Selection–mutation dynamics with asymmetrical reproduction kernels
We study a family of selection–mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents: we assume that each individual inherits mostly its trait from the female or that the trait act...
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| Published in | Nonlinear analysis Vol. 222; p. 112947 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.09.2022
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| Abstract | We study a family of selection–mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents: we assume that each individual inherits mostly its trait from the female or that the trait acts on the female fecundity but does not affect male. Following previous works inspired from principles of adaptive dynamics, we rescale time and assume that mutations have limited effects on the phenotype. Our goal is to study the asymptotic behavior of the population distribution. We derive non-extinction conditions and BV estimates on the total population. We also obtain Lipschitz estimates on the solutions of Hamilton–Jacobi equations that arise from the study of the population distribution concentration at fittest traits. Concentration results are obtained in some special cases by using a Lyapunov functional. |
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| AbstractList | We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual inherits mostly its trait from the female or that the trait acts on the female fecundity but does not affect male. Following previous works inspired from principles of adaptive dynamics, we rescale time and assume that mutations have limited effects on the phenotype. Our goal is to study the asymptotic behavior of the population distribution. We derive non-extinction conditions and BV estimates on the total population. We also obtain Lipschitz estimates on the solutions of Hamilton-Jacobi equations that arise from the study of the population distribution concentration at fittest traits. Concentration results are obtained in some special cases by using a Lyapunov functional. |
| ArticleNumber | 112947 |
| Author | Strugarek, Martin Perthame, Benoît Taing, Cécile |
| Author_xml | – sequence: 1 givenname: Benoît orcidid: 0000-0002-7091-1200 surname: Perthame fullname: Perthame, Benoît email: benoit.perthame@sorbonne-universite.fr organization: Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, F-75005 Paris, France – sequence: 2 givenname: Martin surname: Strugarek fullname: Strugarek, Martin email: martin.strugarek@agriculture.gouv.fr organization: Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, F-75005 Paris, France – sequence: 3 givenname: Cécile surname: Taing fullname: Taing, Cécile email: cecile.taing@univ-poitiers.fr organization: Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, F-86073 Poitiers, France |
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| Cites_doi | 10.1512/iumj.2008.57.3398 10.1093/oxfordjournals.jhered.a023035 10.1006/jeth.2000.2696 10.1371/journal.pone.0123961 10.3934/mbe.2018043 10.1007/s10440-011-9603-0 10.5802/jep.100 10.1016/j.jde.2011.03.007 10.1007/s00285-017-1175-9 10.1007/s10955-014-1062-3 10.1016/S0764-4442(98)80161-4 10.1017/S0016672300004742 10.1016/j.jet.2014.07.001 10.1080/03605302.2010.538784 10.1098/rspb.2006.3725 10.1007/s00526-020-01819-0 10.1007/s00285-012-0562-5 10.1007/s00285-010-0370-8 10.1090/S0273-0979-1992-00266-5 10.1093/genetics/138.3.913 10.1554/06-291.1 10.2307/2640805 10.1016/j.tpb.2012.12.003 10.1038/22521 10.1090/S0273-0979-03-00988-1 10.1137/21M1397313 10.1007/s00285-017-1181-y 10.1016/j.tpb.2004.12.003 10.1088/1361-6544/aa85da 10.1016/j.geb.2016.08.003 10.4310/CMS.2008.v6.n3.a10 10.1007/s11538-014-0046-4 |
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| Snippet | We study a family of selection–mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric... We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric... |
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| SubjectTerms | Adaptive dynamics Analysis of PDEs Asymptotic analysis Integro-differential equations Mathematics Population biology |
| Title | Selection–mutation dynamics with asymmetrical reproduction kernels |
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