Communication is fundamental to the organization of animal societies, often resulting in the convergent evolution of similar social behavior across lineages. However, this similarity may conceal underlying functional and mechanistic differences. Here we combined network and information-theoretic analysis to quantify how tandem recruitment is distinguishable between two ant genera, Temnothorax and Diacamma. We show that Temnothorax uses tandem running to recruit additional recruiters, while Diacamma uses it principally to move the passive majority of their colony, a task that Temnothorax accomplishes with a different behavior, social carrying. Accordingly, the network structure of Diacamma tandems was dissimilar to that of Temnothorax, instead resembling the social-carrying networks in Temnothorax. Furthermore, our information-theoretical analysis on movement trajectories revealed that Diacamma tandem runs lack bidirectional information transfer, the signature of route learning in Temnothorax. By quantifying the diversity of similar communication systems, this study increases the resolution of our understanding of animal societies.

Tandem running in ants is a sophisticated form of communication. Precise measurement of movement coordination by the tandem pair can shed light on social interactions. Here, we describe an integrative approach to obtain long movement trajectories of a specific tandem pair within a crowd of ants. We describe a maze-like arena, video recording and editing, and movement tracking. We integrate two pieces of image-based tracking software that have distinct individual assignment strategies. This protocol aids comparative studies of recruitment communication across species. For complete details on the use and execution of this protocol, please refer to Mizumoto et al. (2023)1 and Valentini et al. (2020).2

Deep learning is driving recent advances behind many everyday technologies, including speech and image recognition, natural language processing and autonomous driving. It is also gaining popularity in biology, where it has been used for automated species identification, environmental monitoring, ecological modelling, behavioural studies, DNA sequencing and population genetics and phylogenetics, among other applications. Deep learning relies on artificial neural networks for predictive modelling and excels at recognizing complex patterns. In this review we synthesize 818 studies using deep learning in the context of ecology and evolution to give a discipline‐wide perspective necessary to promote a rethinking of inference approaches in the field. We provide an introduction to machine learning and contrast it with mechanistic inference, followed by a gentle primer on deep learning. We review the applications of deep learning in ecology and evolution and discuss its limitations and efforts to overcome them. We also provide a practical primer for biologists interested in including deep learning in their toolkit and identify its possible future applications. We find that deep learning is being rapidly adopted in ecology and evolution, with 589 studies (64%) published since the beginning of 2019. Most use convolutional neural networks (496 studies) and supervised learning for image identification but also for tasks using molecular data, sounds, environmental data or video as input. More sophisticated uses of deep learning in biology are also beginning to appear. Operating within the machine learning paradigm, deep learning can be viewed as an alternative to mechanistic modelling. It has desirable properties of good performance and scaling with increasing complexity, while posing unique challenges such as sensitivity to bias in input data. We expect that rapid adoption of deep learning in ecology and evolution will continue, especially in automation of biodiversity monitoring and discovery and inference from genetic data. Increased use of unsupervised learning for discovery and visualization of clusters and gaps, simplification of multi‐step analysis pipelines, and integration of machine learning into graduate and postgraduate training are all likely in the near future.

Ants have evolved diverse recruitment methods to guide colony members to valuable resources, such as food or nest sites. One of these methods, tandem running, consists of an informed leader directly guiding a naive follower every step of the way from nest to resource. Although this behavior appears superficially similar in the different ant taxa in which it has independently evolved, this similarity could conceal underlying functional and mechanistic differences. Here we present a combined network and information-theoretic analysis, which reveals fundamental differences in the tandem recruitment between two distantly related ant genera, Temnothorax and Diacamma. Temnothorax uses tandem running to recruit additional recruiters, whereas Diacamma uses it principally to move the passive majority of the colony, a task that Temnothorax accomplishes with a different behavior, social carrying. Accordingly, the structure of the tandem run recruitment networks of Diacamma was different from those of Temnothorax, with Diacamma networks more closely resembling the social carrying networks of Temnothorax. Furthermore, an information-theoretic analysis of the spatial trajectories of leaders and followers revealed that Diacamma tandem runs lack bidirectional information flow, the signature of route-learning in Temnothorax tandem runs. These results suggest that Diacamma uses tandem runs not to share information, but to transport nestmates. By quantifying the cryptic diversity of communication behavior, this study increases the resolution of our understanding of animal societies.

Ants have evolved diverse recruitment methods to guide colony members to valuable resources, such as food or nest sites. One of these methods, tandem running, consists of an informed leader directly guiding a naive follower every step of the way from nest to resource. Although this behavior appears superficially similar in the different ant taxa in which it has independently evolved, this similarity could conceal underlying functional and mechanistic differences. Here we present a combined network and information-theoretic analysis, which reveals fundamental differences in the tandem recruitment between two distantly related ant genera, Temnothorax and Diacamma. Temnothorax uses tandem running to recruit additional recruiters, whereas Diacamma uses it principally to move the passive majority of the colony, a task that Temnothorax accomplishes with a different behavior, social carrying. Accordingly, the structure of the tandem run recruitment networks of Diacamma was different from those of Temnothorax , with Diacamma networks more closely resembling the social carrying networks of Temnothorax . Furthermore, an information-theoretic analysis of the spatial trajectories of leaders and followers revealed that Diacamma tandem runs lack bidirectional information flow, the signature of route-learning in Temnothorax tandem runs. These results suggest that Diacamma uses tandem runs not to share information, but to transport nestmates. By quantifying the cryptic diversity of communication behavior, this study increases the resolution of our understanding of animal societies. ### Competing Interest Statement The authors have declared no competing interest.

