What’s love got to do with it? Stable marriage in microbial ecosystems limited by two essential nutrients

Microbial communities routinely have several alternative stable states observed for the same environmental parameters. A possibility of sudden and irreversible transitions between these states (regime shifts) complicates external manipulation of these systems. Can we predict which specific perturbations may induce such regime shifts and which would have only a transient effect? To study this topic we introduce and study a model of a microbial ecosystem colonized by a large number of specialist species. Each species can be limited by essential nutrients of two types, e.g. carbon and nitrogen, each represented in the environment by multiple metabolites. We demonstrate that our model has an exponentially large number of potential stable states realized for different nutrient fluxes. Using game theoretical methods adapted from the stable marriage problem, we predict all of these states based only on ranked lists of competitive abilities of species for each of the nutrients. We show that several mutually uninvadable stable states are generally feasible for a given set of environmental conditions, and explore an intricate network of discontinuous transitions between these states upon changes of nutrient fluxes.
BioRxiv 439547 https://doi.org/10.1101/439547 (2018).