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Journal Article

Extinction dynamics from meta-stable coexistences in an evolutionary game

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Park, Hye Jin
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Traulsen, Arne
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Park, H. J., & Traulsen, A. (2017). Extinction dynamics from meta-stable coexistences in an evolutionary game. Physical Review E, 96: 042412. doi:10.1103/PhysRevE.96.042412.

Abstract

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that more abundant types in a coexistence can be more likely to go extinct first well agreed with previous results, and also the distance between the coexistence and extinction point is not a good predictor of extinction. Instead, the WKB method correctly predicts the type going extinct first.