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Fundamental Disagreements in Evolutionary DynamicsThe replicator dynamics and Moran process represent the main deterministic and stochastic models employed in evolutionary game theory. However, there are conditions under which their predictions diverge. I demonstrate the divergence between their predictions is a function of standard techniques used in their analysis, and differences in the idealizations involved in each. Specifically, of the assumptions of infinite populations sizes and time horizons, and infinitesimal mutation rates and selection intensities. This analysis reveals problems for stochastic stability analysis of a broad class of games. I demonstrate a novel domain of agreement between the dynamics, and draw broader methodological lessons for evolutionary modeling.
Logic and Philosophy of Science
University of California, Irvine