Density dependent replicator-mutator models in directed evolution

Matthieu Alfaro; Mario Veruete

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arXiv · 1901.07848

Density dependent replicator-mutator models in directed evolution

Matthieu Alfaro·Mario Veruete

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Abstract

We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal rescaling related to the Avron-Herbst formula [1] to give of a complete picture of the Cauchy problem. Besides its well-posedness, we provide an implicit/explicit expression of the solution, and analyze its large time behaviour. As a by product, we also solve a replicator-mutator model where the mutation coefficient is socially determined, in the sense that it is modulated by the mean-fitness. The latter model reveals concentration or anti diffusion/diffusion phenomena.

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Matthieu Alfaro, Mario Veruete. 2019-01-23. Density dependent replicator-mutator models in directed evolution. https://arxiv.org/abs/1901.07848

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