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arXiv · 2412.08178

Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes

Sahani Pathiraja·Philipp Wacker
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Abstract

The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the replicator-mutator equation in continuous time and for continuous traits for a quadratic fitness function. Using these results we can explain and quantify (without the need for numerical in-silico simulations) a series of evolutionary phenomena, in particular the flying kite effect, survival of the flattest, and the ability of a population to sustain itself while tracking an optimal feature which may be fixed, moving with bounded velocity in trait space, oscillating, or randomly fluctuating.

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Sahani Pathiraja, Philipp Wacker. 2024-12-11. Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes. https://arxiv.org/abs/2412.08178

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