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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Replicator-mutator equations with quadratic fitness
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by Matthieu Alfaro and Rémi Carles PDF
Proc. Amer. Math. Soc. 145 (2017), 5315-5327 Request permission

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.
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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