Using multiplex networks to capture the multidimensional nature of social structure

The effect of social structure on vocal flexibility in monk parakeets

The social complexity hypothesis argues that communicative complexity arises as a result of social complexity, with this occurring through mechanisms including plasticity and selection. Most research to date has focused on ultimate drivers of repertoire size, for example finding that cooperative breeding species exhibit larger repertoires. Until this date, to our knowledge, no study has focused on individual-level drivers of vocal diversity. Here, we examine social networks and vocalizations in wild colonial-nesting monk parakeets (Myiopsitta monachus). We recorded social networks for 337 individuals, relatedness for 100 individuals and matched these with 5599 vocalizations from 229 individuals over 2 years. Overall, we found that all individuals exhibited high contact-call diversity; however, individual-level diversity increased with age in 2020 and with number of nest mates in 2021. Call similarity was not predicted by relatedness, but individuals with stronger affiliative bonds had more dissimilar calls, suggesting an active process to sound unique among close associates. Finally, females had more diverse repertoires, producing relatively fewer contact calls across years and individuals living in larger groups had more diverse repertoires in 2021. Our results demonstrate a multi-faceted social influence on call content, diversity and repertoire diversity, exhibiting how fine-scale variation in social structure can influence expressed vocal complexity.

Group identity without social interactions?

We present several arguments for the preeminence of social interactions in determining and giving shape to societies. In our view, a society can emerge from social interaction and relationship patterns without the need for establishing an a priori limit on who actually belongs to it. Markers of group identity are one element among many that allow societies to persist.

Chimpanzees employ context-specific behavioral strategies within fission-fusion societies

Fission-fusion social systems allow individuals to make flexible choices about where, with whom, and in what contexts to spend their time in response to competing social and ecological pressures. The ability for fission-fusion societies to support individual behavioral strategies that vary across contexts has been suggested, but the potential function of such context-specific social choices remains largely understudied. We adopted the concept of social niche construction to explore possible differences in social complexity at the individual and group level across feeding contexts. Specifically, we examined patterns of co-attendance across two common ecological contexts in wild Central African chimpanzees (Pan troglodytes troglodytes) in the Goualougo Triangle, Republic of Congo. From data compiled over 6 years, we used multidimensional social network analysis to study the patterns of co-attendance generated from 436 group scans at Ficus and 4527 visits to termite mounds. These two contexts were chosen, because they are both fixed spatial features across the landscape that serve as well-defined points to compare association patterns. We identified context-specific social niche construction in a fission-fusion chimpanzee society that produce different patterns of relationships and social complexity that are consistent in their expression over many years, and offer functional benefits. While enhancing our understanding of chimpanzee behavioral strategies, culture, and conservation, our investigation also indicates that the social niche construction framework aids in elucidating the evolutionary advantages of fission-fusion sociality by accounting for intra- and interindividual variability, cognition, and choice in newfound ways.

Exploring animal behaviour multilayer networks in immersive environments - a conceptual framework

Animal behaviour is often modelled as networks, where, for example, the nodes are individuals of a group and the edges represent behaviour within this group. Different types of behaviours or behavioural categories are then modelled as different yet connected networks which form a multilayer network. Recent developments show the potential and benefit of multilayer networks for animal behaviour research as well as the potential benefit of stereoscopic 3D immersive environments for the interactive visualisation, exploration and analysis of animal behaviour multilayer networks. However, so far animal behaviour research is mainly supported by libraries or software on 2D desktops. Here, we explore the domain-specific requirements for (stereoscopic) 3D environments. Based on those requirements, we provide a proof of concept to visualise, explore and analyse animal behaviour multilayer networks in immersive environments.

