Dynamics of collective motion across time and species

1. Introduction

The field of collective animal behaviour investigates how and why social animals coordinate their behaviour in space and time [1,2]. Research over the past few decades has shown convincingly that simple repeated interactions between individuals can produce complex adaptive patterns at the level of the group [3–6]. Individuals' sensory capabilities [7], morphology and locomotion [8] shape local interactions among individuals and the emergent properties of groups in motion, such as group density and order [3,5,9–11]. These group properties in turn affect the way information is transferred through the group and the emerging patterns of collective behaviour [9,12]. While a central tenet of collective behaviour is that individual behavioural mechanisms and the properties they produce at a group level can be similar across species and contexts [2], the specifics of interactions (that is, the behavioural ‘rules’ individuals follow) are often found to vary [10,13–18].

The similarity (or uniqueness) of local- and group-level patterns of behaviour for groups in motion across species and contexts is unclear, in part because direct comparisons of collective motion across different species or contexts are rare [19–22], and because most studies of collective motion tend to rely on short-term observations [13,23–25]. As a result, our understanding of intra- and interspecific variation in collective motion over time is limited. By quantifying how species (and populations) vary in the behavioural rules underlying collective motion, we can begin to approach collective behaviour from an evolutionary perspective [26,27]. For example, we can examine how species' ecological environments, social structures and/or phylogenetic histories shape the individual interaction rules underlying their collective motion. Despite wide interest in this topic, it is currently outside our realm of understanding, largely due to the field's current focus on the detailed study of individual populations. We must thus begin to systematically compare collective motion among different species and over different time scales [22,23,28,29].

The rarity of comparative studies on collective behaviour is surprising given the growing number of studies on collective behaviour across species, the commonality of data gathered (i.e. positional information about individuals over time) and the emphasis placed upon open data availability by researchers in collective behaviour [30,31]. Collective motion has been studied in a variety of insect (e.g. [32,33]), fish (e.g. [5,24,34]), bird (e.g. [25,35,36]) and mammal (e.g. [37–39]) species in the laboratory and the wild. In the laboratory, positional data of individuals through time is typically recorded using automated tracking of individuals from video footage (e.g. [24,34]), but inertial measurement unit (IMU) tags are also used (e.g. [40]). In the wild, studies can use video tracking (e.g. [37]) and stereophotography (e.g. [25,35]) but more commonly IMUs (e.g. [39]) and Global Positioning Systems (GPS) (e.g. [18,39,41–43]) to generate positional data. Review articles have made qualitative comparisons of collective motion across species and contexts [28], interpreting similarities or differences according to species' morphology (e.g. [44]), behaviour, social structure, communication, cognition or environment [8,28,45–47]. However, quantitative comparisons of collective behaviour across species are rare [14,19] and, to our knowledge, only a couple have focused on the specifics of collective motion [21,22].

The first goal of this paper is to begin to compare local patterns (inter-neighbour distances and positions), and group patterns (group shape, speed and polarization) during collective motion for different social species. We chose to study the collective motion of four species that are diverse in their locomotion (aquatic, aerial and terrestrial) and social structures (high fission–fusion dynamics versus stable group membership), using previously collected datasets: shoals of stickleback fish (Gasterosteus aculeatus) in the laboratory [24,48], free-ranging flocks of homing pigeons (Columba livia) [4,41], a free-ranging herd of goats (Capra aegagrus hircus) [39,49] and a troop of wild chacma baboons (Papio ursinus) [42,50]. We place data from each species within a ‘swarm space’ and suggest that this framework will be useful for generating predictions about the types of collective motion different species display. For example, researchers may have an expectation of where their data should fall in the swarm space based on the biological or ecological similarities of their study systems (for instance see [22]). Our aim is to provide a case-study with some example species; researchers can apply our swarm space framework to their own data, supporting future comparative work. When the position of new data in the swarm space does not match the initial prediction (i.e. the species or populations differ in their collective motion despite being biologically or ecologically similar), unique aspects of collective motion within and across species can be identified. Such findings may suggest future research directions, such as questions related to the response of these organisms to environmental and/or ecosystem changes.

