Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution
In a (two-type) Wright–Fisher diffusion with directional selection and two-way mutation, let x denote today’s frequency of the beneficial type, and given x, let h(x) be the probability that, among all individuals of today’s population, the individual whose progeny will eventually take over in the po...
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| Veröffentlicht in: | Theoretical population biology 2015-08, Vol.103, p.27-37 |
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| creator | Lenz, Ute Kluth, Sandra Baake, Ellen Wakolbinger, Anton |
| description | In a (two-type) Wright–Fisher diffusion with directional selection and two-way mutation, let x denote today’s frequency of the beneficial type, and given x, let h(x) be the probability that, among all individuals of today’s population, the individual whose progeny will eventually take over in the population is of the beneficial type. Fearnhead (2002) and Taylor (2007) obtained a series representation for h(x). We develop a construction that contains elements of both the ancestral selection graph and the lookdown construction and includes pruning of certain lines upon mutation. Besides being interesting in its own right, this construction allows a transparent derivation of the series coefficients of h(x) and gives them a probabilistic meaning. |
| doi_str_mv | 10.1016/j.tpb.2015.01.005 |
| format | Article |
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Fearnhead (2002) and Taylor (2007) obtained a series representation for h(x). We develop a construction that contains elements of both the ancestral selection graph and the lookdown construction and includes pruning of certain lines upon mutation. 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Besides being interesting in its own right, this construction allows a transparent derivation of the series coefficients of h(x) and gives them a probabilistic meaning.</description><subject>Ancestral selection graph</subject><subject>Common ancestor type distribution</subject><subject>Lookdown graph</subject><subject>Mutation</subject><subject>Probability</subject><subject>Pruning</subject><subject>Selection, Genetic</subject><subject>Wright–Fisher diffusion with selection and mutation</subject><issn>0040-5809</issn><issn>1096-0325</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkcFO3DAURa0KVKbQD-gGeckm6XMcOw6sEGpppZG6gbXl2C-MhyRO7QyIv6-nQ1nSlWXp3KOnewn5wqBkwOTXbbnMXVkBEyWwEkB8ICsGrSyAV-KIrABqKISC9oR8SmkLAIpx_pGcVEK1jFdyReZ1CI9-eqAuPE_UT3TZIDWTxbREM9CEA9rFh4k-RDNvLuk1nWPoTOcHnxZvqZnz39gNXcLfqA3jmOmDIUS6vMxIXWaj73Z70Rk57s2Q8PPre0ruv3-7u_lRrH_d_ry5XheWK7kUQri6l2i4cqJta1OLrumQ9db0spISUdSK2xpN1zRW8J5BlSPWVY00rm8FPyUXB2--7_cuH6NHnywOg5kw7JJmTS2VUg2D_6OylUxJyfZWdkBtDClF7PUc_Wjii2ag95vorc6b6P0mGpjOm-TM-at-143o3hL_RsjA1QHA3MeTx6iT9ZgbdD7m9rUL_h39H2IPnjM</recordid><startdate>201508</startdate><enddate>201508</enddate><creator>Lenz, Ute</creator><creator>Kluth, Sandra</creator><creator>Baake, Ellen</creator><creator>Wakolbinger, Anton</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><scope>7SN</scope><scope>C1K</scope></search><sort><creationdate>201508</creationdate><title>Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution</title><author>Lenz, Ute ; Kluth, Sandra ; Baake, Ellen ; Wakolbinger, Anton</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-55d4f6ea38d5994a45b7be1fcaf6266ee5483c4eab77c53f10255dcd276adf953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Ancestral selection graph</topic><topic>Common ancestor type distribution</topic><topic>Lookdown graph</topic><topic>Mutation</topic><topic>Probability</topic><topic>Pruning</topic><topic>Selection, Genetic</topic><topic>Wright–Fisher diffusion with selection and mutation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lenz, Ute</creatorcontrib><creatorcontrib>Kluth, Sandra</creatorcontrib><creatorcontrib>Baake, Ellen</creatorcontrib><creatorcontrib>Wakolbinger, Anton</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><collection>Ecology Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><jtitle>Theoretical population biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lenz, Ute</au><au>Kluth, Sandra</au><au>Baake, Ellen</au><au>Wakolbinger, Anton</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution</atitle><jtitle>Theoretical population biology</jtitle><addtitle>Theor Popul Biol</addtitle><date>2015-08</date><risdate>2015</risdate><volume>103</volume><spage>27</spage><epage>37</epage><pages>27-37</pages><issn>0040-5809</issn><eissn>1096-0325</eissn><abstract>In a (two-type) Wright–Fisher diffusion with directional selection and two-way mutation, let x denote today’s frequency of the beneficial type, and given x, let h(x) be the probability that, among all individuals of today’s population, the individual whose progeny will eventually take over in the population is of the beneficial type. 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| ispartof | Theoretical population biology, 2015-08, Vol.103, p.27-37 |
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| source | MEDLINE; ScienceDirect Journals (5 years ago - present) |
| subjects | Ancestral selection graph Common ancestor type distribution Lookdown graph Mutation Probability Pruning Selection, Genetic Wright–Fisher diffusion with selection and mutation |
| title | Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution |
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