GROUP DECISIONS. Shared decision-making drives collective movement in wild baboons

Shared decision-making drives collective movement in wild baboons

Authors: Ariana Strandburg-Peshkin1*†, Damien R. Farine2,3,4,*†, Iain D. Couzin1,5,6, Margaret C. Crofoot2,3,*

*Correspondence: [email protected], [email protected], [email protected]

†equal contributors

Affiliations:

1Department of Ecology & Evolutionary Biology, Princeton University, USA. 2Department of Anthropology, University of California Davis, USA. 3Smithsonian Tropical Research Institute, Panama. 4Edward Grey Institute of Field Ornithology, Department of Zoology, University of Oxford, UK. 5Department of Collective Behaviour, Max Planck Institute for Ornithology, Konstanz, Germany. 6Chair of Biodiversity and Collective Behaviour, Department of Biology, University of Konstanz, Germany.

Abstract: Conflicts of interest about where to go and what to do are a primary challenge of group

living. However, it remains unclear how consensus is achieved in stable groups with stratified social relationships. Tracking wild baboons with high-resolution GPS and analyzing their movements relative to one another reveals that a process of shared decision-making governs baboon movement. Rather than preferentially following dominant individuals, baboons are more likely to follow when multiple initiators agree. When conflicts arise over the direction of movement, baboons choose one direction over the other when the angle between them is large, but compromise if not. These results are consistent with models of collective motion, suggesting that democratic collective action emerging from simple rules is widespread, even in complex, socially-stratified societies.

Main Text: Individuals living in stable social groups may often disagree about where to go, but must

reconcile their differences to maintain cohesion and thus the benefits of group living. Consensus decisions could be dominated by a single despotic leader (1), determined by a hierarchy of influence (2), or emerge from a shared, democratic process (3). Because decisions are typically more accurate when information is pooled (4, 5), theory predicts that shared decision-making should be widespread in nature (6). However, in species that form long-term social bonds, considerable asymmetries in dominance and social power often exist, and some have proposed that these differences give high-ranking individuals increased influence over group decisions (1, 7, 8). Determining how consensus is achieved in these types of societies remains a core challenge for understanding the evolution of social complexity (6, 9, 10).

We studied the collective movement of a troop of wild olive baboons (Papio anubis) at Mpala Research Centre in Kenya to examine how group members reach consensus about whether and where to move. Baboons, long a model system for studying the evolutionary consequences of social bonds (11–13), live in stable multi-male, multi-female troops of up to 100 individuals (11). Despite differing needs, capabilities and preferred foraging strategies (14–16), troop-members remain highly cohesive, travelling long distances each day as a unit, while foraging for diverse but widely dispersed foods. How troops make collective movement decisions, and whether specific individuals determine decision outcomes, remains unclear. Attempts to identify influential individuals by observing which animals initiate departures from sleeping sites (17, 18) or are found at the front of group progressions (19) have yielded conflicting results (9). Studying collective decision-making events requires many potential decision-makers in a group to be monitored simultaneously–a significant logistical challenge.

To tackle this “observational task of daunting dimensions” (8), we analyzed data from 25 wild baboons (~80% of our study troop’s adult and subadult members, Table S1), each fitted with a custom-designed GPS collar that recorded its location every second (Fig. 1, Movies S1-2 (20)). We developed an automated procedure for extracting “movement initiations” based on the relative movements of pairs of individuals (20). These were defined as sequences in which one individual (the initiator) moved away from another (the potential follower), and was either followed (a “pull”, Fig. 1 inset, left), or was not and subsequently returned (an “anchor”, Fig. 1). This definition is agnostic to individual intention and motivation. While any particular movement sequence may or may not reflect a causal relationship between initiator and follower

(Supplementary Online Text), analyzing aggregate patterns across many sequences nonetheless yields insight into the processes driving collective movement.

Our method is based on finding all minima and maxima in the distance between pairs of individuals, allowing it to capture pulls and anchors occurring over a range of timescales, from seconds to minutes (Fig. S8, (21)). It also detects simultaneous movement initiations. We aggregated concurrent pulls and anchors on the same potential follower into “events” (20). We then examined the behavior of potential followers during these events, including if they followed any initiators, and if so in which direction they moved.

Our data show that the probability of following depends on both the number of initiators and their level of directional agreement. To quantify directional agreement among concurrent initiators in an event, we calculated the circular variance (cv) of the unit vectors pointing from the potential follower to each initiator, and defined agreement as 1-cv. This measure approaches 0 when individuals initiate in opposing directions (low agreement), and 1 when all individuals initiate in the same direction (high agreement). Fitting a binomial Generalized Estimating Equation (GEE) model revealed a baboon’s probability of following depends on an interaction between the number of initiators and their directional agreement (Fig. 2, Table S2). Overall, baboons are most likely to follow when there are many initiators with high agreement. However, when agreement is low, having more concurrent initiators decreases the likelihood that a baboon will follow anyone. This pattern suggests that decisions are delayed when opinions are split.

If social dominance plays a role in determining the outcomes of movement decisions (1), the disproportionate influence of high-ranking animals should be easiest to observe when single individuals make movement initiations (single-initiator events). We found no evidence of this. The dominant male did not have the highest probability of being followed, dominance rank (20) did not correlate with initiation success, and no sex differences existed in initiation success (Fig. S1, binomial GLMM: coefficient (male)±SE=-0.222±0.159, z=-1.402, P=0.161, initiator and follower fit as random effects), despite males being dominant over females (11). Instead, we found that baboons are more likely to follow initiators who move in a highly directed manner (Fig. S2), consistent with the findings of a previous study (17).