Collective signalling is shaped by feedbacks between signaller variation, receiver perception and acoustic environment in a simulated communication network

Communication takes place within a network of multiple signallers and receivers. Social network analysis provides tools to quantify how an individual's social positioning affects group dynamics and the subsequent biological consequences. However, network analysis is rarely applied to animal communication, likely due to the logistical difficulties of monitoring natural communication networks. We generated a simulated communication network to investigate how variation in individual communication behaviours generates network effects, and how this communication network's structure feeds back to affect future signalling interactions. We simulated competitive acoustic signalling interactions among chorusing individuals and varied several parameters related to communication and chorus size to examine their effects on calling output and social connections. Larger choruses had higher noise levels, and this reduced network density and altered the relationships between individual traits and communication network position. Hearing sensitivity interacted with chorus size to affect both individuals' positions in the network and the acoustic output of the chorus. Physical proximity to competitors influenced signalling, but a distinctive communication network structure emerged when signal active space was limited. Our model raises novel predictions about communication networks that could be tested experimentally and identifies aspects of information processing in complex environments that remain to be investigated. This article is part of the theme issue 'The power of sound: unravelling how acoustic communication shapes group dynamics'.

Motif-based community detection in heterogeneous multilayer networks

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

Modelling animal network data in R using STRAND

There have been recent calls for wider application of generative modelling approaches in applied social network analysis. At present, however, it remains difficult for typical end users-for example, field researchers-to implement generative network models, as there is a dearth of openly available software packages that make application of such models as simple as other, permutation-based approaches. Here, we outline the STRAND R package, which provides a suite of generative models for Bayesian analysis of animal social network data that can be implemented using simple, base R syntax. To facilitate ease of use, we provide a tutorial demonstrating how STRAND can be used to model proportion, count or binary network data using stochastic block models, social relation models or a combination of the two modelling frameworks. STRAND facilitates the application of generative network models to a broad range of data found in the animal social networks literature.

Social situations differ in their contribution to population-level social structure in griffon vultures

Social relationships among animals emerge from interactions in multiple ecological and social situations. However, we seldom ask how each situation contributes to the global structure of a population, and whether different situations contribute different information about social relationships and the position of individuals within the social fabric. Griffon vultures (Gyps fulvus) interact socially in multiple situations, including communal roosting, joint flights, and co-feeding. These social interactions can influence population-level outcomes, such as disease transmission and information sharing that determine survival and response to changes. We examined the unique contribution of each social and ecological situation to the social structure of the population and individuals' positions within the overall social network using high-resolution GPS tracking. We found that the number of individuals each vulture interacted with (degree) was best predicted by diurnal interactions-both during flights and on the ground (such as when feeding). However, the strength of social bonds, that is, the number of interactions an individual had (strength), was best predicted by interactions on the ground-both during the day (e.g., while feeding) and at night (e.g., while roosting) but not by interactions while flying. Thus, social situations differ in their impact on the relationships that individuals form. By incorporating the ecological situations in which social interactions occur we gain a more complete view of how social relationships are formed and which situations are important for different types of interactions.

Overview of methods for characterization and visualization of a protein-protein interaction network in a multi-omics integration context

At the heart of the cellular machinery through the regulation of cellular functions, protein-protein interactions (PPIs) have a significant role. PPIs can be analyzed with network approaches. Construction of a PPI network requires prediction of the interactions. All PPIs form a network. Different biases such as lack of data, recurrence of information, and false interactions make the network unstable. Integrated strategies allow solving these different challenges. These approaches have shown encouraging results for the understanding of molecular mechanisms, drug action mechanisms, and identification of target genes. In order to give more importance to an interaction, it is evaluated by different confidence scores. These scores allow the filtration of the network and thus facilitate the representation of the network, essential steps to the identification and understanding of molecular mechanisms. In this review, we will discuss the main computational methods for predicting PPI, including ones confirming an interaction as well as the integration of PPIs into a network, and we will discuss visualization of these complex data.

Not just females: the socio-ecology of social interactions between spider monkey males

Male-male relationships are mostly characterized by competition. However, males also cooperate with one another if socio-ecological conditions are suitable. Due to their male philopatry, the need for cooperation in home range defence and high degree of fission-fusion dynamics, spider monkeys provide an opportunity to investigate how male-male interactions are associated with socio-ecological factors, such as the presence of potentially receptive females, the degree of food availability and the likelihood of home range defence. We tested predictions about changes in social interactions between wild spider monkey males in relation to these factors. First, males did not change their interaction patterns when potentially receptive females were in the subgroup compared to when they were absent. Second, males tended to be less tolerant of one another when feeding, but spent more time grooming, in contact and proximity with one another when food availability was lower than when it was higher. Third, males exchanged fewer embraces, spent less time grooming, in proximity and in contact with one another, and spent more time vigilant at the home range boundary area than at other locations. Our findings contribute to the understanding of social flexibility and the importance of considering males in socio-ecological models of any group-living species.

