Impact of COVID-19 lockdown measures on waste production behavior in Lisbon.

The recent restrictions on mobility and economic activities imposed by governments due to the COVID-19 pandemic have significantly affected waste production and recycling patterns in cities worldwide. This effect differed both between cities and within cities as the measures of confinement adopted by governments had diverse impacts in different areas of cities, depending on their characteristics (e.g., touristic, or residential). In the present work, mixed waste collection areas were created, based on waste collection points, that define spatial units in which contextual data such as tourism and residential characteristics were aggregated. The difference in mixed waste collected compared with previous years was analyzed along with the impacts on recycling due to the modification in operations regarding waste collection during the lockdown. The results showed that despite the suspension of the door-to-door recycling system during the lockdown, this did not translate into an increase in the production of mixed waste, and the recycling levels of previous years have not been reached after the lockdown, indicating a possible change in recycling habits in Lisbon. The touristic and non-residential mixed waste circuits presented significantly reduced mixed waste production compared to the non-pandemic context. Also, tourist, mobility, and economic activity were measured to understand which factors contributed to waste production changes during the COVID-19 pandemic. While little evidence of a relationship with these exogenous variables was found at the citywide level, evidence was found at the waste collection circuit level.

Scaling behavior of public procurement activity.

Public procurement refers to the purchase by public sector entities-such as government departments or local authorities-of Services, Goods, or Works. It accounts for a significant share of OECD countries' expenditures. However, while governments are expected to execute them as efficiently as possible, there is a lack of methodologies for an adequate comparison of procurement activity between institutions at different scales, which represents a challenge for policymakers and academics. Here, we propose using methods borrowed from urban scaling laws literature to study public procurement activity among 278 Portuguese municipalities between 2011 and 2018. We find that public procurement expenditure scales sublinearly with population size, indicating an economy of scale for public spending as cities increase their population size. Moreover, when looking at the municipal Scale-Adjusted Indicators (the deviations from the scaling law) by contract categories-Works, Goods, and Services-we are able to identify a richer local characterisation of municipalities based on the similarity of procurement activity. These results make up a framework for quantitatively studying local public expenditure by enabling policymakers a more appropriate foundation for comparative analysis.

Stable leaders pave the way for cooperation under time-dependent exploration rates.

The exploration of different behaviours is part of the adaptation repertoire of individuals to new environments. Here, we explore how the evolution of cooperative behaviour is affected by the interplay between exploration dynamics and social learning, in particular when individuals engage on prisoner's dilemma along the edges of a social network. We show that when the population undergoes a transition from strong to weak exploration rates a decline in the overall levels of cooperation is observed. However, if the rate of decay is lower in highly connected individuals (Leaders) than for the less connected individuals (Followers) then the population is able to achieve higher levels of cooperation. Finally, we show that minor differences in selection intensities (the degree of determinism in social learning) and individual exploration rates, can translate into major differences in the observed collective dynamics.

Consensus and polarization in competing complex contagion processes.

The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the diffusion of human behaviours, innovations and knowledge. Based on that evidence, we propose a model that considers multiple, potentially asymmetric and competing contagion processes and analyse its respective population-wide dynamics, bringing together ideas from complex contagion, opinion dynamics, evolutionary game theory and language competition by shifting the focus from individuals to the properties of the diffusing processes. We show that our model spans a dynamical space in which the population exhibits patterns of consensus, dominance, and, importantly, different types of polarization, a more diverse dynamical environment that contrasts with single simple contagion processes. We show how these patterns emerge and how different population structures modify them through a natural development of spatial correlations: structured interactions increase the range of the dominance regime by reducing that of dynamic polarization, tight modular structures can generate structural polarization, depending on the interplay between fundamental properties of the processes and the modularity of the interaction network.

Structural and temporal patterns of the first global trading market.

Little is known about the structural patterns and dynamics of the first global trading market (FGTM), which emerged during the sixteenth century as a result of the Iberian expansion, let alone how it compares to today's global financial markets. Here we build a representative network of the FGTM using information contained in 8725 (handwritten) Bills of Exchange from that time-which were (human) interpreted and digitalized into an online database. We show that the resulting temporal network exhibits a hierarchical, highly clustered and disassortative structure, with a power-law dependence on the connectivity that remains remarkably robust throughout the entire period investigated. Temporal analysis shows that, despite major turnovers in the number and nature of the links-suggesting fast adaptation in response to the geopolitical and financial turmoil experienced at the time-the overall characteristics of the FGTM remain robust and virtually unchanged. The methodology developed here demonstrates the possibility of building and analysing complex trading and finance networks originating from pre-statistical eras, enabling us to highlight the striking similarities between the structural patterns of financial networks separated by centuries in time.

Optimal diversification strategies in the networks of related products and of related research areas.

