Variability in the estimation of ungulate group sizes complicates ecological inference

Abstract Foundational work has examined adaptive social behavior in animals in relation to the costs and benefits of group living. Within this context, a “group” of animals represents an organizational unit that is integral to the study of animal ecology and evolution. Definitions of animal group sizes are often subjective with considerable variability within and across species. However, investigations of both the extent and implications of such variability in the estimation of animal group sizes are currently lacking. Selecting ungulates as a case study, we conducted a literature review to assess prevailing practices used to determine group sizes among terrestrial Cetartiodactyla and Perissodactyla. Via this process, we examined group size definitions for 61 species across 171 peer‐reviewed studies published between 1962 and 2018. These studies quantified group sizes via estimation of ungulate aggregations in space and time. Spatial estimates included a nearest neighbor distance ranging from 1.4 m to 1,000 m, and this variation was partially explained by a weak positive correlation (|r| = .4, p < .003) with the body size of the ungulate research subjects. The temporal extent over which group size was estimated was even broader, ranging from three minutes to 24 hr. The considerable variability in ungulate group size estimation that we observed complicates efforts to not only compare and replicate studies but also to evaluate underlying theories of group living. We recommend that researchers: (a) clearly describe the spatiotemporal extents over which they define ungulate group sizes, (b) highlight foundational empirical and ecological rationale for these extents, and (c) seek to align such extents among individual species so as to facilitate cross‐system comparisons of ungulate group size dynamics. We believe an integrative approach to ungulate group size estimation would readily facilitate replication, comparability, and evaluation of competing hypotheses examining the tradeoffs of animal sociality.

Thus, social cohesion is an important determinant of fitness for group-living species (Silk, 2007). Ultimately, the cumulative effects of social interactions among group members may lead to long-term adaptations with evolutionary implications (Dunbar & Shultz, 2010;Grodwohl, 2017). For example, dominance hierarchies among males for access to mates may lead to the evolution of sexually selected traits (Qvarnström & Forsgren, 1998). In the same light, sociality across certain prey species represents an evolutionary tradeoff between adaptations to avoid predation and those associated with maximizing the consumption of critical resources (e.g., Bowyer, McCullough, & Belovsky, 2001).
Considerable research has investigated the mechanisms that influence animal group formation (see Aurelli et al., 2008;Dunbar & Shultz, 2010;Gerard et al., 2002;Krause & Ruxton, 2002). Such activities are inherently challenging given fission-fusion social dynamics and spatial variation in density of the animal subjects (Barrette, 1991;Monteith, Sexton, Jenks, & Bowyer, 2007;Reiczigel et al., 2008). These challenges have led to a diversity of group size estimation techniques across ecological studies (see Krause & Ruxton, 2002). However, an understanding of the magnitude and consequences of such variability in animal group size definitions is currently lacking. This is particularly apparent among ungulates, a diverse taxonomic group representing some of the world's most social mammals (Groves & Grubb, 2011;Zurano et al., 2019).
Here, we used research on terrestrial species in the taxonomic orders Cetartiodactyla and Perissodactyla as a case study and conducted a literature review of studies referencing ungulate group size estimation. We synthesized the ways in which researchers estimated ungulate group sizes, highlighted the extent of methodological variation prevalent in the protocols employed, and examined the implications of this variability for inference and comparability across research sites and species. A group is a critical concept underlying animal socio-ecological and evolutionary research (Krause & Ruxton, 2002). Thus, our reflections on the prevailing practices in ungulate group size estimation are critical for future socio-ecological and evolutionary research on these species with subsequent implications for other group-living animals.

| Ungulates
Given that ungulates are among the most social and diverse mammal radiations (Groves & Grubb, 2011;Zurano et al., 2019), we framed our analysis to include studies of free ranging, naturally, or seminaturally occurring terrestrial species in the orders Cetartiodactyla and Perissodactyla. Ungulates in these orders inhabit a wide range of habitats around the world from the Sudanic grassland ecosystems of Africa to the boreal forests of the northern hemisphere ( Figure 1; Groves & Grubb, 2011). This spatial diversity is matched by reciprocal diversity in behavioral traits among ungulate species resulting in a range of grouping patterns (Groves & Grubb, 2011;Ofstad et al., 2016).

