Explosive Cooperation in Social Dilemmas on Higher-Order Networks.

Understanding how cooperative behaviors can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modeled as pairwise networks, the units of many real-world systems can also interact in groups of three or more. Here, we introduce a general framework to extend pairwise games to higher-order networks. By studying social dilemmas on hypergraphs with a tunable structure, we find an explosive transition to cooperation triggered by a critical number of higher-order games. The associated bistable regime implies that an initial critical mass of cooperators is also required for the emergence of prosocial behavior. Our results show that higher-order interactions provide a novel explanation for the survival of cooperation.

Emergence of innovations in networked populations with reputation-driven interactions.

In this work, we analyze how reputation-based interactions influence the emergence of innovations. To do so, we make use of a dynamic model that mimics the discovery process by which, at each time step, a pair of individuals meet and merge their knowledge to eventually result in a novel technology of higher value. The way in which these pairs are brought together is found to be crucial for achieving the highest technological level. Our results show that when the influence of reputation is weak or moderate, it induces an acceleration of the discovery process with respect to the neutral case (purely random coupling). However, an excess of reputation is clearly detrimental, because it leads to an excessive concentration of knowledge in a small set of people, which prevents a diversification of the technologies discovered and, in addition, leads to societies in which a majority of individuals lack technical capabilities.

Effects of human mobility on the spread of Dengue in the region of Caldas, Colombia.

According to the World Health Organization (WHO), dengue is the most common acute arthropod-borne viral infection in the world. The spread of dengue and other infectious diseases is closely related to human activity and mobility. In this paper we analyze the effect of introducing mobility restrictions as a public health policy on the total number of dengue cases within a population. To perform the analysis, we use a complex metapopulation in which we implement a compartmental propagation model coupled with the mobility of individuals between the patches. This model is used to investigate the spread of dengue in the municipalities of Caldas (CO). Two scenarios corresponding to different types of mobility restrictions are applied. In the first scenario, the effect of restricting mobility is analyzed in three different ways: a) limiting the access to the endemic node but allowing the movement of its inhabitants, b) restricting the diaspora of the inhabitants of the endemic node but allowing the access of outsiders, and c) a total isolation of the inhabitants of the endemic node. In this scenario, the best simulation results are obtained when specific endemic nodes are isolated during a dengue outbreak, obtaining a reduction of up to 2.5% of dengue cases. Finally, the second scenario simulates a total isolation of the network, i.e., mobility between nodes is completely limited. We have found that this control measure increases the number of total dengue cases in the network by 2.36%.

Quantifying the heterogeneous impact of lockdown policies on different socioeconomic classes during the first COVID-19 wave in Colombia.

In the absence of vaccines, the most widespread reaction to curb the COVID-19 pandemic worldwide was the implementation of lockdowns or stay-at-home policies. Despite the reported usefulness of such policies, their efficiency was highly constrained by socioeconomic factors determining their feasibility and their associated outcome in terms of mobility reduction and the subsequent limitation of social activity. Here we investigate the impact of lockdown policies on the mobility patterns of different socioeconomic classes in the three major cities of Colombia during the first wave of the COVID-19 pandemic. In global terms, we find a consistent positive correlation between the reduction in mobility levels and the socioeconomic stratum of the population in the three cities, implying that those with lower incomes were less capable of adopting the aforementioned policies. Our analysis also suggests a strong restructuring of the mobility network of lowest socioeconomic strata during COVID-19 lockdown, increasing their endogenous mixing while hampering their connections with wealthiest areas due to a sharp reduction in long-distance trips.

Collapse transition in epidemic spreading subject to detection with limited resources.

Compartmental models are the most widely used framework for modeling infectious diseases. These models have been continuously refined to incorporate all the realistic mechanisms that can shape the course of an epidemic outbreak. Building on a compartmental model that accounts for early detection and isolation of infectious individuals through testing, in this article we focus on the viability of detection processes under limited availability of testing resources, and we study how the latter impacts on the detection rate. Our results show that, in addition to the well-known epidemic transition at R_{0}=1, a second transition occurs at R_{0}^{★}>1 pinpointing the collapse of the detection system and, as a consequence, the switch from a regime of mitigation to a regime in which the pathogen spreads freely. We characterize the epidemic phase diagram of the model as a function of the relevant control parameters: the basic reproduction number, the maximum detection capacity of the system, and the fraction of individuals in shelter. Our analysis thus provides a valuable tool for estimating the detection resources and the level of confinement needed to face epidemic outbreaks.

