Estimating uncertainty and reliability of social network data using Bayesian inference

Modelling animal social networks: New solutions and future directions

Research Highlight: Ross, C. T., McElreath, R., & Redhead, D. (2023). Modelling animal network data in R using STRAND. Journal of Animal Ecology. https://doi.org/10.1111/1365-2656.14021. One of the most important insights in ecology over the past decade has been that the social connections among animals affect a wide range of ecological and evolutionary processes. However, despite over 20 years of study effort on this topic, generating knowledge from data on social associations and interactions remains fraught with problems. Redhead et al. present an R package-STRAND-that extends the current animal social network analysis toolbox in two ways. First, they provide a simple R interfaces to implement generative network models, which are an alternative to regression approaches that draw inference by simulating the data-generating process. Second, they implement these models in a Bayesian framework, allowing uncertainty in the observation process to be carried through to hypothesis testing. STRAND therefore fills an important gap for hypothesis testing using network data. However, major challenges remain, and while STRAND represents an important advance, generating robust results continues to require careful study design, considerations in terms of statistical methods and a plurality of approaches.

Comparative approaches in social network ecology

Social systems vary enormously across the animal kingdom, with important implications for ecological and evolutionary processes such as infectious disease dynamics, anti-predator defence, and the evolution of cooperation. Comparing social network structures between species offers a promising route to help disentangle the ecological and evolutionary processes that shape this diversity. Comparative analyses of networks like these are challenging and have been used relatively little in ecology, but are becoming increasingly feasible as the number of empirical datasets expands. Here, we provide an overview of multispecies comparative social network studies in ecology and evolution. We identify a range of advancements that these studies have made and key challenges that they face, and we use these to guide methodological and empirical suggestions for future research. Overall, we hope to motivate wider publication and analysis of open social network datasets in animal ecology.

Effect of behavioural sampling methods on local and global social network metrics: a case-study of three macaque species

Social network analysis (SNA) is a powerful, quantitative tool to measure animals' direct and indirect social connectedness in the context of social groups. However, the extent to which behavioural sampling methods influence SNA metrics remains unclear. To fill this gap, here we compare network indices of grooming, huddling, and aggression calculated from data collected from three macaque species through two sampling methods: focal animal sampling (FAS) and all-occurrences behaviour sampling (ABS). We found that measures of direct connectedness (degree centrality, and network density) were correlated between FAS and ABS for all social behaviours. Eigenvector and betweenness centralities were correlated for grooming and aggression networks across all species. By contrast, for huddling, we found a correlation only for betweenness centrality while eigenvector centralities were correlated only for the tolerant bonnet macaque but not so for the despotic rhesus macaque. Grooming and huddling network modularity and centralization were correlated between FAS and ABS for all but three of the eight groups. By contrast, for aggression network, we found a correlation for network centralization but not modularity between the sampling methodologies. We discuss how our findings provide researchers with new guidelines regarding choosing the appropriate sampling method to estimate social network metrics.

BISoN: A Bayesian Framework for Inference of Social Networks

Animal social networks are often constructed from point estimates of edge weights. In many contexts, edge weights are inferred from observational data, and the uncertainty around estimates can be affected by various factors. Though this has been acknowledged in previous work, methods that explicitly quantify uncertainty in edge weights have not yet been widely adopted, and remain undeveloped for many common types of data. Furthermore, existing methods are unable to cope with some of the complexities often found in observational data, and do not propagate uncertainty in edge weights to subsequent statistical analyses.We introduce a unified Bayesian framework for modelling social networks based on observational data. This framework, which we call BISoN, can accommodate many common types of observational social data, can capture confounds and model effects at the level of observations, and is fully compatible with popular methods used in social network analysis.We show how the framework can be applied to common types of data and how various types of downstream statistical analyses can be performed, including non-random association tests and regressions on network properties.Our framework opens up the opportunity to test new types of hypotheses, make full use of observational datasets, and increase the reliability of scientific inferences. We have made both an R package and example R scripts available to enable adoption of the framework.

