Foraging and nest relocation forming a bi-directional traffic of outbound and inbound individuals in one-lane organization are two main activities in an ant's life. In this paper, we conducted an experiment on nest relocation of loaded and unloaded ants, moving back and forth between the old nest and the new one. In the experiment, we observed both uni- and bi-directional traffic flow. The headway–speed relationships indicate that the ants showed the same sensitivity to the distance headway in the two types of flow. For bi-directional traffic flow, head-on encounters and giving-way behavior between ants moving in opposing directions were a common occurrence. It took one unloaded ant 2.61 s to solve a head-on encounter with another unloaded ant. Compared with unloaded ants, loaded ants had a lower moving speed, but were less likely to be impacted by a head-on encounter. In the observation region, both sudden stop and head-on encounters contained two phases: deceleration and acceleration. Our analysis indicates that the relaxation time in the deceleration process is less than that in the acceleration process. The reduction of movement efficiency of encountering two discontinuous ants is larger than that when encountering two successive ants (0.18). This is owing to the absence of head-on encounters with following ants. The bi-directional traffic of ants under experimental conditions investigated in this study may inform future studies of high-efficiency movement in collective behavior and traffic systems.
An ant colony, containing a few dozen to millions of individuals (Oldroyd, 1968), consists of one or more fertile females called queens, fertile males, workers and soldiers (Oster and Wilson, 1978). Ants show a strong division of labor; for example, workers are responsible for establishing buildings, enlarging their nest, collecting food and larvae. All ants residing in one colony are regarded as a unified entity and support their colony by collectively working (Flannery, 2011). Thus, collective motion is the main pattern in an ant’s life (Hölldobler and Wilson, 1990). In recent years, the collective behavior of ants under emergency conditions has been widely studied (Dias et al., 2013; Haghani and Sarvi, 2017; Wang et al., 2015). Experimental evidence for a ‘faster is slower’ effect comes from an evacuation experiment of ants under stressed conditions (Soria et al., 2012), but jamming and clogging were not observed near the exit (Boari et al., 2013).
In the wild, bi-directional traffic of inbound and outbound individuals is formed in ants’ foraging activities (Gravish et al., 2015; John et al., 2004), which differs from that of most animals, whose movements are uni-directional. The formation of a foraging trail benefits from the pheromone that ants deposit it on the ground. This pheromone can attract subsequent ants to follow the trail and ultimately find the food resource, and the final destination of this trip is their nest (Norman and Hughes, 2016; Wilson, 1990). Before workers carry food to the nest, cleared physical trails are built, which can facilitate load transport and increase the rate of foraging efficiency (Bruce et al., 2017). Certainly, it takes time and energy for workers to build and maintain physical trails (Bochynek et al., 2017; Howard, 2001). Thus, wider trails could take workers more time and energy, which decreases foraging efficiency.
As in vehicle traffic, some degree of lane segregation in ant traffic spatial organization is observed, i.e. the trails of inbound and outbound ants are not intermingled completely. This is good for reducing the rate of head-on encounters. In some ant traffic, three-lane trails are common, such as in the army ant Eciton burchelli (Couzin and Franks, 2003). Compared with the two-lane organization, three-lane traffic would probably increase flow because there would be fewer head-on encounters (Fourcassié et al., 2010). Moreover, the three-lane organization is useful from a functional point of view as it can protect the loaded ants from being robbed. However, because of width limitation of their trails, such as for arboreal ants traveling on small branches or lianas, or litter ants walking on fallen branches or using structural guidelines (natural cracks, furrows or walls), one-lane organization also occurs in ant trails (Dussutour et al., 2005a). Taking Atta colombica as an example, the inbound and outbound trails show a weak degree of lane separation (Dussutour, 2004). One hypothesis for explaining the intermingled trail is that the high rate of head-on encounters observed in forging trails of A. colombica is beneficial for information exchange and helps outbound workers to find food easily. Furthermore, it is not necessary to take more time and energy to build and enlarge the trail and clear the obstacles in it. Additionally, narrow paths can maintain the pheromone in a high concentration, which can select following ants strongly for foraging. In this way, it contributes to improving foraging efficiency. Alternatively, in one-lane bi-directional traffic, the outbound ants make head-on encounters with loaded ants but not with unloaded inbound ants. These head-on encounters result in the transfer of food between workers and this multistage transport is called ‘bucket brigades’ (Anderson et al., 2002; Lee and Kim, 2017). This suggests that the foraging efficiency is greater with a narrow path than with a wide path (Dussutour et al., 2007).
