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arXiv · 1611.06119

Replicator-mutator equations with quadratic fitness

Matthieu Alfaro·Rémi Carles
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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 non-positive (harmonic potential), solutions converge to a universal stationary Gaussian for large time, whereas when the fitness is non-negative (inverted harmonic potential), solutions always become extinct in finite time.

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Matthieu Alfaro, Rémi Carles. 2016-11-18. Replicator-mutator equations with quadratic fitness. https://doi.org/10.1090/proc%2F13669

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