Biodiversity of marine microbes is safeguarded by phenotypic heterogeneity in ecological traits

predation, and other, ecologically relevant factors. The cumulative outcome of competition between individuals, no matter how biologically complex, can be reduced to three possibilities: win, lose, or draw. Since microorganisms reproduce asexually, success or failure in competi- tion corresponds directly to population increase or decrease, respectively, as shown in Fig 1. At each round of competition, each individual is assigned a competitive ability according to the strategy of its species. Biologically, a strategy represents the probability distribution of com- petitive abilities (e.g. traits) for all individuals of the species. Different trait distributions can be the result of random phenotypic noise, plasticity, or the genetic variation that inevitably exists in large, actively-dividing microbial populations [33]. Leveraging theoretical mathematics, we are able to simultaneously consider all traits and all types of distributions, rather than single traits with close to normal distributions as done previously [34]. In the game theoretic sense, a trait distribution is a mixed strategy for the species, considered as a player in a non-cooperative game. Representing competitive ability as a distribution, rather than a mean value exemplifies our approach of incorporating phenotypic heterogeneity in the assessment of competition outcomes. Game theory is uniquely suited to examine the effects of phenotypic heterogeneity on sur- vival of competing microbial species because game theory evaluates population-level outcomes

of individual-level interactions as depicted in Fig 2. In our application of game theory, we define species-level strategies from which we derive the outcomes of individual-level competi- tions that ultimately determine the population-level survival and abundance. This approach is in contrast with population-level assessments, like Lotka-Volterra type models, where pheno- typic heterogeneity is accounted for by using stochastic differential equations [35]. The game theoretic framework provides a quantitative means to evaluate the success of species compet- ing according to their strategies. Below, we obtain tractable equations for each individual Fig 1. Competition occurs on a cell-to-cell level. When two asexually reproducing individuals compete in a zero-sum game, there are three possible outcomes for each individual: win = self-replicate; draw = maintain status quo for each competitor; lose = die/competitor replicates. The table shows the pay-off function of individual-level competition. A payoff of 1 corresponds to win, a payoff of -1 corresponds to lose, and a payoff of 0 corresponds to a draw. https://doi.org/10.1371/journal.pone.0254799.g001 PLOS ONE Biodiversity of marine microbes is safeguarded by phenotypic heterogeneity in ecological traits PLOS ONE | https://doi.org/10.1371/journal.pone.0254799 August 4, 2021 3 / 18