Group-level differences in social network structure remain repeatable after accounting for environmental drivers

Individuals show consistent between-individual behavioural variation when they interact with conspecifics or heterospecifics. Such patterns might underlie emergent group-specific behavioural patterns and between-group behavioural differences. However, little is known about (i) how social and non-social drivers (external drivers) shape group-level social structures and (ii) whether animal groups show consistent between-group differences in social structure after accounting for external drivers. We used automated tracking to quantify daily social interactions and association networks in 12 colonies of zebra finches (Taeniopygia guttata). We quantified the effects of five external drivers (group size, group composition, ecological factors, physical environments and methodological differences) on daily interaction and association networks and tested whether colonies expressed consistent differences in day-to-day network structure after controlling for these drivers. Overall, we found that external drivers contribute significantly to network structure. However, even after accounting for the contribution of external drivers, there remained significant support for consistent between-group differences in both interaction (repeatability R: up to 0.493) and association (repeatability R: up to 0.736) network structures. Our study demonstrates how group-level differences in social behaviour can be partitioned into different drivers of variation, with consistent contributions from both social and non-social factors.

Changes in social interaction, social relatedness, and friendships in Education Outside the Classroom: A social network analysis

Introduction

Social interaction is associated with many effects on the psychological level of children such as mental health, self-esteem, and executive functions. Education Outside the Classroom (EOtC) describes regular curricular classes/lessons outside the school building, often in natural green and blue environments. Applied as a long-term school concept, EOtC has the potential to enable and promote social interaction. However, empirical studies on this topic have been somewhat scant.

Methods

One class in EOtC (N  = 24) and one comparison class (N = 26) were examined in this study to explore those effects. Statistical Actor-Oriented Models and Exponential Random Graph Models were used to investigate whether there are differences between EOtC and comparison class regarding changes over time in social interaction parameters; whether a co-evolution between social interaction during lessons and breaks and attendant social relatedness and friendships exists; whether students of the same gender or place of residence interact particularly often (homophily).

Results

Besides inconsistent changes in social interaction parameters, no co-evolutional associations between social interaction and social relatedness and friendships could be determined, but grouping was evident in EOtC. Both classes showed pronounced gender homophily, which in the case of EOtC class contributes to a fragmentation of the network over time.

Discussion

The observed effects in EOtC could be due to previously observed tendencies of social exclusion as a result of a high degree of freedom of choices. It therefore seems essential that in future studies not only the quality of the study design and instruments should be included in the interpretation - rather, the underlying methodological-didactic concept should also be evaluated in detail. At least in Germany, it seems that there is still potential for developing holistic concepts with regards to EOtC in order to maximize the return on the primarily organizational investment of implementing EOtC in natural environments.

Research Paradigm of Network Approaches in Construction Safety and Occupational Health

Construction safety accidents seriously threaten the lives and health of employees; however, the complexity of construction safety problems continues to increase. Network approaches have been widely applied to address accident mechanics. This study aims to review related studies on construction safety and occupational health (CSOH) and summarize the research paradigm of recent decades. We solicited 119 peer-reviewed journal articles and performed a bibliometric analysis as the foundation of the future directions, application bottlenecks, and research paradigm. (1) Based on the keyword cluster, future directions are divided into four layers: key directions, core themes, key problems, and important methods. (2) The network approaches are not independently applied in the CSOH research. It needs to rely on different theories or be combined with other methods and models. However, in terms of approach applications, there are still some common limitations that restrict its application and development. (3) The research paradigm of network analysis process can be divided into four stages: description, explanation, prediction, and control. When the same network method encounters different research objects, it focuses on different analysis processes and plays different roles.

Social responses to the natural loss of individuals in Barbary macaques

In recent years, there has been considerable interest in investigating how animal social structure is affected by the loss of individuals. This is often achieved using simulations that generate predictions regarding how the removal of ‘key’ individuals from a group affects network structure. However, little is known about the effects of such removals in wild and free-ranging populations, particularly the extent to which naturally occurring mortality events and the loss of a large proportion of individuals from a social group affects the overall structure of a social network. Here, we used data from a population of wild Barbary macaques (Macaca sylvanus) that was exposed to an exceptionally harsh winter, culminating in the death of 64% of the adults from two groups. We analysed how social interaction patterns among surviving individuals were affected by the natural loss of group members using social networks based on affiliative (i.e., grooming) and aggressive social interactions. We show that only the structure of the pre-decline grooming networks was conserved in the post-decline networks, suggesting that grooming, but not aggression networks are resilient against the loss of group members. Surviving group members were not significantly different from the non-survivors in terms of their affiliative and agonistic relationships, and did not form assorted communities in the pre-decline networks. Overall, our results suggest that in primates, patterns of affiliative interactions are more resilient to changes in group composition than aggressive interaction patterns, which tend to be used more flexibly in new conditions.

