Long Time Evolutionary Dynamics of Phenotypically Structured Populations in Time-Periodic Environments
| Autor: | Sepideh Mirrahimi, Susely Figueroa Iglesias |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
Hamilton-Jacobi equation with constraint
Population 01 natural sciences [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] Mathematics - Analysis of PDEs FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Quantitative Biology::Populations and Evolution Applied mathematics Growth rate 0101 mathematics Evolutionary dynamics education Selection (genetic algorithm) Mathematics education.field_of_study Time periodic coefficients Applied Mathematics Dirac (video compression format) 010102 general mathematics Dynamics (mechanics) 35B27 Dirac concentrations Time-periodic coefficients Adaptive evolution AMS subject classifications: 35B10 92D15 010101 applied mathematics Constraint (information theory) Computational Mathematics Distribution (mathematics) 35K57 Parabolic integro-differential equations Analysis Analysis of PDEs (math.AP) |
| Zdroj: | SIAM Journal on Mathematical Analysis SIAM Journal on Mathematical Analysis, 2018, ⟨10.1137/18M1175185⟩ SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, ⟨10.1137/18M1175185⟩ |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/18m1175185 |
| Popis: | International audience; We study the long time behavior of a parabolic Lotka-Volterra type equation considering a time-periodic growth rate with non-local competition. Such equation describes the dynamics of a phenotypically struc-tured population under the effect of mutations and selection in a fluctuating environment. We first prove that, in long time, the solution converges to the unique periodic solution of the problem. Next, we describe this periodic solution asymptotically as the effect of the mutations vanish. Using a theory based on Hamilton-Jacobi equations with constraint, we prove that, as the effect of the mutations vanishes, the solution concentrates on a single Dirac mass, while the size of the population varies periodically in time. When the effect of the mutations are small but nonzero, we provide some formal approximations of the moments of the population's distribution. We then show, via some examples, how such results could be compared to biological experiments. |
| Databáze: | OpenAIRE |
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