%0 Journal Article
%T Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer
%+ Institut Élie Cartan de Lorraine (IECL)
%+ Biology, genetics and statistics (BIGS)
%+ Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
%+ Laboratoire Analyse et Mathématiques Appliquées (LAMA)
%A Champagnat, Nicolas
%A Méléard, Sylvie
%A Tran, Viet Chi
%Z N.C., S.M. and V.C.T. have been supported by the Chair "Modélisation Mathématique et Bio-diversité" of Veolia Environnement - Ecole Polytechnique -Museum National d'Histoire Naturelle - Fondation X.V.C.T. also acknowledges support from ANR CADENCE (ANR-16-CE32-0007) and Labex Bézout (ANR-10-LABX-58).
%< avec comité de lecture
%@ 1050-5164
%J Annals of Applied Probability
%I Institute of Mathematical Statistics (IMS)
%V 31
%N 4
%P 1820-1867
%8 2021
%D 2021
%R 10.1214/20-AAP1635
%K stochastic individual-based models
%K bacterial conjugation
%K long time behavior
%K large population approximation
%K logistic competition
%K branching processes with immigration
%K horizontal gene transfer
%K coupling
%Z MSC 2000 subject classification : 92D25, 92D15, 60J80, 60K35, 60F99
%Z Mathematics [math]/Probability [math.PR]
%Z Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE]Journal articles
%X Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the population towards lower birth rates. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration. For the latter processes, we derive several results of independent interest.
%G English
%2 https://hal.inria.fr/hal-01974289v3/document
%2 https://hal.inria.fr/hal-01974289v3/file/Transfert-oaxaca-02-10-2020.pdf
%L hal-01974289
%U https://hal.inria.fr/hal-01974289
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