Stochastic dynamics of invasion and fixation.

By Arne Traulsen, Martin A. Nowak, Jorge M. Pacheco. Physical review. E, Statistical, nonlinear, and soft matter physics, 2006

600 citations recorded by the source corpus.

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 a simple closed formula that 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 counterintuitive results at different intensities of selection.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/0457df8fb449602811b8c06b180a2f758498d995

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

In Public Health, Environmental and Occupational Health

In Sociology and Political Science

Citations in the corpus

EVOLUTIONARY DYNAMICS OF CLIMATE CHANGE UNDER COLLECTIVE-RISK DILEMMAS (2012, background): “state.(52,54) Hence, in addition to the analysis of the shape of G(k/Z), often one of the quantities of interest in studying the evolutionary dynamics in finite populations is the probability φk that the system fixates in a monomorphic cooperative state, starting from, for instance, a given number k”
Fixation times in evolutionary games under weak selection (2008, background): “(13) For large N , the sums in equation (13) can be approximated by integrals, which yields a closed expression for the probabilities φi [33, 37].”
Modeling, Analysis and Control of Networked Evolutionary Games (2015, methodology): “There are several commonly used rules such as Unconditional Imitation [37], Fermi Rule [47], [50], Moran Rule [29], [42], etc.”
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics (2009, methodology): “Finally, an update rule that has been widely used in the literature, because of being analytically tractable, is the Fermi rule, based on the Fermi distribution function [82,117,118].”
α-Rank: Multi-Agent Evaluation by Evolution (2019, methodology): “, [16–20]) capture the macro-dynamics of interacting agents, but involve a large number of evolutionary parameters and are not yet grounded in a game-theoretic solution concept.”
Cooperation Prevails When Individuals Adjust Their Social Ties (2006, methodology): “Indeed, especially for the SG, the time for reaching an absorbing state may be prohibitively large [27].”
Games on graphs (2014, neutral): “1C e / 1 [96], [36], [113] and .”