Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models
Abstract
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it possible to bridge individual-level mechanisms with population-scale evolutionary dynamics. We start by formulating a stochastic agent-based model, which describes the dynamics of single population members undergoing proliferation, death, and phenotype changes. Then, we formally derive the corresponding mesoscopic model, which consists of an integro-differential equation for the distribution of population members over the space of phenotypes, where phenotype changes are modelled via an integral kernel. Finally, considering a quasi-invariant regime of small but frequent phenotype changes, we rigorously derive a non-local Fokker-Planck-type equation counterpart of this model, wherein phenotype changes are taken into account by an advection-diffusion term. The theoretical results obtained are illustrated through a sample of results of numerical simulations.
Keywords
Cite
@article{arxiv.2510.15646,
title = {Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models},
author = {Emanuele Bernardi and Tommaso Lorenzi and Andrea Tosin},
journal= {arXiv preprint arXiv:2510.15646},
year = {2025}
}