When multiple members of the troop initiate movement simultaneously, followers must decide in which direction to move. Theory (22) predicts that, when preferred directions conflict, the type of consensus achieved will depend on the angle between these directions (angle of disagreement, Fig. 3A). When this angle is large, the group travels in one direction or the other (“choose”). Below a critical angle, the same individual rules result in the group moving in the average of preferred directions (“compromise”). Our data reveal that baboon followers exhibit these two predicted regimes. In events with two initiators, followers consistently choose one direction or the other when the angle between the initiators’ directions is greater than approximately 90 degrees, but compromise when the angle falls below this threshold (Fig. 3B, (20)). The same pattern emerges in events with multiple initiators clustered into two subgroups (Fig. 3C).

When initiators have strongly conflicting directions, how do followers choose which direction to take? When facing a choice between two subgroups of initiators, followers are more likely to move towards the direction of the majority. This tendency grows stronger as the numeric difference between the two subgroups increases (Fig. 4), consistent with theoretical (3, 6, 22) and empirical studies (3, 5, 23). Individuals’ choices also scale up to group movement.

Following such conflicts, the troop’s travel direction is positively correlated with the direction associated with successful (but not failed) subgroups of initiators (Fig. S4). Thus, failed initiators ultimately move in the direction of the majority (away from their original initiation directions), maintaining cohesion with others.

The failure of high-ranking individuals to dominate movement decisions highlights an important distinction between social status and leadership in wild baboons. Although field-based experiments suggest that dominant individuals, when highly motivated, can shape group movement patterns to their advantage (1), our results provide evidence that the decision-making process driving day-to-day movement patterns in baboons is fundamentally shared. Our study emphasizes the power of using high-resolution GPS tracking data to uncover the interdependencies of animal movements. In conjunction with the rich individual-level data that long-term observational studies provide, these methods open up a new window into the social dynamics of wild animal groups.

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20. Materials and methods are available as supplementary materials on Science Online.

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Acknowledgments: We thank Kenya National Science and Technology Council, Kenyan Wildlife Service and

Mpala Research Centre for permission to conduct research. All procedures received IACUC approval (2012.0601.2015). We thank M. Wikelski, E. Bermingham, D. Rubenstein and M. Kinnaird for logistical support; R. Kays, S. Murray, M. Mutinda, R. Lessnau, S. Alavi, J. Nairobi, F. Kuemmeth, W. Heidrich and I. Brugere for assistance; and T. Berger-Wolf, J. Silk, J. Fischer, B. Sheldon, L. Aplin, D. Pappano, M. Grobis, B. Rosenthal, A. Hein, B. Ziebart, L. Polansky and J. Li for feedback. We acknowledge funding from NSF (EAGER-IOS-1250895), the Max Planck Institute for Ornithology, the Smithsonian Tropical Research Institute, and Princeton University. ASP and DRF received additional support from NIH (T32HG003284), NSF (GRF to ASP) and BBSRC (BB/L006081/1 to B.C. Sheldon). IDC acknowledges support from: NSF (PHY-0848755, IOS-1355061, EAGER-IOS-1251585), ONR (N00014-09-1-1074, N00014-14-1-0635), ARO (W911NG-11-1-0385, W911NF-14-1-0431), and Human Frontier Science Program (RGP0065/2012). Data are deposited at www.datarepository.movebank.org/ (doi:10.5441/001/1.kn0816jn).

Fig. 1. Extracting pulls and anchors from movement data. Baboon trajectories (25 individuals) during the first day of tracking. (inset, left) Successful initiation (pull), where the initiator (blue) recruits the follower (red). (inset, right) Failed initiation (anchor), where the initiator (red) fails to recruit the potential follower (blue). Other individuals’ trajectories are in gray.

Fig. 2. Probability of following depends on the number of initiators and their directional agreement. Baboons are most likely to follow when there is high agreement among many initiators. When agreement is low, additional initiators do not improve the chances of following, and may decrease them. Surface plot shows a GEE fit to the data (Table S2).

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Fig. 3. As predicted by collective movement models (A), as the angle between initiation directions increases, baboon followers exhibit a transition from compromising (moving in the average of the two directions) to choosing one direction over the other. (B-D). Plots show the empirical distribution of follower movement directions as a function of the angle of disagreement between two initiators (B) or two clusters of initiators (C). Regions divided by dotted lines are statistically assigned to (i) compromise, (ii) transitional, and (iii) choose (see Fig. S9). Solid white lines show the median of the directions taken for each mode. Dashed white lines represent the expected direction when compromising (middle line) or choosing (top/bottom lines). When the number of individuals in the clusters differs by 1, followers are more likely to move towards the majority (i.e. along the horizontal line) (D).

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Fig. 4. When initiation directions conflict, followers choose the direction of the largest subgroup of initiators. (A) Empirical data are in black; error bars are 95% confidence intervals estimated by 1000 bootstrapped replications of the data. Red line shows a sigmoidal fit to the data. The tendency to follow the majority is maintained regardless of the total number of initiators (B-D), or whether the troop is moving or stationary (Fig. S6).