Part of the reason that comparisons of collective motion across species are rare may be because data are collected for different time scales depending on the study species and often represent ‘snapshots’ of species behaviour [23]. For example, research undertaken in the laboratory is optimized for short periods of filming because of computationally heavy tracking [51] and benchmark studies of wild groups have used just seconds of data at particular locations [35] often restricted to short time periods or specific locations when collective motion can be observed (e.g. open areas) [25,35]. By contrast, while data on ungulate or primate group motion may extend over consecutive days or weeks (e.g. [38]) and make comparisons of behaviour in different habitats [42,52], periods of collective motion make up only a small proportion of these data.

The second goal of this paper is to investigate intraspecific variation in collective motion over time, using the four species datasets mentioned above. The stickleback fish and pigeon data come from experimentally designed observations—trials of 20 min for the fish shoals [24], and flights of just 30 s on average for the birds [41]. By contrast, the goat and baboon data come from continuous recording of their movements during the daytime—over 10 consecutive days in the case of the goats [39], and over nearly 50 days for the baboons [42]. This provides us with datasets of very different time periods across the four species, and thus different numbers and durations of consecutive periods of collective motion within these datasets. We therefore investigate if and how the metrics describing local and group patterns (group shape, speed and polarization) during collective motion change with the absolute time they are observed, or with the number of defined ‘events’ (samples) of collective movement. Our aim is to provide information about how reliable some common metrics of collective motion are when making observations over different time scales, and across different species.

2. Methods

(b) Collective motion

To enable among-species comparisons, we first identified periods of (uninterrupted) collective motion, defined by high speed and polarization (degree of alignment) of groups. We refer to each such period as an ‘event’ of collective motion. Thresholds for speed and polarization were selected based upon the relationship between them for each species (figure 1a and electronic supplementary material, figure S1). Each group's polarization was calculated as in Attanasi et al. [54] and the group's speed from averaging the smoothed speed of all group members. For details, see our supporting information methods. Collective motion represented different proportions of the full datasets across species, with 58 min of fish swimming over 548 discrete events, 7 min of pigeons flying over 16 events, 57 min of goat motion over 35 events and 35 h for baboon motion over 262 events (figure 1b). Our events are evenly distributed over time (electronic supplementary material, figure S8). Examples of collective motion events for each species are provided in figure 1c–f, and summary statistics for events are provided in electronic supplementary material, table S1. For sticklebacks, groups always consisted of five individuals from six different shoals, and goat data included the same 10 individuals. Pigeon flock size and composition varied, and baboon group size varied across time depending on the number of functioning collars.

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Because the collective motion events we identified vary in duration (electronic supplementary material, table S1), and we aimed to compare collective motion across events (time) and species, we checked how long an event should be to be ‘representative’ of collective motion in our study groups. We therefore randomly sampled ‘snapshots’ from these events ranging from 1 to 30 s and calculated the group's polarization and shape for each snapshot separately. Group shape was defined simply, as the angle (0°–90°) between the group's heading and the direction of the short side of a minimum bounding box that includes all group members [53,55,56]. An angle of 0^° thus represents a group that is perfectly wider than longer, while an angle for 90° a group that is perfectly oblong (elongated in the moving direction). We normalized values by dividing angles by 90° and averaged over time to calculate the mean shape of a group during an event, which thus varies from 0 to 1. The bounding box calculations were performed using the ‘shotGroups’ package in R [57].

We then used a two-way intraclass correlation coefficient (ICC) (using the ‘irr’ package in R [58]) to test agreement between the distribution of real and sampled means for these two metrics [59]. As expected, we see an improvement of agreement (increasing ICC) with increasing duration of snapshot for all species (electronic supplementary material, figures S2 and S3). Aiming to select a single ‘minimum representative time-window’ across all four species, we based our selection on the species showing the larger increase in agreement with increasing ICC, namely pigeons (electronic supplementary material, figure S2). We thus chose a ‘minimum representative time-window’ of 15 s as the minimum sampling window needed across all four species for a sample to be representative of the real mean. According to these criteria, some events of less than 15 s (518 for sticklebacks, 2 for pigeons, 8 for goats and 88 for baboons) were not used in any further analyses. Our final dataset included approximately 15 min of collective motion for sticklebacks, 7 min for pigeons, 56 min for goats and 28 h for baboons.