Agta hunter-gatherer oral microbiomes are shaped by contact network structure.

Here we investigate the effects of extensive sociality and mobility on the oral microbiome of 138 Agta hunter-gatherers from the Philippines. Our comparisons of microbiome composition showed that the Agta are more similar to Central African BaYaka hunter-gatherers than to neighbouring farmers. We also defined the Agta social microbiome as a set of 137 oral bacteria (only 7% of 1980 amplicon sequence variants) significantly influenced by social contact (quantified through wireless sensors of short-range interactions). We show that large interaction networks including strong links between close kin, spouses and even unrelated friends can significantly predict bacterial transmission networks across Agta camps. Finally, we show that more central individuals to social networks are also bacterial supersharers. We conclude that hunter-gatherer social microbiomes are predominantly pathogenic and were shaped by evolutionary tradeoffs between extensive sociality and disease spread.

Network bypasses sustain complexity.

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

Socioeconomic determinants of stay-at-home policies during the first COVID-19 wave.

Introduction: The COVID-19 pandemic has had a significant impact on public health and social systems worldwide. This study aims to evaluate the efficacy of various policies and restrictions implemented by different countries to control the spread of the virus. Methods: To achieve this objective, a compartmental model is used to quantify the "social permeability" of a population, which reflects the inability of individuals to remain in confinement and continue social mixing allowing the spread of the virus. The model is calibrated to fit and recreate the dynamics of the epidemic spreading of 42 countries, mainly taking into account reported deaths and mobility across the populations. Results: The results indicate that low-income countries have a harder time slowing the advance of the pandemic, even if the virus did not initially propagate as fast as in wealthier countries, showing the disparities between countries in their ability to mitigate the spread of the disease and its impact on vulnerable populations. Discussion: This research contributes to a better understanding of the socioeconomic and environmental factors that affect the spread of the virus and the need for equitable policy measures to address the disparities in the global response to the pandemic.

Joint Analysis of the Epidemic Evolution and Human Mobility During the First Wave of COVID-19 in Spain: Retrospective Study.

BACKGROUND: The initial wave of the COVID-19 pandemic placed a tremendous strain on health care systems worldwide. To mitigate the spread of the virus, many countries implemented stringent nonpharmaceutical interventions (NPIs), which significantly altered human behavior both before and after their enactment. Despite these efforts, a precise assessment of the impact and efficacy of these NPIs, as well as the extent of human behavioral changes, remained elusive. OBJECTIVE: In this study, we conducted a retrospective analysis of the initial wave of COVID-19 in Spain to better comprehend the influence of NPIs and their interaction with human behavior. Such investigations are vital for devising future mitigation strategies to combat COVID-19 and enhance epidemic preparedness more broadly. METHODS: We used a combination of national and regional retrospective analyses of pandemic incidence alongside large-scale mobility data to assess the impact and timing of government-implemented NPIs in combating COVID-19. Additionally, we compared these findings with a model-based inference of hospitalizations and fatalities. This model-based approach enabled us to construct counterfactual scenarios that gauged the consequences of delayed initiation of epidemic response measures. RESULTS: Our analysis demonstrated that the pre-national lockdown epidemic response, encompassing regional measures and heightened individual awareness, significantly contributed to reducing the disease burden in Spain. The mobility data indicated that people adjusted their behavior in response to the regional epidemiological situation before the nationwide lockdown was implemented. Counterfactual scenarios suggested that without this early epidemic response, there would have been an estimated 45,400 (95% CI 37,400-58,000) fatalities and 182,600 (95% CI 150,400-233,800) hospitalizations compared to the reported figures of 27,800 fatalities and 107,600 hospitalizations, respectively. CONCLUSIONS: Our findings underscore the significance of self-implemented prevention measures by the population and regional NPIs before the national lockdown in Spain. The study also emphasizes the necessity for prompt and precise data quantification prior to enacting enforced measures. This highlights the critical interplay between NPIs, epidemic progression, and human behavior. This interdependence presents a challenge in predicting the impact of NPIs before they are implemented.

Characterization of interactions' persistence in time-varying networks.

