Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.
cooperation; public goods; pattern formation; self-organization; coevolution
Chronic blood shortages in the U.S. would be alleviated by small increases, in percentage terms, of people donating blood. The current research investigated the effects of subtle changes in charity-seeking messages on the likelihood of people responses to a call for help. We predicted that “avoid losses” messages would lead to more helping behavior than “promote gains” messages would.
Two studies investigated the effects of message framing on helping intentions and behaviors. With the help and collaboration of the Red Cross, Study 1, a field experiment, directly assessed the effectiveness of a call for blood donations that was presented as either death-preventing (losses) or life-saving (gains), and as being of either more or less urgent need. With the help and collaboration of a local charity, Study 2, a lab experiment, assessed the effects of the gain-versus-loss framing of a donation-soliciting flyer on individuals’ expectations of others’ monetary donations as well their own volunteering behavior. Study 2 also assessed the effects of three emotional motivators - feelings of empathy, positive affect, and relational closeness.
Study 1 indicated that, on a college campus, describing blood donations as a way to “prevent a death” rather than “save a life” boosted the donation rate. Study 2 showed that framing a charity’s appeals as helping people to avoid a loss led to larger expected donations, increased intentions to volunteer, and more helping behavior, independent of other emotional motivators.
This research identifies and demonstrates a reliable and effective method for increasing important helping behaviors by providing charities with concrete ideas that can effectively increase helping behavior generally and potentially death-preventing behavior in particular.
Social movements rely in large measure on networked communication technologies to organize and disseminate information relating to the movements’ objectives. In this work we seek to understand how the goals and needs of a protest movement are reflected in the geographic patterns of its communication network, and how these patterns differ from those of stable political communication. To this end, we examine an online communication network reconstructed from over 600,000 tweets from a thirty-six week period covering the birth and maturation of the American anticapitalist movement, Occupy Wall Street. We find that, compared to a network of stable domestic political communication, the Occupy Wall Street network exhibits higher levels of locality and a hub and spoke structure, in which the majority of non-local attention is allocated to high-profile locations such as New York, California, and Washington D.C. Moreover, we observe that information flows across state boundaries are more likely to contain framing language and references to the media, while communication among individuals in the same state is more likely to reference protest action and specific places and times. Tying these results to social movement theory, we propose that these features reflect the movement’s efforts to mobilize resources at the local level and to develop narrative frames that reinforce collective purpose at the national level.
Network models extend evolutionary game theory to settings with spatial or social structure and have provided key insights on the mechanisms underlying the evolution of cooperation. However, network models have also proven sensitive to seemingly small details of the model architecture. Here we investigate two popular biologically motivated models of evolution in finite populations: Death-Birth (DB) and Birth-Death (BD) processes. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Although superficially similar, under DB cooperation may be favoured in structured populations, while under BD it never is. This is especially troubling as natural populations do not follow a strict one birth then one death regimen (or vice versa); such constraints are introduced to make models more tractable. Whether structure can promote the evolution of cooperation should not hinge on a simplifying assumption. Here, we propose a mixed rule where in each time step DB is used with probability and BD is used with probability . We derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. We find that the only qualitatively different outcome occurs when using just BD (). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally we show that, for any mixed BD-DB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma, including the Snowdrift Game.
We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with “specialist” individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents “generalist” individuals not affected by environmental changes. The rest of the landscape is occupied by “maladapted” individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change.
We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod's model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.
Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, records of civil unrest of 170 countries during the period 1919–2008 are analyzed. It is demonstrated that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network’s degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
The Ultimatum game, in which one subject proposes how to share a pot and the other has veto power on the proposal, in which case both lose everything, is a paradigmatic scenario to probe the degree of cooperation and altruism in human subjects. It has been shown that if individuals are empathic, i.e., they play the game having in mind how their opponent will react by offering an amount that they themselves would accept, then non-rational large offers well above the smallest possible ones are evolutionarily selected. We here show that empathy itself may be selected and need not be exogenously imposed provided that interactions take place only with a fraction of the total population, and that the role of proposer or responder is randomly changed from round to round. These empathic agents, that displace agents with independent (uncorrelated) offers and proposals, behave far from what is expected rationally, offering and accepting sizable fractions of the amount to be shared. Specific values for the typical offer depend on the details of the interacion network and on the existence of hubs, but they are almost always significantly larger than zero, indicating that the mechanism at work here is quite general and could explain the emergence of empathy in very many different contexts.