| Literature review
In August of 2018, we conducted a literature review examining ungulate group size definitions. We used the Web of Science, Scopus, Wildlife Studies Worldwide, and the Michigan State University libraries search engines to conduct this review. To obtain as many peer-reviewed studies as possible across all search engines, we used a combination of terms via a multi-step process including primary, secondary, and tertiary searches. We used "ungulate AND group size AND group dynamics OR herd size OR herd composition AND sociality OR group living" as our primary search terms. We then combined these primary search terms with "fusion-fission OR aggregation OR population structure OR social structure OR herbivore behavior" in the secondary search. Finally, in the tertiary search we combined the primary and secondary search terms with "predation risk OR group associations OR plasticity OR seasonal grouping OR social bonds." We included studies that assessed group dynamics for both conspecific and heterospecific interactions. We discarded studies that did not assess ungulate grouping patterns, those that involved domesticated ungulates, and studies of recently reintroduced ungulates. We F I G U R E 1 Spatial extent of the field study locations featured among 171 studies, published between 1962 and 2018, assessing ungulate group size dynamics F I G U R E 2 A framework for ungulate group size estimation. Studies describing ungulate group sizes fall into one of four standardized objective categories. The study objectives determine the field techniques for group size estimation. The field techniques used for group size estimation determine the metrics employed and ultimately the group sizes reported by studies. Arrows depict the sequence of events that lead to observed ungulate group sizes did so based on the consideration that domesticated and recently reintroduced ungulates may not exhibit natural grouping patterns.

| A framework for ungulate group size estimation
Scientific studies of social ungulates often require some enumeration or description of ungulate group sizes. We compared definitions of ungulate group sizes as inferred from each study's research objectives and methodological descriptions. We placed the studies in one of four standardized objective categories to compare group size definitions ( Figure 2). These objective categories included (a) social behavior, (b) animal-habitat relationships, (c) predation risk, and (d) disease/parasite prevalence. We then recorded all metrics used to define ungulate groups across all species, data collection techniques, and study objectives ( Figure 2; Table 1).

| Relationship between body size and spatial extent
Body size is an important factor that influences ecological processes across spatiotemporal scales (Smith & Lyons, 2011). Furthermore, there are three orders of magnitude between the smallest and largest terrestrial species in the taxonomic orders Cetartiodactyla and Perissodactyla. Thus, we hypothesized that the relative body size of the ungulate research subjects might correlate with the spatial extent used to define their group sizes across studies. We obtained body mass data of all species included in our study from the Phylogenetic Atlas of Mammal Macroecology (Faurby et al., 2019). This database contains the most up-to-date trait data for all 5,831 known mammal species from the last interglacial period (~130,000 years ago) until present (Faurby et al., 2018). We then used the nonparametric Spearman's rank correlation test to examine the correlation between body size and spatial extent of group size estimation.

| RE SULTS
In total, our literature review returned 534 studies. Upon review, we eliminated 363 studies from consideration given that they did not meet our criteria for inclusion in the analysis, as described in the methods. Thus, we retained 171 studies, published between 1962 and 2018, that directly examined ungulate grouping behavior (see Table S1).
We detected a weak positive correlation between body size of the research species and the spatial extent used to define their group sizes (|r| = .4, p < .003, Spearman's rank correlation, Figure 5).  Alados, 1985;Mooring et al., 2005), telemetry data (e.g., Deacon & Bercovitch, 2018;Wal, Laforge, & McLoughlin, 2014), or statistical reconstruction (e.g., Hebblewhite & Pletscher, 2002;Stanley & Dunbar, 2013). A common theme among group size definitions from all studies was the description and/or calculation of the factors affecting behavioral cohesion of group members across spatiotemporal dimensions.

