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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Bibliographic Details
Published inNonlinear analysis Vol. 222; p. 112947
Main Authors Perthame, Benoît, Strugarek, Martin, Taing, Cécile
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2022
Elsevier
Subjects
Adaptive dynamics
Analysis of PDEs
Asymptotic analysis
Integro-differential equations
Mathematics
Population biology
35F21
Adaptive dynamics
Population biology
Integro-differential equations
45K05
35B40
Asymptotic analysis
35Q92
Mathematical biology
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Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2022.112947