One-lane organization in ant traffic is common. The associated foraging or nest relocation efficiency is higher than that with wide paths in which lane segregation occurs. In bi-directional ant traffic, head-on encounters, as the main pattern for ants moving in opposite directions, play an important role in foraging and nest relocation efficiency. In previous studies (Couzin and Franks, 2003; Dussutour et al., 2004; Schultheiss et al., 2015), the researchers were interested in qualitative analysis of the spatial organization of trails. In this paper, the main goal was to study the bi-directional flow of ants (Camponotus japonicus) in a narrow path quantitatively. We conducted nest relocation experiments and ants were stimulated to emigrate from their nest by changing the environmental conditions (illumination and humidity) and supplying food.
MATERIALS AND METHODS
Nest relocation experiments were performed on Camponotus japonicus Mayr 1866, a species of black ant native to East Asia, to investigate the collective behavior of ants; 427 worker ants from one colony (without a queen) were collected in Shaanxi Province of China and transported to the laboratory. They were placed in a plaster box with a plastic lid and the wall of the box was painted with Fluon to prevent the ants from escaping. The box was kept at room temperature (24±2°C) under natural light/dark cycles with sufficient water and honey provided. When the experiment started, the ants had been raised in the laboratory for 3 months and the average length of their bodies was 1.03±0.11 cm (mean±s.d.).
Fig. 1A shows the arena for the experiments. Two polypropylene boxes of the same size (41 cm long×29 cm wide×23 cm high), with walls coated with Fluon, were used as the new and the old nests. A transparent plastic pipe (100 cm long and 0.8 cm in diameter) connected the two nests from the bottom corners; its width allowed two ants to move side by side. The old nest had no food or water in it and it was placed in a well-lit environment, whereas the new nest was in a comfortable environment (dark and damp surroundings) with an adequate supply of food (honey) and water. Thus, the ants were easily persuaded to move from the old nest to the new one. A digital video camera with a frame rate of 25 frames s−1 placed over the pipe was used to record the experiment. A 20 cm-long area located at the middle of the pipe was selected as the observation region (see Fig. 1B). When the experiment began, we put the whole colony including dead ants into the old nest.
Time, speed and distance headway in ant traffic
The old nest was in a poor environment, whereas the new nest was suitable for ants to live in. The strong contrast made ants relocate from their old nest to the new one spontaneously. When the ants were introduced into the old nest, they became active and displayed irregular movements within the box. Those near the entrance to the pipe spent less time finding it and arrived at the new nest through this pipe. The first ant entered the observation region 2.23 min after the experiment began. As time elapsed, most ants in the old nest were attracted by pheromones deposited by the pioneer ants and eventually found the new nest as shown in Fig. 2. In order to exchange information with ants in the old nest, ants in the new nest returned to the old one. Thus, outbound and inbound ants encountered each other at some point within the pipe. After a period of time, a stable concentration of pheromone was formed, so that workers began to carry the dead bodies of ants to the new nest through the pipe. The first of these ‘loaded’ ants (see below) appeared in the observation region at 64.28 min. No inbound loaded ant was observed.
Because of the division of labor, some ants are just responsible for exploring trails whilst carrying nothing, i.e. they are unloaded ants. In contrast, the main job for others (the loaded ants) is carrying dead bodies from the old nest to the new one in this nest relocation experiment. In the observation region, the free speed of unloaded ants was 2.87±0.76 cm s−1 while that for loaded ants was 2.22±0.43 cm s−1, as displayed in Fig. 3. There was a significant difference in the average free speed of loaded and unloaded ants (t-test: T=8.32, P<0.05).
