The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes

Blath, Jochen; Tóbiás, András

doi:10.1016/j.tpb.2021.05.001

Cited by 2 publications

(5 citation statements)

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“…Putting together Propositions 4.1 and 2.4 and Corollary 2.5, we now prove our main results, employing some arguments from Section 3.4 of [13], somewhat similarly to the case of stable coexistence in Section 6.4 of [9]. The differences from these proofs stem from the fact that in the model of the present paper there is no case where the formerly resident type (here type 1a) goes extinct, and that we cannot verify a convergence of the dynamical system to the convergence equilibrium.…”

Section: 33)mentioning

confidence: 62%

“…Now, a standard approach (following e.g. [9,13]) in order to describe the invasion probability of the newly arrived virus particle is to couple its behaviour to that of a suitable branching process that is independent of the behaviour of the resident type 1a population as long as the virus population is still small. However, in our case we run into technical problems with this approach.…”

Section: The Approximating Branching Process(es) In the Initial Stoch...mentioning

confidence: 99%

“…However, in our setting, when one wants to treat the early stochastic phase, a technical problem emerges. The proof techniques of the papers [9,13] strongly rely on the irreducibility of the mean matrix of the branching process under consideration. This condition implies that the branching process survives with positive probability when started from any initial condition with at least one positive coordinate.…”

Section: The Approximating Branching Process(es) In the Initial Stoch...mentioning

confidence: 99%

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Microbial virus epidemics in the presence of contact-mediated host dormancy

Blath

Tóbiás

2023

ESAIM: PS

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We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the microbial hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a contact-mediated defence mechanism was described in Bautista&al. (2015) for an archaeal host, while Jackson-Fineran (2019) and Meeske&al. (2019) describe a related, CRISPR-Cas induced, dormancy defense of bacterial hosts to curb phage epidemics. We first analyse the effect of the dormancy-related model parameters on the probability and time of invasion of a newly arriving virus into a resident host population. Given successful invasion, we then show that the emergence (with high probability) of a persistent virus infection (‘epidemic’) in a large host population can be determined by the existence of a coexistence equilibrium for the underlying dynamical system. That is an extension of a dynamical system considered by Beretta-Kuang (1998), known to exhibit a Hopf bifurcation, giving rise to a ‘paradox of enrichment’. We verify that the additional dormancy component can, for certain parameter ranges, prevent the associated loss of stability. Moreover, the presence of contact-mediated dormancy enables the host population to attain higher equilibrium sizes - and still avoid a persistent epidemic - than hosts without this trait.

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Section: 33)mentioning

confidence: 62%

Section: The Approximating Branching Process(es) In the Initial Stoch...mentioning

confidence: 99%

Section: The Approximating Branching Process(es) In the Initial Stoch...mentioning

confidence: 99%

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Microbial virus epidemics in the presence of contact-mediated host dormancy

Blath

Tóbiás

2023

ESAIM: PS

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“…The interplay with competition has been investigated in [BT20], where it is shown that dormancy traits responding to competitive pressure can invade and fixate in a resident population despite a substantial reproductive trade-off. One step further, the interplay of dormancy with competition and directional HGT has been investigated in [BT21], where coexistence regimes of HGT and dormancy traits are being established.…”

Section: Introduction and Biological Motivationmentioning

confidence: 99%

“…Here, we can also make use of the ideas from [BT20], since we are interested in showing that after some time an initially resident trait is driven towards a small population size, while an invasive species becomes resident. As there are many cases of this competition to be distinguished, we also make use of the ideas in [BT21] in the case of competition between a bi-type process and a single-type process.…”

Section: Introduction and Biological Motivationmentioning

confidence: 99%

A Stochastic Adaptive Dynamics Model for Bacterial Populations with Mutation, Dormancy and Transfer

Blath¹,

Paul²,

Tóbiás³

2021

Preprint

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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, Méléard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and Tóbiás (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 nonmonotone 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.MSC 2010. 60J85, 92D25.

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The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes

Cited by 2 publications

References 26 publications

Microbial virus epidemics in the presence of contact-mediated host dormancy

Microbial virus epidemics in the presence of contact-mediated host dormancy

A Stochastic Adaptive Dynamics Model for Bacterial Populations with Mutation, Dormancy and Transfer

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