Using collective motion events that are judged representative for each species (electronic supplementary material, table S1), we then calculated some local (pairwise) metrics. Specifically, we calculated the Euclidean distance between all individuals and recorded the rank distance of each neighbour from a given focal (first closest, second closest, etc). In addition to inter-individual distances, we calculated the angle between the heading of each individual and the position of each of its neighbours, namely their ‘bearing angle’, ranging from 0° (the focal individual is positioned directly behind a neighbour) to ±180° (directly in front of a neighbour to the left or to the right). We also used bearing angles to calculate ‘frontness’ which captures whether an individual is positioned in front of a neighbour, as follows:

$$f_{ij}={\displaystyle \frac{|{\beta }_{ij}|}{{180}^{\circ }},}$$

where β_ij is the bearing angle between a focal individual i and its neighbour j. Thus, a frontness value of 1 means that the focal individual is directly in front of its neighbour (bearing angle close to 180°) and a value of 0 that the focal individual is directly behind. We calculate the average frontness of each focal individual in relation to all neighbours.

3. Results

(a) Collective motion across species

We defined an ‘event’ of collective motion as an uninterrupted period during which individuals move (high speed) together in the same direction (polarized). We used dimensionality-reduction methods, a PCA and a t-SNE, to transform a large set of variables describing local and global characteristics of a group and create a visualization of the across and within species differences in collective motion. The first three principal components of our PCA explained approximately 70% of the variance in our collective motion event data. The eigenvalues of these first three dimensions are all higher than 1 (PC1: 3.02, PC2: 1.8, PC3: 1.48). Conceptually, this variation in collective motion reflects: the groups' cohesion and order (PC1, 33.6% variance explained; figure 2a,b), their temporal plasticity (PC2, 20% variance explained; figure 2a,c), and the groups’ structure and shape (PC3, 16.5% variance explained; figure 2b,c). All metrics showed an important contribution to the first three principal components, except for the average bearing angle; it explained the same variation as our measure of frontness with small contribution to the principal components (electronic supplementary material, figure S4) and was thus excluded from our analysis. The contributions of individual metrics are provided in the electronic supplementary material, table S2.

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Plotting the position of each event with reference to PC1 and PC2 (figure 2a) and using the t-SNE (figure 2d) provides the ‘swarm space’. Species data are clustered together, but with some overlap, especially between the baboon and goat data (figure 2a–c). Group size does not seem to influence the positioning of an event in the swarm space (figure 2a and electronic supplementary material, figure S5), and there is little evidence of consecutive events not being independent (electronic supplementary material, figure S7). Pigeon events were the most distinct from the other species in the PCA (figure 2a), as well as in our t-SNE space that reflects the local similarity between events (figure 2d). The t-SNE analysis suggests that the goats show the largest variation in their collective motion, with their events appearing within the clusters of the other species (and even neighbouring events of pigeons). The events of stickleback fish also share similarities in collective motion not only with goats (as seen also in the PCA space) but also with some baboon events (figure 2d). Note that unlike the PCA space, the global structure of the t-SNE space is uninformative (i.e. the relative position of further away points is not representative of the real structure of the data) hence both analyses should be viewed together.

The variation in collective motion within and between species can be investigated further by examining the metrics that load heavily onto the principal components. For example, the nearest neighbour of an individual is more often in the forward direction for baboons, goats and sticklebacks, and in the lateral direction for pigeons (figure 2e–h). In fact, baboons show a strong front–back formation especially with the first two nearest neighbours (figure 2h). Goats also show a higher density of nearest neighbours (first–fourth) in front, but with a wider distribution than baboons (figure 2g). By contrast, pigeons have their nearest neighbours more often to the left or the right than in front or behind, especially for further away neighbours (fourth) (figure 2f). Stickleback fish show a strong difference between their first nearest neighbour (usually positioned diagonally) and the ones further away (positioned in front or behind) (figure 2e). These differences in how individuals are positioned is further evidenced by our new metric of frontness (see electronic supplementary material, figure S5 for the distributions of the metrics of figure 2).

(b) Collective motion through time

How much data (events) are required to quantify the metrics that contribute to our PCA space? Change-points to a plateau are identified in the majority of the time series, with some however being stationary (KPSS tests with p > 0.05, figure 3a). This is particularly the case for the metrics concerning the groups' shape and structure (PC3). The estimates from our bootstrap analysis fall within the 90% confidence interval of our change-point estimation (see electronic supplementary material, figure S10).