In the process of nest relocation, two interactions were observed among ants: following behavior for homodromous ants (uni-directional traffic) and head-on encounters with ants moving in the opposite direction (bi-directional traffic). Experiments with pedestrians (Cao et al., 2016; Jelić et al., 2012) revealed that speed is dependent on distance headway with several linear relationships. Here, we also investigated the relationship between distance headway and speed. Here, distance headway is defined as the available distance between neighboring ants, i.e. the distance between the head of the following ant and the tail of the preceding one in uni-directional traffic and the distance between the heads of two opposite-moving ants in bi-directional traffic. In uni-directional ant traffic, several ants moving in the same direction passed through the observation region, and the relationship between distance headway and speed is plotted in Fig. 4A. Similarly, the distance headway in bi-directional traffic also affects the speed of ants, as shown in Fig. 4B. However, according to the fitted curve, there are two linear regimes (a strongly constrained regime and a free regime) with different slopes for uni-directional traffic and three linear regimes (a strongly constrained regime, a weakly constrained regime and a free regime) for bi-directional traffic. Comparison of the slope and intercept for uni-directional and bi-directional traffic flow shows that they have the same slopes (0.095, 0.094), while the intercept (0.306) of uni-directional traffic is larger than that of bi-directional traffic (0.0723). In the free regime, the average values of speed were 3.0 and 2.85 cm s−1 for uni-directional and bi-directional traffic, respectively.
At 9.73 min, the first inbound ant entered the observation region. Gradually, more and more inbound ants moved in the pipe, which induced more head-on encounters between outbound and inbound ants in the observation region (see Fig. 2). Their trajectories were displayed in Fig. 5. When the ants moving in opposite directions encountered each other, they gave way by shifting to the left or the right side. The trajectories clearly present a wavy form, and a remarkable detour emerged when the ants gave way to those from the opposite direction.
Deceleration and acceleration
Fig. 6A,C,E,G depicts the temporal–spatial diagram of ant movement in the observation region for one outbound unloaded ant encountering another, inbound unloaded ant, two inbound discontinuous unloaded ants (decreasing speed twice), two inbound successive unloaded ants (just decreasing speed once) and one inbound loaded ant, respectively. Correspondingly, the evolution of speed with position in the observation region is shown in Fig. 6B,D,F,H. In this experiment, we observed that when two unloaded ants encountered each other, their antennae were in contact for a period of time. We hypothesize that the purpose of antennae contact is information exchange. As can be seen from Fig. 6, the head-on encounter of unloaded ants resulted in a decrease of their speed. After opposite-moving ants separated completely, unloaded ants restored their speed rapidly. Fig. 6B,D,F shows that the head-on encounter process consists of three phases: deceleration due to the encounter, stop for information exchange and then acceleration to free speed. In the deceleration phase, unloaded ants decrease their speed from free speed to zero. Correspondingly, during the acceleration phase, the ants regain their speed. In addition, the time spent in the deceleration phase is less than that in the acceleration phase. In this work, we tracked 49 loaded ants, involving 23 encounters with other ants. As shown in Fig. 6G,H, the speed of the outbound loaded ant did not decrease significantly, unlike that of unloaded ants when they make head-on encounters with others. Thus, head-on encounters have less effect on the motion of loaded ants. This may be because loaded ants have a higher mass; therefore, head-on encounters may have less effect on the speed of loaded ants due to inertia. Furthermore, loaded ants utilize their two strong jaws, which are attached to the head below the antennae, when they carry dead bodies (Borror et al., 1989); thus, dead bodies of large size may affect the function of the antennae to some degree. Additionally, the presence of a dead body meant that the process of antennae contact, i.e. information exchange, was not observed clearly. Furthermore, without external interference, loaded ants did not stop suddenly.
