Multiscale eco-evolutionary models: from individuals to populations - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2023

Multiscale eco-evolutionary models: from individuals to populations

Résumé

Motivated by recent biological experiments, we emphasize the effects of small populations in various biological/medical contexts related to evolution such as invasion of mutant cells or emergence of antibiotic resistances. Our main mathematical challenge is to quantify such effects in particular on macroscopic approximations. In order to track individuals and to take into account small populations, we are led to stochastic multiscale models while the limiting macroscopic equations should involve non local non linear partial differential equations. Such approximations are used to analyse the conditions for a mutant invasion from a monotype population and to provide the mutant probability of fixation and its time to fixation. That allows to exhibit a rare mutation scale assumption yielding a timescale separation between competition and mutation. Under these assumptions, the stochastic measure-valued process at the mutation timescale converges to a jump process which describes the successive invasions of successful mutants. The gene transfer can drastically affect the evolutionary outcomes. For fast mutation timescales, preliminary numerical simulations indicate that these models should exhibit many surprising asymptotic behaviours such as cyclic behaviours. These phenomena are mathematically explored on a simple model. Population sizes and times are considered in a log scale to keep track of small subpopulations that have negligible sizes compared with the size of the resident population. Explicit criteria on the model parameters are given to characterise the possible evolutionary outcomes. An important ingredient for the proofs lies in comparison of the stochastic population process with linear or logistic birth-death processes with immigration. The impact of these time and size scales on macroscopic approximations is also investigated, leading to a new class of Hamilton-Jacobi equations with constraint boundary conditions.
Fichier principal
Vignette du fichier
ICM-Champagnat-Meleard-Tran.pdf (1.86 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-04407958 , version 1 (22-01-2024)

Licence

Paternité

Identifiants

Citer

Nicolas Champagnat, Sylvie Méléard, Viet Chi Tran. Multiscale eco-evolutionary models: from individuals to populations. International Congress of Mathematicians, ICM 2022, Jul 2022, fully virtually, Russia. pp.5656-5678, ⟨10.4171/ICM2022/24⟩. ⟨hal-04407958⟩
26 Consultations
11 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More