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Supplementary Materials: Materials and Methods

Supplementary Text Figures S1-S9

Table S1 Movies S1-S2

References (24-30)

Materials and Methods Sections

1. Data collection 2. Pre-processing of GPS data 3. Extracting successful and failed initiation attempts at the dyadic level 4. Extracting and clustering simultaneous pulls and anchors into ‘events’ 5. Overview of pull and anchor data 6. Estimating the dominance hierarchy 7. Testing whether followers average the directions of pulling or choose one or the other

direction 8. Analyses of movement decisions in different contexts 9. Correlated movement preferences

Section 1. Data collection Fieldwork was conducted at the Mpala Research Center (MRC), a conservancy consisting of nearly 200 km2 of savannah and dry woodland habitats in central Kenya. All research activities described in this paper were approved by the Republic of Kenya’s National Council for Science and Technology (Permit # NCTS/RCD/12B/012/26B), Kenya Wildlife Services (KWS/BRM/5001) and the Smithsonian Tropical Research Institute’s Animal Care and Use Committee (IACUC # 2012.0601.2015). From July 21st – 29th, 2012, we captured 33 out of 46 members of a troop of wild olive baboons (Papio anubis) using two arrays of individual traps (1 m3), which we baited with maize and placed at sites near the troop’s sleeping trees. Seven of these individuals were too small to be fit with a collar and were immediately released. We chemically immobilized the rest of the baboons using Ketamine (15 mg/kg). We estimated the age of each individual based on patterns of dental eruption and evidence of sexual maturation. Individuals with deciduous dentition were classified as juveniles. Sub-adult and adult males were distinguished based on their body size and the development of secondary sexual characteristics, including their mantle, musculature and canine size and morphology. Females were considered adult if they had full, permanent dentition and were parous (based on the elongation and darkening of their nipples) or showed evidenced of cycling (based on the morphology of their sexual skin). Nulliparous females that were cycling but still had one or more deciduous teeth were classified as sub-adult (see Table S1). We fit 26 baboons (14 adults, 10 subadults and 2 large juveniles) with GPS collars (e-Obs Digital Telemetry, Gruenwald, German). One of the adults’ collars failed almost immediately, so analyses reported here are based on movement data from 25 individuals. Collared adults and subadults represented approximately 80% (23/29) of the total number of adults and subadults in the troop. Adults and large subadults were fit with D-cell battery collars weighing 300 g while smaller, C-cell collars (230 g) were used on small subadults and juveniles. Following best practice recommendations, all collars weighed less than 5% of individual body weight (24), and were equipped with a break-away mechanism (Advanced Telemetry Solutions, Isanti, MN) that automatically detached the collar at the end of the study.

GPS collars were programmed to record location estimates continuously at 1 Hz during daylight hours (06-18h). Sampling at this rate, C-cell collars had sufficient charge to collect data for 14 days, while D-cell collars remained active for approximately 30 days. Due to limitations in the onboard memory (16 MB), we downloaded data from the collars each night via radio-link. All analyses presented here use data from the first 14 days of the study, because the majority of collars remained active during this period. However, several collars failed early due to a programming bug, and so the total number of individuals tracked each day varied between 16 and 25 (Table S1). To quantify the error in the location estimates, we conducted a test walk with a pair of GPS collars fixed 1 m apart. The average relative positional error was 0.26 m (95% CI: 0.03-0.69). We observed that one individual (2457) had slightly higher (approximately double) error than the others for part of the tracking period due to temporary misalignment of the GPS antenna. The study troop was observed each morning and each evening at their sleep site by MCC and an assistant for the duration of the study. Attempts were made to census the group each day as the troop members left and entered their sleeping trees; group size did not change between the start and end of the study. Not all individuals in the group were individually recognized, making systematic, focal-individual sampling impossible. However, the adult males were easily distinguished, and the alpha male (2427) was identifiable based on his interactions with other members of the troop, including receiving formal signs of submission, supplanting other members of the troop at food patches and, more rarely, based on the outcomes of fights and chases. Section 2. Pre-processing of GPS data GPS devices were capable of logging data at a resolution of 1 Hz (or 1 point per second). We did not apply any smoothing to the data downloaded from the devices. Occasionally, some devices failed to log one or a few points. In those cases, we linearly interpolated missing points based on the existing data around that point from the same device. Randomly selecting 5000 points from the data suggested that the expected error from linear interpolation was significantly less than the GPS error (< 0.2m difference between the observed and interpolated points in cases of a single missing data point). We also found a few cases of unrealistic speeds in the data, where an individual trajectory moved a large distance off a stable trajectory for a single second before resuming the trajectory. We used the same linear interpolation algorithm to identify the 99.9th percentile error (equivalent to speeds in excess of 3.56 m/sec) between the interpolated and observed GPS points, and replaced these points with the interpolated data instead. In total, 7.4% of the data used was interpolated, most of which (7.2%) were replacements of missing values. Section 3. Extracting successful and failed initiation attempts at the dyadic level Our method of extracting successful and failed initiation attempts (pulls and anchors) focused on the dyadic distance between a pair of individuals, i and j, over time. Note that in both successful and failed initiation attempts, the dyadic distance between i and j first increases (as i moves away from j) and then decreases (as j moves toward i, or i moves back toward j). Thus, we extracted candidate sequences by computing the local minima and maxima of the dyadic distance between i and j over time. Any sequence of local minimum, local maximum, local minimum (min-max-