A new word, phylodynamics, was coined to emphasize the interconnection between phylogenetic properties, as observed for instance in a phylogenetic tree, and the epidemic dynamics of viruses, where selection, mediated by the host immune response, and transmission play a crucial role. The challenges faced when investigating the evolution of RNA viruses call for a virtuous loop of data collection, data analysis and modeling. This already resulted both in the collection of massive sequences databases and in the formulation of hypotheses on the main mechanisms driving qualitative differences observed in the (reconstructed) evolutionary patterns of different RNA viruses. Qualitatively, it has been observed that selection driven by the host immune response induces an uneven survival ability among co-existing strains. As a consequence, the imbalance level of the phylogenetic tree is manifestly more pronounced if compared to the case when the interaction with the host immune system does not play a central role in the evolutive dynamics. While many imbalance metrics have been introduced, reliable methods to discriminate in a quantitative way different level of imbalance are still lacking. In our work, we reconstruct and analyze the phylogenetic trees of six RNA viruses, with a special emphasis on the human Influenza A virus, due to its relevance for vaccine preparation as well as for the theoretical challenges it poses due to its peculiar evolutionary dynamics. We focus in particular on topological properties. We point out the limitation featured by standard imbalance metrics, and we introduce a new methodology with which we assign the correct imbalance level of the phylogenetic trees, in agreement with the phylodynamics of the viruses. Our thorough quantitative analysis allows for a deeper understanding of the evolutionary dynamics of the considered RNA viruses, which is crucial in order to provide a valuable framework for a quantitative assessment of theoretical predictions.
We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon.
The topological analysis of biological networks has been a prolific topic in network science during the last decade. A persistent problem with this approach is the inherent uncertainty and noisy nature of the data. One of the cases in which this situation is more marked is that of transcriptional regulatory networks (TRNs) in bacteria. The datasets are incomplete because regulatory pathways associated to a relevant fraction of bacterial genes remain unknown. Furthermore, direction, strengths and signs of the links are sometimes unknown or simply overlooked. Finally, the experimental approaches to infer the regulations are highly heterogeneous, in a way that induces the appearance of systematic experimental-topological correlations. And yet, the quality of the available data increases constantly.
In this work we capitalize on these advances to point out the influence of data (in)completeness and quality on some classical results on topological analysis of TRNs, specially regarding modularity at different levels.
In doing so, we identify the most relevant factors affecting the validity of previous findings, highlighting important caveats to future prokaryotic TRNs topological analysis.
Biological networks; Transcriptional regulatory networks; Motifs significance; Community structure; Network superfamilies
Altruistic behaviour varies across human populations and this variation is likely to be partly explained by variation in the ecological context of the populations. We hypothesise that area level socio-economic characteristics will determine the levels of altruism found in individuals living in an area and we use a lost letter experiment to measure altruism across 20 neighbourhoods with a wide range of income deprivation scores in London, UK. The results show a strong negative effect of neighbourhood income deprivation on altruistic behaviour, with letters dropped in the poorest neighbourhoods having 91% lower odds of being returned than letters dropped in the wealthiest neighbourhoods. We suggest that measures of altruism are strongly context dependant.
We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closest‐friendship between nodes in the network using the recently proposed Generalized Erds Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a system‐size resolution limit. Our closest‐friend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi‐level structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as real‐world networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.
