The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: the case of stacked underdominant clines
We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of allele frequencies and linkage disequilibrium between the two...
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| Veröffentlicht in: | Journal of mathematical biology 2022-02, Vol.84 (3), p.20-20, Article 20 |
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| creator | Alfaro, Matthieu Griette, Quentin Roze, Denis Sarels, Benoît |
| description | We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of allele frequencies and linkage disequilibrium between the two loci, and use a quasi-linkage equilibrium approximation in order to reduce the number of variables. We investigate the solutions of this system and demonstrate the existence of a solution in which the two clines in allele frequency remain stacked together. In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. We obtain an approximation for the speed of this wave which, in particular, is decreased by recombination between the two loci but is always larger than the speed of “one cline alone”. |
| doi_str_mv | 10.1007/s00285-022-01722-6 |
| format | Article |
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In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. We obtain an approximation for the speed of this wave which, in particular, is decreased by recombination between the two loci but is always larger than the speed of “one cline alone”.</description><identifier>ISSN: 0303-6812</identifier><identifier>EISSN: 1432-1416</identifier><identifier>DOI: 10.1007/s00285-022-01722-6</identifier><identifier>PMID: 35166930</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Alleles ; Analysis of PDEs ; Applications of Mathematics ; Approximation ; Clines ; Differential equations ; Diploids ; Diploidy ; Gene Frequency ; Linkage Disequilibrium ; Loci ; Mathematical analysis ; Mathematical and Computational Biology ; Mathematics ; Mathematics and Statistics ; Models, Genetic ; Partial differential equations ; Recombination ; Selection, Genetic ; Traveling waves</subject><ispartof>Journal of mathematical biology, 2022-02, Vol.84 (3), p.20-20, Article 20</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022</rights><rights>2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c453t-7c64721d8efd2865a96334fb773049298630218069feeb1aba4b3c3855846bf13</citedby><cites>FETCH-LOGICAL-c453t-7c64721d8efd2865a96334fb773049298630218069feeb1aba4b3c3855846bf13</cites><orcidid>0000-0002-8227-4448 ; 0000-0001-5978-9358 ; 0000-0001-6872-920X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00285-022-01722-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00285-022-01722-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/35166930$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-03109887$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Alfaro, Matthieu</creatorcontrib><creatorcontrib>Griette, Quentin</creatorcontrib><creatorcontrib>Roze, Denis</creatorcontrib><creatorcontrib>Sarels, Benoît</creatorcontrib><title>The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: the case of stacked underdominant clines</title><title>Journal of mathematical biology</title><addtitle>J. Math. Biol</addtitle><addtitle>J Math Biol</addtitle><description>We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of allele frequencies and linkage disequilibrium between the two loci, and use a quasi-linkage equilibrium approximation in order to reduce the number of variables. We investigate the solutions of this system and demonstrate the existence of a solution in which the two clines in allele frequency remain stacked together. In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. 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Academic</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alfaro, Matthieu</au><au>Griette, Quentin</au><au>Roze, Denis</au><au>Sarels, Benoît</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The spatio-temporal dynamics of interacting genetic incompatibilities. 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In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. We obtain an approximation for the speed of this wave which, in particular, is decreased by recombination between the two loci but is always larger than the speed of “one cline alone”.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><pmid>35166930</pmid><doi>10.1007/s00285-022-01722-6</doi><tpages>1</tpages><orcidid>https://orcid.org/0000-0002-8227-4448</orcidid><orcidid>https://orcid.org/0000-0001-5978-9358</orcidid><orcidid>https://orcid.org/0000-0001-6872-920X</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of mathematical biology, 2022-02, Vol.84 (3), p.20-20, Article 20 |
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| language | eng |
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| source | MEDLINE; SpringerLink Journals - AutoHoldings |
| subjects | Alleles Analysis of PDEs Applications of Mathematics Approximation Clines Differential equations Diploids Diploidy Gene Frequency Linkage Disequilibrium Loci Mathematical analysis Mathematical and Computational Biology Mathematics Mathematics and Statistics Models, Genetic Partial differential equations Recombination Selection, Genetic Traveling waves |
| title | The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: the case of stacked underdominant clines |
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