min) was considered as a candidate sequence. This method eliminates the need to define a time scale of interactions a priori. Rather, the time scale for each sequence is determined by the scale at which minima and maxima in the dyadic distance between individuals occurred. The ability to extract pulls and anchors across a range of time-scales is important given that a feature of initiation attempts is that they can occur over short or long periods of time (21). To reduce the effects of noise due to GPS jitter, and to control the spatial scale at which we extracted interactions, we first applied a threshold to remove local movements. This noise threshold represents the minimum amount that the dyadic distance between a pair of individuals must change before it is considered as part of a candidate sequence. Decreasing this threshold causes more, and smaller, local movements to be extracted as pulls and anchors, while increasing it leads to fewer, and more global, movements being extracted. In all of our analyses, we set this threshold at 5 m, as this is well above the error in our GPS data, and also represents what we believe to be a biologically meaningful spatial scale for the system. After extracting candidate sequences, we determined whether they represented successful pulls, failed pulls (anchors), or neither. To be considered a successful pull, individual i had to move more than individual j during the first segment (min to max) and less than individual i during the second segment (max to min). For a failed pull (or anchor), individual i moved more than individual j during both segments. Candidate sequences in which the distance moved by both individuals was too similar (in either segment) were excluded. To do this, we started by defining the times of the min - max - min sequence as t1, t2, and t3 respectively. To quantify the difference between the movements of i and j in these two segments (t1 → t2 and t2 → t3) we defined the disparity:

d =Δdi (t1→ t2 )−Δdj (t1→ t2 ) Δdi (t2 → t3)−Δdj (t2 → t3)Δdi (t1→ t2 )+Δdj (t1→ t2 ) Δdi (t2 → t3)+Δdj (t2 → t3)

where Δdi(t1→ t2) indicates the displacement of individual i during the time period between t1 and t2 (and likewise for the other terms). The disparity for each candidate sequence therefore ranges from 0 (both individuals move equally during both time segments) to 1 (one individual moves in each time segment while the other stays still). We defined a minimum disparity threshold dmin, below which the candidate sequence was considered to be ambiguous (neither a successful nor a failed pull). This threshold ensured that sequences in which both individuals moved substantially in either or both of the time segments were not included as pulls or anchors in the analysis. For all of our analyses, we set this threshold at 0.1. Note that the use of a disparity threshold ensures that one individual has moved substantially more than the other during each phase of the candidate sequence, but does not require the individual moving less to be completely still. In addition, it is not required that either individual is stationary prior to the beginning of an initiation attempt. In addition to disparity, candidate sequences can also be characterized by their strength, defined as

€

s =sij (t2) − sij (t1) sij (t3) − sij (t2)

sij (t2) + sij (t1) sij (t3) + sij (t2)

where sij(t) gives the dyadic distance between individuals i and j at time t. The strength represents how much the dyadic distance changed during each time segment compared to how large it was overall. This measure approaches 0 when the change in dyadic distance is negligible compared to the total dyadic distance, and 1 when the change is very large compared to the total distance (e.g. when the individuals were first very close together, then very far apart, then very close together again). We set the minimum strength at 0.1. To extract pulls and anchors from our data, we implemented this method for every pair of individuals over the first 14 days of data in R version 3.1.0. These rules characterized pulls where the follower moved within approximately 50 degrees of the trajectory of the initiator (Fig. S7), occurring across a range of timescales (Fig. S8). Code for extracting pulls and anchors from trajectory data will be made available online. Section 4. Extracting and clustering simultaneous pulls and anchors into ‘events’ a) Definition of “events” To investigate the dynamics of pulling beyond the dyadic level, we grouped together pulls and anchors happening at the same time and involving the same potential follower into “events.” New initiation attempts (pulls and anchors) involving the same follower that started before previous initiation attempts finished, were considered as part of the same event. Thus, once one initiation was attempted, all subsequent initiations were classed as the same event until either the potential follower started moving towards at least one of the initiators (resulting in a successful pull) or all initiators had returned (all were failed initiations). Note that each “event” can involve any number of initiators (from 1 to the number of other collared individuals in the group), but by definition involves only one follower. Events were classified as being either successful (the follower was pulled by at least one initiator) or failed (all initiators were anchored). b) The direction of initiations and subsequent follower movement To investigate the geometry of events, we calculated the direction of each initiator from the potential follower and (in cases where at least one initiation was successful) the subsequent direction of movement of the follower. We defined the direction of initiation for each initiator as the vector pointing from the potential follower’s position to the initiator’s position at the time of its maximum distance (t2). When an event was successful, we defined the vector of movement by the follower as its position at the minimum t2 value across all initiators (to capture the earliest time the follower could have made its decision) to its position at the end of the event (the maximum value of t3 over all pullers). For unsuccessful events, the average position of the potential follower (in this case, an ‘anchorer’) was taken over the period from the minimum t2 to the maximum t2. All vectors were normalized to have length 1. c) Clustering of initiation directions To identify subgroups of initiations made in a similar direction, we grouped initiators within the same event into clusters using Gaussian mixture models (following (25)). This method uses machine learning to identify peaks in the distributions of events, exploiting the nonhomogeneity of biological events. In our case, we modified the method to identify peaks in pulling directions

