dorsal/arxiv
View SchemaStochastic Dynamics of Invasion and Fixation
| Authors | Arne Traulsen, Martin A. Nowak, Jorge M. Pacheco |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0609020 |
| URL | https://arxiv.org/abs/q-bio/0609020 |
| DOI | 10.1103/PhysRevE.74.011909 |
| Journal | Physical Review E 74, 011909, 2006 |
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.
{
"annotation_id": "3dc4eaed-8800-46bb-b274-c1b71af068cd",
"date_created": "2026-03-02T18:01:34.979000Z",
"date_modified": "2026-03-02T18:01:34.979000Z",
"file_hash": "1450db6c15cbcbf4010cd5af9eb979caef6004d087fccf74555878f5ab4a0daa",
"private": false,
"record": {
"abstract": "We study evolutionary game dynamics in finite populations. We analyze an\nevolutionary process, which we call pairwise comparison, for which we adopt the\nubiquitous Fermi distribution function from statistical mechanics. The inverse\ntemperature in this process controls the intensity of selection, leading to a\nunified framework for evolutionary dynamics at all intensities of selection,\nfrom random drift to imitation dynamics. We derive, for the first time, a\nsimple closed formula which determines the feasibility of cooperation in finite\npopulations, whenever cooperation is modeled in terms of any symmetric\ntwo-person game. In contrast with previous results, the present formula is\nvalid at all intensities of selection and for any initial condition. We\ninvestigate the evolutionary dynamics of cooperators in finite populations, and\nstudy the interplay between intensity of selection and the remnants of interior\nfixed points in infinite populations, as a function of a given initial number\nof cooperators, showing how this interplay strongly affects the approach to\nfixation of a given trait in finite populations, leading to counter-intuitive\nresults at different intensities of selection.",
"arxiv_id": "q-bio/0609020",
"authors": [
"Arne Traulsen",
"Martin A. Nowak",
"Jorge M. Pacheco"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1103/PhysRevE.74.011909",
"journal_ref": "Physical Review E 74, 011909, 2006",
"title": "Stochastic Dynamics of Invasion and Fixation",
"url": "https://arxiv.org/abs/q-bio/0609020"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "eefbcd87-8a41-40d9-aaaa-b14bf1226edc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}