Many patterns displayed by the distribution of human linguistic groups are similar to the ecological organization described for biological species. It remains a challenge to identify simple and meaningful processes that describe these patterns. The population size distribution of human linguistic groups, for example, is well fitted by a log-normal distribution that may arise from stochastic demographic processes. As we show in this contribution, the distribution of the area size of home ranges of those groups also agrees with a log-normal function. Further, size and area are significantly correlated: the number of speakers and the area spanned by linguistic groups follow the allometric relation , with an exponent varying accross different world regions. The empirical evidence presented leads to the hypothesis that the distributions of and , and their mutual dependence, rely on demographic dynamics and on the result of conflicts over territory due to group growth. To substantiate this point, we introduce a two-variable stochastic multiplicative model whose analytical solution recovers the empirical observations. Applied to different world regions, the model reveals that the retreat in home range is sublinear with respect to the decrease in population size, and that the population-area exponent grows with the typical strength of conflicts. While the shape of the population size and area distributions, and their allometric relation, seem unavoidable outcomes of demography and inter-group contact, the precise value of could give insight on the cultural organization of those human groups in the last thousand years.
A relationship between people’s mobility and their social networks is presented based on an analysis of calling and mobility traces for one year of anonymized call detail records of over one million mobile phone users in Portugal. We find that about 80% of places visited are within just 20km of their nearest (geographical) social ties’ locations. This figure rises to 90% at a ‘geo-social radius’ of 45km. In terms of their travel scope, people are geographically closer to their weak ties than strong ties. Specifically, they are 15% more likely to be at some distance away from their weak ties than strong ties. The likelihood of being at some distance from social ties increases with the population density, and the rates of increase are higher for shorter geo-social radii. In addition, we find that area population density is indicative of geo-social radius where denser areas imply shorter radii. For example, in urban areas such as Lisbon and Porto, the geo-social radius is approximately 7km and this increases to approximately 15km for less densely populated areas such as Parades and Santa Maria da Feira.
We show that world trade network datasets contain empirical evidence that the dynamics of innovation in the world economy indeed follows the concept of creative destruction, as proposed by J.A. Schumpeter more than half a century ago. National economies can be viewed as complex, evolving systems, driven by a stream of appearance and disappearance of goods and services. Products appear in bursts of creative cascades. We find that products systematically tend to co-appear, and that product appearances lead to massive disappearance events of existing products in the following years. The opposite–disappearances followed by periods of appearances–is not observed. This is an empirical validation of the dominance of cascading competitive replacement events on the scale of national economies, i.e., creative destruction. We find a tendency that more complex products drive out less complex ones, i.e., progress has a direction. Finally we show that the growth trajectory of a country’s product output diversity can be understood by a recently proposed evolutionary model of Schumpeterian economic dynamics.
We present a model of disease transmission on a regular and small world network and compare different control options. Comparison is based on a total cost of epidemic, including cost of palliative treatment of ill individuals and preventive cost aimed at vaccination or culling of susceptible individuals. Disease is characterized by pre-symptomatic phase, which makes detection and control difficult. Three general strategies emerge: global preventive treatment, local treatment within a neighborhood of certain size and only palliative treatment with no prevention. While the choice between the strategies depends on a relative cost of palliative and preventive treatment, the details of the local strategy and, in particular, the size of the optimal treatment neighborhood depend on the epidemiological factors. The required extent of prevention is proportional to the size of the infection neighborhood, but depends on time till detection and time till treatment in a non-nonlinear (power) law. The optimal size of control neighborhood is also highly sensitive to the relative cost, particularly for inefficient detection and control application. These results have important consequences for design of prevention strategies aiming at emerging diseases for which parameters are not nessecerly known in advance.
Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies—we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure—future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.
By applying a technique previously developed to study ecosystem assembly [Capitán et al., Phys. Rev. Lett. 103, 168101 (2009)] we study the evolutionary stable strategies of iterated 22 games. We focus on memory-one strategies, whose probability to play a given action depends on the actions of both players in the previous time step. We find the asymptotically stable populations resulting from all possible invasions of any known stable population. The results of this invasion process are interpreted as transitions between different populations that occur with a certain probability. Thus the whole process can be described as a Markov chain whose states are the different stable populations. With this approach we are able to study the whole space of symmetric 22 games, characterizing the most probable results of evolution for the different classes of games. Our analysis includes quasi-stationary mixed equilibria that are relevant as very long-lived metastable states and is compared to the predictions of a fixation probability analysis. We confirm earlier results on the success of the Pavlov strategy in a wide range of parameters for the iterated Prisoner's Dilemma, but find that as the temptation to defect grows there are many other possible successful strategies. Other regions of the diagram reflect the equilibria structure of the underlying one-shot game, albeit often some non-expected strategies arise as well. We thus provide a thorough analysis of iterated 22 games from which we are able to extract some general conclusions. Our most relevant finding is that a great deal of the payoff parameter range can still be understood by focusing on win-stay, lose-shift strategies, and that very ambitious ones, aspiring to obtaining always a high payoff, are never evolutionary stable.