A new method for characterising shared space use networks using animal trapping data

Abstract

Studying the social behaviour of small or cryptic species often relies on constructing networks from sparse point-based observations of individuals (e.g. live trapping data). A common approach assumes that individuals that have been detected sequentially in the same trapping location will also be more likely to have come into indirect and/or direct contact. However, there is very little guidance on how much data are required for making robust networks from such data. In this study, we highlight that sequential trap sharing networks broadly capture shared space use (and, hence, the potential for contact) and that it may be more parsimonious to directly model shared space use. We first use empirical data to show that characteristics of how animals use space can help us to establish new ways to model the potential for individuals to come into contact. We then show that a method that explicitly models individuals’ home ranges and subsequent overlap in space among individuals (spatial overlap networks) requires fewer data for inferring observed networks that are more strongly correlated with the true shared space use network (relative to sequential trap sharing networks). Furthermore, we show that shared space use networks based on estimating spatial overlap are also more powerful for detecting biological effects. Finally, we discuss when it is appropriate to make inferences about social interactions from shared space use. Our study confirms the potential for using sparse trapping data from cryptic species to address a range of important questions in ecology and evolution.

Significance statement

Characterising animal social networks requires repeated (co-)observations of individuals. Collecting sufficient data to characterise the connections among individuals represents a major challenge when studying cryptic organisms—such as small rodents. This study draws from existing spatial mark-recapture data to inspire an approach that constructs networks by estimating space use overlap (representing the potential for contact). We then use simulations to demonstrate that the method provides consistently higher correlations between inferred (or observed) networks and the true underlying network compared to current approaches and requires fewer observations to reach higher correlations. We further demonstrate that these improvements translate to greater network accuracy and to more power for statistical hypothesis testing.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00265-022-03222-5.

Permutation tests for hypothesis testing with animal social network data: Problems and potential solutions

Permutation tests are widely used to test null hypotheses with animal social network data, but suffer from high rates of type I and II error when the permutations do not properly simulate the intended null hypothesis.

Two common types of permutations each have limitations. Pre‐network (or datastream) permutations can be used to control ‘nuisance effects’ like spatial, temporal or sampling biases, but only when the null hypothesis assumes random social structure. Node (or node‐label) permutation tests can test null hypotheses that include nonrandom social structure, but only when nuisance effects do not shape the observed network.

We demonstrate one possible solution addressing these limitations: using pre‐network permutations to adjust the values for each node or edge before conducting a node permutation test. We conduct a range of simulations to estimate error rates caused by confounding effects of social or non‐social structure in the raw data.

Regressions on simulated datasets suggest that this ‘double permutation’ approach is less likely to produce elevated error rates relative to using only node permutations, pre‐network permutations or node permutations with simple covariates, which all exhibit elevated type I errors under at least one set of simulated conditions. For example, in scenarios where type I error rates from pre‐network permutation tests exceed 30%, the error rates from double permutation remain at 5%.

The double permutation procedure provides one potential solution to issues arising from elevated type I and type II error rates when testing null hypotheses with social network data. We also discuss alternative approaches that can provide robust inference, including fitting mixed effects models, restricted node permutations, testing multiple null hypotheses and splitting large datasets to generate replicated networks. Finally, we highlight ways that uncertainty can be explicitly considered and carried through the analysis.

A guide to choosing and implementing reference models for social network analysis

Analysing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the observed data. Here we review a variety of randomization procedures that generate reference models for social network analysis. Reference models provide an expectation for hypothesis testing when analysing network data. We outline the key stages in producing an effective reference model and detail four approaches for generating reference distributions: permutation, resampling, sampling from a distribution, and generative models. We highlight when each type of approach would be appropriate and note potential pitfalls for researchers to avoid. Throughout, we illustrate our points with examples from a simulated social system. Our aim is to provide social network researchers with a deeper understanding of analytical approaches to enhance their confidence when tailoring reference models to specific research questions.

