Determining association networks in social animals: choosing spatial–temporal criteria and sampling rates

Social Network Analysis has become an important methodological tool for advancing our understanding of human and animal group behaviour. However, researchers tend to rely on arbitrary distance and time measures when defining ‘contacts’ or ‘associations’ between individuals based on preliminary observation. Otherwise, criteria are chosen on the basis of the communication range of sensor devices (e.g. bluetooth communication ranges) or the sampling frequencies of collection devices (e.g. Global Positioning System devices). Thus, researchers lack an established protocol for determining both relevant association distances and minimum sampling rates required to accurately represent the network structure under investigation. In this paper, we demonstrate how researchers can use experimental and statistical methods to establish spatial and temporal association patterns and thus correctly characterise social networks in both time and space. To do this, we first perform a mixing experiment with Merino sheep (Ovis aries) and use a community detection algorithm that allows us to identify the spatial and temporal distance at which we can best identify clusters of previously familiar sheep. This turns out to be within 2–3 m of each other for at least 3 min. We then calculate the network graph entropy rate—a measure of ease of spreading of information (e.g. a disease) in a network—to determine the minimum sampling rate required to capture the variability observed in our sheep networks during distinct activity phases. Our results indicate the need for sampling intervals of less than a minute apart. The tools that we employ are versatile and could be applied to a wide range of species and social network datasets, thus allowing an increase in both the accuracy and efficiency of data collection when exploring spatial association patterns in gregarious species.     

Animal social networks: an introduction

Network analysis has a long history in the mathematical and social sciences and the aim of this introduction is to provide a brief overview of the potential that it holds for the study of animal behaviour. One of the most attractive features of the network paradigm is that it provides a single conceptual framework with which we can study the social organisation of animals at all levels (individual, dyad, group, population) and for all types of interaction (aggressive, cooperative, sexual etc.). Graphical tools allow a visual inspection of networks which often helps inspire ideas for testable hypotheses. Network analysis itself provides a multitude of novel statistical tools that can be used to characterise social patterns in animal populations. Among the important insights that networks have facilitated is that indirect social connections matter. Interactions between individuals generate a social environment at the population level which in turn selects for behavioural strategies at the individual level. A social network is often a perfect means by which to represent heterogeneous relationships in a population. Probing the biological drivers for these heterogeneities, often as a function of time, forms the basis of many of the current uses of network analysis in the behavioural sciences. This special issue on social networks brings together a diverse group of practitioners whose study systems range from social insects over reptiles to birds, cetaceans, ungulates and primates in order to illustrate the wide-ranging applications of network analysis. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

Potential banana skins in animal social network analysis

Social network analysis is an increasingly popular tool for the study of the fine-scale and global social structure of animals. It has attracted particular attention by those attempting to unravel social structure in fission–fusion populations. It is clear that the social network approach offers some exciting opportunities for gaining new insights into social systems. However, some of the practices which are currently being used in the animal social networks literature are at worst questionable and at best over-enthusiastic. We highlight some of the areas of method, analysis and interpretation in which greater care may be needed in order to ensure that the biology we extract from our networks is robust. In particular, we suggest that more attention should be given to whether relational data are representative, the potential effect of observational errors and the choice and use of statistical tests. The importance of replication and manipulation must not be forgotten, and the interpretation of results requires care. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

Social network theory: new insights and issues for behavioral ecologists

Until recently, few studies have used social network theory (SNT) and metrics to examine how social network structure (SNS) might influence social behavior and social dynamics in non-human animals. Here, we present an overview of why and how the social network approach might be useful for behavioral ecology. We first note four important aspects of SNS that are commonly observed, but relatively rarely quantified: (1) that within a social group, differences among individuals in their social experiences and connections affect individual and group outcomes; (2) that indirect connections can be important (e.g., partners of your partners matter); (3) that individuals differ in their importance in the social network (some can be considered keystone individuals); and (4) that social network traits often carry over across contexts (e.g., SN position in male–male competition can influence later male mating success). We then discuss how these four points, and the social network approach in general, can yield new insights and questions for a broad range of issues in behavioral ecology including: mate choice, alternative mating tactics, male–male competition, cooperation, reciprocal altruism, eavesdropping, kin selection, dominance hierarchies, social learning, information flow, social foraging, and cooperative antipredator behavior. Finally, we suggest future directions including: (1) integrating behavioral syndromes and SNT; (2) comparing space use and SNS; (3) adaptive partner choice and SNS; (4) the dynamics and stability (or instability) of social networks, and (5) group selection shaping SNS. This contribution is part of the special issue “Social networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

