Dynamic Flux Balance Analysis Game

Flux balance analysis (FBA) for microbial communities often assumes a global objective function that all species cooperatively maximize in addition to maximizing their own growth. Combining community FBA with dynamic FBA to understand the time course and steady states of communities typically entails discretizing time and solving a community FBA model at each time point, a time-intensive process. We propose a dynamic community FBA model where species compete for metabolites to grow off of without needing to cooperate to maximize a community-level objective. An efficient method for computing steady state community compositions is provided, as well as methods for determining the stability of a steady state community to perturbations in biomass and invasion by species outside the community. The model and methods are applied to a model of four E. Coli. mutants with elements of competition (for shared metabolites) and cooperation (via mutants being auxotrophic for metabolites exported by other mutants). ### Competing Interest Statement The authors have declared no competing interest.