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Principal axes for stochastic dynamics

Published in Phys. Rev. E, 2011

We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. We apply our algorithm to two examples of systems showing Hopf bifurcation. We argue it enables one to define vector fields of stochastic eigendirections which can be used assess the path of minimum stochastic forcing in phase space, increasing the predictability of the system.

Recommended citation: Vítor V. Vasconcelos, et al.. "Principal axes for stochastic dynamics" Phys. Rev. E (2011) 84, 031103. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.031103

Evolutionary dynamics of climate change under collective-risk dilemmas

Published in M3AS, 2012

Preventing global warming requires overall cooperation. We show that decisions within small groups under high risk and stringent requirements toward success significantly raise the chances of coordinating to save the planet's climate. We discuss both deterministic dynamics in infinite populations, and stochastic dynamics in finite populations."

Recommended citation: Francisco C. Santos, Vítor V. Vasconcelos, Marta D. Santos, P. N. B. Neves, Jorge M. Pacheco. "Evolutionary dynamics of climate change under collective-risk dilemmas" Mathematical Models and Methods in Applied Sciences (2012) 22 No. supp01 1140004 https://www.worldscientific.com/doi/10.1142/S0218202511400045

A bottom-up institutional approach to cooperative governance of risky commons

Published in Nature Climate Change, 2013

We investigate the emergence and impact of different types of sanctioning to deter non-cooperative behaviour in climate agreements. We show that a bottom-up approach, in which parties create local institutions that punish free-riders, promotes the emergence of widespread cooperation, mostly when risk perception is low, as it is at present. Global institutions provide, at best, marginal improvements regarding overall cooperation. Our results clearly suggest that a polycentric approach involving multiple institutions is more effective than that associated with a single, global one."

Recommended citation: Vítor V. Vasconcelos, Francisco C. Santos, and Jorge M. Pacheco. "A bottom-up institutional approach to cooperative governance of risky commons" Nature Climate Change (2013) 3 9 p797-801 https://www.nature.com/articles/nclimate1927

Climate policies under wealth inequality

Published in Proceedings of the National Academy of Sciences, 2014

This paper incorporates wealth inequality into a public goods dilemma, including an asymmetric distribution of wealth representative of existing inequalities among nations. Without homophily (imitation of like agents), inequality actually makes cooperation easier to achieve; homophily, however, can undercut this, leading to collapse because poor agents may contribute less. Understanding such effects may enhance the ability to achieve agreements on climate change and other issues."

Recommended citation: Vítor V. Vasconcelos, Francisco C. Santos, Jorge M. Pacheco, and Simon A. Levin. "Climate policies under wealth inequality" PNAS (2014) 111 (6) 2212-2216 https://www.pnas.org/content/111/6/2212.short

Evolution of All-or-None strategies in repeated public goods dilemmas

Published in PLoS computational biology, 2014

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.

Recommended citation: Flávio L Pinheiro, Vítor V Vasconcelos, Francisco C Santos, and Jorge M Pacheco. "Evolution of All-or-None strategies in repeated public goods dilemmas" PLoS computational biology (2014) 3 11 e1003945 https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003945

Climate change governance, cooperation and self-organization

Published in Physics of Life Review, 2014

We introduce a simple approach to address dilemmas in which the risk of failure plays a central role in individual decisions. This model can be shown to capture some of the essential features discovered in recent key experiments, while allowing one to extend in non-trivial ways the experimental conditions to regions of more practical interest. Our results suggest that global coordination for a common good should be attempted by segmenting tasks in many small to medium sized groups, in which perception of risk is high and uncertainty in collective goals is minimized. Moreover, our results support the conclusion that sanctioning institutions may further enhance the chances of coordinating to tame the planet's climate, as long as they are implemented in a decentralized and polycentric manner."

Recommended citation: Jorge M Pacheco, Vítor V Vasconcelos, and Francisco C Santos. "Climate change governance, cooperation and self-organization" Phys. Life Rev. (2015) 11 4 573-586 https://www.sciencedirect.com/science/article/pii/S1571064514000268

Co-evolutionary dynamics of collective action with signaling for a quorum

Published in PLoS computational biology, 2015

We address the general question of the evolution of collective signaling at a high level of abstraction. We investigate the evolutionary dynamics of a population engaging in a signaling N-person game theoretic model. Parameter settings allow for loners and cheaters, and for costly or costless signals. We find a rich dynamics, showing how natural selection, operating on a population of individuals endowed with the simplest strategies, is able to evolve a costly signaling system that allows individuals to respond appropriately to different states of Nature. Signaling robustly promotes cooperative collective action, in particular when coordinated action is most needed and difficult to achieve. Two different signaling systems may emerge depending on Nature’s most prevalent states.

