Grooming network cohesion and the role of individuals in a captive chimpanzee group

Social network analysis offers new tools to study the social structure of primate groups. We used social network analysis to investigate the cohesiveness of a grooming network in a captive chimpanzee group (N = 17) and the role that individuals may play in it. Using data from a year-long observation, we constructed an unweighted social network of preferred grooming interactions by retaining only those dyads that groomed above the group mean. This choice of criterion was validated by the finding that the properties of the unweighted network correlated with the properties of a weighted network (i.e. a network representing the frequency of grooming interactions) constructed from the same data. To investigate group cohesion, we tested the resilience of the unweighted grooming network to the removal of central individuals (i.e. individuals with high betweenness centrality). The network fragmented more after the removal of individuals with high betweenness centrality than after the removal of random individuals. Central individuals played a pivotal role in maintaining the network's cohesiveness, and we suggest that this may be a typical property of affiliative networks like grooming networks. We found that the grooming network correlated with kinship and age, and that individuals with higher social status occupied more central positions in the network. Overall, the grooming network showed a heterogeneous structure, yet did not exhibit scale-free properties similar to many other primate networks. We discuss our results in light of recent findings on animal social networks and chimpanzee grooming.     

Violating social norms when choosing friends: how rule-breakers affect social networks

Social networks rely on basic rules of conduct to yield functioning societies in both human and animal populations. As individuals follow established rules, their behavioral decisions shape the social network and give it structure. Using dynamic, self-organizing social network models we demonstrate that defying conventions in a social system can affect multiple levels of social and organizational success independently. Such actions primarily affect actors' own positions within the network, but individuals can also affect the overall structure of a network even without immediately affecting themselves or others. These results indicate that defying the established social norms can help individuals to change the properties of a social system via seemingly neutral behaviors, highlighting the power of rule-breaking behavior to transform convention-based societies, even before direct impacts on individuals can be measured.     

Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

The impacts of network topology on disease spread

Individuals in a population susceptible to a disease may be represented as vertices in a network, with the edges that connect vertices representing social and/or spatial contact between individuals. Networks, which explicitly included six different patterns of connection between vertices, were created. Both scale-free networks and random graphs showed a different response in path level to increasing levels of clustering than regular lattices. Clustering promoted short path lengths in all network types, but randomly assembled networks displayed a logarithmic relationship between degree and path length; whereas this response was linear in regular lattices. In all cases, small-world models, generated by rewiring the connections of a regular lattice, displayed properties, which spanned the gap between random and regular networks.Simulation of a disease in these networks showed a strong response to connectance pattern, even when the number of edges and vertices were approximately equal. Epidemic spread was fastest, and reached the largest size, in scale-free networks, then in random graphs. Regular lattices were the slowest to be infected, and rewired lattices were intermediate between these two extremes. Scale-free networks displayed the capacity to produce an epidemic even at a likelihood of infection, which was too low to produce an epidemic for the other network types. The interaction between the statistical properties of the network and the results of epidemic spread provides a useful tool for assessing the risk of disease spread in more realistic networks.     

Emergence of complex social networks from spatial structure and rules of thumb: a modelling approach

Individual-based computer models show that simple heuristic governing individuals’ behavior may suffice to generate complex patterns of social behavior at the group level such as those observed in animal societies. ‘GrooFiWorld’ is an example of such kind of computer models. In this model, self-organization and simple behavioral rules generate complex patterns of social behavior like those described in tolerant and intolerant societies of macaques. Social complexity results from the socio-spatial structure of the group, the nature of which is, in turn, a side-effect of intensity of aggression. The model suggests that a similar mechanism may give rise to complex social structures in macaques. It is, however, unknown if the spatial structure of the model and that of macaques are indeed similar. Here we used social networks analysis as a proxy for spatial structure of the group. Our findings show that the social networks of the model share similar qualitative features with those of macaques. As group size increases, the density and the average individual eigenvector centrality decrease and the modularity and centralization of the network increase. In social networks emerging from simulations resembling intolerant societies the density is lower, the modularity and centralization are higher, and the individuals ranking higher in the dominance hierarchy are more central than in the social networks emerging from simulations resembling egalitarian societies. Given the qualitative similarity between the social networks of the model and that of empirical data, our results suggest that the spatial structure of macaques is similar to that of the model. It seems thus plausible that, as in the model, the spatial structure combined with simple behavioral rules plays a role in the emergence of complex social networks and complex social behavior in macaques.     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

