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arXiv · 2511.12141

Concentration in selection-mutation models: error estimates and asymptotic expansions

Caroline Guinet·Sepideh Mirrahimi·Jean-Michel Roquejoffre
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Abstract

In this paper, we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We provide an asymptotic analysis of the model, assuming that the mutations have small effects. A standard approach for the analysis of the qualitative properties of the solutions of such an equation is to apply a logarithmic transformation, which yields a Hamilton-Jacobi equation with constraint. When the reproduction term is a concave function of the trait, it has been established that the solution is classical. We rigorously derive a first-order asymptotic expansion of the solution. This expansion allows us to approximate the moments of the phenotypic density. This result establishes a connection between the approximations of the phenotypic density obtained via the Hamilton-Jacobi approach and relevant biological quantities, which are more suitable from a modeling perspective.

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Caroline Guinet, Sepideh Mirrahimi, Jean-Michel Roquejoffre. 2025-11-15. Concentration in selection-mutation models: error estimates and asymptotic expansions. https://arxiv.org/abs/2511.12141

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