Many complex networked systems exhibit volatile dynamic interactions among their vertices, whose order and persistence reverberate on the outcome of dynamical processes taking place on them. To quantify and characterize the similarity of the snapshots of a time-varying network-a proxy for the persistence,-we present a study on the persistence of the interactions based on a descriptor named temporality. We use the average value of the temporality, [Formula: see text], to assess how "special" is a given time-varying network within the configuration space of ordered sequences of snapshots. We analyse the temporality of several empirical networks and find that empirical sequences are much more similar than their randomized counterparts. We study also the effects on [Formula: see text] induced by the (time) resolution at which interactions take place.

Emergence of protective behaviour under different risk perceptions to disease spreading.

The behaviour of individuals is a main actor in the control of the spread of a communicable disease and, in turn, the spread of an infectious disease can trigger behavioural changes in a population. Here, we study the emergence of individuals' protective behaviours in response to the spread of a disease by considering two different social attitudes within the same population: concerned and risky. Generally speaking, concerned individuals have a larger risk aversion than risky individuals. To study the emergence of protective behaviours, we couple, to the epidemic evolution of a susceptible-infected-susceptible model, a decision game based on the perceived risk of infection. Using this framework, we find the effect of the protection strategy on the epidemic threshold for each of the two subpopulations (concerned and risky), and study under which conditions risky individuals are persuaded to protect themselves or, on the contrary, can take advantage of a herd immunity by remaining healthy without protecting themselves, thanks to the shield provided by concerned individuals. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

The interconnection between independent reactive control policies drives the stringency of local containment.

The lack of medical treatments and vaccines upon the arrival of the SARS-CoV-2 virus has made non-pharmaceutical interventions the best allies in safeguarding human lives in the face of the COVID-19 pandemic. Here we propose a self-organized epidemic model with multi-scale control policies that are relaxed or strengthened depending on the extent of the epidemic outbreak. We show that optimizing the balance between the effects of epidemic control and the associated socio-economic cost is strongly linked to the stringency of control measures. We also show that non-pharmaceutical interventions acting at different spatial scales, from creating social bubbles at the household level to constraining mobility between different cities, are strongly interrelated. We find that policy functionality changes for better or worse depending on network connectivity, meaning that some populations may allow for less restrictive measures than others if both have the same resources to respond to the evolving epidemic.

Behavioural response to heterogeneous severity of COVID-19 explains temporal variation of cases among different age groups.

Together with seasonal effects inducing outdoor or indoor activities, the gradual easing of prophylaxis caused second and third waves of SARS-CoV-2 to emerge in various countries. Interestingly, data indicate that the proportion of infections belonging to the elderly is particularly small during periods of low prevalence and continuously increases as case numbers increase. This effect leads to additional stress on the health care system during periods of high prevalence. Furthermore, infections peak with a slight delay of about a week among the elderly compared to the younger age groups. Here, we provide a mechanistic explanation for this phenomenology attributable to a heterogeneous prophylaxis induced by the age-specific severity of the disease. We model the dynamical adoption of prophylaxis through a two-strategy game and couple it with an SIR spreading model. Our results also indicate that the mixing of contacts among the age groups strongly determines the delay between their peaks in prevalence and the temporal variation in the distribution of cases. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.

Structured interactions as a stabilizing mechanism for competitive ecological communities.

How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from theoretical ecology to mathematics and physics. In this context, modeling the stable coexistence of species competing for limited resources is a particularly challenging task. From a mathematical point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species' relative abundances neutrally cycling without converging to a stable equilibrium. Although in recent years several mechanisms have been proposed, models able to explain species coexistence in competitive communities are still limited. Here we identify locality in the interactions as one of the simplest mechanisms leading to stable species coexistence. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes within a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate, within the scope of our model, that species coexist reaching a stable equilibrium when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance. On the contrary, when one of these ingredients is missing, large oscillations and neutral cycles emerge.

Connecting intercity mobility with urban welfare.

While significant effort has been devoted to understand the role of intraurban characteristics on sustainability and growth, much remains to be understood about the effect of interurban interactions and the role cities have in determining each other's urban welfare. Here we consider a global mobility network of population flows between cities as a proxy for the communication between these regions, and analyze how it correlates with socioeconomic indicators. We use several measures of centrality to rank cities according to their importance in the mobility network, finding PageRank to be the most effective measure for reflecting these prosperity indicators. Our analysis reveals that the characterization of the welfare of cities based on mobility information hinges on their corresponding development stage. Namely, while network-based predictions of welfare correlate well with economic indicators in mature cities, for developing urban areas additional information about the prosperity of their mobility neighborhood is needed. We develop a simple generative model for the allocation of population flows out of a city that balances the costs and benefits of interaction with other cities that are successful, finding that it provides a strong fit to the flows observed in the global mobility network and highlights the differences in flow patterns between developed and developing urban regions. Our results hint towards the importance of leveraging interurban connections in service of urban development and welfare.