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We see a large variation in the estimated change-points across metrics and species. Change-points are identified for all metrics in the baboons, the largest dataset in our study. The fewest change-points were identified in the species with the shorter time series, i.e. pigeons. The estimated change-points in the metrics of the first two components are given in figure 3b. Average polarization and frontness are both stationary according to the KPSS tests, with an identified change-point in almost all species, meaning that they are perhaps the most robust metrics of collective motion even when little data is available. By contrast, temporal plasticity during events (variation in speed and polarization) required the most data to be stabilized (almost 10 h in baboons and 20 min in goats). Examples of the time series across metrics with the identified change-point and confidence interval are given in figure 3c–h. For the exact change-point estimation across all metrics, see electronic supplementary material, figure S9.

4. Discussion

Our investigation of collective motion has illustrated the similarities and differences across different time scales and for different species. There are, of course, many more and different aspects to be investigated relating to how collective motion varies across the species and time scales we study here. Nevertheless, taken together, we hope that our work can (i) guide researchers on what type of data to collect and for how long, (ii) provide insight into the self-organized dynamics that link the interaction rules that different species are likely to use and the collective patterns they exhibit and (iii) encourage future comparative work to understand the causes and consequences of collective behaviour in ecological systems. We address each aim in turn.

Our analysis placed ‘events’ (uninterrupted periods) of collective motion of stickleback fish, homing pigeons, goats and chacma baboons in a ‘swarm space’. We showed that variation in collective motion across species comes not only from absolute group characteristics (e.g. their polarization and shape) and internal structure (e.g. positioning of individuals), but also from the consistency of those characteristics across time. Based on our ICC (representative snapshots) and change-point (minimum samples size) analyses, we found that average measurements from snapshots of a few seconds are often representative of the true mean of the full time series and that most key metrics require a certain number of events (repetitions) in order to stabilize. We can thus conclude that sampling a few seconds of collective motion (in our datasets 15 s) over a larger number of days (rather than collecting long trajectories over few days), may be a more advantageous way to capture the true characteristics of a species' collective motion.

There are also important differences in the reliability of metrics over time, which may be affected by differences in the number of events identified for each species within our datasets. For example, the baboon data took the most time to stabilize, but this time is still a small proportion of the whole time series available (figure 3g). Therefore, a smaller dataset (less events) than the one we used here should provide accurate results for baboons, if similar metrics are investigated. Stickleback fish and goat data also tended to stabilize over time but required a much higher proportion of our total data available. Therefore, in the case of the goats and fish, it seems that the datasets available (time, events) were sufficient for estimating the metrics we presented. In contrast with the other species, the pigeon time series tended to be stationary over our increasing sample size (that is, from the first event studied). This indicates that the collective motion of the pigeons showed less variation than our other species, but whether this was because of the context the data were collected in (initiating their homing flight) or the small duration of the time series remains to be tested.

Based on our findings, we can also hypothesize on the underlying interaction rules of group members, which were not considered explicitly here. For instance, the specifics of locomotion may be responsible for many differences we see across species [9], especially for pigeon flocks that showed the largest differentiation from the other three species. The wide shape of pigeon flocks with nearest neighbours positioned on the side of a focal individual may emerge from a cohesion mechanism based on acceleration [18] in combination with turning to avoid collisions [4]. Stickleback fish, goats and baboons share a more oblong group shape and front–back internal structure (figure 3e,g,h), but the nearest neighbour of sticklebacks is rarely directly in front of a focal individual (in contrast with the goats and baboons). This may again be attributed to turning to avoid collisions while swimming, while goats and baboons may mediate collision avoidance mostly by changes in their speed. Additionally, having a nearest neighbour positioned directly in front may indicate pairwise attraction dynamics instead of attraction to the centre of a number of neighbours (as identified in some fish and bird species [13,67]). Given that differences in interaction rules across species and contexts are increasingly found in the literature [10,13,16,68], keeping a species- and context-specific level seems necessary when drawing conclusions about collective behaviour. For instance, whether the behaviour of sticklebacks is representative of fish species (see for instance [21]) or whether the behaviour of pigeons while homing is representative of pigeons during free flight are assumptions that need more data to be tested.