Connectivity for conservation: a framework to classify network measures

Graph theory, network theory, and circuit theory are increasingly being used to quantify multiple aspects of habitat connectivity and protected areas. There has been an explosive proliferation of network (connectivity) measures, resulting in over 60 measures for ecologists to now choose from. Conceptual clarification on the ecological meaning of these network measures and their interrelationships is overdue. We present a framework that categorizes network measures based on the connectivity property that they quantify (i.e., route-specific flux, route redundancy, route vulnerability, and connected habitat area) and the structural level of the habitat network to which they apply. The framework reveals a lack of network measures in the categories of "route-specific flux among neighboring habitat patches" and "route redundancy at the level of network components." We propose that network motif and path redundancy measures can be developed to fill the gaps in these categories. The value of this framework lies in its ability to inform the selection and application of network measures. Ultimately, it will allow a better comparison among graph, network, and circuit analyses, which will improve the design and management of connected landscapes.     

Network-based exploration and visualisation of ecological data

Networks – structured graphs consisting of sets of nodes connected by edges – provide a rich framework for data visualisation and exploratory analyses. Although rarely used for the visualisation of ecological data, networks are well suited to this purpose, including data that one might not normally think of as a network. We present a simple method for transforming a data matrix into network format, and show how this can be used as the basis for interactive exploratory analyses of ecological data.The method is demonstrated using a database of marine zooplankton samples acquired in the Southern Ocean. The network analyses revealed zooplankton community structures that are in good agreement with previously published results. Variations in community structure were observed to be related to the temporal and spatial pattern of sampling, as well as to physical environmental factors such as sea ice cover. The analyses also revealed a number of errors in the data, including taxon identification errors and instrument failures.The method allows the analyst to generate networks from different combinations of variables in the data set, and to examine the effects of varying parameters such as the scales of spatial, temporal, and taxonomic aggregation. This flexibility allows the analyst to rapidly gain a number of perspectives on the data and provides a powerful mechanism for exploration.     

Using home range estimates to construct social networks for species with indirect behavioral interactions

Social network analysis has become a vital tool for studying patterns of individual interactions that influence a variety of processes in behavior, ecology, and evolution. Taxa in which interactions are indirect or whose social behaviors are difficult to observe directly are being excluded from this rapidly expanding field. Here, we introduce a method that uses a probabilistic and spatially implicit technique for delineating social interactions. Kernel density estimators (KDE) are nonparametric techniques that are often used in home range analyses and allow researchers studying social networks to generate interaction matrices based on shared space use. We explored the use of KDE analysis and the effects of altering KDE input parameters on social network metrics using data from a natural population of the spatially persistent forked fungus beetle, Bolitotherus cornutus.     

Social networks and models for collective motion in animals

The theory of collective motion and the study of animal social networks have, each individually, received much attention. Currently, most models of collective motion do not consider social network structure. The implications for considering collective motion and social networks together are likely to be important. Social networks could determine how populations move in, split up into and form separate groups (social networks affecting collective motion). Conversely, collective movement could change the structure of social networks by creating social ties that did not exist previously and maintaining existing ties (collective motion affecting social networks). Thus, there is a need to combine the two areas of research and examine the relationship between network structure and collective motion. Here, we review different modelling approaches that combine social network structures and collective motion. Although many of these models have not been developed with ecology in mind, they present a current context in which a biologically relevant theory can be developed. We argue that future models in ecology should take inspiration from empirical observations and consider different mechanisms of how social preferences could be expressed in collectively moving animal groups.     

