Michael Assaf, Mauro Mobilia, Elijah Roberts
We present a novel approach allowing the accurate study of rare events in a broad class of evolutionary processes under fluctuating environments. Our approach consists of mapping these processes, not necessarily displaying metastability, onto auxiliary models characterized by metastability that can be analyzed semiclassically. This enables us to study the interplay between extrinsic (environmental) noise and intrinsic (demographic) fluctuations on the statistics of interest. We illustrate our theory for the paradigmatic prisoner's dilemma game whose evolution is described by the probability that cooperators take over and fixate the entire population. We demonstrate both analytically and by using Monte Carlo simulations that extrinsic noise may drastically enhance such a fixation probability. In particular, we show that under strong, short-correlated extrinsic noise, the cooperation fixation probability decays algebraically with the population size, rather than exponentially. Finally, we show how our approach generalizes earlier works, notably in population genetics.
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http://arxiv.org/abs/1305.6580
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