Measuring dominance certainty and assessing its impact on individual and societal health in a nonhuman primate model: a network approach

The notion of dominance is ubiquitous across the animal kingdom, wherein some species/groups such relationships are strictly hierarchical and others are not. Modern approaches for measuring dominance have emerged in recent years taking advantage of increased computational power. One such technique, named Percolation and Conductance (Perc), uses both direct and indirect information about the flow of dominance relationships to generate hierarchical rank order that makes no assumptions about the linearity of these relationships. It also provides a new metric, known as 'dominance certainty', which is a complimentary measure to dominance rank that assesses the degree of ambiguity of rank relationships at the individual, dyadic and group levels. In this focused review, we will (i) describe how Perc measures dominance rank while accounting for both nonlinear hierarchical structure as well as sparsity in data-here we also provide a metric of dominance certainty estimated by Perc, which can be used to compliment the information dominance rank supplies; (ii) summarize a series of studies by our research team reflecting the importance of 'dominance certainty' on individual and societal health in large captive rhesus macaque breeding groups; and (iii) provide some concluding remarks and suggestions for future directions for dominance hierarchy research. This article is part of the theme issue 'The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies'.

Multilayer social networks reveal the social complexity of a cooperatively breeding bird

The social environment of individuals affects various evolutionary and ecological processes. Their social environment is affected by individual and environmental traits. We assessed the effects of these traits on nodes and dyads in six layers of networks of Arabian babblers, representing different interaction types. Additionally, we tested how traits affect social niches in the multilayer networks using the t-distributed stochastic neighbor embedding (tSNE) dimensionality reduction algorithm. The effect of group size and season was similar across network layers, but individual traits had different effects on different layers. Additionally, we documented assortativity with respect to individual traits in the dominance display and allopreening networks. The joint analysis of all six layers revealed that most traits did not affect individuals' social niches. However, older individuals occupied fewer social niches than younger ones. Our results suggest that multilayer social networks are an important tool for understanding the complex social systems of cooperative breeders and intragroup interactions.

Social network changes during the development of immature capuchin monkeys (Sapajus spp.)

Immature indivuduals influence the formation and maintenance of social relationships within groups in diverse ways. Because of the increased interest of group members toward newborns, lactating females may use infants as social tools to temporally gain rank positions in matrilineal societies, and differential support received by the mothers may bias the network of immatures born to females of different ranks. In this study, we investigated the changes in proximity, grooming, play, and agonism networks of lactating females and immatures of different developmental periods, sex, and mothers' dominance rank. A semi-free-ranging group of 22 capuchin monkeys (Sapajus spp) was monitored for 12 months, totaling over 300 hours of observation. During this period, the age changes of 13 immatures were monitored and recorded. Best regression models showed that an increased number of grooming partners while lactating did not translate into changes in the proximity or agonistic network positions for females. Age was the main predictor of social network changes, while sex had a minor influence on the play network and no influence on the grooming or agonistic networks. Finally, mothers' rank predicted differences in the affiliative but not the agonistic social network. This pattern points to a more affiliative and individual-based rather than agonistic and nepotism-based strategy for social network insertion, which can be explained by the decreased competition faced by the focal group and by the behavioral flexibility of the clade.

MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach

Network embedding approaches are gaining momentum to analyse a large variety of networks. Indeed, these approaches have demonstrated their effectiveness in tasks such as community detection, node classification, and link prediction. However, very few network embedding methods have been specifically designed to handle multiplex networks, i.e. networks composed of different layers sharing the same set of nodes but having different types of edges. Moreover, to our knowledge, existing approaches cannot embed multiple nodes from multiplex-heterogeneous networks, i.e. networks composed of several multiplex networks containing both different types of nodes and edges. In this study, we propose MultiVERSE, an extension of the VERSE framework using Random Walks with Restart on Multiplex (RWR-M) and Multiplex-Heterogeneous (RWR-MH) networks. MultiVERSE is a fast and scalable method to learn node embeddings from multiplex and multiplex-heterogeneous networks. We evaluate MultiVERSE on several biological and social networks and demonstrate its performance. MultiVERSE indeed outperforms most of the other methods in the tasks of link prediction and network reconstruction for multiplex network embedding, and is also efficient in link prediction for multiplex-heterogeneous network embedding. Finally, we apply MultiVERSE to study rare disease-gene associations using link prediction and clustering. MultiVERSE is freely available on github at https://github.com/Lpiol/MultiVERSE .