Reconstruction of plant-pollinator networks from observational data

Empirical measurements of ecological networks such as food webs and mutualistic networks are often rich in structure but also noisy and error-prone, particularly for rare species for which observations are sparse. Focusing on the case of plant-pollinator networks, we here describe a Bayesian statistical technique that allows us to make accurate estimates of network structure and ecological metrics from such noisy observational data. Our method yields not only estimates of these quantities, but also estimates of their statistical errors, paving the way for principled statistical analyses of ecological variables and outcomes. We demonstrate the use of the method with an application to previously published data on plant-pollinator networks in the Seychelles archipelago and Kosciusko National Park, calculating estimates of network structure, network nestedness, and other characteristics.

Reconstruction of plant–pollinator networks from observational data

Empirical measurements of ecological networks such as food webs and mutualistic networks are often rich in structure but also noisy and error-prone, particularly for rare species for which observations are sparse. Focusing on the case of plant–pollinator networks, we here describe a Bayesian statistical technique that allows us to make accurate estimates of network structure and ecological metrics from such noisy observational data. Our method yields not only estimates of these quantities, but also estimates of their statistical errors, paving the way for principled statistical analyses of ecological variables and outcomes. We demonstrate the use of the method with an application to previously published data on plant–pollinator networks in the Seychelles archipelago and Kosciusko National Park, calculating estimates of network structure, network nestedness, and other characteristics.

Influence of number of individuals and observations per individual on a model of community structure

Social network analysis is increasingly applied to understand animal groups. However, it is rarely feasible to observe every interaction among all individuals in natural populations. Studies have assessed how missing information affects estimates of individual network positions, but less attention has been paid to metrics that characterize overall network structure such as modularity, clustering coefficient, and density. In cases such as groups displaying fission-fusion dynamics, where subgroups break apart and rejoin in changing conformations, missing information may affect estimates of global network structure differently than in groups with distinctly separated communities due to the influence single individuals can have on the connectivity of the network. Using a bat maternity group showing fission-fusion dynamics, we quantify the effect of missing data on global network measures including community detection. In our system, estimating the number of communities was less reliable than detecting community structure. Further, reliably assorting individual bats into communities required fewer individuals and fewer observations per individual than to estimate the number of communities. Specifically, our metrics of global network structure (i.e., graph density, clustering coefficient, Rcom) approached the 'real' values with increasing numbers of observations per individual and, as the number of individuals included increased, the variance in these estimates decreased. Similar to previous studies, we recommend that more observations per individual should be prioritized over including more individuals when resources are limited. We recommend caution when making conclusions about animal social networks when a substantial number of individuals or observations are missing, and when possible, suggest subsampling large datasets to observe how estimates are influenced by sampling intensity. Our study serves as an example of the reliability, or lack thereof, of global network measures with missing information, but further work is needed to determine how estimates will vary with different data collection methods, network structures, and sampling periods.

Consistency of Social Interactions in Sooty Mangabeys and Chimpanzees

Predictability of social interactions can be an important measure for the social complexity of an animal group. Predictability is partially dependent on how consistent interaction patterns are over time: does the behavior on 1 day explain the behavior on another? We developed a consistency measure that serves two functions: detecting which interaction types in a dataset are so inconsistent that including them in further analyses risks introducing unexplained error; and comparatively quantifying differences in consistency within and between animal groups. We applied the consistency measure to simulated data and field data for one group of sooty mangabeys (Cercocebus atys atys) and to groups of Western chimpanzees (Pan troglodytes verus) in the Taï National Park, Côte d'Ivoire, to test its properties and compare consistency across groups. The consistency measures successfully identified interaction types whose low internal consistency would likely create analytical problems. Species-level differences in consistency were less pronounced than differences within groups: in all groups, aggression and dominance interactions were the most consistent, followed by grooming; spatial proximity at different levels was much less consistent than directed interactions. Our consistency measure can facilitate decision making of researchers wondering whether to include interaction types in their analyses or social networks and allows us to compare interaction types within and between species regarding their predictability.

How to make methodological decisions when inferring social networks

Social network analyses allow studying the processes underlying the associations between individuals and the consequences of those associations. Constructing and analyzing social networks can be challenging, especially when designing new studies as researchers are confronted with decisions about how to collect data and construct networks, and the answers are not always straightforward. The current lack of guidance on building a social network for a new study system might lead researchers to try several different methods and risk generating false results arising from multiple hypotheses testing. Here, we suggest an approach for making decisions when starting social network research in a new study system that avoids the pitfall of multiple hypotheses testing. We argue that best edge definition for a network is a decision that can be made using a priori knowledge about the species and that is independent from the hypotheses that the network will ultimately be used to evaluate. We illustrate this approach with a study conducted on a colonial cooperatively breeding bird, the sociable weaver. We first identified two ways of collecting data using different numbers of feeders and three ways to define associations among birds. We then evaluated which combination of data collection and association definition maximized (a) the assortment of individuals into previously known "breeding groups" (birds that contribute toward the same nest and maintain cohesion when foraging) and (b) socially differentiated relationships (more strong and weak relationships than expected by chance). This evaluation of different methods based on a priori knowledge of the study species can be implemented in a diverse array of study systems and makes the case for using existing, biologically meaningful knowledge about a system to help navigate the myriad of methodological decisions about data collection and network inference.

