Replicator-mutator equations with quadratic fitness
Copyright policy )Replicator-mutator equations with quadratic fitness
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.
12 pages
long-time behaviour, nonlocal reaction diffusion equation, evolutionary genetics, Solutions to PDEs in closed form, Integro-partial differential equations, Mathematics - Analysis of PDEs, Problems related to evolution, extinction in finite time, FOS: Mathematics, Genetics and epigenetics, Initial value problems for second-order parabolic equations, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], explicit solution, Analysis of PDEs (math.AP)
long-time behaviour, nonlocal reaction diffusion equation, evolutionary genetics, Solutions to PDEs in closed form, Integro-partial differential equations, Mathematics - Analysis of PDEs, Problems related to evolution, extinction in finite time, FOS: Mathematics, Genetics and epigenetics, Initial value problems for second-order parabolic equations, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], explicit solution, Analysis of PDEs (math.AP)
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