Although the definition of a multilevel society more or less varies among studies, there are three main conditions by which a multilevel society is recognized; (1) The existence of a stable core unit: members of the same unit are physically closer to each other than to individuals who are not [21,26,28,30,32]. Membership is usually very stable, and the composition does not change for months or even several years [27,39,40]; (2) Aggregation of multiple units: different units usually exhibit fission–fusion characteristics and gather to create a temporal multiple-unit group [27,33,34]; (3) Social relationships among units: associations among units are determined not only by environmental, but also by social factors. Certain units are more likely to associate with or avoid each other than for randomly interacting situations to occur [26,32,40]. When animals have more than two levels of social hierarchy, Conditions 2 and 3 are also applicable to higher-level social groups, and members of lower-level groups have stronger bonds than those of higher-level groups [25].

As mentioned in the above sections, most of the studies used the association index (AI), the ratio of inter-individual distance that is smaller than a certain threshold, and subsequent cluster analysis to verify that the subject species has a multilevel society [26,29,40,41]; however, the threshold for ascertaining AI is often determined without any objective basis (but see studies on golden snub-nosed monkeys [34]). In several cases, the results of clustering are supported by behavioral data, such as movement or membership stability [26]. However, the lack of a unified definition makes inter-population and species comparisons difficult. Drone observations can help obtain accurate positional data and enable a more quantitative assessment of the population structure of multilevel societies, which may facilitate more rigorous detection and comparisons among studies.

To date, there is only one case in which a drone was used to examine whether there is a multilevel society and to measure its social relationships [42]. Regarding the horses included in this study, more than 100 individuals were scattered over an area of several hundred meters. To capture all of them in one frame, a drone needs to fly at an altitude of over one hundred meters, which is too high for individual identification, and the distortion of the lens makes it difficult to calculate the exact distance. To solve these problems and to accurately calculate the identified positions, the present study applied the orthomosaic technique. An orthomosaic is a non-distorted map-like image created by connecting a series of successive photographs. Detailed 3D shape recovery is performed by: (1) Automatic acquisition of feature points; (2) Camera position and orientation estimation and calculation of three-dimensional coordinates of feature points; (3) Point cloud generation using multiview image measurement; (4) Automatic surface shape modeling [43,44,45]. Each image was captured at a low altitude of approximately 40–50 m, so that the resolution was sufficiently high for individual identification. The horse population was primarily identified by direct observation from the ground, and their features were matched with the aerial images. In addition, each pixel in the orthomosaic is embedded in the GPS information, which enables accurate distance measurements. This technique has been primarily used for vegetation [46,47,48], topographic surveys [49,50] and population surveys of wild animals [4,11,51]. Thus, it was the first attempt to apply it to animal social studies. Combined with individual identification, this orthomosaic method has the advantage of being able to monitor social associations in the long term by adding individual information on positional data, whereas previous drone studies could not track individuals.

This study indicates that different thresholds are necessary for the evaluation of intra- and inter-unit relationships. In measuring intra-unit relationships, it would be appropriate to set the threshold around the first peak of the histogram of inter-individual distances, whereas it should be around the second peak for the inter-unit relationship to be measured; otherwise, the network can become too sparse. Horses form a two-layered multilevel society (only core unit and second-level social organization), but for a three- or four-layered society, such as the gelada society, it is even more difficult to evaluate every type of proximity relationship with a single threshold. Obtaining continuous interindividual distances could provide objective reasoning for selecting the threshold and enable a more accurate assessment of stratified relationships in a complex society. Accurate inter-individual distance data are difficult to obtain by direct observations from the ground; thus, aerial observations from drones will contribute to a more precise evaluation and detection of multilevel societies.

Furthermore, the aerial observation provided positional information on individuals and units in a multiple-unit group. It would have been feasible to identify to whom an individual was close using the previous methodology; however, it was impossible to know where individuals were located in a group. The individual was positioned heterogeneously in a multi-unit group, and this also raises a question about their collective behavior because most of the models for such studies assumed a homogeneous inter-individual distance in a group. How do multilevel social animals maintain the cohesion of a specific group structure?