New dimensions for animal communication networks: space and time

Communication is a social process and usually occurs in a network of signalers and receivers. While social network analysis has received enormous recent attention from animal behaviorists, there have been relatively few attempts to apply these techniques to communication networks. Communication networks have the potential to offer novel insights into social network studies, and yet are especially challenging subjects, largely because of their unique spatiotemporal characteristics. Namely, signals propagate through the environment, often dissociating from the body of the signaler, to influence receiver behavior. The speed of signal propagation and the signal's active space will affect the congruence of communication networks and other types of social network; in extreme cases the signal may persist and only first be detected long after the signaler has left the area. Other signals move more rapidly and over greater distances than the signaler could possibly move to reach receivers. We discuss the spatial and temporal consequences of signaling in networks and highlight the distinction between the physical location of the signaler and the spread of influence of its signals, the effects of signal modality and receiver sensitivity on communication network properties, the potential for feedbacks between network layers, and approaches to analyzing spatial and temporal change in communication networks in conjunction with other network layers.

A framework to evaluate whether to pool or separate behaviors in a multilayer network

A multilayer network approach combines different network layers, which are connected by interlayer edges, to create a single mathematical object. These networks can contain a variety of information types and represent different aspects of a system. However, the process for selecting which information to include is not always straightforward. Using data on 2 agonistic behaviors in a captive population of monk parakeets (Myiopsitta monachus), we developed a framework for investigating how pooling or splitting behaviors at the scale of dyadic relationships (between 2 individuals) affects individual- and group-level social properties. We designed 2 reference models to test whether randomizing the number of interactions across behavior types results in similar structural patterns as the observed data. Although the behaviors were correlated, the first reference model suggests that the 2 behaviors convey different information about some social properties and should therefore not be pooled. However, once we controlled for data sparsity, we found that the observed measures corresponded with those from the second reference model. Hence, our initial result may have been due to the unequal frequencies of each behavior. Overall, our findings support pooling the 2 behaviors. Awareness of how selected measurements can be affected by data properties is warranted, but nonetheless our framework disentangles these efforts and as a result can be used for myriad types of behaviors and questions. This framework will help researchers make informed and data-driven decisions about which behaviors to pool or separate, prior to using the data in subsequent multilayer network analyses.

Using multilayer network analysis to explore the temporal dynamics of collective behavior

Social organisms often show collective behaviors such as group foraging or movement. Collective behaviors can emerge from interactions between group members and may depend on the behavior of key individuals. When social interactions change over time, collective behaviors may change because these behaviors emerge from interactions among individuals. Despite the importance of, and growing interest in, the temporal dynamics of social interactions, it is not clear how to quantify changes in interactions over time or measure their stability. Furthermore, the temporal scale at which we should observe changes in social networks to detect biologically meaningful changes is not always apparent. Here we use multilayer network analysis to quantify temporal dynamics of social networks of the social spider Stegodyphus dumicola and determine how these dynamics relate to individual and group behaviors. We found that social interactions changed over time at a constant rate. Variation in both network structure and the identity of a keystone individual was not related to the mean or variance of the collective prey attack speed. Individuals that maintained a large and stable number of connections, despite changes in network structure, were the boldest individuals in the group. Therefore, social interactions and boldness are linked across time, but group collective behavior is not influenced by the stability of the social network. Our work demonstrates that dynamic social networks can be modeled in a multilayer framework. This approach may reveal biologically important temporal changes to social structure in other systems.