without the need for a fixed threshold. Because the method was initially developed for temporal time series (operating on a single dimension), it is highly applicable to directions as well. To identify these peaks, we simply started the model searching for peaks from the center of the largest angle between individuals. A toy example of this method is shown in Fig. S9A. Section 5. Overview of pull and anchor data We extracted 123,773 pulls and 62,782 anchors from our data at the dyadic level. These formed 57,053 events (made up of concurrent pulls and anchors). Of these events, 22,215 involved a single initiator (39%), 10,985 involved two initiators (19%), and 23,853 involved more than two initiators (42%). Of the latter, in 3,786 (16%) of cases the initiators formed one subgroup (a cluster of initiators pulling in similar directions) 9,376 (39%) involved two subgroups, and 10,691 (45%) involved three or more subgroups. Section 6. Estimating the dominance hierarchy We inferred the dominance relationships among members of the study group based on approach-avoid interactions (i.e. displacements) extracted from the GPS tracking data (following (26)). Although this measure of dominance is necessarily coarse, rankings derived from displacements are known to correlate strongly with other types of dominance interactions, including supplants, presentations, formal submission, and overt aggression, and are a standard method for assessing rank relationships in observational studies (27, 28). We extracted approach-avoid interactions from the GPS data using a three-step procedure. In step 1, we used a set of heuristics (based on (26)) to extract candidate interactions. In previous work, approach-avoid interactions have been classified directly by human observers but the heuristics used for identifying them have been primarily based on animals’ movements. Once candidate interactions had been extracted, they were manually verified by MCC using animations of the movement trajectories exported to Google Earth (step 2). We then used these approach avoid interactions to estimate the dominance hierarchy, using a method based on Elo scores (29) (step 3). Step 1: Automated extraction of candidate approach-avoid interactions from movement data We used the following criteria to extract candidate approach-avoid interactions between each pair of individuals:

1. Within a 20-second interval (the approach), the distance between individuals i (the approacher) and j (the avoider) changed from being greater than or equal to 3 meters apart to less than or equal to 2 meters apart.

2. In the 10 seconds preceding the approach, individual j moved less than 1.5 meters (i.e. remained stationary).

3. During the approach, individual i moved more than 3 meters. 4. In the subsequent 20-second interval following the approach (the avoid), individuals i and

j went from being less than or equal to 2 meters apart to being greater than or equal to 3 meters apart.

5. During the avoid, individual i (the approacher) moved less than 1.5 meters (i.e. remained stationary).

6. During the avoid, individual j (the avoider) moved at least 3 meters.

Implementing these rules identified 777 candidate approach-avoid interactions.

Step 2: Manual curation of approach-avoid interactions using Google Earth For each candidate interaction, we created animations viewable in Google Earth. These files contained the data (movement trajectories) of all baboons during each potential interaction, superimposed on a satellite image of the area in which the event took place. The approacher and avoider were colored in red and blue respectively to distinguish them from the rest of the troop (which were colored black), but information about the identity of these focal individuals was not visible when assessing the event. Using this interface, an independent observer (MCC) blind to the identities of individuals could scroll through each event in real time and if necessary, view each potential interaction multiple times. Potential interactions were classified by the observer into one of three categories: 290 were classified as “clear approach-avoids,” 249 as “potential approach-avoids” and 238 as “not approach avoids”. In the subsequent analyses, we used all “clear approach avoids”, and those that were classified as being “potential approach-avoids” but with additional comments suggesting that they were good candidates. Step 3: Estimation of the dominance hierarchy from approach-avoid interactions Using the approach-avoid interactions between all pairs of individuals, we constructed a dominance hierarchy using Elo scores. Elo score-based ranking is a standard method of ranking, originally used for ranking competitors in sports events, that has gained increasing popularity in the literature on animal dominance hierarchies in recent years (29). Elo scores are computed based on wins and losses between pairs of individuals, and can provide a dynamical measure of an individual’s ranking over time. The basic principle of this ranking algorithm is that wins against competitors who are much more highly ranked result in a larger increase in score than wins against closely-ranked competitors. Individuals that repeatedly win contests (in this case displace others) will gain high scores, whereas the score of those that are displaced will drop (as a result of losing these contests). Thus, higher scores mean that individuals are more dominant (they were the “approacher” more often than the “avoider”). Because the dominance hierarchy is likely to have remained stable during the 14 days of the study, and observers did not report any escalation of dominance dispute while the baboons were collared, we looked only at the final Elo score rather than using the scores as a dynamic measure. In addition, because the order of events affects Elo scores (and in a short study such as ours the ordering of events is largely an artifact of when we started the study) we repeatedly measured the Elo scores while randomizing the order of the approach-avoid interactions (1000 randomizations). This enabled us to compute a mean score for each individual. Scores were computed within each sex separately. Although we did not collect systematic data on dominance interactions during the study, observations by MCC and an assistant identified individual 2427 as the dominant male. This provided a verification test for our method, which successfully identified this male as the most dominant. Section 7. Testing whether followers average the directions of pulling or choose one or the other direction