Programming robot swarms is hard because system requirements are formulated at the swarm level (i.e., globally) while control rules need to be coded at the individual robot level (i.e., locally). Connecting global to local levels or vice versa through mathematical modeling to predict the system behavior is generally assumed to be the grand challenge of swarm robotics. We propose to approach this problem by programming directly at the swarm level. Key to this solution is the use of heterogeneous swarms that combine appropriate subsets of agents whose hard-coded agent behaviors have known global effects. Our novel global-to-local design methodology allows to compose heterogeneous swarms for the example application of self-organized task allocation. We define a large but finite number of local agent controllers and focus on the global dynamics of behaviorally heterogeneous swarms. The user inputs the desired global task allocation for the swarm as a stationary probability distribution of agents allocated over tasks. We provide a generic method that implements the desired swarm behavior by mathematically deriving appropriate compositions of heterogeneous swarms that approximate these global user requirements. We investigate our methodology over several task allocation scenarios and validate our results with multiagent simulations. The proposed global-to-local design methodology is not limited to task allocation problems and can pave the way to formal approaches to design other swarm behaviors.

Group-living animals that rely on stable foraging or migratory routes can develop behavioural traditions to pass route information down to inexperienced individuals. Striking a balance between exploitation of social information and exploration for better alternatives is essential to prevent the spread of maladaptive traditions. We investigated this balance during cumulative route development in the homing pigeon Columba livia. We quantified information transfer within pairs of birds in a transmission-chain experiment and determined how birds with different levels of experience contributed to the exploration–exploitation trade-off. Newly introduced naïve individuals were initially more likely to initiate exploration than experienced birds, but the pair soon settled into a pattern of alternating leadership with both birds contributing equally. Experimental pairs showed an oscillating pattern of exploration over generations that might facilitate the discovery of more efficient routes. Our results introduce a new perspective on the roles of leadership and information pooling in the context of collective learning.

Quorum sensing (QS) is ubiquitous in distributed, multi-agent systems in nature—from bacteria to arthropods to primates—and has been proposed as a useful distributed algorithm in engineered systems—from multi-robot systems to Internet server farms. Achieving QS requires groups to collectively integrate information about their numbers and reach consensus on an action contingent upon those numbers. In nest-site selection tasks that employ QS in ants, sensitivity to encounter rate has been implicated as a mechanism for how individuals sense that quorum has been reached. However, little is known about how individual ants estimate proximity to the critical rate. Ant-inspired QS algorithms proposed by computer scientists either heavily depend on communication between agents or the ability for individual agents to accumulate information over many encounters with others. Both communication and significant memory storage may be beyond the simple capabilities of small-scale robots in large collectives. Alternatively, if cognition was embodied across the group of agents and their physical environment, cognitive abilities could far exceed the abilities of each individual. Toward this end, we propose a novel bio-inspired algorithm for QS on mobile agents within a confined space. Our approach does not require individuals to communicate or count over long sequences of encounters; instead, QS emerges from the random interaction of mobile excitable agents with each other and the physical cavity. We validate theoretical predictions for our algorithm’s performance in simulation, and we also show that it has good qualitative agreement with accuracy and response-time data from real ants. More broadly, our algorithm provides a new, concrete example of how ants can serve as conceptual models for hypothetical dynamic networks of mobile neurons.

Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Materials and methods Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract Group-living animals that rely on stable foraging or migratory routes can develop behavioural traditions to pass route information down to inexperienced individuals. Striking a balance between exploitation of social information and exploration for better alternatives is essential to prevent the spread of maladaptive traditions. We investigated this balance during cumulative route development in the homing pigeon Columba livia. We quantified information transfer within pairs of birds in a transmission-chain experiment and determined how birds with different levels of experience contributed to the exploration–exploitation trade-off. Newly introduced naïve individuals were initially more likely to initiate exploration than experienced birds, but the pair soon settled into a pattern of alternating leadership with both birds contributing equally. Experimental pairs showed an oscillating pattern of exploration over generations that might facilitate the discovery of more efficient routes. Our results introduce a new perspective on the roles of leadership and information pooling in the context of collective learning. Editor's evaluation This study in the field of collective behavior addresses how naïve and experienced individuals (i.e., homing pigeons) pool information in order to navigate while flying back home. The authors show that the passage of information is largely democratic, meaning information passes both ways, and that, unexpectedly, exploration of the route is initiated both by naïve and experienced birds. The work provides a new perspective on information sharing during collective learning. https://doi.org/10.7554/eLife.68653.sa0 Decision letter Reviews on Sciety eLife's review process Introduction The coordinated motion of groups is a widespread phenomenon observed in multiple taxa (Vicsek and Zafeiris, 2012). Among other adaptive advantages, such as increased energetic efficiency and decreased odds of predation (Krause and Ruxton, 2002), collective motion also allows group members to increase their sensory and cognitive capacity (Berdahl et al., 2013; Gelblum et al., 2020) and to acquire valuable social information for navigation (Couzin, 2009; Couzin et al., 2011). In many animals, this social information concerns well-established foraging or migratory routes that can, in some species, persist over successive generations (Helfman and Schultz, 1984; Sasaki and Biro, 2017; Jesmer et al., 2018). Knowledge and skills that accumulate over generations can provide groups with an enhanced ability to solve difficult problems (Biro et al., 2016). Not only can later generations build on the success of earlier ones, but the introduction of new members, even those with no prior knowledge, adds diversity that can enhance the group’s behavioural solutions (Mehlhorn et al., 2015). As is often the case (Hills et al., 2015), behavioural patterns that lead to a search for improvement, whether individually, socially, or over multiple generations, involve an exploration–exploitation trade-off. In navigation problems, both solitary individuals and groups have to balance between exploiting previously acquired information necessary to navigate a known route and exploring for additional information that might allow them to approach the optimal route (Fu and Gray, 2006). However, how moving collectives compromise between these tasks has received limited attention. Understanding the exploration–exploitation trade-off is complicated by ambiguity about group leadership (Couzin et al., 2005; Garland et al., 2018). Although some collectives (e.g., ants, honeybees) can allocate certain individuals to spatial exploration while others continue to exploit accumulated information (Hills et al., 2015), individuals in cohesively moving groups are highly coupled and can only benefit from compromising between exploring and exploiting if they do so in unison. For example, dominant guineafowls displace subordinates to monopolize a foraging patch (i.e., exploitation) but, to benefit from the safety of group cohesion, are then forced to follow subordinates in their exploration for alternative patches (Papageorgiou and Farine, 2020). Baboons can also compromise between movement decisions. When they travel together, they follow one member’s directional preference over another if the angle of disagreement between conflicting preffered directions is large but compromise by averaging alternative proposed directions when this angle is small (Strandburg-Peshkin et al., 2015). If individuals are to stay together, the group must reach consensus between following a known route or departing from it to find better routes, foraging patches, or temporary resting locations. Elucidating whether different group members contribute differently to this process is crucial to understanding how groups compromise between exploration and exploitation. We investigate this question in the context of navigation through natural landscapes using the homing pigeon Columba livia as our model system. After successive homing journeys from a given release site, pigeons develop stable idiosyncratic routes that are followed with high fidelity (Meade et al., 2005; Guilford and Biro, 2014). These birds rely on sequences of localized visual landmarks to recapitulate familiar yet individually distinct routes (Biro et al., 2004; Meade et al., 2005). Each route is learned in a gradual process starting with an exploration phase that samples new landmarks, from which the bird eventually converges upon a stable sequence of landmarks (Biro et al., 2004). Experiments with paired birds show that route information can be passed from experienced birds to naïve individuals through social learning (Pettit et al., 2013a) and can be modified through information pooling when individuals with different idiosyncratic routes share information to reach a compromise between their routes (Biro et al., 2006). Although learning generally improves route efficiency, both social learning and information pooling tend to reach a plateau beyond which further improvement in efficiency is not seen. However, for birds flying together, the introduction of a naïve individual in place of an experienced one effectively leads to the resumption of exploratory behaviour and further route improvement (Sasaki and Biro, 2017). Yet, it remains unclear to what extent a bird’s prior experience influences the balance between exploration and exploitation and how birds with potentially different route preferences jointly shape a route. Indeed, the mechanisms underlying how different individual preferences are combined into a collective outcome is one of the key foci in studies of collective animal behaviour. Broadly, group decisions can range from despotic with a single leader to democratic in which input from different individuals is aggregated to reach consensus (Conradt and Roper, 2003). Some animal groups make both despotic and democratic decisions, and researchers have been investigating what determines reliance on one collective decision-making strategy over the other (King and Cowlishaw, 2014). For example, baboons live in despotic societies where the alpha male is most often responsible for group decisions between alternative foraging destinations (King et al., 2008), but they can also decide democratically in certain situations, such as during daily ranging activities (Strandburg-Peshkin et al., 2015). Evidence of both despotic and democratic decisions also exists in homing pigeons (Biro et al., 2006; Nagy et al., 2010; Jorge and Marques, 2012). When leadership is defined as disproportionate input into collective navigational decisions, either through spatial position (Pettit et al., 2013b), route similarity (Flack et al., 2012), or directional correlation delay (Nagy et al., 2010), a number of different factors have been shown to play a role in it. Leadership dynamics are influenced by individual differences among birds in fidelity to their own routes (Freeman et al., 2011), their typical flight speed (Pettit et al., 2015), their personality (Sasaki et al., 2018), as well as their level of experience (Flack et al., 2012). Moreover, equally experienced birds are known to come to a compromise by averaging their idiosyncratic routes so long as the pair’s route remains within a threshold distance from each bird’s favoured one – a low level of conflict. Higher levels of conflict lead instead to a splitting of the pair or to the emergence of a single leader (Biro et al., 2006). Nonetheless, experience alone is unable to fully recover the leadership structure characteristic of larger flocks (Watts et al., 2016). Spatial position offers some insight into leadership; on average, birds flying closer to the front of the flock have a stronger influence on the flock’s directional choices than birds flying at the back (Nagy et al., 2010; Pettit et al., 2013b). Even so, the moment-to-moment relationship between leadership and level of experience remains unclear. Leader–follower interactions of this sort can be accurately captured using information-theoretic measures that quantify causal relations in terms of predictive information (Butail et al., 2016; Kim et al., 2018; Crosato et al., 2018; Ray et al., 2019; Valentini et al., 2020). This methodological approach, which generally requires large amounts of data (but see Porfiri and Ruiz Marín, 2020), is gaining popularity among behavioural ecologists (Strandburg-Peshkin et al., 2018; Pilkiewicz et al., 2020) as tools for automatic monitoring and extraction of the necessary volumes of behavioural data become increasingly available (Egnor and Branson, 2016). One of these measures, transfer entropy, quantifies information about the future behaviour of a focal individual