Fission-fusion events, i.e. changes to the size and composition of animal social groups, are a mechanism to adjust the social environment in response to short-term changes in the cost-benefit ratio of group living. Furthermore, the time and location of fission-fusion events provide insight into the underlying drivers of these dynamics. Here, we describe a method for identifying group membership over time and for extracting fission-fusion events from animal tracking data. We applied this method to high-resolution GPS data of free-ranging sheep (Ovis aries). Group size was highest during times when sheep typically rest (mid-day and at night), and when anti-predator benefits of grouping are high while costs of competition are low. Consistent with this, fission and fusion frequencies were highest during early morning and late evening, suggesting that social restructuring occurs during periods of high activity. However, fission and fusion events were not more frequent near food patches and water resources when adjusted for overall space use. This suggests a limited role of resource competition. Our results elucidate the dynamics of grouping in response to social and ecological drivers, and we provide a tool for investigating these dynamics in other species.

The study was conducted at Fowler's Gap Arid Zone Research Station in Australia, in 2018. Our study tracked a herd of 50 female merino sheep (Ovis aries) interacting in a paddock over 16 days. The paddock did not include any other conspecifics, and was approximately 6 km2 in size. It contained one water trough and 10 food locations consisting of bales of hay. The region was severely affected by drought and most of the annual vegetation that sheep would graze on was absent. Thus, the provided hay constituted the vast majority of food resources available to the study animals. We recorded the locations of all 50 sheep every 6 seconds for 24 hours each day using GPS collars. Every four days, sheep were captured to change GPS collar batteries. The data from these capture time periods were excluded from the analysis. Sheep were undisturbed during the 4-day tracking periods (86 to 88h each). GPS collars (GPS, i-gotU GT-120 by MobileAction, with a larger battery CE04381 by Core Electronics) weighed 700g, approximately 1.9% of the sheep’s body mass, falling well below the common 5% threshold for fitting scientific devices. 

We followed the data processing procedure described in Leu et al. (2021) to increase overall data quality. Briefly, we first plotted all GPS locations and removed obvious outlier locations outside the paddock boundaries. We also removed all locations that were determined with fewer than three satellites, which is the minimum required for triangulation. Second, we removed locations that could not have been reached if the animal moved at maximum speed, taking the two previous and two following locations into consideration. We used a maximum movement speed of 1.5m/s, which was determined in a simulated predation event (Manning et al., 2014). Lastly, because GPS units differed slightly in their recording times for each fix, we linearly interpolated the data such that each sheep’s location was estimated at exactly 6 second intervals. We also filled small gaps in the data using the data interpolation (maximum of two consecutive missing locations). The processed data comprised 10,362,043 data points, representing 97% of the possible maximum number of data points across all sheep and time steps.

Data was further processed with the modified DBSCAN algorithm also described in our paper. Groups are built through an iterative process, based on DBSCAN. We outline the original DBSCAN before adding our modification. The algorithm starts with a randomly picked focal sheep and connects all sheep within the given radius to the focal sheep and to each other. This approach reflects the “gambit of the group”, an assumption that all individuals in a group are associated with each other, thus ignoring internal group structure (Franks et al., 2010). Then, the algorithm identifies and connects all further individuals that are within the radius of any group member. This is repeated until no additional sheep can be added to the group. Then, a new focal sheep, not yet a member of any group, is chosen, and the iteration starts again. The process is repeated until all sheep are assigned to a group or are identified as unconnected solitary individuals. The algorithm returns a list of the groups for each time step. In its original form, the inputs to DBSCAN are 1) a radius that describes the maximum Euclidean distance between two individuals considered associated with each other, and 2) an integer representing the minimum group size. In our study, we set the minimum group size to 1, thus considering groups of any size.

Defining membership in a social group based on a spatial radius can result in group membership fluctuating with small changes in the distance between individuals, although the social link is likely still present. Such fluctuations can be problematic in the context of identifying fission-fusion events, because they can lead to the detection of many small events that are not biologically/socially meaningful. To limit the effect of such fluctuations, we applied a “sticky DBSCAN” algorithm, which uses two radii – an inner radius and an outer radius. An individual is considered to join another individual in a group only if their dyadic distance is smaller than the inner radius. However, the time at which the individual joins is identified as the moment when the dyadic distance falls below the outer radius. Similarly, an individual is considered to leave the group at the time it crosses the outer radius of all group members after it has previously been within the inner radius.  

In practice, the “Sticky” DBSCAN algorithm starts with a list of the distances of two particular sheep over time. It splits at each step where the larger radius r2 is crossed. Now, these time spans are dedicated as "connections" or "not connections" based on whether they contain at least one distance smaller than the small radius r1. The traditional DBSCAN is run now but instead of using a radius to determine whether two sheep are connections, it uses the Boolean "connection" value. While splitting the groups, we ignore any missing data as we will filter out these points in the interpolation of group membership step. Since a missing sheep at time t will not appear in any of the groups at time t (just as with traditional DBSCAN), ignoring them in the "connections" data set only means that sheep stay "sticky" associated with their groups during GPS outage.

The sticky DBSCAN algorithm was applied with different combinations of radii, which are included in the label. If no radii are mentioned in the label, the radii were 30m and 50m.
 
Franks DW, Ruxton GD, James R. Sampling animal association networks with the gambit of the group. Behav Ecol Sociobiol. 2010 Jan 1;64(3):493–503. Available from: https://doi.org/10.1007/s00265-009-0865-8

Leu ST, Quiring K, Leggett KEA, Griffith SC. Consistent behavioural responses to heatwaves provide body condition benefits in rangeland sheep. Appl Anim Behav Sci . 2021 Jan 1;234:105204. Available from: https://doi.org/10.1016/j.applanim.2020.105204

Manning JK, Fogarty ES, Trotter MG, Schneider DA, Thomson PC, Bush RD, et al. A pilot study into the use of global navigation satellite system technology to quantify the behavioural responses of sheep during simulated dog predation events. Anim Prod Sci. 2014 Aug 28; 54(10):1676–81. Available from: https://doi.org/10.1071/AN14221

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