Ants acknowledge information to control its rate of transfer

Signals whose function is solely to coordinate communication are so far known only in human conversations1 and telecommunication networks2. Utterances like “mm-hmm”3, gestures such as the nodding of one’s head, or “ACK” packets used in Internet protocols to confirm the reception of a message4 all coordinate communication. Rather than carrying domain-specific information5–7, these signals are generic acknowledgements used by receivers to control the flow of sender information when the rate of information transfer could possibly be overwhelming. Here, we show the first evidence of the use of acknowledgements to control information transfer rates outside human society. Quantitative comparison of information flows between sender-receiver pairs demonstrates that acknowledgements are used by pairs of ants during tandem running8,9—a social behaviour where the sender facilitates the receiver’s intake of navigational information—but not by pairs of termites that also tandem run10,11 to maintain cohesion but not to share large amounts of information. Our analysis provides a quantitative framework for identifying in other animal taxa hidden patterns of information flow with implications for uncovering cryptic signals within complex communication behaviours that are still poorly understood12,13.

explore in search of a nest site. Despite having different function, in both ants and termites the follower is attracted to volatile pheromones emitted by the leader 16,17 and the leader responds to the touch of the follower's antennae by resuming or continuing motion 16,18,19 . This mutual communication may serve merely to maintain proximity between the pair, but we hypothesize that it has an additional role in ants, because of their need to transfer a large amount of information 20,21 . Under this hypothesis (Figs. 1c and 1d), the leader acts as a filter of the environment, setting the path and directing the follower to useful navigational cues.
The follower, in turn, actively regulates the speed of the run through acknowledgement signals, by interrupting and resuming physical contact with the leader, so that she can acquire information at a manageable rate.
Both the cohesion and acknowledgement hypotheses predict that leaders will pause and wait if the follower's tactile input is lost, consistent with the results of experiments 16,18,19 and with the occurrence of spontaneous pauses in unmanipulated tandems of both ants and termites. To distinguish between these explanations, we employ information theory 22 to formally quantify the directionality of information flow between leaders and followers. Given time series of behavioural observations of two parties that may be communicating, transfer entropy quantifies the reduction of uncertainty about the future state of the putative receiver given knowledge of the present state of the corresponding sender 23 . Transfer entropy is well suited for studying message passing as it naturally incorporates temporal ordering, from the sender's present to the receiver's future, and quantifies the additional predictive power gained from the sender beyond what is contained in the receiver's past. It is a measure of predictive information 24 that allows us to make rigorous statements about the directionality of information flow without altering the studied behaviour through experimental interventions. Using transfer entropy, we first studied whether the leader's or the follower's behaviour better predicts the direction of motion of the other runner along the route. We expect the leader's behaviour to be more informative about that of the follower both in ants, because the leader is showing a known route to the follower, and in termites, because the leader is directing a random search. To test this, we coarsegrained the spatial trajectories of each runner into sequences of clockwise and counter-clockwise turns ( Fig. 1e and Methods). Then, we measured the flow of information between the pair and found that, as expected, the leader better predicts the rotation pattern of the follower than the other way around across all three species (Fig. 1f, rotation bars).
Next, to analyse the regulation of speed, we focused on the frequent brief interruptions that give tandem runs a distinctive stop-and-go appearance. During these interruptions, the follower breaks tactile contact with the leader, who then pauses while the follower performs a local random search 19,25 . When the follower again touches the leader, the latter resumes motion, and the pair continues on their way. If our hypothesis about acknowledgment signals is correct, we would expect the follower's pausing pattern of ants to differ from that of termites. This is because the ant follower likely triggers each pause by breaking contact to acquire navigational information 15,26 , while the termite follower should not interrupt tandem runs deliberately but only as a result of accidental separation from the leader. To test this, we analysed the same spatial trajectories but instead coarse-grained them as sequences of pauses and movements (Fig. 1e). We found that the leader remains the best source of predictive information in termites, but in ants the follower instead controls the flow of information and better predicts the future pausing behaviour of the leader (Fig.   1f, pausing bars). Communication is therefore bidirectional in ants (from leader to follower for rotations and from follower to leader for pauses) and unidirectional in termites (from leader to follower for both rotations and pauses).
