Replicator-mutator equations with quadratic fitness
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- by Matthieu Alfaro and Rémi Carles PDF
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Abstract:
This work completes our previous analysis on models arising in evolutionary genetics. We consider the so-called replicator-mutator equation, when the fitness is quadratic. This equation is a heat equation with a harmonic potential, plus a specific nonlocal term. We give an explicit formula for the solution, thanks to which we prove that when the fitness is nonpositive (harmonic potential), solutions converge to a universal stationary Gaussian for large time, whereas when the fitness is nonnegative (inverted harmonic potential), solutions always become extinct in finite time.References
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Additional Information
- Matthieu Alfaro
- Affiliation: CNRS and Université de Montpellier, IMAG, CC 051, 34095 Montpellier, France
- MR Author ID: 801390
- Email: matthieu.alfaro@umontpellier.fr
- Rémi Carles
- Affiliation: CNRS and Université de Montpellier, IMAG, CC 051, 34095 Montpellier, France
- ORCID: 0000-0002-8866-587X
- Email: remi.carles@math.cnrs.fr
- Received by editor(s): November 18, 2016
- Received by editor(s) in revised form: January 15, 2017
- Published electronically: August 29, 2017
- Communicated by: Catherine Sulem
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5315-5327
- MSC (2010): Primary 92D15, 35K15, 45K05, 35C05
- DOI: https://doi.org/10.1090/proc/13669
- MathSciNet review: 3717959