Adding more data from events of collective motion will now enable across-species comparisons and deepen our understanding of self-organized patterns of collective behaviour. Just considering our small sample of four species, we can begin to hypothesize about ‘higher level’ collective behaviour, such as collective navigation, decision-making and escape. For instance, if we take the metric of ‘frontness’, which we introduced here, its variation could be related to the function of collective motion in different species or be an inevitable outcome of their environment [24,42,52,69]. If differences are functional, we could speculate that species with a clear front–back structure in motion may have stronger ‘leadership’ dynamics [24,42,70,71] associated with collective motion that is linked to decision-making concerning navigation. By contrast, species with low frontness could be organized to maximize information transfer [54] with collective motion linked to anti-predatory functions [41,43,53]. If differences are the result of environment, then front–back structures may reflect constraints of moving through largely two-dimensional terrestrial environments that present more physical and energetic constraints upon movement in space [52,72] compared to three-dimensional environments that are more open [73]. Furthermore, our t-SNE space that highlights the similarities between events of different species also suggests potential links in dynamics of collective motion across species. For example, the surprisingly wide distribution of events of collective motion of goats in the t-SNE space (i.e. their resemblance with events of all other species in our datasets) indicates the variation in collective motion that goats exhibit, making them an interesting, and to date not well studied, species.

We now encourage colleagues in collective behaviour research to use our swarm space framework with events of collective motion of their study species. This will allow us to identify ‘model’ species of collective behaviour that are representative of their taxa, but also those species that are functionally unique. A wide range of important ecological questions can then be addressed in terms of the diversity of collective behaviour (where events and species fall in the swarm space). Simple questions around the variation in collective motion for studies in controlled laboratory environments versus experiments or observations conducted in the wild can be tackled. But perhaps most interesting are questions about the evolutionary and ecological determinants of diversity in collective behaviour and the potential links to ecosystem level processes [23,29,74–77]. It will be possible to begin to test whether specific collective motion is correlated to locomotion (e.g. swimming versus flying), or socio-ecological variables (e.g. social system), and measure how strongly phylogenetic relatedness predicts the distribution of collective behaviour across species.

There are challenges associated with future comparative work, though, as highlighted by our study. Differences in the specifics of each species' dataset may pose constrains for the generalization of conclusions reached from their comparison. First, the stickleback data are collected in the laboratory [24] while pigeon, goat and baboon data are collected in the field [39,41,42]. Second, the duration of our pigeon trajectories is much shorter than the trajectories of the other species (this however may not affect our across-species analysis, since pigeons show the highest percentage of collective motion, figure 1b). Third, the sampling frequency used across our datasets varies. Given that the frequency of observations at each study tends to be made at biologically relevant scales, sampling frequency may not have a significant effect on how groups are placed within the swarm space, but it should nevertheless be considered in future research. Fourth, in the datasets of sticklebacks and pigeons, each group consists of a different combination of individuals, while in goats and baboons the same individuals are being tracked as a group. Thus, we may underestimate the variability in collective motion for goats and baboons. Lastly, as is common when deploying tags in wild group-living animals, the data of baboons and goats do not cover all the individuals of their groups. It therefore remains to be seen how these differences may introduce noise or confound future comparative work. However, if we continue to focus on characteristics of collective motion (local and global metrics), these potential issues can be overcome, either by directly testing for their effects in any analyses (e.g. laboratory versus wild data; see above), or keeping these issues in the forefront when making interpretations.

Overall, our study provides a starting ground for future research on collective behaviour under a more unifying framework. Identifying the differences in self-organized dynamics across species is a necessary step before generalizing identified patterns from one or a few species. Similarly, identifying the time scales of each characteristic of collective motion can facilitate our search for the interaction rules that underlie group-level patterns and can help ensure the validity of past findings. Knowledge of dynamics of collective motion across species and time, as presented in our work, can inform the design of data collection in future research (in a manner that relates to research in other species) which in turn can ensure valid comparisons across study systems.

Data accessibility

Data on metrics of collective motion across species and time are stored in the Zenodo repository: https://doi.org/10.5281/zenodo.7457770, and the code to reproduce our figures and analysis is available at the GitHub repository: https://github.com/marinapapa/ColMotion-Species-Time (https://doi.org/10.5281/zenodo.7566410).

Authors' contributions

M.P.: conceptualization, data curation, formal analysis, investigation, methodology, software, visualization, writing—original draft and writing—review and editing; I.F.: data curation, funding acquisition, project administration and resources; L.O.: data curation and methodology; S.G.: data curation and methodology; D.G.G.: data curation and methodology; A.M.B.: data curation and methodology; C.C.: data curation and methodology; A.J.K.: conceptualization, funding acquisition, investigation, project administration, resources, writing—original draft and writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work is supported by an Office for Naval Research (ONR) Global Grant (grant no. N629092112030) awarded to A.J.K.