Side-by-side comparison of tandem run trajectories (Figs. 2c and 2f) shows that ants, but not termites, evince a tension between cohesion and information acquisition. Leader and follower ants repeatedly switch in and out of proximity regulation under the control of the follower (Figs. 2a and 2b). The predictive power of the leader's rotation pattern dominates at close distances up to two body lengths, when the pair is undergoing sustained motion and seeking cohesion (point 1, rotation regime); when their distance increases further, the follower becomes more informative, predicting pauses in the motion of the leader (point 2, pausing regime). Their separation then decreases as the follower approaches the stationary leader (point 3) and predicts her resumption of motion. When leader and follower are again in close proximity and the leader begins to move away (point 4), this pattern repeats. Large separations are evidently generated by the follower ant and are unrelated to rotational course corrections.
In contrast to ants, the termite leader dominates both regimes of predictive information (Fig. 2d-f and Extended Data Fig. 6). Even more, these regimes are inverted with respect to ants with rotation being predicted at larger distances and pausing of motion at shorter distances. The distance between leader and follower is characterised by oscillations with higher frequency but lower amplitude than those of the ants (cf. Fig. 2c and Fig. 2f). These oscillations are largely within the rotation regime due to sustained motion. In this regime, tandem runners frequently alternate between a phase in which the leader is the faster of the two and their distance increases (point 1a) and a phase in which the follower moves faster than the leader, reducing the gap (point 2a). Sporadically, leader and follower can be found very close to each other (less than 0.89 body lengths, Fig. 2d) where they enter the pausing regime. When this happens, the leader's motion initially predicts the decrease and then the increase in speed of the follower (points 1b and 2b). The pausing regime is then quickly abandoned, and rotation information regains dominance. This behaviour is consistent with relatively close proximity facilitating momentary large course corrections ( Fig.   2f, right inset). Leader-initiated pauses in termites might serve some unknown function (e.g., motor planning 27,28 ); however, we have no evidence that they facilitate follower control over any aspects of the trajectory.
Both ants and termites rely on physical contact as a feedback mechanism to maintain cohesion.
However, whereas termites separate sporadically and can be likened to a person leading another by the hand, ants show a more complex coordination of social behaviour as they alternate between close contact and separation. We suggest that the ants' intermittent motion and bidirectional feedback is akin to the pausing for acknowledgment observed between machines on a computer network. In this case, communication theory can aid in understanding the frequency of acknowledgments in terms of the receiver's informational capacity and the complexity of the information being received. The selective exposure of a follower to navigational information is the sending of a complex message over a simple Although social insects use cue-based mechanisms to regulate the flow of physical material (e.g., food or nesting material 30,31 ), our study is the first to reveal signalling mechanisms that control the flow of a non-physical quantity-information-in a non-human organism. This opens questions about the evolution of flow regulation: tandem running has evolved multiple times in the ants, and not all instances necessarily require acknowledgment signals 32 ; thus a comparison across systems may provide insights into how signals that regulate other signals evolve. The methodology we put forward, which applies advanced information-theoretic measures to different coarse-grainings of the same dataset, can enable the discovery of cryptic signalling behaviours in other taxa and can reveal deeper insights into behaviours that have poorly or partially understood functions (e.g., turn-taking 12,13 , complex coordinated dances in avian 33 ). The pausing pattern is encoded using two states: the motion state (M) and the pause state (P). The motivation for this coding scheme is to capture when a tandem runner pauses while waiting for the other to re-join the tandem run or to react to physical contact. Pauses, small adjustments of the position of the runner, or changes due to noise in the sampled trajectories may each accidentally be considered as genuine acts of motion. To prevent these spurious classifications, we used a threshold to distinguish segments of the trajectory into those identifying motion and those identifying pauses. The distribution of step sizes, i.e., the distance travelled by a runner between two consecutive sampled positions ( and (=# , shows two distinct modes: short steps representing pauses and long steps representing sustained motion (see Extended Data Fig. 2). The 10 th percentile was used as a threshold for separating the two modes for all sampling periods. We therefore encoded steps in the trajectory in the 10 th size percentile as pause states and the remaining steps as motion states. This threshold was varied in the interval {5%, 6%, … , 15%}