| D ISCUSS I ON
Studies based their group size definitions on rates of individual movements among group members, interindividual distances, properties of attraction, and synchrony of behavior (Caro, 2005;Dagg, 2014;Gerard & Richard-Hansen, 1992;Krause & Ruxton, 2002;Miquelle, Peek, & Ballenberghe, 1992;Salazar et al., 2016). We detected considerable variation in the metrics used to define ungulate group sizes across these dimensions (i.e., spatial extent of group members and observation time; Figure 4).
Furthermore, we detected a weak positive correlation between body size and spatial extent ( Figure 5). Groups for large species that occupy large areas such as giraffes (Giraffa camelopardalis) tended to be defined by higher spatial extents than smaller species during field observations ( Figure 4). This aligned with our expectation that spatial extent used to define group size positively correlates with species body size. Correspondingly, even fewer studies specified the temporal window over which they estimated group sizes. Spatial extent and observation time are important factors given that they delimit the extent over which group sizes are enumerated (Altmann, 1974;Jarman, 1974). Observation time bounds are critical because individuals under observation are active entities that switch between activities across space and time. Thus, a group defined within a given period reflects a partial record of the behavior of the animals under observation (Altmann, 1974). This is especially important in identification of subgroups within large groups, defining grouping rates, and consequently understanding fission-fusion dynamics.
Across studies, the empirical and ecological rationale used to justify choice of spatial and temporal extents used to define ungulate group sizes was rare (e.g., Balmford, 1992;Bowyer et al., 2001;Marino, 2010). Specifically, the only rationale we found for choice of a spatial extent was constrained by technical designs of telemetry equipment (see Wal et al., 2014;Wal, Paquet, et al., 2012;Wal, Paquet, Messier, & McLoughlin, 2013;Wal, Yip, & McLoughlin, 2012) rather than the ecology of species under study. These studies programmed proximity-logging collars to activate and collect data on elk (Cervus elaphus) interaction rates when the collared elk individuals came within 1.4 m of each other (Wal et al., 2013(Wal et al., , 2014Wal, Paquet, et al., 2012;Wal, Yip, et al., 2012). Unlike distance, time bound employed for group definitions derived from telemetry studies was not constrained by technical design of telemetry equipment (Wal et al., 2013(Wal et al., , 2014Wal, Paquet, et al., 2012;Wal, Yip, et al., 2012). Overall, uncertainty to the ecological or empirical basis for the choice of spatial and temporal extents for defining ungulate group sizes remains.
The lack of empirical and ecological rationale for choice of spatial extent and observation time for ungulate group size estimation challenges cross-system comparisons and problematizes the development of theory. Spatial extent is critical when there is clear separation among groups with little to no observable movement of individuals among the groups (Cross, Lloyd-Smith, & Getz, 2005). Within this context, distance-based group definitions may be problematic for characterizing herds for highly active species. For instance, highly mobile species may perceive groups at larger spatial scales than less mobile and sedentary species (Cross et al., 2005). Additionally, large spatial extent may be limited by detectability of animal groups across large spatial scales and may only be suited to air surveys for species that occur in very large congregations. We found only one study that F I G U R E 5 The relationship between ungulate body size and spatial extent used to define ungulate group sizes from a review of 171 studies, published between 1962 and 2018, assessing ungulate group size dynamics restricted its group definition to the number of individuals within sight of the observer(s) (see Bercovitch & Berry, 2014).
Additionally, the subjectivity inherent among ungulate group size definitions may make studies susceptible to observer bias. While subjective criteria such as "involvement in same general activity," "awareness among group members," and "movement in the same general direction" are not implausible, they are hard to practically contextualize among several observers, species, survey periods, or across study sites. We suggest that definitions of ungulate group sizes be rooted in empirical foundational structures with clearly articulated descriptions that can be readily replicated across studies. This is particularly important for the comparison of animal ecology across species and study sites. For example, the species included in our analysis inhabit different habitats in different locations (Figure 1) and adopt a variety of social behaviors. For instance, the beira (Dorcatragus megalotis) is a rare antelope that mostly lives in very small mixed-sex family groups in arid mountainous ecosystems in East Africa (Giotto, Laurent, Mohamed, Prevot, & Gerard, 2008). In contrast, the caribou/ reindeer (Rangifer tarandus) is a highly gregarious species with a circumpolar distribution extending across northern North America and Europe (Gunn, 2016). While the group size definitions of these two species might logically vary, there is little utility in having intraspecies variation as well. Furthermore, interspecies variation in life history traits and range dynamics complicate efforts to make species-level inferences for ecological and conservation purposes.

ACK N OWLED G M ENTS
We thank E. Tans of the Michigan State University library for assisting with the literature review. We also thank D. Kramer, E.
Liljestrand, R. Moll, and an anonymous reviewer for constructive comments on earlier drafts of the manuscript. We are grateful to K.
Quigley for her assistance with data analysis. HK was supported by a World Wildlife Fund Russell E Train Education For Nature fellowship (Agreement #SZ86). Project support was also provided by the National Geographic Society NGS-56533C-19.

CO N FLI C T O F I NTE R E S T
The authors report no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
Supplementary data are provided in the supporting information.