Theoretical models predict that, when a group contains two subgroups that are biased to move toward two different directions, the group as a whole will move in the average of the directions when the angle between the directions (the “angle of disagreement”) is small, but will choose one direction or the other when this angle is large (22). To test the predictions of this model at the individual level, we quantified whether followers (in events where the follower is pulled by at least one initiator) average the pulling directions of concurrent initiators or choose between them, as a function of the angle between the initiation directions. We used the dip test of bimodality (30) to determine if the distribution of directions taken by followers, over all events within a given range of angles (bin), was bimodal (Fig. S9B). For large angles, the distribution of subsequent directions taken by the follower was significantly bimodal (Fig. S9C, red points), indicating that followers move in the direction of one or the other initiator in these situations. For small angles, distributions did not differ from unimodality. However unimodality alone does not necessarily indicate that followers are averaging the directions of initiators. As the angle between initiation directions decreases, if followers were actually choosing one direction or the other, the overall distribution of angles chosen would eventually appear unimodal as these two distributions began to overlap. This fact is obvious if one considers the limiting case, when the angle between initiation directions is 0, and the two distributions have completely converged. To test whether followers are actually averaging at small angles, it is necessary to account for this converging-modes effect. In other words, to show evidence of averaging, the distribution of follower directions must be more unimodal than expected based on the baseline effect of the converging modes. We used the observed data at large angles (where the distribution is clearly bimodal) to construct null distributions for each small angle difference. We then determined whether the empirical distributions at each angle were significantly more unimodal than expected based on this null model. When the angle between clusters of initiators is large, each mode of the distribution is well-fit by a Gaussian with mean equal to the initiation direction and standard deviation equal to the standard deviation of follower directions. For angles above ~120 degrees (well above the point where the distributions converge), the standard deviation remains approximately constant (Fig. S9B). For our null model, we therefore assumed that the distributions at each angle difference consisted of the sum of two Gaussians, one at each pulling direction, each with a standard deviation 0.37 (computed based on the data above 120 degrees). In Fig. S9C, we show the expected distribution that results from this null model for each bin of the angle of disagreement (shown in black). We then overlay the observed data from Fig. 3B in red (the case of an individual following two initiators). The empirical distributions match the null distributions well when the angle between initiators is large. However they begin to disagree at smaller angles. In particular, the empirical distributions appear to be more peaked than the null distributions, in support of the idea that they representing true averaging of directions by the follower. To quantify this effect, we used Sarle’s bimodality coefficient, defined as

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b =g2 +1

k +3(n −1)2

(n − 2)(n − 3)

where g is the sample skewness, k is the sample excess kurtosis, and n is the sample size. For each angle difference (binned as shown in Fig. S9C), we created 1000 null distributions, each constructed from the same amount of data as was actually observed in that bin. We then computed the bimodality coefficient for each of these distributions, and counted how many times it was lower than the bimodality coefficient of the empirical distribution. This yielded a P-value, representing the probability that one would observe a value as or more unimodal than the empirical value based on the converging-modes null model (Fig. S9D, black points). In order for a distribution to be considered in the “compromise” or “averaging” regime, we required that two conditions were met: (1) the distribution was not significantly bimodal, as measured by the dip test for bimodality (30) (Fig. S9D, red points above 0.05), and (2) the distribution was more unimodal than expected based on our converging-modes null distributions described above (Fig. S9D, black points below 0.05). For angles below 72 degrees (Fig. S9D, gray region), both of these conditions were met, indicating that below 72 degrees, followers tend to average the directions of pullers. For angles above 96 degrees (Fig. S9D, red region), neither of these two conditions held, indicating that followers tend to choose one direction or the other. Between 72 and 96 degrees, one condition holds but not the other, and we therefore classified this region as transitional (Fig. S9D, dark red region). We repeated the same process for the case of two clusters, finding that individuals transitioned from averaging to choosing at between 60 and 72 degrees difference between the centers of the clusters. Section 8. Analyses of movement decisions in different contexts To determine whether our findings remain consistent in different situations, we repeated our analysis of majority rule in different group contexts. We compared periods where the group was relatively stationary (bottom 90% of troop speeds, as defined by the average speed of the troop centroid over the course of a minute) vs. moving (top 10% of speeds - above a troop speed of approximately 0.26 m/s). For each context, we computed the probability of following as a function of the difference between the number of individuals in each cluster (Fig. S6).

Supplementary Text

The results reported in this paper strongly suggest that baboon collective movement is driven by a shared decision-making process. However, these same results could theoretically arise via an alternative mechanism: independent but correlated movement preferences of troop-mates.

This alternative hypothesis suggests that if the baboons in the study troop (which are moving in a natural context) each made independent, but highly correlated, movement decisions (to optimize foraging, for instance), a pattern of ‘majority rule’ could arise without individuals having any influence on each other. However, for this process to underlie baboon collective movements, individuals’ preferences would have to be extremely highly correlated--even slight differences in the timing of movement or direction of departure would, over time, lead to group dissolution. Baboon troops in general maintain strong group cohesion. In our study the troop remained highly cohesive throughout the study period. The upper 97.5% threshold of dyadic distances is 126 m, despite the troop having travelled over an area 3161 m (east-to-west) by 3746 m (north-to-south). Thus there exists strong cohesion, and hence temporal contingency, in their movements.

