Asymptotic analysis of a quantitative genetics model with nonlinear integral operator

DOI10.5802/jep.100zbMath1420.35167arXiv1811.01779OpenAlexW2965521458MaRDI QIDQ2315131

Vincent Calvez, Florian Patout, Jimmy Garnier

Publication date: 1 August 2019

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01779

zbMATH Keywords

integro-differential equationsasymptotic analysisquantitative geneticsnon linear spectral theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Integro-differential operators (47G20)

Related Items (10)

Dynamics of Dirac concentrations in the evolution of quantitative alleles with sexual reproduction ⋮ Selection-mutation dynamics with asymmetrical reproduction kernels ⋮ Ancestral lineages in mutation selection equilibria with moving optimum ⋮ Ergodicity of the Fisher infinitesimal model with quadratic selection ⋮ Adaptation of a quantitative trait to a changing environment: new analytical insights on the asexual and infinitesimal sexual models ⋮ The best of both worlds: combining population genetic and quantitative genetic models ⋮ The Cauchy problem for the infinitesimal model in the regime of small variance ⋮ Front Propagation of a Sexual Population with Evolution of Dispersion: A Formal Analysis ⋮ A Nonexpanding Transport Distance for Some Structured Equations ⋮ Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

Cites Work

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• Dynamics of sexual populations structured by a space variable and a phenotypical trait
• Local stability of perfect alignment for a spatially homogeneous kinetic model
• An integro-PDE model for evolution of random dispersal
• A Hamilton-Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations
• A Hamilton-Jacobi approach for a model of population structured by space and trait
• Asymptotic analysis of a selection model with space
• Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result
• The effects of density dependence and immigration on local adaptation and niche evolution in a black-hole sink environment
• Commentary: ``Fisher's infinitesimal model: a story for the ages
• The infinitesimal model: definition, derivation, and implications
• Adaptation and migration of a population between patches
• Non-local competition slows down front acceleration during dispersal evolution
• Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation
• Singular limits for models of selection and mutations with heavy-tailed mutation distribution
• Uniqueness in a class of Hamilton-Jacobi equations with constraints
• A note on a nonlinear Krein-Rutman theorem
• The dynamics of adaptation: An illuminating example and a Hamilton--Jacobi approach
• Modelling wild-domestic interbreeding: how selection on a quantitative trait affects gene flow at a neutral locus
• Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Thin Front Limit of an Integro-differential Fisher-KPP Equation with Fat-Tailed Kernels
• A Hamilton–Jacobi approach to characterize the evolutionary equilibria in heterogeneous environments
• Singular Limits for Reaction-Diffusion Equations with Fractional Laplacian and Local or Nonlocal Nonlinearity

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