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  When the mean is not enough: calculating fixation time distributions in birth-death processes

Ashcroft, P., Traulsen, A., & Galla, T. (2015). When the mean is not enough: calculating fixation time distributions in birth-death processes. Physical Review E, 92: 042154.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0026-CC95-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-CC4E-0
Genre: Journal Article

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http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042154 (Publisher version)
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 Creators:
Ashcroft, Peter, Author
Traulsen, Arne1, Author              
Galla, Tobias, Author
Affiliations:
1Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

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 Abstract: Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.

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Language(s): eng - English
 Dates: 2015-10-092015-04-162015-10-28
 Publication Status: Published online
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 Rev. Method: -
 Identifiers: arXiv: 1504.04249
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: - Volume / Issue: 92 Sequence Number: 042154 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012