Multilayer network analyses as a toolkit for measuring social structure

The formalization of multilayer networks allows for new ways to measure sociality in complex social systems, including groups of animals. The same mathematical representation and methods are widely applicable across fields and study systems, and a network can represent drastically different types of data. As such, in order to apply analyses and interpret the results in a meaningful way the researcher must have a deep understanding of what their network is representing and what parts of it are being measured by a given analysis. Multilayer social networks can represent social structure with more detail than is often present in single layer networks, including multiple "types" of individuals, interactions, or relationships, and the extent to which these types are interdependent. Multilayer networks can also encompass a wider range of social scales, which can help overcome complications that are inherent to measuring sociality. In this paper, I dissect multilayer networks into the parts that correspond to different components of social structures. I then discuss common pitfalls to avoid across different stages of multilayer network analyses-some novel and some that always exist in social network analysis but are magnified in multi-layer representations. This paper serves as a primer for building a customized toolkit of multilayer network analyses, to probe components of social structure in animal social systems.

The consistency of individual centrality across time and networks in wild vervet monkeys

Previous primate social network studies largely limited their focus to grooming and/or aggression networks, particularly among adult females. In addition, the consistency of individuals' network centrality across time and/or different networks has received little attention, despite this being critical for a global understanding of dynamic social structure. Here, we analyzed the grooming, aggression, and play social networks of a group of 26-28 wild vervet monkeys (Chlorocebus pygerythrus), including adults and juveniles, over two periods of 6 months. We collected data on grooming, play, and aggression using focal animal sampling with instantaneous recording and ad libitum sampling. We examined whether individuals' network centralities were consistent over the two periods and across networks, as well as the effect of age, sex, and dominance rank on three individual centrality metrics in each network and within each study period. We found that individuals were quite consistent in their network position from 1 year to the next despite changes in group composition. However, their network centralities were not correlated across networks, except for Strength and weighted Eigenvector centrality between grooming and aggression networks. We also found that in the aggression network, high-rankers showed the highest centrality in most network metrics (e.g., Degree, Strength, and Eigenvector centrality) and compared to males, females were most central in 2017 but not in 2018. In the grooming network, high-ranking females had the highest Eigenvector centrality, whereas in the play network, juvenile males had the highest Eigenvector centrality. Our findings corroborate previous findings on vervet monkeys. In addition, they show that individuals' network centralities may vary among networks and over time; thus highlighting the effect of sociodemographics and behaviors' functions on the group level dynamics of social behavior.

Assessing the sociability of former pet and entertainment chimpanzees by using multiplex networks

Advances in the field of social network analysis facilitate the creation of multiplex networks where several interaction types can be analysed simultaneously. In order to test the potential benefits of this approach, we investigated the sociability of atypically raised chimpanzees by constructing and analysing 4-layered multiplex networks of two groups of former pet and entertainment chimpanzees (Pan troglodytes). These networks are based on four social interaction types (stationary vicinity, affiliative behaviour, allogrooming, passive close proximity) representing low- to high-level interaction types in terms of sociability. Using the tools provided by the MuxViz software, we could assess and compare the similarity and information gain of each these social interaction types. We found some social interaction types to be more similar than other ones. However, each social interaction type imparted different information. We also tested for a possible impact of the chimpanzees’ biographical background on the social interaction types and found affiliative behaviour as well as allogrooming to be affected by adverse early life experiences. We conclude that this multiplex approach provides a more realistic framework giving detailed insight into the sociability of these chimpanzees and can function as a tool to support captive care management decisions.

Social Network Analysis of a Chimpanzee (Pan troglodytes) Group in Captivity Following the Integration of a New Adult Member

Management of primates in captivity often presents the challenge of introducing new individuals into a group, and research investigating the stability of the social network in the medium term after the introduction can help inform management decisions. We investigated the behavior of a group of chimpanzees (Pan troglodytes) housed at Chester Zoo, UK over 12 months (divided into three periods of 4 months) following the introduction of a new adult female. We recorded grooming, proximity, other affiliative behaviors, and agonistic behaviors and used social network analysis to investigate the stability, reciprocity, and structure of the group, to examine the effect of rearing history on grooming network position and the role of sex in agonistic behavior. Both the grooming and agonistic networks correlated across all three periods, while affiliative networks correlated only between periods 2 and 3. Males had significantly higher out-degree centrality in agonistic behaviors than females, indicating that they carried out agonistic behaviors more often than females. There was no significant difference in centrality between hand-reared and mother-reared chimpanzees. Overall, the group structure was stable and cohesive during the first year after the introduction of the new female, suggesting that this change did not destabilize the group. Our findings highlight the utility of social network analysis in the study of primate sociality in captivity, and how it can be used to better understand primate behavior following the integration of new individuals.

