Despite extensive research into the behavioral ecology of free-ranging animal groups, questions remain about how group members integrate information about their physical and social surroundings. This is because a) tracking of multiple group members is limited to a few easily manageable species; and b) the tools to simultaneously quantify physical and social influences on an individual’s movement remain challenging, especially across large geographic scales. A relevant example of a widely-ranging species with a complex social structure and of conservation concern is the African savanna elephant. We evaluate highly synchronized GPS tracks from five male elephants in Etosha National Park in Namibia by incorporating their dynamic social landscape into an established resource selection model. The fitted model predicts movement patterns based simultaneously on the physical landscape (e.g., repeated visitation of waterholes) and the social landscape (e.g., avoidance of a dominant male). Combining the fitted models for multiple focal individuals produces landscape-dependent social networks that vary over space (e.g., with distance from a waterhole) and time (e.g., as the seasons change). The networks, especially around waterholes, are consistent with dominance patterns determined from previous behavioral studies.  Models that combine physical landscape and social effects based on remote tracking can augment traditional methods for determining social structure from intensive behavioral observations. More broadly, these models will be essential to effective, in-situ conservation and management of wide-ranging social species in the face of anthropogenic disruptions to their physical surroundings and social connections.

Study subjects and the social landscape: The five individuals considered in this study belong to a large elephant subpopulation residing in the northeastern region of Etosha National Park, Namibia. As a part of a different research effort, these individuals were classified into several age, dominance, social, and reproductive categories (O’Connell-Rodwell et al. 2011; O’Connell et al. 2024a). The age structure in this population was determined on the basis of several morphological features and can be found in the original publication (O’Connell-Rodwell et al. 2011; O’Connell et al. 2022).  The dominance categories are reported from a population-level, ordinal dominance hierarchy based on the frequency of agonistic dyadic interactions (i.e., displacement) observed during all-occurrence sampling, over multiple field seasons (O’Connell-Rodwell et al. 2024a). The social categories were approximated using social network analysis (i.e., eigenvector centrality—an index expressing how influential an individual is based on the frequency of associating with other influential conspecifics) (O’Connell-Rodwell et al. 2024a; O’Connell-Rodwell et al. 2024b;). The reproductive category expresses whether an elephant was in musth at the time of behavioral data collection. 

Tracking data: In September 2009, ENP personnel fitted five elephants with Global Positioning System (GSP) and satellite Global System for Mobile Communication (GSM) tracking devices. The trackers recorded positional data (i.e., longitude, latitude) every 15 minutes over approximately 24 months. Prior to analysis, we converted tracking data to Cartesian units (i.e., meters) using the Universal Transverse Mercator coordinate system (UTM) projection. We also filtered the data to remove outlier movements as follows: we kept only movements (pairs of GPS fixes) in which 1) the interval was 15 minutes, 2) the focal individual moved ≤ 300 m in that time, and 3) all four of the other tracked elephants were within 20 km. Criterion 1 eliminates missed fixes; criterion 2 eliminates a small number of unusually fast movements which could represent startle responses to rare stimuli; and criterion 3 ensures that there is at least the potential for social interactions between all five elephants. The resulting datasets (one for each focal individual) had between 27,397 and 30,584 movements.

The physical landscape: To evaluate tracking data in the context of the physical landscape, we constructed a map of vegetation productivity using data from the 16-day 250 m Normalized Difference Vegetation Index (NDVI) MODIS imagery. We also created a map of the perennial waterholes by extracting coordinate information from existing geospatial records generated by ENP personnel. Finally, we compiled a map of ‘frequently visited areas’ (FVAs) as the centroids of the top 20 clusters of large turning angles (>90 degrees) in the movement data. These locations broadly correlate with the presence of shade and proximity to fruiting trees (Kilian, W. personal communication), which in other populations affect elephant movement.

The Social Resource Selection Function (SRSF) model: Our approach extends the existing Resource Selection Function framework in which an individual’s location, when fixed (by a GPS device or other tracking methodology) is considered a choice made from a set of possible locations. This set of locations is bounded in space by how far from its previously known location the individual could reasonably be expected to move in the time between the two fixes. The relative probability of ending up at different destinations, relative to one’s current location, is modeled using conditional logistic regression (CLR) as a function of various environmental parameters that differ between locations (e.g., ‘vegetation density’, ‘distance to water’, distance to the previous location). The SRSF model adds to the RSF framework by considering the locations of other individuals in a moving group as time-varying point features of the landscape. One individual (the focal individual) is modeled, and the locations of the others (nonfocal individuals) are incorporated as ‘distance to neighbor’ values that can be calculated for all the possible locations in the CLR. Assuming that each elephant responds differently to different conspecifics, we calculate a set of social predictors by determining the distance to each neighbor separately.

