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  How small are small mutation rates?

Wu, B., Gokhale, C. S., Wang, L., & Traulsen, A. (2012). How small are small mutation rates? Journal of Mathematical Biology, 64(5), 803-827. doi:10.1007/s00285-011-0430-8.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-D352-A Version Permalink: http://hdl.handle.net/21.11116/0000-0003-3B25-2
Genre: Journal Article

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Wu2012_Article_HowSmallAreSmallMutationRates.pdf (Publisher version), 577KB
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 Creators:
Wu, Bin1, Author              
Gokhale, Chaitanya S.1, Author              
Wang, Long, Author
Traulsen, Arne1, Author              
Affiliations:
1Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

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Free keywords: evolutionary game theory; mutation rates; perturbation analysis
 Abstract: We consider evolutionary game dynamics in a finite population of size N. When mutations are rare, the population is monomorphic most of the time. Occasionally a mutation arises. It can either reach fixation or go extinct. The evolutionary dynamics of the process under smallmutation rates can be approximated by an embedded Markov chain on the pure states. Here we analyze how small the mutation rate should be to make the embedded Markov chain a good approximation by calculating the difference between the real stationary distribution and the approximated one. While for a coexistence game, where the best reply to any strategy is the opposite strategy, it is necessary that the mutation rate μ is less than N−1/2 exp[−N] to ensure that the approximation is good, for all other games, it is sufficient if themutation rate is smaller than (N ln N) −1. Our results also hold for a wide class of imitation processes under arbitrary selection intensity.

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Language(s): eng - English
 Dates: 2012
 Publication Status: Published in print
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 Rev. Method: -
 Identifiers: eDoc: 610655
DOI: 10.1007/s00285-011-0430-8
Other: 2918/S 39263
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Title: Journal of Mathematical Biology
Source Genre: Journal
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Pages: - Volume / Issue: 64 (5) Sequence Number: - Start / End Page: 803 - 827 Identifier: ISSN: 0303-6812 (print)
ISSN: 1432-1416 (online)