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Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches

Abstract : Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to their offspring. Consistent experimental evidence report that this phenomenon plays an essential role in the evolution of certain bacterias. In particular, HT is believed to be the main instrument of developing the antibiotic resistance. In this work, we consider several models which describe this phenomenon: a stochastic jump process (individual-based) and the deterministic nonlinear integrod-ifferential equation obtained as a limit for large populations. We also consider a Hamilton-Jacobi equation, obtained as a limit of the deterministic model under the assumption of small mutations. The goal of this paper is to compare these models with the help of numerical simulations. More specifically, our goal is to understand to which extent the Hamilton-Jacobi model reproduces the qualitative behavior of the stochastic model and the phenomenon of evolutionary rescue in particular.
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https://hal.archives-ouvertes.fr/hal-02166168
Contributor : Anna Melnykova <>
Submitted on : Wednesday, June 26, 2019 - 3:23:43 PM
Last modification on : Wednesday, March 10, 2021 - 3:04:06 PM

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Vincent Calvez, Susely Figueroa Iglesias, Hélène Hivert, Sylvie Méléard, Anna Melnykova, et al.. Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches. ESAIM: Proceedings and Surveys, EDP Sciences, 2020, CEMRACS 2018 - Numerical and mathematical modeling for biological and medical applications: deterministic, probabilistic and statistical descriptions, 67, pp.135-160. ⟨10.1051/proc/202067009⟩. ⟨hal-02166168⟩

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