Cooperation dilemma in finite populations under fluctuating environments

We present a novel approach allowing the study of rare events, like fixation, under fluctuating environments in evolutionary processes characterized by the dominance of one species. Our treatment consists of mapping the system at hand onto an auxiliary model, exhibiting metastable species coexistence, that can be analyzed semiclassically. This approach enables us to study the interplay between environmental and demographic noise on the statistics of interest. We illustrate our theory on 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 environmental noise may drastically enhance the cooperation fixation probability and even change its functional dependence on the population size. These results indicate that fluctuating environments may sustain and promote a much higher level of cooperation than static settings. We also show that our approach generalizes earlier works, notably in population genetics.