Cooperation dilemma in finite populations under fluctuating environments

Abstract

We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of mapping the system onto an auxiliary model, exhibiting metastable species coexistence, that can be analyzed semiclassically. This approach enables us to study the interplay between extrinsic and demographic noise on the statistics of interest. We illustrate our theory by considering the paradigmatic prisoner's dilemma game whose evolution is described by the probability that cooperators fixate the population and replace all defectors. We analytically and numerically demonstrate that extrinsic noise may drastically enhance the cooperation fixation probability and even change its functional dependence on the population size. These results, which generalize earlier works in population genetics, indicate that extrinsic noise may help sustain and promote a much higher level of cooperation than static settings.

7 pages, 5 figures - final version

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• Ecological feedback in quorum-sensing microbial populations can induce heterogeneous production of autoinducers
• Intrinsic fluctuations of reinforcement learning promote cooperation
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• Evolutionary games with facilitators: When does selection favor cooperation?
• Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
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• Lotka-Volterra predator-prey model with periodically varying carrying capacity
• Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
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• Beyond the adiabatic limit in systems with fast environments: a $\tau$-leaping algorithm