Countries and cities are likely to enter economic activities that are related to those that are already present in them. Yet, while these path dependencies are universally acknowledged, we lack an understanding of the diversification strategies that can optimally balance the development of related and unrelated activities. Here, we develop algorithms to identify the activities that are optimal to target at each time step. We find that the strategies that minimize the total time needed to diversify an economy target highly connected activities during a narrow and specific time window. We compare the strategies suggested by our model with the strategies followed by countries in the diversification of their exports and research activities, finding that countries follow strategies that are close to the ones suggested by the model. These findings add to our understanding of economic diversification and also to our general understanding of diffusion in networks.

Intermediate Levels of Network Heterogeneity Provide the Best Evolutionary Outcomes.

Complex networks impact the diffusion of ideas and innovations, the formation of opinions, and the evolution of cooperative behavior. In this context, heterogeneous structures have been shown to generate a coordination-like dynamics that drives a population towards a monomorphic state. In contrast, homogeneous networks tend to result in a stable co-existence of multiple traits in the population. These conclusions have been reached through the analysis of networks with either very high or very low levels of degree heterogeneity. In this paper, we use methods from Evolutionary Game Theory to explore how different levels of degree heterogeneity impact the fate of cooperation in structured populations whose individuals face the Prisoner's Dilemma. Our results suggest that in large networks a minimum level of heterogeneity is necessary for a society to become evolutionary viable. Moreover, there is an optimal range of heterogeneity levels that maximize the resilience of the society facing an increasing number of social dilemmas. Finally, as the level of degree heterogeneity increases, the evolutionary dominance of either cooperators or defectors in a society increasingly depends on the initial state of a few influential individuals. Our findings imply that neither very unequal nor very equal societies offer the best evolutionary outcome.

Linking Individual and Collective Behavior in Adaptive Social Networks.

Adaptive social structures are known to promote the evolution of cooperation. However, up to now the characterization of the collective, population-wide dynamics resulting from the self-organization of individual strategies on a coevolving, adaptive network has remained unfeasible. Here we establish a (reversible) link between individual (micro)behavior and collective (macro)behavior for coevolutionary processes. We demonstrate that an adaptive network transforms a two-person social dilemma locally faced by individuals into a collective dynamics that resembles that associated with an N-person coordination game, whose characterization depends sensitively on the relative time scales between the entangled behavioral and network evolutions. In particular, we show that the faster the relative rate of adaptation of the network, the smaller the critical fraction of cooperators required for cooperation to prevail, thus establishing a direct link between network adaptation and the evolution of cooperation. The framework developed here is general and may be readily applied to other dynamical processes occurring on adaptive networks, notably, the spreading of contagious diseases or the diffusion of innovations.

Evolution of all-or-none strategies in repeated public goods dilemmas.

Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games (PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

Origin of peer influence in social networks.

Social networks pervade our everyday lives: we interact, influence, and are influenced by our friends and acquaintances. With the advent of the World Wide Web, large amounts of data on social networks have become available, allowing the quantitative analysis of the distribution of information on them, including behavioral traits and fads. Recent studies of correlations among members of a social network, who exhibit the same trait, have shown that individuals influence not only their direct contacts but also friends' friends, up to a network distance extending beyond their closest peers. Here, we show how such patterns of correlations between peers emerge in networked populations. We use standard models (yet reflecting intrinsically different mechanisms) of information spreading to argue that empirically observed patterns of correlation among peers emerge naturally from a wide range of dynamics, being essentially independent of the type of information, on how it spreads, and even on the class of underlying network that interconnects individuals. Finally, we show that the sparser and clustered the network, the more far reaching the influence of each individual will be.

Reward from punishment does not emerge at all costs.

The conundrum of cooperation has received increasing attention during the last decade. In this quest, the role of altruistic punishment has been identified as a mechanism promoting cooperation. Here we investigate the role of altruistic punishment on the emergence and maintenance of cooperation in structured populations exhibiting connectivity patterns recently identified as key elements of social networks. We do so in the framework of Evolutionary Game Theory, employing the Prisoner's Dilemma and the Stag-Hunt metaphors to model the conflict between individual and collective interests regarding cooperation. We find that the impact of altruistic punishment strongly depends on the ratio q/p between the cost of punishing a defecting partner (q) and the actual punishment incurred by the partner (p). We show that whenever q/p<1, altruistic punishment turns out to be detrimental for cooperation for a wide range of payoff parameters, when compared to the scenario without punishment. The results imply that while locally, the introduction of peer punishment may seem to reduce the chances of free-riding, realistic population structure may drive the population towards the opposite scenario. Hence, structured populations effectively reduce the expected beneficial contribution of punishment to the emergence of cooperation which, if not carefully dosed, may in fact hinder the chances of widespread cooperation.

