dorsal/arxiv
View SchemaFixation of strategies for an evolutionary game in finite populations
| Authors | Tibor Antal, Istvan Scheuring |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0509008 |
| URL | https://arxiv.org/abs/q-bio/0509008 |
| DOI | 10.1007/s11538-006-9061-4 |
| Journal | Bulletin of Mathematical Biology 68, 1923 (2006) |
Abstract
A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with arbitrary hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.
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"abstract": "A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix\ngames is studied in finite populations. We focus on stochastic properties of\nfixation: how a strategy represented by a single individual wins over the\nentire population. The process is discussed in the framework of a random walk\nwith arbitrary hopping rates. The time of fixation is found to be identical for\nboth strategies in any particular game. The asymptotic behavior of the fixation\ntime and fixation probabilities in the large population size limit is also\ndiscussed. We show that fixation is fast when there is at least one pure\nevolutionary stable strategy (ESS) in the infinite population size limit, while\nfixation is slow when the ESS is the coexistence of the two strategies.",
"arxiv_id": "q-bio/0509008",
"authors": [
"Tibor Antal",
"Istvan Scheuring"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech"
],
"doi": "10.1007/s11538-006-9061-4",
"journal_ref": "Bulletin of Mathematical Biology 68, 1923 (2006)",
"title": "Fixation of strategies for an evolutionary game in finite populations",
"url": "https://arxiv.org/abs/q-bio/0509008"
},
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