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A tragedy of the commons (TOC) occurs when individuals acting in their own self-interest deplete commonly-held resources, leading to a worse outcome than had they cooperated. Over time, the depletion of resources can change incentives for subsequent actions. Here, we investigate long-term feedback between game and environment across a continuum of incentives in an individual-based framework. We identify payoff-dependent transition rules that lead to oscillatory TOC-s in stochastic simulations and the mean field limit. Further extending the stochastic model, we find that spatially explicit interactions can lead to emergent, localized dynamics, including the propagation of cooperative wave fronts and cluster formation of both social context and resources. These dynamics suggest new mechanisms underlying how TOCs arise and how they might be averted.
We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. We establish the tragedy in the context of a general chemostat model with two species, the cooper
We study the coevolutionary dynamics of the diversity of phenotype expression and the evolution of cooperation in the Prisoners Dilemma game. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating
While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible enough to capt
Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infe
Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact with a host