Partitioning of reproduction in animal societies

A key feature differentiating cooperative animal societies Is the apportionment of reproduction among individuals. Only recently have studies started to focus on intraspecific variability in the distribution of reproduction within animal societies, and the available data suggest that this variability might be greater than previously suspected. How can one account for intra-and interspecific variability in partitioning of reproduction? This Is one of the most intriguing problems in the study of social behaviour, and understanding the factors underlying this variability is one of the keys to understanding the properties of complex animal societies.     

Social Structure of a Semi-Free Ranging Group of Mandrills (Mandrillus sphinx): A Social Network Analysis

The difficulty involved in following mandrills in the wild means that very little is known about social structure in this species. Most studies initially considered mandrill groups to be an aggregation of one-male/multifemale units, with males occupying central positions in a structure similar to those observed in the majority of baboon species. However, a recent study hypothesized that mandrills form stable groups with only two or three permanent males, and that females occupy more central positions than males within these groups. We used social network analysis methods to examine how a semi-free ranging group of 19 mandrills is structured. We recorded all dyads of individuals that were in contact as a measure of association. The betweenness and the eigenvector centrality for each individual were calculated and correlated to kinship, age and dominance. Finally, we performed a resilience analysis by simulating the removal of individuals displaying the highest betweenness and eigenvector centrality values. We found that related dyads were more frequently associated than unrelated dyads. Moreover, our results showed that the cumulative distribution of individual betweenness and eigenvector centrality followed a power function, which is characteristic of scale-free networks. This property showed that some group members, mostly females, occupied a highly central position. Finally, the resilience analysis showed that the removal of the two most central females split the network into small subgroups and increased the network diameter. Critically, this study confirms that females appear to occupy more central positions than males in mandrill groups. Consequently, these females appear to be crucial for group cohesion and probably play a pivotal role in this species.     

Modelling disease spread and control in networks: implications for plant sciences

Networks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed.     

Epidemic threshold and network structure: The interplay of probability of transmission and of persistence in small-size directed networks

A growing number of studies are investigating the effect of contact structure on the dynamics of epidemics in large-scale complex networks. Whether findings thus obtained apply also to networks of small size, and thus to many real-world biological applications, is still an open question. We use numerical simulations of disease spread in directed networks of 100 individual nodes with a constant number of links. We show that, no matter the type of network structure (local, small-world, random and scale-free), there is a linear threshold determined by the probability of infection transmission between connected nodes and the probability of infection persistence in an infected node. The threshold is significantly lower for scale-free networks compared to local, random and small-world ones only if super-connected nodes have a higher number of links both to and from other nodes. The starting point, the node at which the epidemic starts, does not affect the threshold conditions, but has a marked influence on the final size of the epidemic in all kinds of network. There is evidence that contact structure has an influence on the average final size of an epidemic across all starting nodes, with significantly lower values in scale-free networks at equilibrium. Simulations in scale-free networks show a distinctive time-series pattern, which, if found in a real epidemic, can be used to infer the underlying network structure. The findings have relevance also for meta-population ecology and species conservation.     

Evolution of cooperation on dynamical graphs

There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner's dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change.     

How scale-free are biological networks.

The concept of scale-free network has emerged as a powerful unifying paradigm in the study of complex systems in biology and in physical and social studies. Metabolic, protein, and gene interaction networks have been reported to exhibit scale-free behavior based on the analysis of the distribution of the number of connections of the network nodes. Here we study 10 published datasets of various biological interactions and perform goodness-of-fit tests to determine whether the given data is drawn from the power-law distribution. Our analysis did not identify a single interaction network that has a nonzero probability of being drawn from the power-law distribution.     