Timbre is a key perceptual feature that allows discrimination between different sounds. Timbral sensations are highly dependent on the temporal evolution of the power spectrum of an audio signal. In order to quantitatively characterize such sensations, the shape of the power spectrum has to be encoded in a way that preserves certain physical and perceptual properties. Therefore, it is common practice to encode short-time power spectra using psychoacoustical frequency scales. In this paper, we study and characterize the statistical properties of such encodings, here called timbral code-words. In particular, we report on rank-frequency distributions of timbral code-words extracted from 740 hours of audio coming from disparate sources such as speech, music, and environmental sounds. Analogously to text corpora, we find a heavy-tailed Zipfian distribution with exponent close to one. Importantly, this distribution is found independently of different encoding decisions and regardless of the audio source. Further analysis on the intrinsic characteristics of most and least frequent code-words reveals that the most frequent code-words tend to have a more homogeneous structure. We also find that speech and music databases have specific, distinctive code-words while, in the case of the environmental sounds, this database-specific code-words are not present. Finally, we find that a Yule-Simon process with memory provides a reasonable quantitative approximation for our data, suggesting the existence of a common simple generative mechanism for all considered sound sources.
During the last few years, much research has been devoted to strategic interactions on complex networks. In this context, the Prisoner's Dilemma has become a paradigmatic model, and it has been established that imitative evolutionary dynamics lead to very different outcomes depending on the details of the network. We here report that when one takes into account the real behavior of people observed in the experiments, both at the mean-field level and on utterly different networks, the observed level of cooperation is the same. We thus show that when human subjects interact in a heterogeneous mix including cooperators, defectors and moody conditional cooperators, the structure of the population does not promote or inhibit cooperation with respect to a well mixed population.
We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits.
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks based on both endogenous and exogenous factors, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We address this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges have continuous values (bounded or unbounded), thus greatly expanding the scope of networks applied researchers can subject to statistical analysis.
Information technology (IT) adoption enables biomedical research. Publications are an accepted measure of research output, and network models can describe the collaborative nature of publication. In particular, ecological networks can serve as analogies for publication and technology adoption. We constructed network models of adoption of bioinformatics programming languages and health IT (HIT) from the literature.
We selected seven programming languages and four types of HIT. We performed PubMed searches to identify publications since 2001. We calculated summary statistics and analyzed spatiotemporal relationships. Then, we assessed ecological models of specialization, cooperativity, competition, evolution, biodiversity, and stability associated with publications.
Adoption of HIT has been variable, while scripting languages have experienced rapid adoption. Hospital systems had the largest HIT research corpus, while Perl had the largest language corpus. Scripting languages represented the largest connected network components. The relationship between edges and nodes was linear, though Bioconductor had more edges than expected and Perl had fewer. Spatiotemporal relationships were weak. Most languages shared a bioinformatics specialization and appeared mutualistic or competitive. HIT specializations varied. Specialization was highest for Bioconductor and radiology systems. Specialization and cooperativity were positively correlated among languages but negatively correlated among HIT. Rates of language evolution were similar. Biodiversity among languages grew in the first half of the decade and stabilized, while diversity among HIT was variable but flat. Compared with publications in 2001, correlation with publications one year later was positive while correlation after ten years was weak and negative.
Adoption of new technologies can be unpredictable. Spatiotemporal relationships facilitate adoption but are not sufficient. As with ecosystems, dense, mutualistic, specialized co-habitation is associated with faster growth. There are rapidly changing trends in external technological and macroeconomic influences. We propose that a better understanding of how technologies are adopted can facilitate their development.