Invasion and fixation of microbial dormancy traits under competitive pressure

Abstract

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-anddeath 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. (2017Coron et al. ( , 2019.MSC 2010. 60J85, 92D25.

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

“…Note that the detailed results behind D 1 have recently been established in [BT20]. The results related to D 2 will be a corollary to the results on mixed populations exhibiting dormancy and HGT in the present paper, see Section 3.…”

“…[KKL01, TLLPS11, BGKW16, BGKW20]), they have only rather recently been considered in a population dynamics framework involving direct competition. Indeed, in our recent preprint [BT20], we introduced an individual-based model for the invasion analysis of a dormancy trait in a resident population lacking this trait. We showed that under suitable assumptions on the model parameters, with asymptotically positive probability, a newly arriving ('mutant') individual having the dormancy trait is able to invade a resident population, even if it has a significantly lower reproductive rate than the residents, and in case of a successful invasion, it will fixate with high probability.…”

“…In the present paper we aim to gain some conceptual understanding of the combined effects of both horizontal transfer and dormancy (at least in a basic scenario based on the previous works mentioned above). To this end we analyse competitive individual-based models with two traits, one of them being one-sided HGT involving a donor and a recipient (similarly as in [BCFMT18, Section 7] or [CMT19]), and the other one being dormancy (as in [BT20]). For concreteness, we say that trait 1 may exhibit dormancy, where switching into a dormant state is triggered by competitive pressure, while switching back (resuscitation) happens spontaneously.…”

“…During the analysis of the invasion (and, if applicable, fixation) of trait 1 in a trait 2 population, we are able to use multiple arguments of our recent paper [BT20] where we investigated competitioninduced dormancy without HGT. The analysis of phases (1) and (if applicable) (3) is a relatively straightforward adaptation of the methods of [BT20], which rely on a number of proof techniques from the papers [CCLS17,CCLLS19].…”

“…During the analysis of the invasion (and, if applicable, fixation) of trait 1 in a trait 2 population, we are able to use multiple arguments of our recent paper [BT20] where we investigated competitioninduced dormancy without HGT. The analysis of phases (1) and (if applicable) (3) is a relatively straightforward adaptation of the methods of [BT20], which rely on a number of proof techniques from the papers [CCLS17,CCLLS19]. Here, the main task is to take into account the additional effect of HGT and the arising coexistence equilibrium, handling also cases that were not included in [BT20] (eg., the case where the probability of mutant extinction tends to 1, the one where there is stable coexistence, and in general the one where a mutant lacking dormancy tries to invade a resident population exhibiting dormancy and not the other way around).…”