Aerial drone observations identified a multilevel society in feral horses

The study of non-human multilevel societies can give us insights into how group-level relationships function and are maintained in a social system, but their mechanisms are still poorly understood. The aim of this study was to apply spatial association data obtained from drones to verify the presence of a multilevel structure in a feral horse society. We took aerial photos of individuals that appeared in pre-fixed areas and collected positional data. The threshold distance of the association was defined based on the distribution pattern of the inter-individual distance. The association rates of individuals showed bimodality, suggesting the presence of small social organizations or “units”. Inter-unit distances were significantly smaller than those in randomly replaced data, which showed that units associate to form a higher-level social organization or “herd”. Moreover, this herd had a structure where large mixed-sex units were more likely to occupy the center than small mixed-sex units and all-male-units, which were instead on the periphery. These three pieces of evidence regarding the existence of units, unit association, and stable positioning among units strongly indicated a multilevel structure in horse society. The present study contributes to understanding the functions and mechanisms of multilevel societies through comparisons with other social indices and models as well as cross-species comparisons in future studies.

recorded roughly half of the areas to reduce the duration of each observations. During the 30 minutes interval of the observations, we observed the field with binoculars and recorded when horses appeared to/disappeared from the field site. Sequential photos were taken by a camera deployed to a drone in regular RGB images (equipped with 12.35 MP sensor, 4000 × 3000 pixels). Focus, shutter speed, and IOS were set automatically. We took the sequential photos every 1-2 second/s so that forward overlap of each images became 60% at least. The data were stored on board in a microSD card.

The relationship of the inter-unit distance and direct interaction
We decided the threshold of inter-unit interaction as p2 = 122.1 m. To investigate this threshold was meaningful to the inter-unit relationships, we examined the direct interaction among units.
Most of the interaction we observed were a ʻritual' among males, which was the behavioural sequence starting from running up with each other, followed by sniffing, tossing of the head while squealing and striking with their force legs 6 , and sometime it escalated to the actual fighting including kicking, biting and chasing. We were able to identify a stallion ritual from the aerial photos because of the unusual proximity between males from different units.
While males were engaging themselves in the ritual, the females in the males' harem usually did not care and kept foraging. Thus, we considered the distance between the females represent the inter-unit distance when the males recognized each other and started the ritual.
We observed 17 male-male interaction, 6 of them occurred between harem males and the rest occurred between a harem male and a bachelor male. The mean ± SD of the inter-harem distance was 55.9 ± 31.9 m (range 22.4 -102.4 m). Although the sample size was small, 122.1 m roughly matched with the maximum distance of the interaction, thus we considered it is appropriate to use for the threshold.
Comparing the spatial structure of two periods.
We compared the network of two periods: June 6 th -July 4 th (Period 1, all units were observed in Zone 2) and July 5 th -July 10 th (Period 2, units were observed in both Zone 1 and 2). The average distance matrix of these two periods show quite high correlation matrix, where r = 0.99 (p < 0.001). Then, we averaged interindividual distances in each day, and calculated the correlation index for all pairs of the daily average distance matrix. According to the Mantel test with 9,999 replicates, all of them showed 5% level significance ( Figure S2a). Each correlation index of each dyad was separated into three categories: Period1-1 (when both of the days were in Period1), Period1-2 (when one was in Period1 and the other is in Period2), and Period2-2 (when both were in Period2). Kruskal-Wallis rank sum test showed significant difference among these three at p < 0.01 level (χ 2 = 50.51; Figure. S2b). Post hoc Dunn's test showed that the correlation of Period1-1 is higher than that of Period1-2 and Period2-2 (p < 0.01). We further compared the nearest unit distance in two period using Welch's test. The distance to nearest units were significantly smaller during Period 1 (mean ± SD: 35.0 ± 32.3 m) than Period 2 (54.4 ± 100.8m; t (980.53) = 5.77, p < 0.001)

Were the units with larger centrality located closer to the herd center?
According to the network analysis, AMUs had lower centrality than harems and larger units had higher centrality than smaller ones. We examined that larger harems were actually located in the central positions, while smaller harems and AMUs were in the periphery of the herd.
We selected the days that all the units were available (June 14 th , 18 th , 20 th , 21 st , 23 rd ), and in total 69 observation were used. We considered the average position of all the units as the centre of the herd. We calculated the distance from it and scored the rank (units with smaller rank is closer to the centre) for each unit in each observation. We first calculated the correlations of the distance from the center and the rank toward strength centrality and both showed negative correlations (r = -0.66 for both of the indices). ANOVA and post-hoc Tukey HSD test were also conducted under R environment to examine the distance from the center and the rank differ according to the unit size and type (harem or bachelor). ANOVA showed significant difference in both distance and rank among the categories (distance from the centre: F(8) = 12.34, p < 0.001; rank F(8) = 14.7, p < 0.001). Tukey's test indicated that AMUs and smaller harems tended to have larger distance from the centre and higher ranks ( Figure S3).   Figure S3. The results of ANOVA and post-hoc Tukey tests of (a) distance from the center and (b) the rank. Higher ranks mean the unit tends to be in the peripheral area of the herd. When two categories have different alphabets above the graph (for example, "a" and "c"), they have significant difference each other at 5% significance level. The graphs were created using R package 'multcomp' 8 .