that can be obtained exclusively from knowledge of the present behaviour of another subject (Schreiber, 2000). Transfer entropy measures information transferred from the present of the sender to the future of the receiver (Lizier and Prokopenko, 2010). It explicitly accounts for autocorrelations characteristic of individual birds’ trajectories (Mitchell et al., 2019) by discounting predictive information available from the sender’s present that is already included in the receiver’s past (see Figure 1). Furthermore, it does not require a model of how sender and receiver interact, and it is well suited to study social interactions both over space and time (Lizier et al., 2008; Strandburg-Peshkin et al., 2018). This aspect of transfer entropy encompasses traditional methods to quantify collective movement that are based on modelling an individual’s behaviour as a combination of three motional tendencies (Couzin et al., 2002) – alignment of direction to nearby group members, attraction towards sufficiently distant members, and repulsion from sufficiently close members – that allow an individual to maintain proximity to the group. In this context, transfer entropy is advantageous as it can capture causal interactions due not only to alignment forces (Nagy et al., 2010) but also to attraction and repulsion forces that result in temporarily unaligned states (Pettit et al., 2013b). Figure 1 Download asset Open asset Illustration of the methodological approach. The spatial trajectories of an experienced (E) and a naïve (N) bird (point 1) are encoded as clockwise and counterclockwise rotations (point 2) which we represent as discrete time series (point 3). The combination of rotations encoded in both series (point 4) is used to estimate the probabilities required to compute transfer entropy (point 5) and to determine the influence of one individual over the future behaviour of the other (point 6). This example illustrates transfer entropy from experienced to naïve, but we also computed it for the opposite direction. We study collective decision-making and the exploration–exploitation trade-off using an experimental analysis of cumulative route development in homing pigeons conducted by Sasaki and Biro, 2017. In their experiments, pairs consisting of a naïve and an experienced bird were required to successively solve the same homing task a total of 12 times. This set of paired flights, which represents a single generation of cumulative route development, allowed the naïve bird to acquire knowledge of localized visual landmarks necessary for homing. At the end of each generation, the more experienced bird was then replaced with a new naïve individual and the learning process was repeated with the newly formed pair. This transmission-chain design, where experienced individuals were repeatedly replaced with naïve ones, lasted five generations and was replicated in 10 independent transmission chains. Route efficiency was measured as the ratio of the beeline distance between the release site and the home loft (i.e., the ideal optimum) and the actual distance travelled by birds. Sasaki and Biro’s (2017) s results showed that, although homing efficiency dropped considerably every time a new naïve bird was introduced, transmission-chain pairs continued to improve within and over generations, eventually outperforming both solo and fixed-pair controls (respectively, 0.92 efficiency versus 0.83 and 0.85). In contrast, the efficiency of solo and fixed pairs plateaued after they had first established their idiosyncratic routes (around the 9th–10th release for the former and the 7th–8th release for the latter). The continued improvement seen in transmission chains might result from a variety of decision-making mechanisms ranging from fully despotic to increasingly democratic. A simplified perspective of this continuum allows us to consider four alternative hypotheses. In two of these alternatives, H1 and H2, and, a single despotic leader, either the naïve (H1) or the experienced (H2) bird, determines the entire homing route. Whereas evidence of social learning (Sasaki and Biro, 2017) suffices to dismiss the possibility of leadership by the naïve individual (H1), leadership by the experienced individual (H2) could still be the only process in place if social learning is unidirectional and the naïve individual merely triggers the experienced bird to resume and lead exploration. Under the other two hypotheses, H3 and H4, birds pool their personal information by means of democratic processes based on moment-by-moment integration of individual preferences or transient, alternating leadership (Conradt, 2012). The third hypothesis (H3) entails the experienced bird contributing only its past route information and relying instead on the naïve individual for the discovery of route innovations. If this hypothesis holds, we expect the naïve bird to disproportionally lead phases of exploration. Otherwise (fourth hypothesis, H4), both experienced and naïve birds might contribute through exploration to the discovery of new information. We discriminated between these alternative hypotheses by using transfer entropy to reveal the extent to which birds influence each other and to investigate if relative spatial position can accurately predict leader–follower dynamics. On this basis, we studied the contribution of each bird to the exploration–exploitation trade-off over different stages of route development. This exploration–exploitation perspective of homing route development allowed us to characterize the efficiency of choices made by birds over the course of the experiment and to shed light on the superior performance of experimental pairs with respect to solo and fixed-pairs controls. Results Birds pool information Whereas previous evidence of social learning (Sasaki and Biro, 2017) suffices to dismiss the possibility of naïve individuals behaving in a despotic manner (H1), the despotic approach remains a possible option for experienced birds (H2). Indeed, the social learning hypothesis under which the naïve bird passively copies the idiosyncratic route of the experienced one (i.e., H2, the despotic leader) entails a transfer of information that is unidirectional – from the experienced to the naïve bird. Instead, under the two alternative hypotheses based on democratic decision-making (H3 and H4), the two birds rely on bidirectional information transfer to pool information and increase the efficiency of their route (Pettit et al., 2013a; Sasaki and Biro, 2017). We rejected the unidirectional social learning hypothesis H2 by finding causal evidence of information pooling; the naïve bird actively influenced the behaviour of the experienced one for a large portion of the parameter space (Appendix 1—figure 1). As is common practice with these measures (Porfiri, 2018), we selected the parameter configuration that maximized the total transfer of information between the two birds (one sample every 0.2 s, history length of 10 samples). This was maximal for the shortest sampling period (i.e., prediction interval) of 0.2 s and progressively decreased towards 0 for larger periods up to 4 s, indicating that the effect of an interaction between birds was transitory and lasted for a limited period of time. Using this configuration, we compared measurements of information transfer against those of a surrogate dataset created by pairing trajectories of birds that were not flown together. We found that levels of mutual influence between birds that flew together were significantly higher than those observed in the surrogate dataset both overall and for each generation separately (Mann–Whitney–Wilcoxon, columns 2 and 3 of Appendix 1—table 1). During the first two generations of paired flights (Figure 2a, paired analysis), when there was a large margin to improve the efficiency of the pair’s trajectory, the naïve bird was more informative than the experienced one, evidenced by a stronger influence of the former over the latter. At generation 4, there was a balance between the two birds, whereas the experienced bird eventually became the better source of predictive information in the last generation. A linear fit over generations of the paired comparison (Figure 2a, red line) showed an increasing influence of the experienced bird over the naïve one (Theil–Sen estimator, slope 0.534, p<0.001). Additionally, a non-paired comparison of the same results revealed that, although the behaviour of the naïve bird resulted, on average, in a marginally higher predictive power than that of the experienced bird (18.7–21.4% versus 17.7–20.5%), variations in each bird’s route explained a large portion of the other bird’s behaviour (Figure 2b), suggesting non-trivial leadership dynamics. These results do not show whether different levels of experience within the pair led to asymmetric contributions of birds to route development, with the experienced bird providing only its past route information and the naïve bird in charge of discovering route innovations, or if both birds contributed to the exploration for possible route alternatives. To discriminate between the remaining hypotheses H3 and H4, we first developed the means to evaluate leadership on a moment-to-moment basis. Figure 2 Download asset Open asset Predictive power of birds over generations. Panel (a) shows the net predictive power of the two birds over generations; it measures the excess predictive information within the pair and highlights which of the two birds is more informative (purple for the experienced bird, green for the naïve bird). The red line corresponds to a linear fit over generations using the Theil–Sen estimator. Panel (b) shows the predictive power of naïve and experienced birds separately from each other as a function of generations. The predictive power of a bird with respect to the other is measured in terms