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Identifying latent structures underlying animal social organization is fundamental in animal ecology [ 1 ], as well as in the social sciences [ 2 ]. In order to infer the biological mechanisms underlying the emergence of complex animal societies, researchers have traditionally recorded animal social data in the multiple dimensions of animal societies; for example, spatial distances Funding: This study was mainly funded by the Japan Science and Technology Agency, Core Research for Evolutional Science and Technology 17941861 (#JPMJCR17A4) and partly by MEXT Grant-in-aid for Scientific Research on Innovative Areas #4903 (Evolinguistics), 17H06380. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. among group members, social relationships (male–female or mother–offspring relationships), and movements based on group decision making.

The recent update of computational models for social network analysis (SNA) enables quantitative evaluation of complex processes of social networks based using big data. The basic framework of SNA envisions multiple nodes as animals, viruses, people, or any other agents within the network and at its edges as a dyadic relation mathematically defined between the two nodes (e.g., [ 3–5 ]). The SNA aims to statistically link network structures with bottom-up rules defining dyadic relations, e.g., affiliations, friendships, proximities, co-occurrences, follower/followee, signal sender/receiver, or communications [ 6 ]. SNA provides a modern powerful interface for visualizing complex biological networks.

One major biological interest for SNA is statistical approximations of modular, clustered or hierarchical structures embedded in animal social groups [ 1, 7 ]. Doubtless, kinship is a basic concept in the theory of the socioecology (for a classical kickoff, e.g., [ 8 ]). A mother invests effort in her offspring, mother and offspring generally maintain proximity, and degrees of the social bonding are reflected by relatedness [ 9, 10 ]. Based on the cumulative effects of such relatedness, social structures are determined by additional social relations, such as male-female sexual interactions and male-male competition [ 11, 12 ]. Consequently, a wide variety of social roles in the animal group are recognized, and multi-layered clustered structures of the group emerge [ 1, 13–15 ]. Some metrics commonly implemented in the modern SNAs provide statistical indices for modularity, centrality or cohesiveness (e.g., [ 16 ]), and have been applied to actual observational data of animals.

For the practical applications of SNA to observational data, dyadic social interactive behaviors or distance-based proximities have been commonly used in ecological analyses of animal societies [ 3, 17 ]. Allogrooming is a typical example of dyadic social interaction that is widely observed in social mammals. Allogrooming is an altruistic behavior and an appropriate behavioral metric for evaluating affiliative interactions (e.g., [ 18–20 ]). Likewise, agonistic interactions, where dominant animals show aggression toward subordinate animals, are also interpretable and countable behaviors that can be used to characterize dominance hierarchies (e.g., [ 21–23 ]). Generally, in the case of dyadic social interactions, researchers calculate the occurrence frequencies of dyadic events using an observational rule; for example, counting the grooming occurrences and recording the identity of the groomer and groomee in a specific observational session. These data obtained for social interactions can be used to construct matrices of social relationship strength by scoring or weighting the obtained data of dyadic relationships [ 17 ]. However, despite the interpretable advantages of social relationships, there are certain disadvantages associated with such data. Behavioral-based metrics such as grooming or fighting are generally unsuitable for the automation of data acquisition or evaluation. Currently, at least, researchers must record animal behaviors via direct observation or video recording for data analysis. Additional disadvantages are the “specializations” of social behaviors; for example, grooming might not always be observed in insects, or we may have little knowledge regarding the agonistic interactions among some animals, thereby limiting the analysis. In contrast, distance-based data lack contextual information and are not perfectly linked to social relationships [ 24 ]. In the case of distance-based proximities, inter-individual distances are recorded using a regular cycle of sampling rates (e.g., recording the distance at 5-min intervals), and proximities are evaluated. Subsequently, a matrix of social relationships is generated in a similar manner, scoring or weighting the proximity. Given that close proximity is assumed to indicate an affiliative relationship, the thresholds of the specific distance defining the social “association” can be used to generate binary data (i.e., association or isolation), and an adjacency matrix is generated from a summation of the binary data [ 17 ]. These data are generally accepted to indirectly reflect social 2 / 16 affiliations [ 25 ]. Affiliated individuals may maintain proximity as typically seen in motheroffspring pairs. The recent advanced tracking methods using high-precision GPS (e.g., [ 26, 27 ]) or Bluetooth beacons (e.g., [ 28 ]) have strongly influenced location-based proximity metrics due to dramatic expansion of data for interactions among “trackable” animals. Realtime distance-based proximities among all animal agents empirically reveal core mechanisms underlying collective movement emergencies. Simultaneous tracking of multiple animals using wearable tags is technologically possible. However, perfect tracking of suitable numbers of animals in groups/units for analyses of collective movement are still limited to laboratory-based animals (e.g., [ 28, 29 ]) or capturable wild animals [ 30–32 ]. Thus, a key analytical step for SNA is selection of appropriate data, which researchers record massively, easily, reliably and precisely.

