Cemracs 2018 project.

Participants: Susely Figueroa Iglesias (Université Paul Sabatier, Toulouse), Anna Melnykova (Université de Cergy-Pontoise and Université de Grenoble Alpes), Samuel Nordmann (CAMS, EHESS, PSL Université, Paris)

Supervisors: Sylvie Méléard, Vincent Calvez

Abstract:

Horizontal Gene Transfer (HGT) enables exchange of genetic material between individuals among the same population without filiation. This modulus operandi is known to play a key role in the evolution of resistance against antibiotics at the population level. The aim of the project is to investigate this fundamental question in the light of recent results at the interface stochastic processes/partial differential equations. The expected outcomes are quantitative results to decipher evolutionary dynamics subject to HGT and especially possible evolutionary rescue of populations that could be driven to extinction under unilateral HGT.

The cornerstone of the project will be the comparative numerical investigation of the individual-based stochastic process introduced in [1,2] with the integro-differential model obtained in the limit of large population size in the same articles. In particular, the probability of evolutionary rescue (population renewal from a pool of few individuals possibly far from the common type) will be carefully estimated from simulations of the stochastic process. It will be compared with a heuristics derived from the analysis of the integro-differential model based on the approximation of small phenotypical variance of its solutions, after [3,4].

This project will be completed by the reconstruction of lineages that led to evolutionary rescue when it happened, based on stochastic simulations.

[1] S Billiard, P Collet, R Ferrière, S Méléard, Viet Chi Tran. Stochastic dynamics for adaptation and evolution of microorganisms, preprint arXiv (2016)

[2] S Billiard, P Collet, R Ferrière, S Méléard, Viet Chi Tran. The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism, Journal of Theoretical Biology (2016)

[3] O Diekmann, PE Jabin, S Mischler, B Perthame. The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theoretical Population Biology (2005)

[4] A Lorz, S Mirrahimi, B Perthame. Dirac mass dynamics in multidimensional nonlocal parabolic equations, Communication in Partial Differential Equations (2011)

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