of densities, we demonstrated that ants seem to be immune to traffic congestion.

The traffic of pedestrians or vehicles is often ruled by external constraints (enforced rules), time consuming interactions (avoidance behavior) and negative feedbacks (jamming). In contrast, in ants, traffic is governed by positive feed-backs (trail following and reinforcement) and interactions which are time consuming but often beneficial for the colony as they promotes information transfer (Bouchebti et al., 2015; Burd and Aranwela, 2003; Farji-Brener et al., 2010; Fourcassié et al., 2010; Gordon, 2019). Nonetheless, time spent interacting with other ants has strong consequences on traffic dynamics (Gravish et al., 2015). Short interaction time allows a smooth traffic over a wide range of densities whereas long interaction time promotes rapid slowing of traffic (Gravish et al., 2015). In fire ants, Gravish et al. (2015) found that interaction time was relatively short (0.45 s) and that the flow was relatively unaffected by density up to a certain critical value beyond which they observed the formation of traffic jams (Gravish et al., 2015). Here, we found that Argentine ants have an interaction time approximately twice shorter than fire ants, which could explain why we observed a smooth and efficient mixing of opposite flows over a broader range of densities.

The exact nature of the mechanisms used by Argentine ants to keep the traffic flowing in this study remains elusive, yet when density on the trail increases, ants seemed to be able to assess crowding locally, and adjusted their speed accordingly to avoid any interruption of traffic flow. Moreover, ants restrained themselves from entering a crowded path and ensured that the capacity of the bridge was never exceeded that is the maximum value of the flow allowed by the bridge width. Traffic regulation on trails ultimately allows Argentine ants to maintain a high rate of food return to the nest, an essential asset in the context of food competition occurring in natural environments. This balance between positive feedback and negative feedback appears to be generic in ants. For instance, in the nest-building context, behaviors such as ‘individual idleness and retreating’ at overcrowded digging sites supports an optimal accessibility of space facilitating excavation during nest construction in fire ants (Aguilar et al., 2018). Similarly, carpenter ants placed under threat and forced to escape through a narrow door distribute themselves uniformly over the space available instead of rushing toward the door and trampling on others (Parisi et al., 2015). As a result, contrary to humans (Helbing et al., 2000), they avoid clogging and evacuate efficiently (Parisi et al., 2015). Lastly, in garden ants, the interplay between trail following behavior and collisions allows ants to cope with bottleneck situations (Dussutour et al., 2006; Dussutour et al., 2005; Dussutour et al., 2004).

Overall, our results extend previous research on ant traffic organization (Aguilar et al., 2018; Burd et al., 2002; Fourcassié et al., 2010; Gravish et al., 2015; Hönicke et al., 2015; John et al., 2009) and show that ant prevented traffic jams from occurring and behaved as a self-organized biological adaptive system (Camazine et al., 2003; Hemelrijk, 2005). Similar phenomena of self-regulation ought to be found in other complex systems such as migrating animals (Buhl et al., 2006), cell machinery (Leduc et al., 2012), swarm of robots (Aguilar et al., 2018) and data traffic (Valverde and Solé, 2004) and could provide inspiration in all disciplines, ranging from molecular biology to automotive engineering. Although comparing ant traffic to human traffic might be a delicate task, as traffic in humans is neatly separated into unidirectional roadways, the rise of autonomous vehicles paves the way for new strategies to optimize traffic flow.

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Author details

1. Laure-Anne Poissonnier

   Research Center on Animal Cognition (CRCA), Center for Integrative Biology (CBI), Toulouse University, CNRS, UPS, 31062 Toulouse, France

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing—review and editing

   Contributed equally with

   Sebastien Motsch

   Competing interests

   No competing interests declared

2. Sebastien Motsch

   Arizona State University, Tempe, United States

   Contribution

   Data curation, Formal analysis, Validation, Visualization, Writing—original draft, Writing—review and editing

   Contributed equally with

   Laure-Anne Poissonnier

   Competing interests

   No competing interests declared

3. Jacques Gautrais

   Research Center on Animal Cognition (CRCA), Center for Integrative Biology (CBI), Toulouse University, CNRS, UPS, 31062 Toulouse, France

   Contribution

   Data curation, Software, Formal analysis, Visualization

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7002-9920

4. Camille Buhl

   School of Agriculture, Food and Wine, The University of Adelaide, Adelaide, Australia

   Contribution

   Validation, Writing—review and editing

   Competing interests

   No competing interests declared

5. Audrey Dussutour

   Research Center on Animal Cognition (CRCA), Center for Integrative Biology (CBI), Toulouse University, CNRS, UPS, 31062 Toulouse, France

   Contribution

   Conceptualization, Data curation, Formal analysis, Supervision, Funding acquisition, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   dussutou@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1377-3550

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