of the percentage reduction in uncertainty, and it has been computed on the basis of transfer entropy as detailed in Materials and methods. Relative position determines temporary leadership Consistent with information sharing within each pair, we found that experienced and naïve birds repeatedly switched their positions at the front and back of the pair (Figure 3a). Previous studies found evidence that birds that spent, on average, more time at the front of the flock had a tendency to assume leadership roles (Nagy et al., 2010; Pettit et al., 2013b). To see whether this average relationship between leadership and position holds at each point in time, we investigated the spatiotemporal dynamics of information transfer (Lizier et al., 2008). We did so by considering the amount of predictive information obtained by each bird as a function of the distance from the experienced to the naïve bird projected over their mean direction of motion (Figure 3b). We found that within a distance of up to 30 m the bird flying ahead was consistently more informative than that flying in the back. This is not only further evidence that the bird flying ahead acts as the leader, influencing the path of the follower behind it, but, because of its finer grain, it also enables relative distance between birds to be used as a (more parsimonious) moment-to-moment measure of causal influence within the pair. Figure 3 Download asset Open asset Predictive power of birds as a function of relative distance. Panel (a) shows sample flight trajectories for a number of different releases, r, of the same pair of birds. Colours highlight which bird is ahead of the other during different segments of the route. Panel (b) shows the local transfer of information (mean and 95% confidence interval) between the experienced bird and the naïve one as a function of their relative distance (colours represent the direction of information transfer) estimated from generations 2–5 using smoothed conditional means. The experienced and the naïve birds alternated leading segments of the route, where leadership durations were consistent with a log-normal distribution (see Supplementary material). Although the naïve bird flew at the front of the pair for longer segments (Whitney–Mann–Wilcoxon, p<0.047, W = 56865638), the difference was very small (0.3 s) and largely driven by the flights of one generation. Indeed, for all generations but the third (p<0.001, W = 6588674), the distribution of consecutive time spent at the front of the pair by the experienced bird cannot be distinguished from that of the naïve individual (Appendix 1—table 2). The tails of these distributions approach that of an exponential distribution and suggest that temporary leadership might be decided randomly (Biro et al., 2006) instead of using deterministic rules such as fixed periods of time. Moreover, with the exception of generation 3 where 54% of the route was led by the naïve bird (Wilcoxon signed-rank test, p=0.03, V = 1851), there was no significant difference in the proportion of a flight spent by each bird at the front of the pair (Appendix 1—table 3), suggesting a relatively egalitarian relation between birds despite differing levels of experience. Exploration–exploitation dynamics explain flight performance Sasaki and Biro, 2017 previously showed that flight efficiency varies across treatments with experimental pairs eventually outperforming both fixed pairs of birds and solo individuals. The discovery of route innovations and, in particular, how birds with different levels of experience contribute to this task, is the key to the superior performance of experimental pairs. To understand this phenomenon and thus shed light on the pair’s information-pooling mechanism, we investigated how pigeons balance between exploitation of known information – closely following (<300 m) their most recent route – and exploration for possible route improvements. To do so, we labelled segments of flight trajectories as a function of the point-to-point distance from each point of a focal trajectory to the closest point of the immediately preceding trajectory (i.e., baseline) and compared the exploration–exploitation dynamics both across treatments and between experienced and naïve birds. During the initial part of the experiment (Figure 4a, first 12 releases), exploration decreased steadily in all conditions with birds that flew individually in the experimental group (i.e., generation 1) performing similarly to those of the solo control (respectively, 36.7 and 34.2%), whereas fixed pairs of birds explored significantly more (51.7%, Whitney–Mann–Wilcoxon, p<0.001, Appendix 1—table 4). However, while exploration steadily decreased for solo and fixed pairs of birds in the successive 48 releases, experimental pairs showed a markedly different pattern of exploration oscillating over generations (Figure 4a, releases 13–60). Each time a new naïve individual was paired with an experienced one (dotted vertical lines), exploration increased for about 5–6 releases, reaching values well beyond those of both solo birds and fixed pairs; then exploration decreased within a few releases (2–4) to the same levels as those of fixed pairs. On average during generations 2–5, experimental pairs explored (32.9%) significantly more than both solo (15.7%, p<0.001) and fixed pairs of birds (29.3%, p=0.0456). These results also held when exploration and exploitation were defined with respect to the last release of the previous generation. Under this model, differences between experimental and fixed pairs were even more pronounced, with the former characterized by 46.6% exploration and the latter by only 32.4% (p<0.001, Appendix 1—table 5 and Appendix 1—figure 6). The inferior flight efficiency of solo and fixed pairs of birds might thus be explained, at least in some measure, by a lower likelihood to discover route improvements due to limited exploration. Figure 4 Download asset Open asset Analysis of exploration and exploitation. Panel (a) shows the proportion of exploration over releases for the experimental group (the red dotted vertical line separates solo flights at generation 1 from paired flights at generations 2–5), the solo control, and the fixed-pairs control. Smoothed lines are computed using generalized additive models using shrinkage cubic regression splines (mean and standard error); points represent averages for individual releases. Panel (b) shows the proportion of a flight led by each bird during phases of exploration and exploitation in the experimental treatment. Darker colours correspond to exploitation, lighter colours to exploration; purple represents the experienced bird, green the naïve one; red lines represent linear fits to data pooled from both birds using the Theil–Sen estimator (slopes and p-values: respectively, 0.0203, p<0.001 for exploitation and –0.0171, p=0 for exploration). Panel (c) shows the probability for the naïve individual to initiate phases of exploration over releases (exact binomial test, p<0.01 for release 1). The dotted vertical line separates the first release, where the naïve bird was significantly more likely to initiate, from the successive releases 2–12 showing no significant difference between the two birds; the red line provides a visual reference indicating an equal likelihood between the two birds to initiate exploration. The superior homing performance of experimental pairs is suggested to be rooted in their ability to select novel portions of a route introduced by the naïve individual that are more efficient while discarding inefficient ones (Sasaki and Biro, 2017). Under this hypothesis, which is an extension of H3, we expect to observe not only increasing homing efficiency over generations but also an asymmetric pattern of leadership in which the naïve individual leads periods of exploration and the experienced one leads periods of exploitation. We found instead no significant difference between the contributions of the experienced bird and those of the naïve one both overall and within generations (Figure 4b, Appendix 1—table 1). The sole exception is represented by generation 3 during which the naïve bird contributed more than the experienced one to exploitation (Wilcoxon signed-rank test, p=0.035, V = 1871). In agreement with our expectations for H4, experienced and naïve birds led the pair with approximately the same frequency in both exploration and exploitation, suggesting that deviations from established routes were not caused only by the naïve bird (see also Appendix 1—figure 4, inset). We did find evidence of behavioural asymmetries, in that transitions from exploitation to exploration were marginally more likely to be initiated by naïve birds (exact binomial test, p=0.042, n = 964, Appendix 1—table 2); however, this result was driven by those of generation 3 (p=0.02, n = 301), whereas no difference was detected in other generations. Transitions from exploration to exploitation were equally likely to be initiated by the two birds both overall and within each generation. However, when transitions are considered over the 12 releases composing each generation (Figure 4c), the naïve individual was more likely to initiate phases of exploration during the first release (p<0.01, n = 44, Appendix 1—table 3) doing so 70.5% of the time compared to 29.5% for the experienced bird. After the first release, transitions that initiate phases of exploration were about as likely to be initiated by either of the two birds independently of their level of experience. Discussion For many group-living animals, searching for optimal travel routes can be a complex task as social information about routes can persist over generations regardless of its quality (Helfman and Schultz, 1984; Sasaki and Biro, 2017; Jesmer et al., 2018; Laland and Williams, 1998). This search is inherently subject to

