Invasion and fixation of microbial dormancy traits under competitive pressure

TL;DR

This paper investigates the conditions under which microbial dormancy traits can invade and become fixed in populations facing resource limitations and competition, using stochastic models to analyze invasion probabilities and fixation times.

Contribution

It provides a mathematical framework for understanding when dormancy traits confer a fitness advantage and can invade populations despite lower reproductive rates.

Findings

Identifies necessary and sufficient conditions for invasion success.

Explicitly calculates invasion probability and fixation time.

Observes classical invasion phases in the stochastic model.

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-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).