Asymptotics in adaptive cluster sampling

In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators.     

Wildlife contact analysis: emerging methods, questions, and challenges

Recent technological advances, such as proximity loggers, allow researchers to collect complete interaction histories, day and night, among sampled individuals over several months to years. Social network analyses are an obvious approach to analyzing interaction data because of their flexibility for fitting many different social structures as well as the ability to assess both direct contacts and indirect associations via intermediaries. For many network properties, however, it is not clear whether estimates based upon a sample of the network are reflective of the entire network. In wildlife applications, networks may be poorly sampled and boundary effects will be common. We present an alternative approach that utilizes a hierarchical modeling framework to assess the individual, dyadic, and environmental factors contributing to variation in the interaction rates and allows us to estimate the underlying process variation in each. In a disease control context, this approach will allow managers to focus efforts on those types of individuals and environments that contribute the most toward super-spreading events. We account for the sampling distribution of proximity loggers and the non-independence of contacts among groups by only using contact data within a group during days when the group membership of proximity loggers was known. This allows us to separate the two mechanisms responsible for a pair not contacting one another: they were not in the same group or they were in the same group but did not come within the specified contact distance. We illustrate our approach with an example dataset of female elk from northwestern Wyoming and conclude with a number of important future research directions.     

Bayesian entropy for spatial sampling design of environmental data

We develop a spatial statistical methodology to design national air pollution monitoring networks with good predictive capabilities while minimizing the cost of monitoring. The underlying complexity of atmospheric processes and the urgent need to give credible assessments of environmental risk create problems requiring new statistical methodologies to meet these challenges. In this work, we present a new method of ranking various subnetworks taking both the environmental cost and the statistical information into account. A Bayesian algorithm is introduced to obtain an optimal subnetwork using an entropy framework. The final network and accuracy of the spatial predictions is heavily dependent on the underlying model of spatial correlation. Usually the simplifying assumption of stationarity, in the sense that the spatial dependency structure does not change location, is made for spatial prediction. However, it is not uncommon to find spatial data that show strong signs of nonstationary behavior. We build upon an existing approach that creates a nonstationary covariance by a mixture of a family of stationary processes, and we propose a Bayesian method of estimating the associated parameters using the technique of Reversible Jump Markov Chain Monte Carlo. We apply these methods for spatial prediction and network design to ambient ozone data from a monitoring network in the eastern US.     

Sampling animal association networks with the gambit of the group

Ecologists increasingly use network theory to examine animal association patterns. The gambit of the group (GoG) is a simple and useful assumption for accumulating the data necessary for a network analysis. The gambit of the group implies that each animal in a group is associating with every other individual in that group. Sampling is an important issue for networks in wild populations collected assuming GoG. Due to time, effort, and resource constraints and the difficulty of tracking animals, sampled data are usually a subset of the actual network. Ecologists often use association indexes to calculate the frequency of associations between individuals. These indexes are often transformed by applying a filter to produce a binary network. We explore GoG sampling using model networks. We examine assortment at the level of the group by a single dichotomous trait, along with many other network measures, to examine the effect of different sampling regimes, and choice of filter on the accuracy and precision with which measures are estimated. We find strong support for the use of weighted, rather than filtered, network measures and show that different filters have different effects depending on the nature of the sampling. We make several practical recommendations for ecologists planning GoG sampling.     

Social network theory in the behavioural sciences: potential applications

Social network theory has made major contributions to our understanding of human social organisation but has found relatively little application in the field of animal behaviour. In this review, we identify several broad research areas where the networks approach could greatly enhance our understanding of social patterns and processes in animals. The network theory provides a quantitative framework that can be used to characterise social structure both at the level of the individual and the population. These novel quantitative variables may provide a new tool in addressing key questions in behavioural ecology particularly in relation to the evolution of social organisation and the impact of social structure on evolutionary processes. For example, network measures could be used to compare social networks of different species or populations making full use of the comparative approach. However, the networks approach can in principle go beyond identifying structural patterns and also can help with the understanding of processes within animal populations such as disease transmission and information transfer. Finally, understanding the pattern of interactions in the network (i.e. who is connected to whom) can also shed some light on the evolution of behavioural strategies.     

