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Mixing times in evolutionary game dynamics
- Source :
- Physical Review Letters
- Publication Year :
- 2012
- Publisher :
- arXiv, 2012.
-
Abstract
- Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics. However, many biological arguments focus on stationary distributions in a mutation-selection equilibrium. Here, we address the equilibration time required to reach stationarity in the presence of mutation, this is known as the mixing time in the theory of Markov processes. We show that mixing times in evolutionary games have the opposite behaviour from fixation times when the intensity of selection increases: In coordination games with bistabilities, the fixation time decreases, but the mixing time increases. In coexistence games with metastable states, the fixation time increases, but the mixing time decreases. Our results are based on simulations and the WKB approximation of the master equation.<br />Comment: 5 pages, 3 figures
- Subjects :
- Physics - Physics and Society
Time Factors
Complex system
General Physics and Astronomy
Markov process
FOS: Physical sciences
Physics and Society (physics.soc-ph)
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Game Theory
Metastability
0103 physical sciences
Master equation
Evolutionary game dynamics
Quantitative Biology::Populations and Evolution
Statistical physics
Coordination game
Quantitative Biology - Populations and Evolution
010306 general physics
Evolutionary dynamics
Condensed Matter - Statistical Mechanics
Physics
Models, Genetic
Statistical Mechanics (cond-mat.stat-mech)
Populations and Evolution (q-bio.PE)
Biological Evolution
Quantitative Biology::Genomics
Fixation (population genetics)
FOS: Biological sciences
Mutation
symbols
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Physical Review Letters
- Accession number :
- edsair.doi.dedup.....ca26eb9a015c1d87815f77f4fc40125b
- Full Text :
- https://doi.org/10.48550/arxiv.1204.0608