Detecting social transmission in networks

In recent years researchers have drawn attention to a need for new methods with which to identify the spread of behavioural innovations through social transmission in animal populations. Network-based analyses seek to recognise diffusions mediated by social learning by detecting a correspondence between patterns of association and the flow of information through groups. Here we introduce a new order of acquisition diffusion analysis (OADA) and develop established time of acquisition diffusion analysis (TADA) methods further. Through simulation we compare the merits of these and other approaches, demonstrating that OADA and TADA have greater power and lower Type I error rates than available alternatives, and specifying when each approach should be deployed. We illustrate the new methods by applying them to reanalyse an established dataset corresponding to the diffusion of foraging innovations in starlings, where OADA and TADA detect social transmission that hitherto had been missed. The methods are potentially widely applicable by researchers wishing to detect social learning in natural and captive populations of animals, and to facilitate this we provide code to implement OADA and TADA in the statistical package R.     

Trust transitivity in social networks

Non-centralized recommendation-based decision making is a central feature of several social and technological processes, such as market dynamics, peer-to-peer file-sharing and the web of trust of digital certification. We investigate the properties of trust propagation on networks, based on a simple metric of trust transitivity. We investigate analytically the percolation properties of trust transitivity in random networks with arbitrary in/out-degree distributions, and compare with numerical realizations. We find that the existence of a non-zero fraction of absolute trust (i.e. entirely confident trust) is a requirement for the viability of global trust propagation in large systems: The average pair-wise trust is marked by a discontinuous transition at a specific fraction of absolute trust, below which it vanishes. Furthermore, we perform an extensive analysis of the Pretty Good Privacy (PGP) web of trust, in view of the concepts introduced. We compare different scenarios of trust distribution: community- and authority-centered. We find that these scenarios lead to sharply different patterns of trust propagation, due to the segregation of authority hubs and densely-connected communities. While the authority-centered scenario is more efficient, and leads to higher average trust values, it favours weakly-connected "fringe" nodes, which are directly trusted by authorities. The community-centered scheme, on the other hand, favours nodes with intermediate in/out-degrees, in detriment of the authorities and its "fringe" peers.     

Effects of deception in social networks

Honesty plays a crucial role in any situation where organisms exchange information or resources. Dishonesty can thus be expected to have damaging effects on social coherence if agents cannot trust the information or goods they receive. However, a distinction is often drawn between prosocial lies (‘white’ lies) and antisocial lying (i.e. deception for personal gain), with the former being considered much less destructive than the latter. We use an agent-based model to show that antisocial lying causes social networks to become increasingly fragmented. Antisocial dishonesty thus places strong constraints on the size and cohesion of social communities, providing a major hurdle that organisms have to overcome (e.g. by evolving counter-deception strategies) in order to evolve large, socially cohesive communities. In contrast, white lies can prove to be beneficial in smoothing the flow of interactions and facilitating a larger, more integrated network. Our results demonstrate that these group-level effects can arise as emergent properties of interactions at the dyadic level. The balance between prosocial and antisocial lies may set constraints on the structure of social networks, and hence the shape of society as a whole.     

Hypothesis testing in animal social networks

Behavioural ecologists are increasingly using social network analysis to describe the social organisation of animal populations and to test hypotheses. However, the statistical analysis of network data presents a number of challenges. In particular the non-independent nature of the data violates the assumptions of many common statistical approaches. In our opinion there is currently confusion and uncertainty amongst behavioural ecologists concerning the potential pitfalls when hypotheses testing using social network data. Here we review what we consider to be key considerations associated with the analysis of animal social networks and provide a practical guide to the use of null models based on randomisation to control for structure and non-independence in the data.     

Threshold learning dynamics in social networks

Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.     

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.     

Entropy of dynamical social networks

Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a large dataset of phone-call interactions we show evidence that the dynamical social network has an entropy that depends on the time of the day in a typical week-day. Moreover we show evidence for adaptability of human social behavior showing data on duration of phone-call interactions that significantly deviates from the statistics of duration of face-to-face interactions. This adaptability of behavior corresponds to a different information content of the dynamics of social human interactions. We quantify this information by the use of the entropy of dynamical networks on realistic models of social interactions.     