Recommended citation: Jorge M. Pacheco, Vítor V. Vasconcelos, and Francisco C. Santos. "Co-evolutionary dynamics of collective action with signaling for a quorum" PLoS computational biology (2015) 11 2 e1004101 https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004101

Incomplete cooperation and co-benefits: deepening climate cooperation with a proliferation of small agreements

Published in Climatic Change, 2015

Case study and model results lend some optimism for the potential of small coalitions with partially excludable public goods to substantially deepen international cooperation on energy and climate issues. Drawing motivation from other issue areas in international relations ranging from nuclear non-proliferation, transboundary air pollution and liberalized trade, we use an evolutionary-game-theoretic model to analyze regimes that yield domestic incentives to contribute to public goods provision (co-benefits). Co-benefits may be limited, but can create a nucleus for formation of coalitions that grow while deepening provision of global public goods. The Climate and Clean Air Coalition (CCAC) is a prime example of an agreement that employs partially excludable club benefits to deepen cooperation on non-CO2 greenhouse gases. This paper lends positive support that a proliferation of small agreements under a building blocks approach at the UNFCCC may be more effective (not just more likely) for deepening climate change cooperation than a fully inclusive approach.

Recommended citation: Phillip M. Hannam, Vítor V. Vasconcelos, Simon A. Levin, and Jorge M. Pacheco. "Incomplete cooperation and co-benefits: deepening climate cooperation with a proliferation of small agreements" Climatic Change (2015) 1-15 https://link.springer.com/article/10.1007/s10584-015-1511-2

Cooperation dynamics of polycentric climate governance

Published in M3AS, 2015

We review a stochastic model which incorporates a threshold game of collective action and the idea of risky goods, capturing essential features unveiled in recent experiments. We show how reducing uncertainty both in terms of the perception of disaster and in terms of goals induce a transition to cooperation. Taking into account wealth inequality, we explore the impact of the homophily, potentially present in the network of influence of the rich and the poor, in the different contributions of the players. Finally, we discuss the impact of polycentric sanctioning institutions, showing how such a scenario also proves to be more efficient than a single global institution.

Recommended citation: Vítor V. Vasconcelos, Francisco C. Santos, and Jorge M. Pacheco. "Cooperation dynamics of polycentric climate governance" M3AS (2015) 25 13 2503-2517 https://www.worldscientific.com/doi/abs/10.1142/S0218202515400163

Stochastic dynamics through hierarchically embedded Markov chains

Published in Phys. Rev. Lett., 2017

We develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Recommended citation: Vítor V. Vasconcelos, Fernando P. Santos, Francisco C. Santos, and Jorge M. Pacheco. "Stochastic Dynamics through Hierarchically Embedded Markov Chains" Phys. Rev. Let. (2017) 118 058301 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.058301

Stability and recovery of coral-algae systems: the importance of recruitment seasonality and grazing influence

Published in Theoretical Ecology, 2018

we use a model of coral-macroalgae dynamics to explore the effects of different assumptions regarding grazing and coral recruitment seasonality in coral-algae systems. We find that the grazing functional form constrains the potential for alternative stable states and coexistence, highlighting the need to further elucidate herbivore dynamics on reef systems. We also show that coral recruitment from external sources facilitates coral persistence and recovery, both when recruitment is assumed to be constant over time, and when recruitment occurs seasonally. In systems with alternative stable states, the total number of larvae that reaches a patch is the primary driver that dictates whether a system with low coral cover can flip into the coral-dominated basin of attraction. However, in a limited parameter space, the duration and timing of this larval pulse can also determine whether coral can recover in a bistable system. These results highlight the multiple factors that influence whether a coral reef is likely to remain in its present state or not, especially as ocean conditions change.

Recommended citation: Lisa C. McManus, James R. Watson, Vítor V. Vasconcelos, and Simon A. Levin. "Stability and recovery of coral-algae systems: the importance of recruitment seasonality and grazing influence" Theoretical Ecology (2018) 12 1 p61-72 https://link.springer.com/article/10.1007/s12080-018-0388-x

Simple property of heterogeneous aspiration dynamics: Beyond weak selection

Published in Phys. Rev. E, 2018

We investigate whether and how heterogeneity in the rules of behavior update alters the evolutionary outcome. We assume that individuals update behaviors by aspiration-based self-evaluation and they do so in their own ways. Under weak selection, we analytically reveal a simple property that holds for any two-strategy multiplayer games in well-mixed populations and on regular graphs: the evolutionary outcome in a population with heterogeneous update rules is the weighted average of the outcomes in the corresponding homogeneous populations, and the associated weights are the frequencies of each update rule in the heterogeneous population. Beyond weak selection, we show that this property holds for public goods games. Our finding implies that heterogeneous aspiration dynamics is additive. This additivity greatly reduces the complexity induced by the underlying individual heterogeneity. Our work thus provides an efficient method to calculate evolutionary outcomes under heterogeneous update rules.

Recommended citation: Lei Zhou, Bin Wu, Vítor V. Vasconcelos, and Long Wang. "Simple property of heterogeneous aspiration dynamics: Beyond weak selection" Phys. Rev. E (2018) 98 062124 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.062124

Consensus and polarization in competing complex contagion processes

Published in J. Roy. Soc. Interface, 2019

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.

