Abstract
A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.
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Tao, Y., Cressman, R. Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics. Bull. Math. Biol. 69, 1377–1399 (2007). https://doi.org/10.1007/s11538-006-9170-0
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DOI: https://doi.org/10.1007/s11538-006-9170-0