Design based estimation for ranked set sampling in finite populations

In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz–Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen–Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen–Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.     

Fundamental insights on when social network data are most critical for conservation planning

As declines in biodiversity accelerate, there is an urgent imperative to ensure that every dollar spent on conservation counts toward species protection. Systematic conservation planning is a widely used approach to achieve this, but there is growing concern that it must better integrate the human social dimensions of conservation to be effective. Yet, fundamental insights about when social data are most critical to inform conservation planning decisions are lacking. To address this problem, we derived novel principles to guide strategic investment in social network information for systematic conservation planning. We considered the common conservation problem of identifying which social actors, in a social network, to engage with to incentivize conservation behavior that maximizes the number of species protected. We used simulations of social networks and species distributed across network nodes to identify the optimal state-dependent strategies and the value of social network information. We did this for a range of motif network structures and species distributions and applied the approach to a small-scale fishery in Kenya. The value of social network information depended strongly on both the distribution of species and social network structure. When species distributions were highly nested (i.e., when species-poor sites are subsets of species-rich sites), the value of social network information was almost always low. This suggests that information on how species are distributed across a network is critical for determining whether to invest in collecting social network data. In contrast, the value of social network information was greatest when social networks were highly centralized. Results for the small-scale fishery were consistent with the simulations. Our results suggest that strategic collection of social network data should be prioritized when species distributions are un-nested and when social networks are likely to be centralized.     

Conservation planning for successional landscapes

The systematic conservation planning literature invariably assumes that the biodiversity features being preserved in sites do not change through time. We develop a conservation planning framework for ecosystems where disturbance events and succession drive vegetation dynamics. The framework incorporates three key attributes of disturbance theory: heterogeneity in disturbance rates, spatial correlation between disturbance events and different impacts of disturbance. In our conservation problem we wish to maximise the chance that we represent a certain number of successional types given a cap on the number of sites we can conserve. Correlation between disturbance events dramatically complicates the problem of choosing the optimal suite of sites. However, in our problem we discover that spatial correlation in disturbances affects the optimal reserve network very little. The reason is twofold: (i) through our probabilistic framework we focus on the long-term effectiveness of reserve networks and (ii) in the dynamics considered in our model the state of a site is not only affected by the most recent (correlated) disturbance event but also by the site's long-term stochastic history which blurs the impact of spatial correlation. If successional states are the conservation target rather than individual species then, conserving a site can only contribute to meeting one target. However, given that correlation of disturbance events may be ignored, we show that if the number of candidate reserves is sufficiently large the statistical dependence of different conservation targets may be ignored, too. We conclude that the computational complexity of reserve selection methods for dynamic ecosystems can be much simpler than they first appear.     

The spatial links tool: Automated mapping of habitat linkages in variegated landscapes

The removal, alteration and fragmentation of habitat in many parts of the world has led to a loss of biodiversity. Within the prevailing societal limitations the process is not easily reversed. Attempts are being made to minimise the fragmentation of remaining habitat by strategically reversing or managing habitat loss. Although their relative usefulness is a topic of debate among ecologists, habitat corridors are seen as one way of maintaining spatially dependent ecological processes within landscapes where habitat has been seriously depleted. Corridors can only be effective if they significantly contribute to the species sustaining processes of gene flow, resource access or the colonisation of vacant patches. We present a spatial habitat modelling methodology for evaluating the contribution and potential contribution of connecting paths to landscape connectivity. We have developed the spatial links tool (SLT), which maps link value across a region. The SLT combines connectivity measures from metapopulation ecology with the least cost path algorithm from graph theory, and can be applied to continuously variable landscape data. Combined with expert judgement, link value maps can be used to delineate habitat corridors. The approach capitalises on some synergies between ecological relevance and computational efficiency to produce an easily applied heuristic tool that has been successfully applied in NSW Australia.     