Predictability and variability of association patterns in sooty mangabeys

Abstract

In many group-living animal species, interactions take place in changing social environments, increasing the information processing necessary to optimize social decision-making. Communities with different levels of spatial and temporal cohesion should differ in the predictability of association patterns. While the focus in this context has been on primate species with high fission-fusion dynamics, little is known about the variability of association patterns in species with large groups and high temporal cohesion, where group size and the environment create unstable subgroups. Here, we use sooty mangabeys as a model species to test predictability on two levels: on the subgroup level and on the dyadic level. Our results show that the entirety of group members surrounding an individual is close to random in sooty mangabeys; making it unlikely that individuals can predict the exact composition of bystanders for any interaction. At the same time, we found predictable dyadic associations based on assortative mixing by age, kinship, reproductive state in females, and dominance rank; potentially providing individuals with the ability to partially predict which dyads can be usually found together. These results indicate that animals living in large cohesive groups face different challenges from those with high fission-fusion dynamics, by having to adapt to fast-changing social contexts, while unable to predict who will be close-by in future interactions. At the same time, entropy measures on their own are unable to capture the predictability of association patterns in these groups.

Significance statement

While the challenges created by high fission-fusion dynamics in animal social systems and their impact on the evolution of cognitive abilities are relatively well understood, many species live in large groups without clear spatio-temporal subgrouping. Nonetheless, they show remarkable abilities in considering their immediate social environment when making social decisions. Measures of entropy of association patterns have recently been proposed to measure social complexity across species. Here, we evaluate suggested entropy measures in sooty mangabeys. The high entropy of their association patterns would indicate that subgroup composition is largely random, not allowing individuals to prepare for future social environments. However, the existence of strong assortativity on the dyadic level indicates that individuals can still partially predict who will be around whom, even if the overall audience composition might be unclear. Entropy alone, therefore, captures social complexity incompletely, especially in species facing fast-changing social environments.

Life history stage explains behavior in a social network before and during the early breeding season in a cooperatively breeding bird

In species with stage-structured populations selection pressures may vary between different life history stages and result in stage-specific behaviors. We use life history stage to explain variation in the pre and early breeding season social behavior of a cooperatively breeding bird, the Florida scrub-jay (Aphelocoma coerulescens) using social network analysis. Life history stage explains much of the variation we observed in social network position. These differences are consistent with nearly 50 years of natural history observations and generally conform to a priori predictions about how individuals in different stages should behave to maximize their individual fitness. Where the results from the social network analysis differ from the a priori predictions suggest that social interactions between members of different groups are more important for breeders than previously thought. Our results emphasize the importance of accounting for life history stage in studies of individual social behavior.

Kinship and reproductive condition correlate with affiliation patterns in female southern Australian bottlenose dolphins

Social relationships in female mammals are usually determined by an interplay among genetic, endogenous, social and ecological factors that ultimately affect their lifetime reproductive success. However, few studies have attempted to control for, and integrate these factors, hampering our understanding of drivers underlying female sociality. Here, we used generalized affiliation indices, combined with social networks, reproductive condition, and genetic data to investigate drivers of associations in female southern Australian bottlenose dolphins. Our analysis is based on photo-identification and genetic data collected through systematic boat surveys over a two-year study period. Female dolphins formed preferred associations and social clusters which ranged from overlapping to discrete home ranges. Furthermore, matrilineal kinship and biparental relatedness, as well as reproductive condition, correlated with the strength of female affiliations. In addition, relatedness for both genetic markers was also higher within than between social clusters. The predictability of resources in their embayment environment, and the availability of same-sex relatives in the population, may have favoured the formation of social bonds between genetically related females and those in similar reproductive condition. This study highlights the importance of genetic, endogenous, social and ecological factors in determining female sociality in coastal dolphins.