Recommended citation: Vítor V. Vasconcelos, Simon A. Levin, and Flávio L. Pinheiro "Consensus and Polarization in Competing Complex Contagion Processes" 16 J. Roy. Soc. Interface (2019) https://royalsocietypublishing.org/doi/full/10.1098/rsif.2019.0196

Extreme temperature events will drive coral decline in the Coral Triangle

Published in Global Change Biology, 2019

In light of rapid environmental change, quantifying the contribution of regional‐ and local‐scale drivers of coral persistence is necessary to characterize fully the resilience of coral reef systems. To assess multiscale responses to thermal perturbation of corals in the Coral Triangle (CT), we developed a spatially explicit metacommunity model with coral‐algal competition, including seasonal larval dispersal and external spatio‐temporal forcing. We tested coral sensitivity in 2083 reefs across the CT region and surrounding areas under potential future temperature regimes, with and without interannual climate variability, exploring a range of 0.5 to 2.0°C overall increase in temperature in the system by 2054. We found that among future projections, reef survival probability and mean percent coral cover over time were largely determined by the presence or absence of interannual sea surface temperature (SST) extremes as well as absolute temperature increase. Overall, reefs that experienced SST time series that were filtered to remove interannual variability had approximately double the chance of survival than reefs subjected to unfiltered SST. By the end of the forecast period, the inclusion of thermal anomalies was equivalent to an increase of at least 0.5°C in SST projections without anomalies. Change in percent coral cover varied widely across the region within temperature scenarios, with some reefs experiencing local extinction while others remaining relatively unchanged. Sink strength and current thermal stress threshold were found to be significant drivers of these patterns, highlighting the importance of processes that underlie larval connectivity and bleaching sensitivity in coral networks.

Recommended citation: Lisa C McManus, Vítor V Vasconcelos, Simon A Levin, Diane M Thompson, Joan A Kleypas, Frederic S Castruccio, Enrique N Curchitser, and James R Watson "Extreme temperature events will drive coral decline in the Coral Triangle" 14972 Global Change Biology (2019) https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.14972

Caring for the future can turn tragedy into comedy for long-term collective action under risk of collapse

Published in Proceeding of the National Academy of Sciences, 2020

We will need collective action to avoid catastrophic climate change, and this will require valuing the long term as well as the short term. Shortsightedness and uncertainty have hindered progress in resolving this collective action problem and have been recognized as important barriers to cooperation among humans. Here, we propose a coupled social–ecological dilemma to investigate the interdependence of three well-identified components of this cooperation problem: 1) timescales of collapse and recovery in relation to time preferences regarding future outcomes, 2) the magnitude of the impact of collapse, and 3) the number of actors in the collective. We find that, under a sufficiently severe and time-distant collapse, how much the actors care for the future can transform the game from a tragedy of the commons into one of coordination, and even into a comedy of the commons in which cooperation dominates. Conversely, we also find conditions under which even strong concern for the future still does not transform the problem from tragedy to comedy. For a large number of participating actors, we find that the critical collapse impact, at which these game regime changes happen, converges to a fixed value of collapse impact per actor that is independent of the enhancement factor of the public good, which is usually regarded as the driver of the dilemma. Our results not only call for experimental testing but also help explain why polarization in beliefs about human-caused climate change can threaten global cooperation agreements.

Recommended citation: Wolfram Barfuss, Jonathan F Donges, Vítor V. Vasconcelos, Jürgen Kurths, and Simon A. Levin "Caring for the future can turn tragedy into comedy for long-term collective action under risk of collapse" 117 (23) 12915-12922 Proceedings of the National Academy of Sciences https://www.pnas.org/content/117/23/12915

Coalition-structured governance improves cooperation to provide public goods

Published in Scientific Reports, 2020

While the benefits of common and public goods are shared, they tend to be scarce when contributions are provided voluntarily. Failure to cooperate in the provision or preservation of these goods is fundamental to sustainability challenges, ranging from local fisheries to global climate change. In the real world, such cooperative dilemmas occur in multiple interactions with complex strategic interests and frequently without full information. We argue that voluntary cooperation enabled across overlapping coalitions (akin to polycentricity) not only facilitates a higher generation of non-excludable public goods, but it may also allow evolution toward a more cooperative, stable, and inclusive approach to governance. Contrary to any previous study, we show that these merits of multi-coalition governance are far more general than the singular examples occurring in the literature, and they are robust under diverse conditions of excludability, congestion of the non-excludable public good, and arbitrary shapes of the return-to-contribution function. We first confirm the intuition that a single coalition without enforcement and with players pursuing their self-interest without knowledge of returns to contribution is prone to cooperative failure. Next, we demonstrate that the same pessimistic model but with a multi-coalition structure of governance experiences relatively higher cooperation by enabling recognition of marginal gains of cooperation in the game at stake. In the absence of enforcement, public-goods regimes that evolve through a proliferation of voluntary cooperative forums can maintain and increase cooperation more successfully than singular, inclusive regimes.

Recommended citation: Vítor V Vasconcelos, Phillip M Hannam, Simon A Levin, and Jorge M Pacheco "Coalition-structured governance improves cooperation to provide public goods" 10 9194 Scientific Reports (2020) https://www.nature.com/articles/s41598-020-65960-8

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