Assessing model structure uncertainty through an analysis of system feedback and Bayesian networks.

Ecological predictions and management strategies are sensitive to variability in model parameters as well as uncertainty in model structure. Systematic analysis of the effect of alternative model structures, however, is often beyond the resources typically available to ecologists, ecological risk practitioners, and natural resource managers. Many of these practitioners are also using Bayesian belief networks based on expert opinion to fill gaps in empirical information. The practical application of this approach can be limited by the need to populate large conditional probability tables and the complexity associated with ecological feedback cycles. In this paper, we describe a modeling approach that helps solve these problems by embedding a qualitative analysis of sign directed graphs into the probabilistic framework of a Bayesian belief network. Our approach incorporates the effects of feedback on the model's response to a sustained change in one or more of its parameters, provides an efficient means to explore the effect of alternative model structures, mitigates the cognitive bias in expert opinion, and is amenable to stakeholder input. We demonstrate our approach by examining two published case studies: a host-parasitoid community centered on a nonnative, agricultural pest of citrus cultivars and the response of an experimental lake mesocosm to nutrient input. Observations drawn from these case studies are used to diagnose alternative model structures and to predict the system's response following management intervention.     

Eigenbehaviors: identifying structure in routine

Longitudinal behavioral data generally contains a significant amount of structure. In this work, we identify the structure inherent in daily behavior with models that can accurately analyze, predict, and cluster multimodal data from individuals and communities within the social network of a population. We represent this behavioral structure by the principal components of the complete behavioral dataset, a set of characteristic vectors we have termed eigenbehaviors. In our model, an individual’s behavior over a specific day can be approximated by a weighted sum of his or her primary eigenbehaviors. When these weights are calculated halfway through a day, they can be used to predict the day’s remaining behaviors with 79% accuracy for our test subjects. Additionally, we demonstrate the potential for this dimensionality reduction technique to infer community affiliations within the subjects’ social network by clustering individuals into a “behavior space” spanned by a set of their aggregate eigenbehaviors. These behavior spaces make it possible to determine the behavioral similarity between both individuals and groups, enabling 96% classification accuracy of community affiliations within the population-level social network. Additionally, the distance between individuals in the behavior space can be used as an estimate for relational ties such as friendship, suggesting strong behavioral homophily amongst the subjects. This approach capitalizes on the large amount of rich data previously captured during the Reality Mining study from mobile phones continuously logging location, proximate phones, and communication of 100 subjects at MIT over the course of 9 months. As wearable sensors continue to generate these types of rich, longitudinal datasets, dimensionality reduction techniques such as eigenbehaviors will play an increasingly important role in behavioral research. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James). An erratum to this article can be found at     

Effects of sampling completeness on the structure of plant-pollinator networks

Plant-animal interaction networks provide important information on community organization. One of the most critical assumptions of network analysis is that the observed interaction patterns constitute an adequate sample of the set of interactions present in plant-animal communities. In spite of its importance, few studies have evaluated this assumption, and in consequence, there is no consensus on the sensitivity of network metrics to sampling methodological shortcomings. In this study we examined how variation in sampling completeness influences the estimation of six network metrics frequently used in the literature (connectance, nestedness, modularity, robustness to species loss, path length, and centralization). We analyzed data of 186 flowering plants and 336 pollinator species in 10 networks from a forest-fragmented system in central Chile. Using species-based accumulation curves, we estimated the deviation of network metrics in undersampled communities with respect to exhaustively sampled communities and the effect of network size and sampling evenness on network metrics. Our results indicate that: (1) most metrics were affected by sampling completeness but differed in their sensitivity to sampling effort; (2) nestedness, modularity, and robustness to species loss were less influenced by insufficient sampling than connectance, path length, and centralization; (3) robustness was mildly influenced by sampling evenness. These results caution studies that summarize information from databases with high, or unknown, heterogeneity in sampling effort per species and should stimulate researchers to report sampling intensity to standardize its effects in the search for broad patterns in plant-pollinator networks.