Methods
during a perturbation analysis of predictive information (see Computation of statistics).
The rotation pattern is also encoded using two states: clockwise (CW) and counter-clockwise (CCW).
The direction of rotation at time is obtained by looking at three consecutive positions, (@# , ( , (=# , in the spatial trajectory of each runner. The rotation is clockwise when the cross product A@# A BBBBBBBBBBBB⃗× A A=# BBBBBBBBBBBB⃗ is positive, counter-clockwise when it is negative, and collinear when it is zero. In the rare occurrences of collinear motion, the direction of rotation at the previous time step, − 1, is copied over in the time series. As a control for our choices of possible behavioural outcomes, we also considered a compound pausing & rotation pattern that simultaneously encodes for both components of tandem running. The pausing & rotation pattern is defined using a ternary coding scheme that encodes motion bouts in the states pause (P), clockwise (CW) and counter-clockwise (CCW). As for the pausing pattern, the shortest 10% of steps in the spatial trajectories are encoded as pausing (see Computation of statistics for a perturbation analysis of this parameter). The remaining 90% of steps are encoded using states clockwise and counter-clockwise following the same methodology used for the rotation pattern.

Measuring predictive information.
Our analysis of communication in tandem running is grounded on the theory of information 22 and on its constructs of entropy, conditional entropy, and transfer entropy. We aim to quantify how knowledge of the current behaviour of the sender allows us to predict the future behaviour of the receiver. We consider the behavioural patterns of leaders and followers as the series of realizations A second step to obtain additional information about the future of the follower is to consider the timedelayed effects of its interaction with the leader. Transfer entropy was introduced for this purpose 23 . It measures the amount of information about the future behaviour of the receiver given by knowledge of the current behaviour of the sender-information that is not contained in the receiver's past. Due to its time directionality (i.e., from the present of the sender to the future of the receiver), it is considered a measure of information transfer or predictive information 24 . Transfer entropy is defined as and measures the reduction of uncertainty of (=# given from knowledge of which is not already given by (U) . The logarithm in the above equation is known as local transfer entropy 39 and tells us whether, at time , the interaction ( | ( (U) → (=# | ( (U) between the two processes is informative (> 0) or misinformative (< 0). In our analysis, we look at local transfer entropy averaged over the distance between leader and follower to understand the spatiotemporal dynamics of communication during tandem running.
Due to the asymmetry of transfer entropy, _→a ≠ a→_ , we can obtain the predominant direction and the magnitude of predictive information by studying the difference _→a − a→_ . This quantity is positive when information flows predominantly from to and negative when it flows from to . Its absolute value is known as net transfer entropy 40  normalised transfer entropy is minimal and equal to 0.

Computation of statistics.
We computed information-theoretic measures for both leaders and followers.
In our computations, we assume that the pausing and rotation patterns of ants and termites are peculiar features of the species rather than of specific pairs of tandem runners. As such, rather than treating each trial separately and then aggregating the results, we estimated the necessary probabilities from all experimental trials together and obtained a single estimate of transfer entropy for each considered species and parameter configuration. Our measures of predictive information are therefore averaged over all trials of the same species. All information-theoretic measures were computed in R 3.4.3 using the rinform- To prevent possible artefacts that may arise due to finite sample sets, we discounted transfer entropy by a correction factor computed over pairs of independent time series therefore obtaining conservative estimates 40 . To do so, we randomly paired the behavioural patterns of leaders and followers belonging to

Additional information
Accession codes: Data that support the findings of this study will be available in "figshare" with identifier "10.6084/m9.figshare.9786260" upon acceptance of the manuscript.

Competing interests:
The authors declare no competing interest.

Extended data
Extended Data Figure  Extended Data Figure 2 Step size distributions. Probability density function of the step size as a function of the sampling period, respectively, (a) for T. rugatulus, (b) for C. formosanus, and (c) R. speratus. Colour blue represents the 10% probability mass used to define the pausing state; colour green represents the remaining 90% of the probability mass defining the motion state. Step size (mm) Sampling period (s) Step size (mm) Sampling period (s)