For such cohesion to arise from independent, but correlated individual decisions, baboons would have to all converge on the same foraging decision each time such a decision is made. Given the diversity of food items baboons consume, the widespread distribution of these food sources on the landscape, and their temporal unpredictability, repeatedly reaching the same decision is not trivial. It is statistically improbable that all individuals in a baboon troop would make exactly the same causally independent decision (despite considerable individual differences), at the same time, across hundreds of such decision events, as would be required to explain observed levels of troop cohesion.

However, it is likely that some level of independent decision-making in baboons forms a part of the dynamics we observe. In our data, we capture pairs or small groups (aka ‘clusters’) of individuals that moved in the same direction at the same time. This is consistent with a subset of individuals that could be moving together in response to causally independent optimality functions, or in response to similar environmental cues and previous experiences. However, we then show that individuals can make movement initiations in different directions, and we identify and explicitly investigate these situations of directional conflict. In conflicts, two or more individuals initiate in different directions at the same time. These conflicts likely arise because not all individuals have made the same decision or have the same preference.

The outcome of the conflicts we investigate is that the baboons remain together and eventually move off together. This stands in contrast to what we would expect if individuals were “following” due to correlated directional preferences - in that case the group would fragment when directional preferences conflicted. Instead, we find that the subsequent heading of the troop is positively correlated with the direction proposed by the subgroup that was followed (Fig. S4). In the case of equally-sized subgroups, we find that the directions are selected with approximately equal probability, whereas the direction associated with the majority of initiators tends to ‘win’ when subgroups differ in size, consistent with social interactions. Thus, the troop ultimately goes in the direction associated with the majority. We also find that the heading associated with the subgroup that is not followed is negatively correlated with the subsequent

movement direction of the troop. Thus, failed initiators ultimately move in the direction of the majority (away from their own initial directions, Fig. S4).

Fig. S1. Individuals with high social dominance ranks are not more likely to be followed. (A) Contrary to the predictions of a despotic leadership model, the known dominant male (white text) was not more likely to be successful in recruiting followers than others. Further, there was no pattern suggesting that dominant females (B, Spearman rank correlation: rho=-0.29, P=0.86) or males (C, Spearman rank correlation: rho=0.21, P=0.30) had greater initiation success. Individuals with grey borders had collars which stopped functioning before the end of the study period (thus greater error in the estimation of dominance rank). Although our method of assigning rank is indirect, and potentially coarse, we also did not find evidence that a few individuals had substantially higher probability of being followed than all others, which is inconsistent with a model of leadership by a small minority. We also found that age/sex classes did not consistently differ in their probability of being followed. Juveniles were removed from these analyses.

Fig. S2. Baboons are more likely to follow initiators who move in a directed manner. The probability that an initiation is successful (color) increases with the directedness of movement of the initiator (defined as the 1-f, where f is the net displacement divided by the total path length). For a given level of directedness, the probability of success is highest for slow to intermediate speeds.

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Fig. S3. Individuals are less likely follow when the angle of disagreement between concurrent initiators is large, and more likely to follow when the angle is small (see also Fig. 3). The shaded region shows the 95% confidence intervals estimated from 1000 bootstrapped replications of the data.

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Fig. S4. The subsequent direction of troop movement is strongly correlated with the initiation direction of the successful subgroup of initiators (chosen by the follower) but slightly negatively correlated with the initiation direction of the unsuccessful (not chosen) subgroup. We measured the heading correlation between the average direction of initiators in each subgroup (limited to cases of two concurrent clusters of initiators), and the movement of the troop centroid. From the point when the follower begins to move (t=0), the heading of the troop centroid between its position at t=0 and current time (along x-axis) becomes positively correlated with the initiation direction of the chosen subgroup. This positive correlation remains even after long periods of time (in excess of 3 hours), suggesting that the decisions made by followers have significant implications for the resulting location of the troop in space.

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Fig. S5. The probability of following as a function of the angle between subgroups of initiators. Individuals are more likely to follow (either by compromising or choosing a cluster) when the numerical difference between competing options is high (i.e. numerical conflict is low). However, this relationship is modulated by the angle of disagreement between competing options, with clusters requiring a greater majority to successfully pull a follower as the angle of disagreement increases. When directional conflict reaches 180 degrees, clusters are typically only successful at recruiting any individual if they have a strong majority.

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Fig. S6. Followers employ a majority rule regardless of whether the troop is currently moving or relatively stationary. In both cases, the probability of following the majority increases as the numerical difference between competing subgroups increases, resulting in the characteristic sigmoidal shape of the curves. However, this sigmoidal response is steeper when the group is moving than when it is stationary, indicating that followers’ sensitivity to small differences in the number of initiators within competing subgroups may vary depending on the context. Points represent raw data for each context (blue = moving, red = stationary, black = all data), and curves represent sigmoidal fits. The troop was considered to be moving if the speed of the troop centroid fell within the top 10% of speeds at the beginning of an event, and was considered stationary otherwise (see Materials and Methods section 8).

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Fig. S7. Histogram of angle between the direction of initiation and the direction taken by the follower over all successful pulls.

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Fig. S8. Histogram of the time scale over which pulls and anchors occurred. Values represent the time between t1, the beginning of the initiation, and t2, the time that either following began (for pulls) or the initiator began to return (for anchors).

