Exact solutions for the selection–mutation equilibrium in the Crow–Kimura evolutionary model
•We find stationary distributions of the Crow–Kimura model for specific fitness landscapes.•We propose a generating function method for the equilibrium distributions.•We give simple analytical expressions for a number of examples.•Our method generalizes the random variable technique. We reformulate...
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| Veröffentlicht in: | Mathematical biosciences 2015-08, Vol.266, p.1-9 |
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| container_title | Mathematical biosciences |
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| creator | Semenov, Yuri S. Novozhilov, Artem S. |
| description | •We find stationary distributions of the Crow–Kimura model for specific fitness landscapes.•We propose a generating function method for the equilibrium distributions.•We give simple analytical expressions for a number of examples.•Our method generalizes the random variable technique.
We reformulate the eigenvalue problem for the selection–mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. |
| doi_str_mv | 10.1016/j.mbs.2015.05.002 |
| format | Article |
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We reformulate the eigenvalue problem for the selection–mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations.</description><identifier>ISSN: 0025-5564</identifier><identifier>EISSN: 1879-3134</identifier><identifier>DOI: 10.1016/j.mbs.2015.05.002</identifier><identifier>PMID: 26005029</identifier><language>eng</language><publisher>United States: Elsevier Inc</publisher><subject>Biological Evolution ; Crow–Kimura model ; Error threshold ; Gene Frequency ; Models, Biological ; Mutation ; Quasispecies model ; Selection, Genetic ; Selection–mutation equilibrium ; Single peaked landscape</subject><ispartof>Mathematical biosciences, 2015-08, Vol.266, p.1-9</ispartof><rights>2015</rights><rights>Copyright © 2015. Published by Elsevier Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-71ad3ba0330399580a89f66776ad594bb0ea3c7a4d91e34b83b7216d504850803</citedby><cites>FETCH-LOGICAL-c396t-71ad3ba0330399580a89f66776ad594bb0ea3c7a4d91e34b83b7216d504850803</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0025556415001029$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26005029$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Semenov, Yuri S.</creatorcontrib><creatorcontrib>Novozhilov, Artem S.</creatorcontrib><title>Exact solutions for the selection–mutation equilibrium in the Crow–Kimura evolutionary model</title><title>Mathematical biosciences</title><addtitle>Math Biosci</addtitle><description>•We find stationary distributions of the Crow–Kimura model for specific fitness landscapes.•We propose a generating function method for the equilibrium distributions.•We give simple analytical expressions for a number of examples.•Our method generalizes the random variable technique.
We reformulate the eigenvalue problem for the selection–mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations.</description><subject>Biological Evolution</subject><subject>Crow–Kimura model</subject><subject>Error threshold</subject><subject>Gene Frequency</subject><subject>Models, Biological</subject><subject>Mutation</subject><subject>Quasispecies model</subject><subject>Selection, Genetic</subject><subject>Selection–mutation equilibrium</subject><subject>Single peaked landscape</subject><issn>0025-5564</issn><issn>1879-3134</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kE1OwzAQRi0EoqVwADYoSzYJ4zh2YrFCVfkRldjA2jjJVLhK6tZOCuy4AzfkJLi0sEQaaUajN5_sR8gphYQCFRfzpC19kgLlCYSCdI8MaZHLmFGW7ZNh2PCYc5ENyJH3cwCaUyoOySAVABxSOSTPkzdddZG3Td8Zu_DRzLqoe8HIY4PVZvX18dn2nd6MEa5605jSmb6NzOKHGzv7GpB70_ZOR7jeBWn3HrW2xuaYHMx04_Fk10fk6XryOL6Npw83d-OraVwxKbo4p7pmpQbGgEnJC9CFnAmR50LXXGZlCahZleuslhRZVhaszFMqag5ZwaEANiLn29yls6sefada4ytsGr1A23tFhRS0CMkioHSLVs5673Cmls604cWKgtqIVXMVxKqNWAWhIA03Z7v4vmyx_rv4NRmAyy2A4ZNrg075yuCiwtq4IFLV1vwT_w2WfItb</recordid><startdate>20150801</startdate><enddate>20150801</enddate><creator>Semenov, Yuri S.</creator><creator>Novozhilov, Artem S.</creator><general>Elsevier Inc</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20150801</creationdate><title>Exact solutions for the selection–mutation equilibrium in the Crow–Kimura evolutionary model</title><author>Semenov, Yuri S. ; Novozhilov, Artem S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-71ad3ba0330399580a89f66776ad594bb0ea3c7a4d91e34b83b7216d504850803</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Biological Evolution</topic><topic>Crow–Kimura model</topic><topic>Error threshold</topic><topic>Gene Frequency</topic><topic>Models, Biological</topic><topic>Mutation</topic><topic>Quasispecies model</topic><topic>Selection, Genetic</topic><topic>Selection–mutation equilibrium</topic><topic>Single peaked landscape</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Semenov, Yuri S.</creatorcontrib><creatorcontrib>Novozhilov, Artem S.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Mathematical biosciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Semenov, Yuri S.</au><au>Novozhilov, Artem S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact solutions for the selection–mutation equilibrium in the Crow–Kimura evolutionary model</atitle><jtitle>Mathematical biosciences</jtitle><addtitle>Math Biosci</addtitle><date>2015-08-01</date><risdate>2015</risdate><volume>266</volume><spage>1</spage><epage>9</epage><pages>1-9</pages><issn>0025-5564</issn><eissn>1879-3134</eissn><abstract>•We find stationary distributions of the Crow–Kimura model for specific fitness landscapes.•We propose a generating function method for the equilibrium distributions.•We give simple analytical expressions for a number of examples.•Our method generalizes the random variable technique.
We reformulate the eigenvalue problem for the selection–mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations.</abstract><cop>United States</cop><pub>Elsevier Inc</pub><pmid>26005029</pmid><doi>10.1016/j.mbs.2015.05.002</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Mathematical biosciences, 2015-08, Vol.266, p.1-9 |
| issn | 0025-5564 1879-3134 |
| language | eng |
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| source | MEDLINE; ScienceDirect Journals (5 years ago - present) |
| subjects | Biological Evolution Crow–Kimura model Error threshold Gene Frequency Models, Biological Mutation Quasispecies model Selection, Genetic Selection–mutation equilibrium Single peaked landscape |
| title | Exact solutions for the selection–mutation equilibrium in the Crow–Kimura evolutionary model |
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