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تسجيل مستخدم جديدA Stochastic Adaptive Dynamics Model for Bacterial Populations with Mutation, Dormancy and Transfer
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This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it combines the recent model of Champagnat, Meleard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and Tobias (2020). Our main result is a convergence theorem which describes the evolution of the different traits in the population on a `doubly logarithmic scale as piece-wise affine functions. Interestingly, even for a relatively small trait space, the limiting process exhibits a non-monotone dependence of the success of the dormancy trait on the dormancy initiation probability. Further, the model establishes a new `approximate coexistence regime for multiple traits that has not been observed in previous literature.
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We investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution called dormancy and horizontal gene transfer. The corresponding traits come in many guises and are ubiquitous in microbial communities, aff
ecting their dynamics in important ways. Recently, they have each moved (separately) into the focus of stochastic individual-based modelling (Billiard et al. 2016, 2018; Champagnat, Meleard and Tran, 2021; Blath and Tobias 2020). Here, we examine their combined effects in a unified model. Indeed, we consider the (idealized) scenario of two sub-populations, respectively carrying trait 1 and trait 2, where trait 1 individuals are able to switch (under competitive pressure) into a dormant state, and trait 2 individuals are able to execute horizontal gene transfer, turning trait 1 individuals into trait 2 ones, at a rate depending on the frequency of individuals. In the large-population limit, we examine the fate of a single trait i individual (a mutant) arriving in a trait j resident population living in equilibrium, for $i,j=1,2,i eq j$. We provide a complete analysis of the invasion dynamics in all cases where the resident population is individually fit and the initial behaviour of the mutant population is non-critical. We identify parameter regimes for the invasion and fixation of the new trait, stable coexistence of the two traits, and founder control (where the initial resident always dominates, irrespective of its trait). The most striking result is that stable coexistence occurs in certain scenarios even if trait 2 (which benefits from transfer at the cost of trait 1) would be unfit when being merely on its own. In the case of founder control, the limiting dynamical system has an unstable coexistence equilibrium. In all cases, we observe the classical (up to 3) phases of invasion dynamics `a la Champagnat (2006).
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Fernando Cordero
, Adrian Gonzalez Casanova
, Jason Schweinsberg andn Maite Wilke-Berenguer
2020
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