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Microbial dormancy is an evolutionary trait that has emerged independently atvarious positions across the tree of life. It describes the ability of amicroorganism to switch to a metabolically inactive state that can withstandunfavorable conditions. However, maintaining such a trait requires additionalresources that could otherwise be used to increase e.g. reproductive rates. Inthis paper, we aim for gaining a basic understanding under which conditionsmaintaining a seed bank of dormant individuals provides a "fitness advantage"when facing resource limitations and competition for resources amongindividuals (in an otherwise stable environment). In particular, we wish tounderstand when an individual with a "dormancy trait" can invade a residentpopulation lacking this trait despite having a lower reproduction rate than theresidents.  To this end, we follow a stochastic individual-based approach employingbirth-and-death processes, where dormancy is triggered by competitive pressurefor resources. In the large-population limit, we identify a necessary andsufficient condition under which a complete invasion of mutants has a positiveprobability. Further, we explicitly determine the limiting probability ofinvasion and the asymptotic time to fixation of mutants in the case of asuccessful invasion. In the proofs, we observe the three classical phases ofinvasion dynamics in the guise of Coron et al. (2017, 2019).

Invasion and fixation of microbial dormancy traits under competitive pressure