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Invasion and fixation of microbial dormancy traits under competitive pressure

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  • Blath, Jochen
  • Tóbiás, András

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 unfavourable 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).

Suggested Citation

  • Blath, Jochen & Tóbiás, András, 2020. "Invasion and fixation of microbial dormancy traits under competitive pressure," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7363-7395.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7363-7395
    DOI: 10.1016/j.spa.2020.07.018
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    References listed on IDEAS

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    1. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.
    2. Koopmann, Bendix & Müller, Johannes & Tellier, Aurélien & Živković, Daniel, 2017. "Fisher–Wright model with deterministic seed bank and selection," Theoretical Population Biology, Elsevier, vol. 114(C), pages 29-39.
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    1. Blath, Jochen & Tóbiás, András, 2021. "The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes," Theoretical Population Biology, Elsevier, vol. 139(C), pages 18-49.
    2. Usman Sanusi & Sona John & Johannes Mueller & Aurélien Tellier, 2022. "Quiescence Generates Moving Average in a Stochastic Epidemiological Model with One Host and Two Parasites," Mathematics, MDPI, vol. 10(13), pages 1-22, June.
    3. Blath, Jochen & Paul, Tobias & Tóbiás, András & Wilke Berenguer, Maite, 2024. "The impact of dormancy on evolutionary branching," Theoretical Population Biology, Elsevier, vol. 156(C), pages 66-76.

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