Cooperation dilemma in finite populations under fluctuating environments.
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.
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Michael
M
Assaf
Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.
Mauro
M
Mobilia
Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Elijah
E
Roberts
D003299:Cooperative Behavior; D004777:Environment; D005716:Game Theory; D008390:Markov Chains; D015233:Models, Statistical; D011157:Population Dynamics