In the observation region, some ants stopped suddenly without any external interference and then started moving again. Fig. 7B shows the deceleration and acceleration phases for these sudden stops. The results show that τ=0.17 s for the deceleration phase and τ=0.42 s for the acceleration phase. Comparison of the head-on encounter process and sudden stops shows the mean relaxation time of the deceleration phase is similar, but ants took less time to restore their speed from zero in the sudden stop condition.
Reduction of movement efficiency
In this ant nest relocation experiment, because of division of labor, the first ‘explorer’ worker went into the observed region at 2.23 min and then found the new nest. The first inbound ant appeared in the observation region at 9.73 min. However, the first loaded ant carrying a dead body appeared at 64.28 min, which was regarded as the beginning of nest relocation. Ants are eusocial insects; therefore, when they relocate their nest, the dead bodies of ants are also carried by workers from the old nest to the new one. It took 62.05 min for nest relocation using the accumulated pheromone trail. In a sealed space, this is enough for pheromone accumulation because of its 30–60 min lifetime (Camazine et al., 2003). We assume that, during this period, a stable concentration of pheromone had been formed in the pipe and the safe state of the environment was ensured. Only under these conditions did the ants begin to relocate the nest. The path from the old nest to the new nest was a 1 m long, sealed transparent pipe, which is effective at reducing the evaporation of pheromone. The formation of a foraging or nest relocation trail would be expected to take more time in nature.
There are two basic types of traffic in nest relocation experiments: uni- and bi-directional. In these two traffic flows, the adaptation times (Jelić et al., 2012), i.e. the slope of the relationship of headway–speed in a strongly constrained regime, are the same, which means that ants have the same sensitivity to the distance headway not only for the tail of the preceding ant but also for the head of the opposite-moving ant. As interpreted in Cao et al. (2016) and Jelić et al. (2012), the intercept can be seen as a minimal individual space. The intercept in uni-directional traffic is 0.306, which is larger than that in bi-directional traffic (0.0723). The reason is that there is no overtaking behavior for following ants as found in John et al. (2009), and they decreased their speed with the distance headway. However, in bi-directional ant traffic, opposite-moving ants made head-on encounters and passed each other. In this way, when the speed was zero, the distance headway could approximate to zero before the ants gave way to each other. In addition, in bi-directional traffic, there is a weakly constrained regime. It is possible that the antennae of opposite-moving ants impacts their speed. In this work, we recorded three free speeds for unloaded ants: 2.87 cm s−1 in the observation region without following and head-on encounters, and 3 cm s−1 and 2.85 cm s−1 in the free regimes of uni-directional and bi-directional traffic, respectively. It was found that the free speed in uni-directional traffic (following behavior) is the greatest of these. This is because the following ants move with high speed owing to the high concentration pheromone deposited by the preceding one. In contrast, in the other two cases, the concentration of pheromone may be low relatively. Moreover, if the types of outbound pheromone (from the old nest to the new nest) and inbound pheromone (from the new nest to the old nest) are different, this would also result in a discrepancy in free speed.
In ant traffic, head-on encounters frequently occur in foraging (Farji-Brener et al., 2010). Similarly, in our experiment, not only head-on encounters but also sudden stops were observed. Sudden stops manifest as single individuals stopping abruptly and quickly without any external interference in the observation region. Both head-on encounters and sudden stops contain phases of deceleration and acceleration. The relaxation time of the deceleration phase is the same for head-on encounters and sudden stops. The reason is that ants are not harmed by collision and a collision avoidance strategy is therefore not required (Moffett, 1987). Furthermore, unlike the behavior of pedestrians, ants have the ability to stop and regain their speed rapidly. In this experiment, the relaxation time of deceleration was 0.16–0.17 s, which means that ants can stop quickly and control themselves effectively. In the acceleration phase, the relaxation time of head-on encounters is larger than that in sudden stops. This may be because in head-on encounters, opposite ants have to share the channel in the initial stage before they accelerate to their former speed, which limits the increase of speed. The relaxation time of deceleration is shorter than that of acceleration for both head-on encounters and sudden stops. The probable reason is that deceleration is a random or sudden procedure, which is mainly determined by the ants’ ability to control their bodies. In contrast, the acceleration phase is arbitrary without any urgency.