The main objectives of this study were (1) to propose a novel approach for obtaining observable data that has not been systematically applied in the estimation of animal social organization, and (2) to provide methodological validation for the proposed approach. The first objective is based on practicality, particularly with respect to those studying wild animals. Dyadic social interactive behaviors or distance-based proximities have been a golden standard used to infer animal social organizations, as mentioned above; however, those studying animal behavior often experience difficulty in obtaining large amounts of high-quality data for such dyadic social interactions or spatial proximity in wild animals. For example, it is extremely difficult to monitor complete behavioral activities, even if wearable sensors are available. Similarly, in most cases, experimental manipulations, such as artificial control of specific individual movements, are not possible for wild animals (for a discussion of the methodological issues, see [ 17 ]). Accordingly, researchers invariably search for alternative promising types of data, together with technological updates. For the generalized application of novel types of data, empirical evidence that can be used to validate the approaches is necessary, which could partly be achieved using numerical simulations.

In this study, another kind of testable data for the SNA is proposed, that is, “animal singlefile movement” generated by bottom-up rules in the theory of collective movements. This topic is currently of great interest in animal ecology (for a recent review, e.g., [ 33 ]). Typically in fish schools, bird flocks, insect swarms, or ungulate herds, large numbers of individual agents show highly-coordinated collective movements [ 34, 35 ]. Theoretically, collective movements do not rely on decision-making of specific individuals, e.g., a “leader”, but emerge in a bottom-up manner such as iterated interactions between animals, either directly (e.g. via visual cues) or indirectly (e.g. via trail formation).

Animal single-file movement, defined as serially ordered patterns of animals that are indirectly determined by degrees of inter-agent relations, is a promising target for data collection for linking SNA linking with recent discussions of collective movement by social animals. First, single-file movements are observable in many free-ranging animal species. Classically, social animals moving in single file provided an excellent opportunity to count group members inhabiting dense forests with poor visibility, and further to infer social structures. Extensive historical fieldwork reveals that such events provide information on latent key factors underlying animal social organizations, e.g., dominance hierarchy [ 36, 37 ], kin relationships [ 38 ], and physiological status, such as breeding cycle [ 39, 40 ]. Additionally, due to the recent human imposed threats such as roads, animals are often forced into singlefile formation to cross risky or dangerous places. Such an aspect of socio-spatial organization under highly risky situations has also been analyzed in meerkat [ 41 ] and elephant [ 42 ]. In fact, recent studies focusing on single-file movement and social system structure have examined several animal taxa, e.g., wolves, Canis lupus: [ 36 ]; zebra, Equus burchellii: [ 39 ], buffalo, Syncems cuffer: [ 40 ], chimpanzee, Pan troglodytes: [ 43 ], mandrill, Mandrillus sphinx: [ 44 ] 3 / 16 and spider monkey, Ateles geoffroyi: [ 45 ]. Second, animal single-file movement can be recorded without capture and release for attachment of location tags, simply by videorecording (e.g., camera-trappings). This advantage for studying collective movement avoids use of GPS collars that are a burden for free-ranging animals, and most cannot be used for threatened and endangered species [ 46 ]. Also, single-file movement is naturally observed even in zebra heading to water holes [ 39 ] or in wolves through snow [ 47 ]. Anywhere such single-file movements are often observable recently developed camera-trapping techniques [ 48 ] would enable collection of a valuable data set. Further, where animal movement is controllable in semi-free range conditions such as narrow gateways to feeders and water, another opportunity exists. Such single-file movement has been recorded for sheep, Ovis aries: [ 37 ]. Third, serial order patterns governed by collective movements allow behavioral ecologists to examine individual-based observation essential for documentation and measurement of animal behavior. Fourth, the methodological advantages listed above compensate for the disadvantages of other metrics commonly used in the previous studies, such as dyadic social interactive behaviors or distance-based proximities.