Personality in the context of social networks

There is great interest in environmental effects on the development and evolution of animal personality traits. An important component of an individual's environment is its social environment. However, few studies look beyond dyadic relationships and try to place the personality of individuals in the context of a social network. Social network analysis provides us with many new metrics to characterize the social fine-structure of populations and, therefore, with an opportunity to gain an understanding of the role that different personalities play in groups, communities and populations regarding information or disease transmission or in terms of cooperation and policing of social conflicts. The network position of an individual is largely a consequence of its interactive strategies. However, the network position can also shape an individual's experiences (especially in the case of juveniles) and therefore can influence the way in which it interacts with others in future. Finally, over evolutionary time, the social fine-structure of animal populations (as quantified by social network analysis) can have important consequences for the evolution of personalities-an approach that goes beyond the conventional game-theoretic analyses that assumed random mixing of individuals in populations.     

Dynamics and topology of idiotypic networks

Jerne's idiotypic network was previously modelled using simple proliferation dynamics and a homogeneous tree as a connection structure. The present paper studies analytically and numerically the genericity of the previous results when the network connection structure is randomized, e.g. with loops and varying connection intensities. The main feature of the dynamics is the existence of different localized attractors that can be interpreted in terms of vaccination and tolerance. This feature is preserved when loops are added to the network, with a few exceptions concerning some regular lattices. Localized attractors might be destroyed by the introduction of a continuous distribution of connection intensities. We conclude by discussing possible modifications of the elementary model that preserve localization of the attractors and functionality of the network.     

Assortative interactions and social networks in fish

The mechanisms underpinning the structure of social networks in multiple fish populations were investigated. To our knowledge this is the first study to provide replication of social networks and therefore probably the first that allows general conclusions to be drawn. The social networks were all found to have a non-random structure and exhibited social cliquishness. A number of factors were observed to contribute to this structuring. Firstly, social network structure was influenced by body length and shoaling tendency, with individuals interacting more frequently with conspecifics of similar body length and shoaling tendency. Secondly, individuals with many social contacts were found to interact with each other more often than with other conspecifics, a phenomenon known as a positive degree correlation. Finally, repeated interactions between pairs of individuals occurred within the networks more often than expected by random interactions. The observed network structures will have ecological and evolutionary implications. For example, the occurrence of positive degree correlations suggests the possibility that pathogens and information (that are socially transmitted) could spread very fast within the populations. Furthermore, the occurrence of repeated interactions between pairs of individuals fulfils an important pre-requisite for the evolution of reciprocal altruism.     

Men's social networks and contraception in Ghana

In this paper, longitudinal data from northern Ghana is used to assess the effects of encouragement to use family planning that men receive from their personal network partners on the adoption of modern contraception by their wives. The study tests a conceptual model that, in addition to the effect of men's network encouragement, incorporates the effect of encouragement to use family planning that women receive from their respective network partners and the effect of spousal communication on reproductive matters and approval of family planning. Results show that encouragement received by men from their social networks significantly increases the likelihood of subsequent contraceptive use by their wives but this effect operates primarily by galvanizing spousal communication on reproductive matters. The effect of encouragement received by women from their respective network partners is largely independent from the effect of male network encouragement but it influences contraceptive adoption both directly and through spousal communication.     

Spreading of healthy mood in adolescent social networks

Depression is a major public health concern worldwide. There is evidence that social support and befriending influence mental health, and an improved understanding of the social processes that drive depression has the potential to bring significant public health benefits. We investigate transmission of mood on a social network of adolescents, allowing flexibility in our model by making no prior assumption as to whether it is low mood or healthy mood that spreads. Here, we show that while depression does not spread, healthy mood among friends is associated with significantly reduced risk of developing and increased chance of recovering from depression. We found that this spreading of healthy mood can be captured using a non-linear complex contagion model. Having sufficient friends with healthy mood can halve the probability of developing, or double the probability of recovering from, depression over a 6–12-month period on an adolescent social network. Our results suggest that promotion of friendship between adolescents can reduce both incidence and prevalence of depression.     