Individual foraging variation drives social organization in bottlenose dolphins

Identifying foraging variation within a population and assessing its relationship with social structure is essential to increase knowledge about the evolution of social systems. Here, we investigated individual foraging variation in bottlenose dolphins and its potential influence on their social organization. We used generalized affiliation indices and applied social network analysis to data collected over four consecutive years of research in a coastal area subject to significant use and pressure by humans. Our findings revealed variation in foraging behavior among individual bottlenose dolphins, which in turn shapes their social organization. Our results indicated that individuals that frequently foraged within human-altered areas (i.e., shellfish farms) exhibited weaker Strength, Reach, and Affinity compared to others. These bottlenose dolphins profit from a reliable and easily located food source, which may increase their energy intake and interindividual competition. In contrast, individuals that foraged less frequently within the shellfish farms occupied a central position within the network and exhibited strong associations. These individuals may benefit from increased cooperation and reduced intragroup competition, thus increasing learning and information sharing, as they may face a patchy and irregular distribution of prey. We also demonstrated that bottlenose dolphins preferred to affiliate with other individuals with similar foraging strategies (i.e., homophily), which could promote, through time, a segregation of the population into behaviorally distinct groups. These findings provide valuable insight into the evolution of bottlenose dolphin social systems and their response to human-induced changes in the marine environment.

Choosing a sensible cut-off point: assessing the impact of uncertainty in a social network on the performance of NBDA

Network-based diffusion analysis (NBDA) has become a widely used tool to detect and quantify social learning in animal populations. NBDA infers social learning if the spread of a novel behavior follows the social network and hence relies on appropriate information on individuals' network connections. Most studies on animal populations, however, lack a complete record of all associations, which creates uncertainty in the social network. To reduce this uncertainty, researchers often use a certain threshold of sightings for the inclusion of animals (which is often arbitrarily chosen), as observational error decreases with increasing numbers of observations. Dropping individuals with only few sightings, however, can lead to information loss in the network if connecting individuals are removed. Hence, there is a trade-off between including as many individuals as possible and having reliable data. We here provide a tool in R that assesses the sensitivity of NBDA to error in the social network given a certain threshold for the inclusion of individuals. It simulates a social learning process through a population and then tests the power of NBDA to reliably detect social learning after introducing observational error into the social network, which is repeated for different thresholds. Our tool can help researchers using NBDA to select a threshold, specific to their data set, that maximizes power to reliably quantify social learning in their study population.

Genetic relatedness delineates the social structure of southern Australian bottlenose dolphins

Social relationships represent an adaptive behavioral strategy that can provide fitness benefits to individuals. Within mammalian societies, delphinids are known to form diverse grouping patterns and show a variety of social systems. However, how ecological and intrinsic factors have shaped the evolution of such diverse societies is still not well understood. In this study, we used photo-identification data and biopsy samples collected between March 2013 and October 2015 in Coffin Bay, a heterogeneous environment in South Australia, to investigate the social structure of southern Australian bottlenose dolphins (Tursiops cf. australis). Based on the data from 657 groups of dolphins, we used generalized affiliation indices, and applied social network and modularity methods to study affiliation patterns among individuals and investigate the potential presence of social communities within the population. In addition, we investigated genetic relatedness and kinship relationships within and between the communities identified. Modularity analysis revealed that the Coffin Bay population is structured into 2 similar sized, mixed-sex communities which differed in ranging patterns, affiliation levels and network metrics. Lagged association rates also indicated that nonrandom affiliations persisted over the study period. The genetic analyses suggested that there was higher relatedness, and a higher proportion of inferred full-sibs and half-sibs, within than between communities. We propose that differences in environmental conditions between the bays and kinship relationships are important factors contributing to the delineation and maintenance of this social structure.