This study aimed to determine if movement order in single-file movements are informative and effective observations for the reconstruction of animal social structures using an agentbased computational simulation model, e.g., [ 49, 50 ]. An initial artificial 2-dimensional spatial distribution was developed using the simple assumption of clustered group structures. Animal agents in a group are composed of independent and dependent agents. Independent agents distribute spatially independently each other, while dependent agents distribute depending movements of independent agents. The artificial spatial distributions aim to represent clustered structures of agent locations—a coupling of “core” or “keystone” subjects and “subordinate” or “follower” subjects. Collective movements were governed by two simple rules, 1) initiators of the movement are randomly chosen, and 2) the next moving agent is always the nearest neighbor of the last moving agents. These bottom-up rules allowed simulation of “single-file movement” data. Finally, we visualized social networks and reconstructed clustered structures using a recent major SNA algorithm, the Louvain algorithm, for rapid unfolding of communities in large networks [ 51 ]. The current idea—that artificial agents are initially generated, collective movements are produced, and collective movements are used to evaluate social networks—is similar to a previous computer experiment [ 52 ]. The current simulation is more generalized. Parameter assumptions are minimum and used mixed normal distributions. Parameter conditions were sought where single-file movement data work well for reconstruction of the latent clustered structures and further discuss possibilities for practical applications in field investigations of wild animal societies.

The simulations described below can be used to examine whether individual-by-individual serially ordered movements, i.e., “animal single-file movements,” provide sufficient information to reconstruct the clustered organization that is typically believed to exist in animal social groups, such as those of primates. Our simulations adopt agent-based models and involve four main steps: (1) animal agents are distributed in two-dimensional space with latent cluster organizations; (2) these generated agents are serially aligned following a simple collective movement rule (generating the “single-file movements”); (3) the social network structure is computed using an association index defined by serial orders of animal singlefile movement; and (4) the cluster organization of the generated social network is evaluated. Fig 1 shows a schematic representation of the simulation process. The details of each step are described below. 4 / 16 Fig 1. Schematic illustration of the simulation process. In this example, the parameters were set as follows: nI = 5, nD = 5, σI = 10, σD = 1, nexp = 10. The simulation started from the spatial distributions of agents generated from one latent state of social group organization, determined by parameters of the mixed Gaussian processes, nI, nD, σI, σD (the two top layers). The “single-file movement” data sets were then generated using the process described in the section on ordered alignment of agents. The vertical chains of the 30 circles represent single-file movement (the number of each circle is the agent id). Adjacency matrices Gk for k 2 {1, 2, . . .10} were generated from orders in the single-file movement data set, and were convolved to a single adjacency matrix G, which was passed to the social network analysis. Finally, a social network graph was produced, with clustering of the local community (bottom graph). This flow is a single simulation process, which is run 1000 times.

Fig 4 is the contour plots of the calculated average score ÿr for some selected sets of parameter values. This suggests that the average score increases as parameters σI and nexp increases, just as expected. It is also observed that the score decreases as nI, the numbers of the independenter, increases. In contrast, it increases as nD, the numbers of the depender, increases. In summary, scores will be better with large σI, nexp, nD and small nI (expect for the case of nI = 1). In the cases of nexp = 30 and σI ÿ 5, scores were often perfect, i.e., ÿr ÿ 1. Thus, cluster size estimations were often successful, if animal single-file movements were observed 30 times.

We appreciate the profound comments and suggestions from Ichiro Tsuda, Aru Toyoda, and Takashi Morita. This study was performed under the Cooperative Research Program at KUPRI (2018-C-27, 2019-B-27).

Conceptualization: Hiroki Koda, Ikki Matsuda.

Data curation: Hiroki Koda.

Formal analysis: Hiroki Koda, Zin Arai.

Funding acquisition: Hiroki Koda, Ikki Matsuda.

Investigation: Hiroki Koda.

Methodology: Hiroki Koda, Zin Arai.

Project administration: Hiroki Koda, Ikki Matsuda. Resources: Hiroki Koda.

Validation: Hiroki Koda.

Visualization: Hiroki Koda.

Writing – original draft: Hiroki Koda, Zin Arai, Ikki Matsuda. 13 / 16 14 / 16 15 / 16