Leadership of animal group movements depends on social feedback, hence leader’s signals and follower’s responses should be attuned to each other. However, leader and follower roles are difficult to disentangle in species with high levels of coordination. To overcome this challenge, we investigated a simple case of movement coordination: termite pairs in which a female leads a male as they search for a nest site. To tease apart leader and follower roles, we created conspecific and heterospecific pairs of Coptotermes gestroi and C. formosanus, which share a pairing pheromone so that males follow females of either species. Conspecific pairs were stable for both species, even though C. gestroi females produce less pheromone than C. formosanus. Heterospecific pairs with C. gestroi males were also stable, but not those with C. formosanus males. We attributed this difference to the C. gestroi male’s unique capacity to follow females that release small amounts of pheromone; C. formosanus males cannot follow or reject C. gestroi females as unsuitable. This conclusion was supported by an information-theoretic analysis that detected information flow from C. formosanus females to C. gestroi males as in conspecific pairs, but not from C. gestroi females to C. formosanus males. Despite their following ability, C. gestroi males lost to C. formosanus males in competitions to follow C. formosanus females. Thus, partner selection has shaped the species-specific association of mating pairs. Our results demonstrate that a similar level of coordination can emerge from distinct sets of complementary sender-receiver interactions.

Collective behavior is widely regarded as a hallmark property of living and intelligent systems. Yet, many examples are known of simple physical systems that are not alive, which nonetheless display collective behavior too, prompting simple physical models to often be adopted to explain living collective behaviors. To understand collective behavior as it occurs in living examples, it is important to determine whether or not there exist fundamental differences in how non-living and living systems act collectively, as well as the limits of the intuition that can be built from simpler, physical examples in explaining biological phenomenon. Here, we propose a framework for comparing non-living and living collectives as a continuum based on their information architecture: that is, how information is stored and processed across different degrees of freedom. We review diverse examples of collective phenomena, characterized from an information-theoretic perspective, and offer views on future directions for quantifying living collective behaviors based on their informational structure.