Infectious disease modeling of social contagion in networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for 'automatic' (or 'spontaneous') non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.     

Automated mapping of social networks in wild birds

Growing interest in the structure and dynamics of animal social networks has stimulated major advances [1-3], but recording reliable association data for wild populations has remained challenging. While animal-borne 'proximity' tags have been available for some time [4], earlier devices were comparatively heavy, had limited detection ranges and/or necessitated recovery for data retrieval. We have developed wireless digital transceiver technology ('Encounternet') that enables automated mapping of social networks in wild birds, yielding datasets of unprecedented size, quality and spatio-temporal resolution. Miniature, animal-borne tags record the proximity and duration of bird encounters, and periodically transfer logs to a grid of fixed receiver stations, from which datasets can be downloaded remotely for real-time analysis. We used our system to chart social associations in New Caledonian crows Corvus moneduloides[5,6]. Analysis of ca. 28,000 encounter logs for 34 crows over a 7-day period reveals a substantial degree of close-range association between non-family birds, demonstrating the potential for horizontal and oblique information exchange.     

Information flow,opinion polling and collective intelligence in house-hunting social insects

The sharing and collective processing of information by certain insect societies is one of the reasons that they warrant the superlative epithet ''super-organisms'' (Franks 1989, Am. Sci. 77, 138-145). We describe a detailed experimental and mathematical analysis of information exchange and decision-making in, arguably, the most difficult collective choices that social insects face: namely, house hunting by complete societies. The key issue is how can a complete colony select the single best nest-site among several alternatives? Individual scouts respond to the diverse information they have personally obtained about the quality of a potential nest-site by producing a recruitment signal. The colony then deliberates over (i.e. integrates) different incoming recruitment signals associated with different potential nest-sites to achieve a well-informed collective decision. We compare this process in honeybees and in the ant Leptothorax albipennis. Notwithstanding many differences - for example, honeybee colonies have 100 times more individuals than L. albipennis colonies - there are certain similarities in the fundamental algorithms these societies appear to employ when they are house hunting. Scout honeybees use the full power of the waggle dance to inform their nest-mates about the distance and direction of a potential nest-site (and they indicate the quality of a nest-site indirectly through the vigour of their dance), and yet individual bees perhaps only rarely make direct comparisons of such sites. By contrast, scouts from L. albipennis colonies often compare nest-sites, but they cannot directly inform one another of their estimation of the quality of a potential site. Instead, they discriminate between sites by initiating recruitment sooner to better ones. Nevertheless, both species do make use of forms of opinion polling. For example, scout bees that have formerly danced for a certain site cease such advertising and monitor the dances of others at random. That is, they act without prejudice. They neither favour nor disdain dancers that advocate the site they had formerly advertised or the alternatives. Thus, in general the bees are less well informed than they would be if they systematically monitored dances for alternative sites rather than spending their time reprocessing information they already have. However, as a result of their lack of prejudice, less time overall will be wasted in endless debate among stubborn and potentially biased bees. Among the ants, the opinions of nest-mates are also pooled effectively when scouts use a threshold population of their nest-mates present in a new nest-site as a cue to switch to more rapid recruitment. Furthermore, the ants'' reluctance to begin recruiting to poor nest-sites means that more time is available for the discovery and direct comparison of alternatives. Likewise, the retirement of honeybee scouts from dancing for a given site allows more time for other scouts to find potentially better sites. Thus, both the ants and the bees have time-lags built into their decision-making systems that should facilitate a compromise between thorough surveys for good nest-sites and relatively rapid decisions. We have also been able to show that classical mathematical models can illuminate the processes by which colonies are able to achieve decisions that are relatively swift and very well informed.     

Dynamics of stochastic epidemics on heterogeneous networks

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a heterogeneous network. Using this, we consider analytically the early asymptotic exponential growth phase of such epidemics, showing how the higher order moments of the network degree distribution enter into the stochastic behaviour of the epidemic. We find that the first three moments of the network degree distribution are needed to specify the variance in disease prevalence fully, meaning that the skewness of the degree distribution affects the variance of the prevalence of infection. We compare these asymptotic results to simulation and find a close agreement for city-sized populations.