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Fig. S9. Procedure for analyzing the geometry of decision-making. (A) Toy example applying the GMM clustering method to initiations by 5 different individuals. In this example, the clustering algorithm first identifies the largest angle between initiators, and then identifies 3 peaks in the directions taken reflecting 3 different clusters. (B) For cases when two clusters of initiators are detected, red and black markers show the standard deviation of followers that chose each cluster (estimated by measuring the standard deviation of the top and bottom half of the distribution of the directions taken by all followers) as a function of the difference in angle between the clusters. The value of the standard deviation of the directions taken by followers in each cluster stabilizes when the angle between the clusters is greater than approximately 90 degrees. This stabilization indicates that the distributions of follower directions for the two clusters are no longer overlapping extensively with one another. We estimated the mean standard deviation at large angles (past the point of stabilization), and used this as the basis for our converging-modes null model (panel C). To be conservative, we used only the values in the shaded region in our estimate of the standard deviation. (C) We generated an expected distribution of following angles by combining samples from two normal distributions with the same standard deviation (taken from above) and with a difference in mean ranging from 0 to 180 degrees. Comparing the expected (black) and empirical (red) probability distributions of the directions taken by followers highlights the strong central peak when the difference in angle is small (top-left), becoming more bimodal to match the expected bimodal distribution when angles are large (bottom-right). (D) Using the converging-modes test (black points) highlights that the distribution is significantly more peaked (unimodal) than expected by chance when the difference in angle between clusters is small (grey shading). This represents the region of the data where, for a given angular difference between initiators (or groups of initiators), the followers moved in a direction that was closer to the average of the initiation directions than expected (c.f. “compromise”). The dip test for unimodality (red points) highlights that the distribution of follower directions is significantly different from unimodal when the difference in angles between clusters is large (red shading). This region represents followers either choosing one or the other of the initiation directions (c.f. “choose”), thus generating two peaks in the distribution of following directions. The region of uncertainty between these two regimes (where the two statistics do not agree, in this case both are significant) represents the “transition” between choosing and compromising, and this region contains the critical angle (Fig. 4).

Collar Number

Sex Age Battery Capture Date

Tracking Start Date

Tracking End Date

Days Tracked

2426 Male Sub-adult D 7/21/2012 8/1/2012 8/31/2012 31

2427 Male Adult D 7/21/2012 8/1/2012 9/4/2012 35

2428 Female Sub-adult C 7/29/2012 8/1/2012 8/15/2012 15

2430 Female Adult D 7/28/2012 8/1/2012 8/3/2012 3

2432 Male Sub-adult C 7/22/2012 8/1/2012 8/5/2012 5

2433 Male Sub-adult D 7/22/2012 8/1/2012 8/6/2012 6

2434 Male Adult D 7/22/2012 8/1/2012 8/2/2012 2

2436 Male Sub-adult D 7/22/2012 8/1/2012 9/2/2012 33

2439 Female Adult D 7/21/2012 8/1/2012 9/4/2012 35

2441 Female Sub-adult C 7/22/2012 8/1/2012 8/29/2012 29

2443 Male Sub-adult D 7/23/2012 8/1/2012 9/2/2012 33

2446 Female Adult D 7/25/2012 8/1/2012 9/2/2012 33

2447 Female Adult D 7/24/2012 8/1/2012 8/31/2012 31

2448 Male Juvenile C 7/22/2012 8/1/2012 8/17/2012 17

2449 Female Adult D 7/23/2012 8/1/2012 8/31/2012 31

2450 Female Sub-adult D 7/24/2012 8/1/2012 8/5/2012 5

2451 Female Adult D 7/22/2012 8/1/2012 9/2/2012 33

2452 Male Sub-adult C 7/21/2012 8/1/2012 8/14/2012 14

2453 Female Adult D 7/25/2012 8/1/2012 8/3/2012 3

2454 Male Juvenile C 7/22/2012 8/1/2012 8/14/2012 14

2455 Female Sub-adult D 7/28/2012 8/1/2012 8/8/2012 8

2456 Female Adult D 7/22/2012 8/1/2012 8/31/2012 31

2457 Male Adult D 7/21/2012 8/1/2012 9/4/2012 35

2458 Female Adult D 7/22/2012 8/1/2012 8/2/2012 1

2460 Female Adult D 7/28/2012 8/1/2012 8/2/2012 1

Table S1. Collar ID, age/sex class and tracking details for GPS-collared baboons.

Effect Coef. SE Wald P

Agreement 0.183 0.045 16.03 <0.001

Number of initiators -0.116 0.006 398.26 <0.001

Interaction 0.534 0.008 4196.05 <0.001 Table S2. Results of fitting GEE model to the number of initiators and their level of agreement (Fig 2). GEE was fit to the binary outcome for a given event (success or not) with an interaction between the number of initiators and their agreement as fixed effects. Because events already include all concurrent initiations, we did not include an autocorrelation structure.

Movie S1. Example of baboon movement data (shown at 25x speed) over a 25-minute period on the morning of the first day, as the baboons departed from their sleep site. Points indicate individual baboons, with colors denoting age/sex class (dark blue = adult male, light blue = subadult male, red = adult female, orange = subadult female, grey = juvenile male).   Movie S2. Example of baboon movement data (shown at 25x speed) over a 25-minute period during the middle of the third day, during a period of directional conflict. Points indicate individual baboons, with colors denoting age/sex class (dark blue = adult male, light blue = subadult male, red = adult female, orange = subadult female, grey = juvenile male).