Inferring influence and leadership in moving animal groups

Collective decision-making is a daily occurrence in the lives of many group-living animals, and can have critical consequences for the fitness of individuals. Understanding how decisions are reached, including who has influence and the mechanisms by which information and preferences are integrated, has posed a fundamental challenge. Here, we provide a methodological framework for studying influence and leadership in groups. We propose that individuals have influence if their actions result in some behavioural change among their group-mates, and are leaders if they consistently influence others. We highlight three components of influence (influence instances, total influence and consistency of influence), which can be assessed at two levels (individual-to-individual and individual-to-group). We then review different methods, ranging from individual positioning within groups to information-theoretic approaches, by which influence has been operationally defined in empirical studies, as well as how such observations can be aggregated to give insight into the underlying decision-making process. We focus on the domain of collective movement, with a particular emphasis on methods that have recently been, or are being, developed to take advantage of simultaneous tracking data. We aim to provide a resource bringing together methodological tools currently available for studying leadership in moving animal groups, as well as to discuss the limitations of current methodologies and suggest productive avenues for future research.This article is part of the theme issue 'Collective movement ecology'.

Evaluating empirical contact networks as potential transmission pathways for infectious diseases

Networks are often used to incorporate heterogeneity in contact patterns in mathematical models of pathogen spread. However, few tools exist to evaluate whether potential transmission pathways in a population are adequately represented by an observed contact network. Here, we describe a novel permutation-based approach, the network k-test, to determine whether the pattern of cases within the observed contact network are likely to have resulted from transmission processes in the network, indicating that the network represents potential transmission pathways between nodes. Using simulated data of pathogen spread, we compare the power of this approach to other commonly used analytical methods. We test the robustness of this technique across common sampling constraints, including undetected cases, unobserved individuals and missing interaction data. We also demonstrate the application of this technique in two case studies of livestock and wildlife networks. We show that the power of the k-test to correctly identify the epidemiologic relevance of contact networks is substantially greater than other methods, even when 50% of contact or case data are missing. We further demonstrate that the impact of missing data on network analysis depends on the structure of the network and the type of missing data.

Environmental disturbance increases social connectivity in a passerine bird

Individual level response to natural and anthropogenic disturbance represents an increasingly important, but as yet little understood, component of animal behavior. Disturbance events often alter habitat, which in turn can modify behaviors of individuals in affected areas, including changes in habitat use and associated changes in social structure. To better understand these relationships, we investigated aspects of habitat selection and social connectivity of a small passerine bird, the red-backed fairywren (Malurus melanocephalus), before vs. after naturally occurring fire disturbance in Northern Territory, Australia. We utilized a social network framework to evaluate changes in social dynamics pre- vs. post-fire. Our study covered the non-breeding season in two consecutive years in which fires occurred, and individuals whose habitat was affected and those that were not affected by fire. Individuals in habitat affected by fires had stronger social ties (i.e. higher weighted degree) after fires, while those that were in areas that were not affected by fire actually had lower weighted degree. We suggest that this change in social connections may be linked to habitat. Before fires, fairywrens used habitat that had similar grass cover to available habitat plots randomly generated within our study site. Fire caused a reduction in grass cover, and fairywrens responded by selecting habitat with higher grass cover relative to random plots. This study demonstrates how changes in habitat and/or resource availability caused by disturbance can lead to substantive changes in the social environment that individuals experience.

Network analysis of the hominin origin of Herpes Simplex virus 2 from fossil data

Herpes simplex virus 2 (HSV2) is a human herpesvirus found worldwide that causes genital lesions and more rarely causes encephalitis. This pathogen is most common in Africa, and particularly in central and east Africa, an area of particular significance for the evolution of modern humans. Unlike HSV1, HSV2 has not simply co-speciated with humans from their last common ancestor with primates. HSV2 jumped the species barrier between 1.4 and 3 MYA, most likely through intermediate but unknown hominin species. In this article, we use probability-based network analysis to determine the most probable transmission path between intermediate hosts of HSV2, from the ancestors of chimpanzees to the ancestors of modern humans, using paleo-environmental data on the distribution of African tropical rainforest over the last 3 million years and data on the age and distribution of fossil species of hominin present in Africa between 1.4 and 3 MYA. Our model identifies Paranthropus boisei as the most likely intermediate host of HSV2, while Homo habilis may also have played a role in the initial transmission of HSV2 from the ancestors of chimpanzees to P.boisei.