Dynamics of N-person snowdrift games in structured populations.

In many real-life situations, the completion of a task by a group toward achieving a common goal requires the cooperation of at least some of its members, who share the required workload. Such cases are conveniently modeled by the N-person snowdrift game, an example of a Public Goods Game. Here we study how an underlying network of contacts affects the evolutionary dynamics of collective action modeled in terms of such a Public Goods Game. We analyze the impact of different types of networks in the global, population-wide dynamics of cooperators and defectors. We show that homogeneous social structures enhance the chances of coordinating toward stable levels of cooperation, while heterogeneous network structures create multiple internal equilibria, departing significantly from the reference scenario of a well-mixed, structureless population.

From local to global dilemmas in social networks.

Social networks affect in such a fundamental way the dynamics of the population they support that the global, population-wide behavior that one observes often bears no relation to the individual processes it stems from. Up to now, linking the global networked dynamics to such individual mechanisms has remained elusive. Here we study the evolution of cooperation in networked populations and let individuals interact via a 2-person Prisoner's Dilemma--a characteristic defection dominant social dilemma of cooperation. We show how homogeneous networks transform a Prisoner's Dilemma into a population-wide evolutionary dynamics that promotes the coexistence between cooperators and defectors, while heterogeneous networks promote their coordination. To this end, we define a dynamic variable that allows us to track the self-organization of cooperators when co-evolving with defectors in networked populations. Using the same variable, we show how the global dynamics--and effective dilemma--co-evolves with the motifs of cooperators in the population, the overall emergence of cooperation depending sensitively on this co-evolution.

Evolutionary dynamics of collective action when individual fitness derives from group decisions taken in the past.

Many actions take some time to have an impact - their effects only appear at some point in the future. Such time lags turn out to be ubiquitous among living organisms. Here we study the impact of time lags in the evolutionary dynamics of cooperative collective action. We consider a population in which individuals interact via a N-Person Stag Hunt dilemma and must opt to cooperate or defect. In the absence of any delay, the replicator dynamics reveals the existence of regimes in which two internal fixed points appear simultaneously. We show that the presence of time delay in the fitness of individuals leads to a delayed replicator equation exhibiting new evolutionary profiles, each profile being separated by critical values of the delay that we determine explicitly. When we break the symmetry in the time lags, we show that, generally, defectors take more advantage from delay than cooperators. Finally, when we take into consideration, approximately, effects associated with the finite population size, we find that counter-intuitive evolutionary outcomes may occur, resulting from the interplay between delay and the basins of attraction in the neighborhood of the internal fixed-points, and which may lead to full cooperation in conditions under which the outcome would be Full Defection in infinite populations.

The role of diversity in the evolution of cooperation.

Understanding the evolutionary mechanisms that promote and maintain cooperative behavior is recognized as a major theoretical problem where the intricacy increases with the complexity of the participating individuals. This is epitomized by the diverse nature of Human interactions, contexts, preferences and social structures. Here we discuss how social diversity, in several of its flavors, catalyzes cooperative behavior. From the diversity in the number of interactions an individual is involved to differences in the choice of role models and contributions, diversity is shown to significantly increase the chances of cooperation. Individual diversity leads to an overall population dynamics in which the underlying dilemma of cooperation is changed, benefiting the society as whole. In addition, we show how diversity in social contexts can arise from the individual capacity for organizing their social ties. As such, Human diversity, on a grand scale, may be instrumental in shaping us as the most sophisticated cooperative entities on this planet.

Population structure induces a symmetry breaking favoring the emergence of cooperation.

The evolution of cooperation described in terms of simple two-person interactions has received considerable attention in recent years, where several key results were obtained. Among those, it is now well established that the web of social interaction networks promotes the emergence of cooperation when modeled in terms of symmetric two-person games. Up until now, however, the impacts of the heterogeneity of social interactions into the emergence of cooperation have not been fully explored, as other aspects remain to be investigated. Here we carry out a study employing the simplest example of a prisoner's dilemma game in which the benefits collected by the participants may be proportional to the costs expended. We show that the heterogeneous nature of the social network naturally induces a symmetry breaking of the game, as contributions made by cooperators may become contingent on the social context in which the individual is embedded. A new, numerical, mean-field analysis reveals that prisoner's dilemmas on networks no longer constitute a defector dominance dilemma--instead, individuals engage effectively in a general coordination game. We find that the symmetry breaking induced by population structure profoundly affects the evolutionary dynamics of cooperation, dramatically enhancing the feasibility of cooperators: cooperation blooms when each cooperator contributes the same cost, equally shared among the plethora of games in which she participates. This work provides clear evidence that, while individual rational reasoning may hinder cooperative actions, the intricate nature of social interactions may effectively transform a local dilemma of cooperation into a global coordination problem.