Evolution in group-structured populations can resolve the tragedy of the commons

Public goods are the key features of all human societies and are also important in many animal societies. Collaborative hunting and collective defence are but two examples of public goods that have played a crucial role in the development of human societies and still play an important role in many animal societies. Public goods allow societies composed largely of cooperators to outperform societies composed mainly of non-cooperators. However, public goods also provide an incentive for individuals to be selfish by benefiting from the public good without contributing to it. This is the essential paradox of cooperation-known variously as the Tragedy of the Commons, Multi-person Prisoner's Dilemma or Social Dilemma. Here, we show that a new model for evolution in group-structured populations provides a simple and effective mechanism for the emergence and maintenance of cooperation in such a social dilemma. This model does not depend on kin selection, direct or indirect reciprocity, punishment, optional participation or trait-group selection. Since this mechanism depends only on population dynamics and requires no cognitive abilities on the part of the agents concerned, it potentially applies to organisms at all levels of complexity.     

Network frailty and the geometry of herd immunity

The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks-Poisson, scale-free and small-world-we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.     

社会网络分析法及其在动物行为学研究中的应用

近年来,社会网络分析法被广泛用于动物行为学研究。它通过量化动物社会关系中的特定属性 (如中心度和中心势),可辨识动物群体中的关键个体及其在群体中的作用,揭示动物社会交往的形成机制,深化人们对动物社会性起源、个体行为与种群动态格局间关系的理解。本文简要介绍了社会网络分析法的发展史和基本概念,然后阐述了如何建立网络及选择常用指标,强调了创建原模型的必要性及途径。最后着重评述了社会网络分析法在动物行为学研究中的应用现状,并提出未来应当关注直接身体接触 (如打斗和理毛) 和非肢体接触 (如声音通讯) 等不同交往形式的变动过程,以此构建社会交往的动态网络。同时也需要加强种间社交网络的研究,以便增进人们对社会行为的生态功能以及合作理论等问题的理解。     

Congruent epidemic models for unstructured and structured populations: analytical reconstruction of a 2003 SARS outbreak

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.     

Systems approach to studying animal sociality: individual position versus group organization in dynamic social network models

Social networks can be used to represent group structure as a network of interacting components, and also to quantify both the position of each individual and the global properties of a group. In a series of simulation experiments based on dynamic social networks, we test the prediction that social behaviors that help individuals reach prominence within their social group may conflict with their potential to benefit from their social environment. In addition to cases where individuals were able to benefit from improving both their personal relative importance and group organization, using only simple rules of social affiliation we were able to obtain results in which individuals would face a trade-off between these factors. While selection would favor (or work against) social behaviors that concordantly increase (or decrease, respectively) fitness at both individual and group level, when these factors conflict with each other the eventual selective pressure would depend on the relative returns individuals get from their social environment and their position within it. The presented results highlight the importance of a systems approach to studying animal sociality, in which the effects of social behaviors should be viewed not only through the benefits that those provide to individuals, but also in terms of how they affect broader social environment and how in turn this is reflected back on an individual's fitness.     

Effectiveness of realistic vaccination strategies for contact networks of various degree distributions

A "contact network" that models infection transmission comprises nodes (or individuals) that are linked when they are in contact and can potentially transmit an infection. Through analysis and simulation, we studied the influence of the distribution of the number of contacts per node, defined as degree, on infection spreading and its control by vaccination. Three random contact networks of various degree distributions were examined. In a scale-free network, the frequency of high-degree nodes decreases as the power of the degree (the case of the third power is studied here); the decrease is exponential in an exponential network, whereas all nodes have the same degree in a constant network. Aiming for containment at a very early stage of an epidemic, we measured the sustainability of a specific network under a vaccination strategy by employing the critical transmissibility larger than which the epidemic would occur. We examined three vaccination strategies: mass, ring, and acquaintance. Irrespective of the networks, mass preventive vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate of the population. Ring post-outbreak vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate, which is the rate confined to the targeted ring comprising the neighbors of an infected node; however, the total number of vaccinated nodes could mostly be fewer than 100 nodes at the critical transmissibility. In combination, mass and ring vaccinations decreased the pathogen's "effective" transmissibility each by the factor of the unvaccinated rate. The amount of vaccination used in acquaintance preventive vaccination was lesser than the mass vaccination, particularly under a highly heterogeneous degree distribution; however, it was not as less as that used in ring vaccination. Consequently, our results yielded a quantitative assessment of the amount of vaccination necessary for infection containment, which is universally applicable to contact networks of various degree distributions.