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Register a new userThe interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes
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Andr\\'as J\\'ozsef T\\'obi\\'as
Publication date
2020
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English
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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, affecting 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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Microbial dormancy is an evolutionary trait that has emerged independently at various positions across the tree of life. It describes the ability of a microorganism to switch to a metabolically inactive state that can withstand unfavorable conditions. However, maintaining such a trait requires additional resources that could otherwise be used to increase e.g. reproductive rates. In this paper, we aim for gaining a basic understanding under which conditions maintaining a seed bank of dormant individuals provides a fitness advantage when facing resource limitations and competition for resources among individuals (in an otherwise stable environment). In particular, we wish to understand when an individual with a dormancy trait can invade a resident population lacking this trait despite having a lower reproduction rate than the residents. To this end, we follow a stochastic individual-based approach employing birth-and-death processes, where dormancy is triggered by competitive pressure for resources. In the large-population limit, we identify a necessary and sufficient condition under which a complete invasion of mutants has a positive probability. Further, we explicitly determine the limiting probability of invasion and the asymptotic time to fixation of mutants in the case of a successful invasion. In the proofs, we observe the three classical phases of invasion dynamics in the guise of Coron et al. (2017, 2019).
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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Fernando Cordero
, Adrian Gonzalez Casanova
, Jason Schweinsberg andn Maite Wilke-Berenguer
2020
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, $N$ individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a $Lambda$-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all $Lambda$-coalescents that can arise in this framework.
In this paper we investigate the spread of advantageous genes in two variants of the F-KPP model with dormancy. The first variant, in which dormant individuals do not move in space and instead form localized seed banks, has recently been introduced in Blath, Hammer and Nie (2020). However, there, only a relatively crude upper bound for the critical speed of potential travelling wave solutions has been provided. The second model variant is new and describes a situation in which the dormant forms of individuals are subject to motion, while the active individuals remain spatially static instead. This can be motivated e.g. by spore dispersal of fungi, where the dormant spores are distributed by wind, water or insects, while the active fungi are locally fixed. For both models, we establish the existence of monotone travelling wave solutions, determine the corresponding critical wave-speed in terms of the model parameters, and characterize aspects of the asymptotic shape of the waves depending on the decay properties of the initial condition. Interestingly, the slow-down effect of dormancy on the speed of propagation of beneficial alleles is often more serious in model variant II (the spore model) than in variant I (the seed bank model), and this can be understood mathematically via probabilistic representations of solutions in terms of (two variants of) on/off branching Brownian motions. Our proofs make rather heavy use of probabilistic tools in the tradition of McKean (1975), Bramson (1978), Neveu (1987), Lalley and Sellke (1987), Champneys et al (1995) and others. However, the two-compartment nature of the model and the special forms of dormancy also pose obstacles to the classical formalism, giving rise to a variety of open research questions that we briefly discuss at the end of the paper.
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extend
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