For any given movement m, the ‘choice’ is a binary response, where a potential location i is either the endpoint at which the individual was recorded (yi = 1) or one of the alternatives (yi = 0). For convenience, we have labeled the chosen location with the subscript j (j ∈ i). The probability of a movement is modeled by where X is a matrix of k predictors derived from the landscape data; β is a k by 1 matrix of parameters to be estimated; c is the total number of locations considered (1 being the actual endpoint and c – 1 being randomly sampled within a circle of fixed radius); and s is the probability of a stochastic, ‘non-choice-type movement’ for which the endpoint is independent to any of the included predictors. One example might be a sudden scare that causes a flight response. In this case, we assign all possible endpoints the same probability 1/c. Including the possibility of non-choice movements is a novel addition to the standard CLR model; we found that for these data it stabilized the parameter estimates (meaning that we obtained similar results with different random subsets of the data when it was included, and disparate estimates when it was not). Overall, pm is the predicted ‘preference value’ for the chosen location divided by (and therefore conditional on) the sum of the preference values for the random sample of possible locations. In practice, depending on the resolution of the landscape and the boundary of possible distances reached, the denominator could include hundreds or even thousands of random locations. This can make computation of the expression, which is repeated for every movement in a dataset, time-consuming—a challenge that then translates into the model fitting. It is thus standard practice to randomly select a fixed number of non-chosen alternative locations on the assumption that they will comprise a representative sample of the landscape variation available to the individual. Given that our landscape features — various distance measures plus an interpolated array of NDVI values — vary smoothly and continuously within our sampling radius, we used 30 random locations (so c = 31). We fit the CLR by maximizing L, the log-likelihood of the entire set of n movements, using quasi-Newton nonlinear maximization.

We performed variable selection by first fitting models with all possible subsets of physical and social landscape variables in their quadratic forms, except for distance to the previous location, which was always included as a linear function as an established proxy for the effort required to move to a new location. We ranked the models using Akaike’s Information Criterion (AIC) and calculated importance scores for each variable as the cumulative Akaike weight of the models in which it appeared. 

Interpretation of the SRSF model outputs depends on the functional form of each variable over the range of its values and its importance score. Because a linear cost-of-movement function is in every model by design, we exclude it from further reporting and discussion. The functional forms of the remaining variables can be divided into five categories: 1) monotonically increasing or 2) decreasing (indicating a preference for large or smaller values of the variable in question); 3) convex with the maximum within the data range (a preference for intermediate values); 4) concave with the minimum within the data range (a preference for large and small values indicating a back-and-forth movement between the locations containing the variable in question); or 5) constant over the data range (lack of preference for a specific value) (Mashintonio et al. 2014).

The SRSF model outputs are expressed as the relative preference for movement towards locations defined by the physical (e.g., NDVI, a proxy for vegetation productivity) and social variables (e.g., distance to a neighbor) (Mashintonio et al. 2014).

Testing the predictions about movements in a sociophysical landscape: Because one of our goals was to see if social interactions previously observed at Mushara waterhole persist in the larger landscape, we fit the SRSF model to three different subsets of movement data: movements within 2 km of waterholes, movements within 2 km of an FVA, and movements more than 2 km away from both kinds of feature. To account for potential seasonal changes in the effect of the sociophysical landscape on individual movement, we divided each data subset into the wet season (November-April) and dry season (May-October). Different numbers of movements remained for each subset for each focal elephant from 371 to 13,555. To achieve a constant sample size for seasonal comparisons, we fit the SRSF model to 350 random movement segments for areas near water and far from water or FVAs; and 450 randomly selected movement segments for areas near the FVAs. To test for consistency, we repeated each model fit ten times using different random samples of movements.

The physical predictors in each fit included time-matched NDVI (vegetation productivity), distance to the nearest waterhole, and distance to the nearest FVA. The social predictors for each focal animal were distance to each of the four nonfocal elephants separately.

References: 

O’Connell-Rodwell CE, Wood JD, Kinzley C, Rodwell TC, Alarcon C, Wasser SK, Sapolsky R. (2011). Male African elephants (Loxodonta africana) queue when the stakes are high. Ethol Ecol Evol. 23: 388–397.

O’Connell-Rodwell CE, Berezin JL, Kinzley C, Freeman PT, Sandri MN, Kieschnick D, Rodwell TC, Abarca M, and Hayssen V. (2024a Preprint). Dynamics of male African elephant 695 character durability across time and social contexts. bioRxiv 2024.05.24.595367

O’Connell-Rodwell CE, Freeman PT, Kinzley C, Sandri MN, Berezin JL, Wiśniewska M, Jessup K, Rodwell TC. (2022). A novel technique for aging male African elephants (Loxodonta africana) using craniofacial photogrammetry and geometric morphometrics. Mamm Biol. 102: 591-613

O’Connell-Rodwell CE, Berezin JL, Kinzley C, Freeman PT, Sandri MN, Kieschnick D, Rodwell TC, Abarca M, and Hayssen V. (2024a Preprint). Dynamics of male African elephant 695 character durability across time and social contexts. bioRxiv 2024.05.24.595367

O’Connell-Rodwell CE. Berezin JL, Pignatelli A, Rodwell TC. (2024b Preprint). The use of vocal coordination in male African elephant group departures: evidence of active leadership and consensus. bioRxiv 2024.05.31.596833.

Mashintonio AF, Pimm SL, Harris GM, van Aarde RJ, Russell GJ. (2014). Data-driven discovery of the spatial scales of habitat choice by elephants. PeerJ. 2: e504.