Hunter-gatherer multilevel sociality accelerates cumulative cultural evolution.

Although multilevel sociality is a universal feature of human social organization, its functional relevance remains unclear. Here, we investigated the effect of multilevel sociality on cumulative cultural evolution by using wireless sensing technology to map inter- and intraband social networks among Agta hunter-gatherers. By simulating the accumulation of cultural innovations over the real Agta multicamp networks, we demonstrate that multilevel sociality accelerates cultural differentiation and cumulative cultural evolution. Our results suggest that hunter-gatherer social structures [based on (i) clustering of families within camps and camps within regions, (ii) cultural transmission within kinship networks, and (iii) high intercamp mobility] may have allowed past and present hunter-gatherers to maintain cumulative cultural adaptation despite low population density, a feature that may have been critical in facilitating the global expansion of Homo sapiens.

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks.

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience.

Resource heterogeneity leads to unjust effort distribution in climate change mitigation.

Climate change mitigation is a shared global challenge that involves collective action of a set of individuals with different tendencies to cooperation. However, we lack an understanding of the effect of resource inequality when diverse actors interact together towards a common goal. Here, we report the results of a collective-risk dilemma experiment in which groups of individuals were initially given either equal or unequal endowments. We found that the effort distribution was highly inequitable, with participants with fewer resources contributing significantly more to the public goods than the richer -sometimes twice as much. An unsupervised learning algorithm classified the subjects according to their individual behavior, finding the poorest participants within two "generous clusters" and the richest into a "greedy cluster". Our results suggest that policies would benefit from educating about fairness and reinforcing climate justice actions addressed to vulnerable people instead of focusing on understanding generic or global climate consequences.

The structure of plant spatial association networks is linked to plant diversity in global drylands.

1. Despite commonly used to unveil the complex structure of interactions within ecological communities and their value to assess their resilience against external disturbances, network analyses have seldom been applied in plant communities. We evaluated how plant-plant spatial association networks vary in global drylands, and assessed whether network structure was related to plant diversity in these ecosystems. 2. We surveyed 185 dryland ecosystems from all continents except Antarctica and built networks using the local spatial association between all the perennial plants species present in the communities studied. Then, for each network we calculated four descriptors of network structure (link density, link weight mean and heterogeneity, and structural balance), and evaluated their significance with null models. Finally, we used structural equation models to evaluate how abiotic factors (including geography, topography, climate and soil conditions) and network descriptors influenced plant species richness and evenness. 3. Plant networks were highly variable worldwide, but at most study sites (72%) presented common structures such as a higher link density than expected. We also find evidence of the presence of high structural balance in the networks studied. Moreover, all network descriptors considered had a positive and significant effect on plant diversity, and on species richness in particular. Synthesis. Our results constitute the first empirical evidence showing the existence of common network architectures structuring dryland plant communities at the global scale, and suggest a relationship between the structure of spatial networks and plant diversity. They also highlight the importance of system-level approaches to explain the diversity and structure of interactions in plant communities, two major drivers of terrestrial ecosystem functioning.

Epidemics on plants: Modeling long-range dispersal on spatially embedded networks.

Here we develop an epidemic model that accounts for long-range dispersal of pathogens between plants. This model generalizes the classical compartmental models-Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR)-to take into account those factors that are key to understand epidemics in real plant populations. These ingredients are the spatial characteristics of the plots and fields in which plants are embedded and the effect of long-range dispersal of pathogens. The spatial characteristics are included through the use of random rectangular graphs which allow to consider the effects of the elongation of plots and fields, while the long-range dispersal is implemented by considering transformations, such as the Mellin and Laplace transforms, of a generalization of the adjacency matrix of the geometric graph. Our results point out that long-range dispersal favors the propagation of pathogens while the elongation of plant plots increases the epidemic threshold and decreases dramatically the number of affected plants. Interestingly, our model is able of reproducing the existence of patchy regions of infected plants and the absence of a clear propagation front centered in the initial infected plants, as it is observed in real plant epidemics.