Stochastic Dynamics of Invasion and Fixation

Abstract

We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive, for the first time, a simple closed formula which determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counter-intuitive results at different intensities of selection.

References in corpus (1)

• Coevolutionary Dynamics: From Finite to Infinite Populations

Cited by in corpus (8)

• Co-evolution of strategy and structure in complex networks with dynamical linking
• Mutation-selection equilibrium in games with multiple strategies
• Fixation times in evolutionary games under weak selection
• Noise-guided evolution within cyclical interactions
• Strategy abundance in 2x2 games for arbitrary mutation rates
• Promotion of cooperation induced by the interplay between structure and game dynamics
• Influence of initial distributions on robust cooperation in evolutionary Prisoner's Dilemma
• Dynamic origin of species