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A moment-based approach for the analysis of the infinitesimal model

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Abstract : We provide an asymptotic analysis of a nonlinear integro-differential equation which describes the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is modeled via a nonlinear integral term, known as the 'infinitesimal model'. We consider a regime of small segregational variance, where a parameter in the infinitesimal operator, which measures the deviation between the trait of the offspring and the mean parental trait, is small. We prove that in this regime the phenotypic distribution remains close to a Gaussian profile with a fixed small variance and we characterize the dynamics of the mean phenotypic trait via an ordinary differential equation. We also briefly discuss the extension of the method to the study of steady solutions and their stability.

MSC Codes :
35B40 - Asymptotic behavior of solutions of PDE
47G20 - Integro-differential operators, See also {45J05, 45K05}
92D15 - Problems related to evolution
35Q92 - PDEs in connection with biology and other natural sciences

    Information on the Video

    Language : English
    Available date : 11/10/2024
    Conference Date : 26/09/2024
    Subseries : Research talks
    arXiv category : Analysis of PDEs ; Combinatorics
    Mathematical Area(s) : PDE
    Format : MP4 (.mp4) - HD
    Video Time : 00:46:50
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-09-25_Mirrahimi.mp4

Information on the Event

Event Title : Non-local branching processes / Processus de branchement non local
Dates : 23/09/2024 - 27/09/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3109.html

Citation Data

DOI : 10.24350/CIRM.V.20249103
Cite this video as: (2024). A moment-based approach for the analysis of the infinitesimal model. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20249103
URI : http://dx.doi.org/10.24350/CIRM.V.20249103

See Also

Bibliography

  • GUERAND, J., HILLAIRET, M., et MIRRAHIMI, S. A moment-based approach for the analysis of the infinitesimal model in the regime of small variance. arXiv preprint arXiv:2309.09567, 2023. - https://doi.org/10.48550/arXiv.2309.09567



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