Network analysis as a tool to understand social development in spider monkeys

The emerging field of network science has demonstrated that an individual's connectedness within their social network has cascading effects to other dimensions of life. Like humans, spider monkeys live in societies with high fission-fusion dynamics, and are remarkably social. Social network analysis (SNA) is a powerful tool for quantifying connections that may vary as a function of initiating or receiving social behaviors, which has been described as shifting social roles. In primatology, the SNA literature is dominated by work in catarrhines, and has yet to be applied to the study of development in a platyrrhine model. Here, SNA was utilized in combination with R-Index social role calculation to characterize social interaction patterns in juvenile and adult Colombian spider monkeys (Ateles fusciceps rufiventris). Connections were examined across five behaviors: embrace, face-embrace, grooming, agonism, and tail-wrapping from 186 hr of observation and four network metrics. Mann-Whitney U tests were utilized to determine differences between adult and juvenile social network patterns for each behavior. Face-embrace emerged as the behavior with different network patterns for adults and juveniles for every network metric. With regard to social role, juveniles were receivers, not initiators, for embrace, face-embrace, and grooming (ps < .05). Network and social role differences are discussed in light of social development and aspects of the different behaviors.

Collective Computation in Animal Fission-Fusion Dynamics

Recent work suggests that collective computation of social structure can minimize uncertainty about the social and physical environment, facilitating adaptation. We explore these ideas by studying how fission-fusion social structure arises in spider monkey (Ateles geoffroyi) groups, exploring whether monkeys use social knowledge to collectively compute subgroup size distributions adaptive for foraging in variable environments. We assess whether individual decisions to stay in or leave subgroups are conditioned on strategies based on the presence or absence of others. We search for this evidence in a time series of subgroup membership. We find that individuals have multiple strategies, suggesting that the social knowledge of different individuals is important. These stay-leave strategies provide microscopic inputs to a stochastic model of collective computation encoded in a family of circuits. Each circuit represents an hypothesis for how collectives combine strategies to make decisions, and how these produce various subgroup size distributions. By running these circuits forward in simulation we generate new subgroup size distributions and measure how well they match food abundance in the environment using transfer entropies. We find that spider monkeys decide to stay or go using information from multiple individuals and that they can collectively compute a distribution of subgroup size that makes efficient use of ephemeral sources of nutrition. We are able to artificially tune circuits with subgroup size distributions that are a better fit to the environment than the observed. This suggests that a combination of measurement error, constraint, and adaptive lag are diminishing the power of collective computation in this system. These results are relevant for a more general understanding of the emergence of ordered states in multi-scale social systems with adaptive properties-both natural and engineered.

The multidimensionality of female mandrill sociality-A dynamic multiplex network approach

The structure and dynamics of primate social groups are shaped by the social relationships of its members. These relationships are based on different types of interactions and vary in relation to the identity of the interactants and over time. Social network analysis tools represent a powerful and comprehensive method to characterise social interactions and recent methodological advances now allow the study of the multidimensionality of sociality via multilayer networks that incorporate multiple types of interactions. Here, we use a multidimensional network approach to investigate the multidimensionality of sociality of females in a captive group of mandrills. We constructed two multiplex networks based on agonistic, proximity and grooming interactions of 6-7 mature females to analyse the multidimensionality of relationships within two independent observation periods; and three multiplex networks (one for each interaction type) to examine how relationships changed between periods. Within each period, different individuals were the most central in each layer and at the multiplex level, and different layers (i.e., interaction types) contributed non-redundant information to the multilayer structure. Across periods, relationships based on the same interaction type also contained non-redundant information. These results indicate that female mandrills engage in multidimensional and dynamic relationships, suggesting that in order to represent the full complexity of relationships, networks need to be constructed from more than a single type of interaction and across time. Our results provide evidence for the potential value of the multilayer network approach to characterise the multidimensionality of primate sociality.