As plotted in Fig. 3, there was a significant discrepancy in speed of loaded and unloaded ants. The moving speed was influenced by the mass of the load that the ants carried (Burd and Aranwela, 2003) and their body size (Wang and Song, 2016). For some ants, head-on encounters cost them more time than carrying load in foraging. Taking A. colombica as an example, a quantitative analysis showed that the time cost for head-on encounters was twice as that for carrying things (Dussutour et al., 2009). In this experiment, the speed of loaded ants was smaller than that of unloaded ants as displayed in Fig. 3. However, the reduction of movement efficiency of loaded ants was smaller than that of unloaded ants when two opposite-moving ants encountered each other (see Fig. 9). One possible reason is that the higher mass of loaded ants means that their speed is less affected by head-on encounters. Another reason may be that loaded ants take less time for information exchange because of the influence of the dead body. When a loaded ant encountered an unloaded ant, it was observed that the unloaded ant stopped and gave way to the loaded ant (see Fig. 6G,H). This behavior of unloaded ants embodies the social attribute of collective cooperation, which can ensure high movement efficiency in nest relocation traffic.
Compared with bi-directional pedestrian and vehicle traffic, an ant with weak sight would not decelerate on the basis of vision as pedestrians or drivers would. Ants stop rapidly when they perceive the presence of others through their antennae. In the pedestrian experiment, when a interferer (pedestrian or obstacle) appeared in the planned route, the pedestrian adjusted their speed and direction to avoid collision (without physical contact) (Ma et al., 2010; Moussaïd et al., 2009). However, in ant bi-directional traffic, head-on encounters between opposite-moving ants are a common occurrence for information exchange, which takes ants 2.61 s. Thus, the decrease in speed due to the limits of space and time on information exchange lead to a reduction of movement efficiency. From this point of view, the pedestrian motion has higher efficiency than ant in bi-directional traffic.
In the observation region, one ant may meet one or more opposite-moving ants. The reduction of movement efficiency was 0.71 and 0.53 when one unloaded ant encountered two discontinuous ants and two successive ants, respectively. The reason for this smaller reduction of movement efficiency for encountering two successive ants is that the ant just decreased speed once and made a head-on encounter with the leader of the two successive ants, as the subsequent ant followed the leader one closely. In ant traffic, the following phenomenon is common, and it is beneficial to improving movement efficiency because of the attraction of the pheromone. In addition, the following ants can avoid head-on encounters with opposite-moving ants which gave way to them in bi-directional traffic. Thus, the following behavior for successive ants can improve movement efficiency in bi-direction traffic. Like workers of the black garden ant Lasius niger, they can maintain a high foraging efficiency in a narrow path with alternating clusters of inbound and outbound ants (Dussutour et al., 2005b). Furthermore, in the control experiment with pedestrians, the same phenomenon that clusters of pedestrians rather than single individuals passed the bottleneck from one side to the other was observed. After a period of time, pedestrians from the other side had a chance to pass this bottleneck (Helbing et al., 2005). Analogous to pedestrian or vehicle traffic in daily life, in some places, because of limitations of the environment, there are parts of the road that only one vehicle or pedestrian can pass at a time. In this case, the best way to enhance transportation efficiency is by giving way to opposite-moving vehicles or pedestrians at a particular time, and then exchange. This embodies the importance of cooperation.
Conceptualization: W.S.; Methodology: Q.W.; Software: Q.W.; Formal analysis: Q.W.; Investigation: Q.W.; Resources: Q.W.; Data curation: Q.W.; Writing - original draft: Q.W.; Writing - review & editing: J.Z., W.S., S.L.; Visualization: J.Z.; Supervision: W.S., S.L.; Project administration: W.S.
This research was supported by Key Research and Development Program of China (2016YFC0802508), and Fundamental Research Funds for the Central Universities (WK2320000035).
The authors declare no competing or financial interests.