Behavioral correlations stretching over time are an essential but often neglected aspect of interactions among animals. These correlations pose a challenge to current behavioral-analysis methods that lack effective means to analyze complex series of interactions. Here we show that non-invasive information-theoretic tools can be used to reveal communication protocols that guide complex social interactions by measuring simultaneous flows of different types of information between subjects. We demonstrate this approach by showing that the tandem-running behavior of the ant Temnothorax rugatulus and that of the termites Coptotermes formosanus and Reticulitermes speratus are governed by different communication protocols. Our discovery reconciles the diverse ultimate causes of tandem running across these two taxa with their apparently similar signaling mechanisms. We show that bidirectional flow of information is present only in ants and is consistent with the use of acknowledgement signals to regulate the flow of directional information.

The fitness of group-living animals often depends on how well members share information needed for collective decision-making. Theoretical studies have shown that collective choices can emerge in a homogeneous group of individuals following identical rules, but real animals show much evidence for heterogeneity in the degree and nature of their contribution to group decisions. In social insects, for example, the transmission and processing of information is influenced by a well-organized division of labour. Studies that accurately quantify how this behavioural heterogeneity affects the spread of information among group members are still lacking. In this paper, we look at nest choices during colony emigrations of the ant Temnothorax rugatulus and quantify the degree of behavioural heterogeneity of workers. Using clustering methods and network analysis, we identify and characterize four behavioural castes of workers—primary, secondary, passive and wandering—covering distinct roles in the spread of information during an emigration. This detailed characterization of the contribution of each worker can improve models of collective decision-making in this species and promises a deeper understanding of behavioural variation at the colony level.