A multiplex centrality metric for complex social networks: sex, social status, and family structure predict multiplex centrality in rhesus macaques

Members of a society interact using a variety of social behaviors, giving rise to a multi-faceted and complex social life. For the study of animal behavior, quantifying this complexity is critical for understanding the impact of social life on animals' health and fitness. Multilayer network approaches, where each interaction type represents a different layer of the social network, have the potential to better capture this complexity than single layer approaches. Calculating individuals' centrality within a multilayer social network can reveal keystone individuals and more fully characterize social roles. However, existing measures of multilayer centrality do not account for differences in the dynamics and functionality across interaction layers. Here we validate a new method for quantifying multiplex centrality called consensus ranking by applying this method to multiple social groups of a well-studied nonhuman primate, the rhesus macaque. Consensus ranking can suitably handle the complexities of animal social life, such as networks with different properties (sparse vs. dense) and biological meanings (competitive vs. affiliative interactions). We examined whether individuals' attributes or socio-demographic factors (sex, age, dominance rank and certainty, matriline size, rearing history) were associated with multiplex centrality. Social networks were constructed for five interaction layers (i.e., aggression, status signaling, conflict policing, grooming and huddling) for seven social groups. Consensus ranks were calculated across these five layers and analyzed with respect to individual attributes and socio-demographic factors. Generalized linear mixed models showed that consensus ranking detected known social patterns in rhesus macaques, showing that multiplex centrality was greater in high-ranking males with high certainty of rank and females from the largest families. In addition, consensus ranks also showed that females from very small families and mother-reared (compared to nursery-reared) individuals were more central, showing that consideration of multiple social domains revealed individuals whose social centrality and importance might otherwise have been missed.

Ecological and social determinants of association and proximity patterns in the fission-fusion society of spider monkeys (Ateles geoffroyi)

Some social species exhibit high levels of fission-fusion dynamics (FFD) that improve foraging efficiency. In this study, we shed light on the way that FFD allows animal groups to cope with fluctuations in fruit availability. We explore the relative contribution of fruit availability and social factors like sex in determining association and proximity patterns in spider monkeys. We tested the influence of fruit availability and social factors on the association and proximity patterns using three-year data from a group of spider monkeys in the Yucatan Peninsula of Mexico. We identified subgroup members and estimated their Interindividual distances through instantaneous scan sampling. We evaluated fruit availability by monitoring the phenology of the 10 most important food tree species for spider monkeys in the study site. Social network analyses allowed us to evaluate association and proximity patterns in subgroups. We showed that association patterns vary between seasons, respond to changes in fruit availability, and are influenced by the sex of individuals, likely reflecting biological and behavioral differences between sexes and the interplay between ecological and social factors. In contrast, proximity patterns were minimally affected by changes in fruit availability, suggesting that social factors are more important than food availability in determining cohesion within subgroups.

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as multilayer network analysis, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour through connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population and evolutionary levels of organization. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.

The dynamics of grooming interactions: maintenance of partner choice and the consequences of demographic variation for female mandrills

A large body of evidence suggests that female Old World monkeys maintain selective long-term grooming interactions with fitness benefits. The last two decades have produced evidence that the regulation of social interactions among primates can be, in part, explained by the Biological Markets theory, with grooming behaviour as the focus of these studies. Grooming facilitates bonding between individuals, constituting an essential part of the regulation of social relationships among female cercopithecids. In contrast to the well-studied baboons (Papio spp), knowledge about the nature of grooming interactions and their regulation is generally lacking for the large, terrestrial species of mandrills (Mandrillus sphinx). We used a combination of social network analysis tools and well-established methods for assessing partner diversity and reciprocity to characterise grooming networks, partner choice and patterns of trade (be groomed, give grooming) among females in a captive group of mandrills, both within and across two separate observation periods. Our results suggest that, even though the relatively stable conditions of captivity allowed the studied females to maintain selective grooming interactions across time, small scale demographic changes affected the grooming dynamics of the group in accordance with the expectations of the Biological Markets theory. In particular, the maturation and consequent integration of a high ranking female into the group's grooming network from one period to the next resulted in a more pronounced effect of rank on the regulation of grooming interactions. In addition, the influence of the maturation of a dependent infant on the grooming interactions of his mother were evident between periods. Our results also demonstrate that grooming networks are dynamic and that high ranking individuals are not necessarily the most central in grooming networks. Finally, we discuss the potential of social network analysis to identify cases of social exclusion and its consequences for captive management.