Male great tits assort by personality during the breeding season

Animal personalities can influence social interactions among individuals, and thus have major implications for population processes and structure. Few studies have investigated the significance of the social context of animal personalities, and such research has largely focused on the social organization of nonterritorial populations. Here we address the question of whether exploratory behaviour, a well-studied personality trait, is related to the social structure of a wild great tit, Parus major, population during the breeding season. We assayed the exploration behaviour of wild-caught great tits and then established the phenotypic spatial structure of the population over six consecutive breeding seasons. Network analyses of breeding proximity revealed that males, but not females, show positive assortment by behavioural phenotype, with males breeding closer to those of similar personalities. This assortment was detected when we used networks based on nearest neighbours, but not when we used the Thiessen polygon method where neighbours were defined from inferred territory boundaries. Further analysis found no relationship between personality assortment and local environmental conditions, suggesting that social processes may be more important than environmental variation in influencing male territory choice. This social organization during the breeding season has implications for the strength and direction of both natural and sexual selection on personality in wild animal populations.

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We assess whether a great tit breeding population is structured by personality.

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Network analyses were conducted on a 6-year data set from this wild bird population.

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Males show positive assortment, nesting nearer to similar personalities (bold/shy).

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This assortment was not found to be related to local environmental variation.

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We discuss implications for natural and sexual selection on personality in the wild.

A guide to null models for animal social network analysis

Null models are an important component of the social network analysis toolbox. However, their use in hypothesis testing is still not widespread. Furthermore, several different approaches for constructing null models exist, each with their relative strengths and weaknesses, and often testing different hypotheses.

In this study, I highlight why null models are important for robust hypothesis testing in studies of animal social networks. Using simulated data containing a known observation bias, I test how different statistical tests and null models perform if such a bias was unknown.

I show that permutations of the raw observational (or ‘pre‐network’) data consistently account for underlying structure in the generated social network, and thus can reduce both type I and type II error rates. However, permutations of pre‐network data remain relatively uncommon in animal social network analysis because they are challenging to implement for certain data types, particularly those from focal follows and GPS tracking.

I explain simple routines that can easily be implemented across different types of data, and supply R code that applies each type of null model to the same simulated dataset. The R code can easily be modified to test hypotheses with empirical data. Widespread use of pre‐network data permutation methods will benefit researchers by facilitating robust hypothesis testing.

Analysing animal social network dynamics: the potential of stochastic actor-oriented models

Animals are embedded in dynamically changing networks of relationships with conspecifics. These dynamic networks are fundamental aspects of their environment, creating selection on behaviours and other traits. However, most social network‐based approaches in ecology are constrained to considering networks as static, despite several calls for such analyses to become more dynamic.

There are a number of statistical analyses developed in the social sciences that are increasingly being applied to animal networks, of which stochastic actor‐oriented models (SAOMs) are a principal example. SAOMs are a class of individual‐based models designed to model transitions in networks between discrete time points, as influenced by network structure and covariates. It is not clear, however, how useful such techniques are to ecologists, and whether they are suited to animal social networks.

We review the recent applications of SAOMs to animal networks, outlining findings and assessing the strengths and weaknesses of SAOMs when applied to animal rather than human networks. We go on to highlight the types of ecological and evolutionary processes that SAOMs can be used to study.

SAOMs can include effects and covariates for individuals, dyads and populations, which can be constant or variable. This allows for the examination of a wide range of questions of interest to ecologists. However, high‐resolution data are required, meaning SAOMs will not be useable in all study systems. It remains unclear how robust SAOMs are to missing data and uncertainty around social relationships.

Ultimately, we encourage the careful application of SAOMs in appropriate systems, with dynamic network analyses likely to prove highly informative. Researchers can then extend the basic method to tackle a range of existing questions in ecology and explore novel lines of questioning.

Measuring the robustness of network community structure using assortativity

The existence of discrete social clusters, or 'communities', is a common feature of social networks in human and nonhuman animals. The level of such community structure in networks is typically measured using an index of modularity, Q. While modularity quantifies the degree to which individuals associate within versus between social communities and provides a useful measure of structure in the social network, it assumes that the network has been well sampled. However, animal social network data is typically subject to sampling errors. In particular, the associations among individuals are often not sampled equally, and animal social network studies are often based on a relatively small set of observations. Here, we extend an existing framework for bootstrapping network metrics to provide a method for assessing the robustness of community assignment in social networks using a metric we call community assortativity (rcom). We use simulations to demonstrate that modularity can reliably detect the transition from random to structured associations in networks that differ in size and number of communities, while community assortativity accurately measures the level of confidence based on the detectability of associations. We then demonstrate the use of these metrics using three publicly available data sets of avian social networks. We suggest that by explicitly addressing the known limitations in sampling animal social network, this approach will facilitate more rigorous analyses of population-level structural patterns across social systems.