Throughout evolution, living systems have developed mechanisms to make adaptive decisions in the face of complex and changing environmental conditions. Most organisms make such decisions despite lacking a neural architecture. This is the case of the acellular slime mold Physarum polycephalum that has demonstrated remarkable information processing and problem-solving abilities. Previous studies suggest that the membrane of P. polycephalum plays an important role in integrating and processing information leading to the selection of a resource to exploit. The cyclical contraction-relaxation pattern of the membrane changes with the local quality of the environment, and individual contractile regions within a P. polycephalum can entrain neighboring regions, providing a potential mechanism for information processing and propagation. In this study, we use an information-theoretic tool, transfer entropy, to study the flow of information in single tubule segments of P. polycephalum in a binary choice between two food sources. We test P. polycephalum tubules in two food choice conditions, where the two available options are either symmetric in their nutrient concentrations or with one more concentrated in nutrients than the other (i.e., asymmetric). We measure the contractile pattern of the P. polycephalum membrane and use these data to explore the direction and amount of information transfer along the tubule as a function of the cell's final decision. We find that the direction of information transfer is different in the two experimental conditions, and the amount of information transferred is inversely proportional to the distance between different contractile regions. Our results show that regions playing a leading role in information transfer changes with the decision-making challenges faced by P. polycephalum.

Signals whose function is solely to coordinate communication are so far known only in human conversations1 and telecommunication networks2. Utterances like mm-hmm3, gestures such as the nodding of ones 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 receivers 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.

Nature provides us with abundant examples of how large numbers of individuals can make decisions without the coordination of a central authority. Social insects, birds, fishes, and many other living collectives, rely on simple interaction mechanisms to do so. They individually gather information from the environment; small bits of a much larger picture that are then shared locally among the members of the collective and processed together to output a commonly agreed choice. Throughout evolution, Nature found solutions to collective decision-making problems that are intriguing to engineers for their robustness to malfunctioning or lost individuals, their flexibility in face of dynamic environments, and their ability to scale with large numbers of members. In the last decades, whereas biologists amassed large amounts of experimental evidence, engineers took inspiration from these and other examples to design distributed algorithms that, while maintaining the same properties of their natural counterparts, come with guarantees on their performance in the form of predictive mathematical models. In this paper, we review the fundamental processes that lead to a collective decision. We discuss examples of collective decisions in biological systems and show how similar processes can be engineered to design artificial ones. During this journey, we review a framework to design distributed decision-making algorithms that are modular, can be instantiated and extended in different ways, and are supported by a suit of predictive mathematical models.

Collective decision-making systems rely on many agents to gather, process and exchange information to arrive at a group decision. Critical to group success is the transfer of information among agents and between agents and their environment. Without information transfer, no consensus can be achieved. Yet, the role of individual rules in determining information transfer at the group level is poorly understood. With the aim to shed a light on how the decision mechanism of individuals affects information transfer in collectives, we analyze the information landscape of two decision-making strategies: one based on the majority rule and one based on the voter model. For each strategy, we consider a binary site-selection scenario and use transfer entropy to measure the flow of information in a spatial, multi-agent system. We find that information transferred among agents is dependent on the decision mechanism, increases with the time necessary to make a collective decision, and is loosely modulated by the uncertainty of the final outcome. This is the first study that compares collective decision making mechanisms through the lens of information dynamics. Although this approach is limited to simulated agents, similar approaches could in principle be used to study collective decisions in biological systems.

The study of collective behavior has traditionally relied on a variety of different methodological tools ranging from more theoretical methods such as population or game-theoretic models to empirical ones like Monte Carlo or multi-agent simulations. An approach that is increasingly being explored is the use of information theory as a methodological framework to study the flow of information and the statistical properties of collectives of interacting agents. While a few general purpose toolkits exist, most of the existing software for information theoretic analysis of collective systems is limited in scope. We introduce Inform, an open-source framework for efficient information theoretic analysis that exploits the computational power of a C library while simplifying its use through a variety of wrappers for common higher-level scripting languages. We focus on two such wrappers here: PyInform (Python) and rinform (R). Inform and its wrappers are cross-platform and general-purpose. They include classical information-theoretic measures, measures of information dynamics and information-based methods to study the statistical behavior of collective systems, and expose a lower-level API that allow users to construct measures of their own. We describe the architecture of the Inform framework, study its computational efficiency and use it to analyze three different case studies of collective behavior: biochemical information storage in regenerating planaria, nest-site selection in the ant Temnothorax rugatulus , and collective decision making in multi-agent simulations.